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.
258 C<isl> is released under the MIT license.
262 Permission is hereby granted, free of charge, to any person obtaining a copy of
263 this software and associated documentation files (the "Software"), to deal in
264 the Software without restriction, including without limitation the rights to
265 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
266 of the Software, and to permit persons to whom the Software is furnished to do
267 so, subject to the following conditions:
269 The above copyright notice and this permission notice shall be included in all
270 copies or substantial portions of the Software.
272 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
273 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
274 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
275 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
276 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
277 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
282 Note that by default C<isl> requires C<GMP>, which is released
283 under the GNU Lesser General Public License (LGPL). This means
284 that code linked against C<isl> is also linked against LGPL code.
286 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
287 will link against C<imath>, a library for exact integer arithmetic released
288 under the MIT license.
292 The source of C<isl> can be obtained either as a tarball
293 or from the git repository. Both are available from
294 L<http://isl.gforge.inria.fr/>.
295 The installation process depends on how you obtained
298 =head2 Installation from the git repository
302 =item 1 Clone or update the repository
304 The first time the source is obtained, you need to clone
307 git clone git://repo.or.cz/isl.git
309 To obtain updates, you need to pull in the latest changes
313 =item 2 Optionally get C<imath> submodule
315 To build C<isl> with C<imath>, you need to obtain the C<imath>
316 submodule by running in the git source tree of C<isl>
321 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
323 =item 2 Generate C<configure>
329 After performing the above steps, continue
330 with the L<Common installation instructions>.
332 =head2 Common installation instructions
336 =item 1 Obtain C<GMP>
338 By default, building C<isl> requires C<GMP>, including its headers files.
339 Your distribution may not provide these header files by default
340 and you may need to install a package called C<gmp-devel> or something
341 similar. Alternatively, C<GMP> can be built from
342 source, available from L<http://gmplib.org/>.
343 C<GMP> is not needed if you build C<isl> with C<imath>.
347 C<isl> uses the standard C<autoconf> C<configure> script.
352 optionally followed by some configure options.
353 A complete list of options can be obtained by running
357 Below we discuss some of the more common options.
363 Installation prefix for C<isl>
365 =item C<--with-int=[gmp|imath|imath-32]>
367 Select the integer library to be used by C<isl>, the default is C<gmp>.
368 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
369 for values out of the 32 bit range. In most applications, C<isl> will run
370 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
373 =item C<--with-gmp-prefix>
375 Installation prefix for C<GMP> (architecture-independent files).
377 =item C<--with-gmp-exec-prefix>
379 Installation prefix for C<GMP> (architecture-dependent files).
387 =item 4 Install (optional)
393 =head1 Integer Set Library
395 =head2 Memory Management
397 Since a high-level operation on isl objects usually involves
398 several substeps and since the user is usually not interested in
399 the intermediate results, most functions that return a new object
400 will also release all the objects passed as arguments.
401 If the user still wants to use one or more of these arguments
402 after the function call, she should pass along a copy of the
403 object rather than the object itself.
404 The user is then responsible for making sure that the original
405 object gets used somewhere else or is explicitly freed.
407 The arguments and return values of all documented functions are
408 annotated to make clear which arguments are released and which
409 arguments are preserved. In particular, the following annotations
416 C<__isl_give> means that a new object is returned.
417 The user should make sure that the returned pointer is
418 used exactly once as a value for an C<__isl_take> argument.
419 In between, it can be used as a value for as many
420 C<__isl_keep> arguments as the user likes.
421 There is one exception, and that is the case where the
422 pointer returned is C<NULL>. Is this case, the user
423 is free to use it as an C<__isl_take> argument or not.
424 When applied to a C<char *>, the returned pointer needs to be
429 C<__isl_null> means that a C<NULL> value is returned.
433 C<__isl_take> means that the object the argument points to
434 is taken over by the function and may no longer be used
435 by the user as an argument to any other function.
436 The pointer value must be one returned by a function
437 returning an C<__isl_give> pointer.
438 If the user passes in a C<NULL> value, then this will
439 be treated as an error in the sense that the function will
440 not perform its usual operation. However, it will still
441 make sure that all the other C<__isl_take> arguments
446 C<__isl_keep> means that the function will only use the object
447 temporarily. After the function has finished, the user
448 can still use it as an argument to other functions.
449 A C<NULL> value will be treated in the same way as
450 a C<NULL> value for an C<__isl_take> argument.
451 This annotation may also be used on return values of
452 type C<const char *>, in which case the returned pointer should
453 not be freed by the user and is only valid until the object
454 from which it was derived is updated or freed.
458 =head2 Initialization
460 All manipulations of integer sets and relations occur within
461 the context of an C<isl_ctx>.
462 A given C<isl_ctx> can only be used within a single thread.
463 All arguments of a function are required to have been allocated
464 within the same context.
465 There are currently no functions available for moving an object
466 from one C<isl_ctx> to another C<isl_ctx>. This means that
467 there is currently no way of safely moving an object from one
468 thread to another, unless the whole C<isl_ctx> is moved.
470 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
471 freed using C<isl_ctx_free>.
472 All objects allocated within an C<isl_ctx> should be freed
473 before the C<isl_ctx> itself is freed.
475 isl_ctx *isl_ctx_alloc();
476 void isl_ctx_free(isl_ctx *ctx);
478 The user can impose a bound on the number of low-level I<operations>
479 that can be performed by an C<isl_ctx>. This bound can be set and
480 retrieved using the following functions. A bound of zero means that
481 no bound is imposed. The number of operations performed can be
482 reset using C<isl_ctx_reset_operations>. Note that the number
483 of low-level operations needed to perform a high-level computation
484 may differ significantly across different versions
485 of C<isl>, but it should be the same across different platforms
486 for the same version of C<isl>.
488 Warning: This feature is experimental. C<isl> has good support to abort and
489 bail out during the computation, but this feature may exercise error code paths
490 that are normally not used that much. Consequently, it is not unlikely that
491 hidden bugs will be exposed.
493 void isl_ctx_set_max_operations(isl_ctx *ctx,
494 unsigned long max_operations);
495 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
496 void isl_ctx_reset_operations(isl_ctx *ctx);
498 In order to be able to create an object in the same context
499 as another object, most object types (described later in
500 this document) provide a function to obtain the context
501 in which the object was created.
504 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
505 isl_ctx *isl_multi_val_get_ctx(
506 __isl_keep isl_multi_val *mv);
509 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
511 #include <isl/local_space.h>
512 isl_ctx *isl_local_space_get_ctx(
513 __isl_keep isl_local_space *ls);
516 isl_ctx *isl_set_list_get_ctx(
517 __isl_keep isl_set_list *list);
520 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
521 isl_ctx *isl_multi_aff_get_ctx(
522 __isl_keep isl_multi_aff *maff);
523 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
524 isl_ctx *isl_pw_multi_aff_get_ctx(
525 __isl_keep isl_pw_multi_aff *pma);
526 isl_ctx *isl_multi_pw_aff_get_ctx(
527 __isl_keep isl_multi_pw_aff *mpa);
528 isl_ctx *isl_union_pw_aff_get_ctx(
529 __isl_keep isl_union_pw_aff *upa);
530 isl_ctx *isl_union_pw_multi_aff_get_ctx(
531 __isl_keep isl_union_pw_multi_aff *upma);
532 isl_ctx *isl_multi_union_pw_aff_get_ctx(
533 __isl_keep isl_multi_union_pw_aff *mupa);
535 #include <isl/id_to_ast_expr.h>
536 isl_ctx *isl_id_to_ast_expr_get_ctx(
537 __isl_keep isl_id_to_ast_expr *id2expr);
539 #include <isl/point.h>
540 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
543 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
546 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
548 #include <isl/vertices.h>
549 isl_ctx *isl_vertices_get_ctx(
550 __isl_keep isl_vertices *vertices);
551 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
552 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
554 #include <isl/flow.h>
555 isl_ctx *isl_restriction_get_ctx(
556 __isl_keep isl_restriction *restr);
557 isl_ctx *isl_union_access_info_get_ctx(
558 __isl_keep isl_union_access_info *access);
559 isl_ctx *isl_union_flow_get_ctx(
560 __isl_keep isl_union_flow *flow);
562 #include <isl/schedule.h>
563 isl_ctx *isl_schedule_get_ctx(
564 __isl_keep isl_schedule *sched);
565 isl_ctx *isl_schedule_constraints_get_ctx(
566 __isl_keep isl_schedule_constraints *sc);
568 #include <isl/schedule_node.h>
569 isl_ctx *isl_schedule_node_get_ctx(
570 __isl_keep isl_schedule_node *node);
572 #include <isl/band.h>
573 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
575 #include <isl/ast_build.h>
576 isl_ctx *isl_ast_build_get_ctx(
577 __isl_keep isl_ast_build *build);
580 isl_ctx *isl_ast_expr_get_ctx(
581 __isl_keep isl_ast_expr *expr);
582 isl_ctx *isl_ast_node_get_ctx(
583 __isl_keep isl_ast_node *node);
587 C<isl> uses two special return types for functions that either return
588 a boolean or that in principle do not return anything.
589 In particular, the C<isl_bool> type has three possible values:
590 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
591 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
592 C<isl_bool_error> (a negative integer value), indicating that something
593 went wrong. The following function can be used to negate an C<isl_bool>,
594 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
597 isl_bool isl_bool_not(isl_bool b);
599 The C<isl_stat> type has two possible values:
600 C<isl_stat_ok> (the integer value zero), indicating a successful
602 C<isl_stat_error> (a negative integer value), indicating that something
604 See L</"Error Handling"> for more information on
605 C<isl_bool_error> and C<isl_stat_error>.
609 An C<isl_val> represents an integer value, a rational value
610 or one of three special values, infinity, negative infinity and NaN.
611 Some predefined values can be created using the following functions.
614 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
615 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
616 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
617 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
618 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
619 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
621 Specific integer values can be created using the following functions.
624 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
626 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
628 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
629 size_t n, size_t size, const void *chunks);
631 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
632 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
633 The least significant digit is assumed to be stored first.
635 Value objects can be copied and freed using the following functions.
638 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
639 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
641 They can be inspected using the following functions.
644 long isl_val_get_num_si(__isl_keep isl_val *v);
645 long isl_val_get_den_si(__isl_keep isl_val *v);
646 __isl_give isl_val *isl_val_get_den_val(
647 __isl_keep isl_val *v);
648 double isl_val_get_d(__isl_keep isl_val *v);
649 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
651 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
652 size_t size, void *chunks);
654 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
655 of C<size> bytes needed to store the absolute value of the
657 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
658 which is assumed to have been preallocated by the caller.
659 The least significant digit is stored first.
660 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
661 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
662 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
664 An C<isl_val> can be modified using the following function.
667 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
670 The following unary properties are defined on C<isl_val>s.
673 int isl_val_sgn(__isl_keep isl_val *v);
674 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
675 isl_bool isl_val_is_one(__isl_keep isl_val *v);
676 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
677 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
678 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
679 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
680 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
681 isl_bool isl_val_is_int(__isl_keep isl_val *v);
682 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
683 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
684 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
685 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
687 Note that the sign of NaN is undefined.
689 The following binary properties are defined on pairs of C<isl_val>s.
692 isl_bool isl_val_lt(__isl_keep isl_val *v1,
693 __isl_keep isl_val *v2);
694 isl_bool isl_val_le(__isl_keep isl_val *v1,
695 __isl_keep isl_val *v2);
696 isl_bool isl_val_gt(__isl_keep isl_val *v1,
697 __isl_keep isl_val *v2);
698 isl_bool isl_val_ge(__isl_keep isl_val *v1,
699 __isl_keep isl_val *v2);
700 isl_bool isl_val_eq(__isl_keep isl_val *v1,
701 __isl_keep isl_val *v2);
702 isl_bool isl_val_ne(__isl_keep isl_val *v1,
703 __isl_keep isl_val *v2);
704 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
705 __isl_keep isl_val *v2);
707 The function C<isl_val_abs_eq> checks whether its two arguments
708 are equal in absolute value.
710 For integer C<isl_val>s we additionally have the following binary property.
713 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
714 __isl_keep isl_val *v2);
716 An C<isl_val> can also be compared to an integer using the following
717 function. The result is undefined for NaN.
720 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
722 The following unary operations are available on C<isl_val>s.
725 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
726 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
727 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
728 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
729 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
730 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
731 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
733 The following binary operations are available on C<isl_val>s.
736 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
737 __isl_take isl_val *v2);
738 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
739 __isl_take isl_val *v2);
740 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
741 __isl_take isl_val *v2);
742 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
744 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
745 __isl_take isl_val *v2);
746 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
748 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
749 __isl_take isl_val *v2);
750 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
752 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
753 __isl_take isl_val *v2);
755 On integer values, we additionally have the following operations.
758 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
759 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
760 __isl_take isl_val *v2);
761 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
762 __isl_take isl_val *v2);
763 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
764 __isl_take isl_val *v2, __isl_give isl_val **x,
765 __isl_give isl_val **y);
767 The function C<isl_val_gcdext> returns the greatest common divisor g
768 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
769 that C<*x> * C<v1> + C<*y> * C<v2> = g.
771 =head3 GMP specific functions
773 These functions are only available if C<isl> has been compiled with C<GMP>
776 Specific integer and rational values can be created from C<GMP> values using
777 the following functions.
779 #include <isl/val_gmp.h>
780 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
782 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
783 const mpz_t n, const mpz_t d);
785 The numerator and denominator of a rational value can be extracted as
786 C<GMP> values using the following functions.
788 #include <isl/val_gmp.h>
789 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
790 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
792 =head2 Sets and Relations
794 C<isl> uses six types of objects for representing sets and relations,
795 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
796 C<isl_union_set> and C<isl_union_map>.
797 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
798 can be described as a conjunction of affine constraints, while
799 C<isl_set> and C<isl_map> represent unions of
800 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
801 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
802 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
803 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
804 where spaces are considered different if they have a different number
805 of dimensions and/or different names (see L<"Spaces">).
806 The difference between sets and relations (maps) is that sets have
807 one set of variables, while relations have two sets of variables,
808 input variables and output variables.
810 =head2 Error Handling
812 C<isl> supports different ways to react in case a runtime error is triggered.
813 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
814 with two maps that have incompatible spaces. There are three possible ways
815 to react on error: to warn, to continue or to abort.
817 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
818 the last error in the corresponding C<isl_ctx> and the function in which the
819 error was triggered returns a value indicating that some error has
820 occurred. In case of functions returning a pointer, this value is
821 C<NULL>. In case of functions returning an C<isl_bool> or an
822 C<isl_stat>, this valus is C<isl_bool_error> or C<isl_stat_error>.
823 An error does not corrupt internal state,
824 such that isl can continue to be used. C<isl> also provides functions to
825 read the last error and to reset the memory that stores the last error. The
826 last error is only stored for information purposes. Its presence does not
827 change the behavior of C<isl>. Hence, resetting an error is not required to
828 continue to use isl, but only to observe new errors.
831 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
832 void isl_ctx_reset_error(isl_ctx *ctx);
834 Another option is to continue on error. This is similar to warn on error mode,
835 except that C<isl> does not print any warning. This allows a program to
836 implement its own error reporting.
838 The last option is to directly abort the execution of the program from within
839 the isl library. This makes it obviously impossible to recover from an error,
840 but it allows to directly spot the error location. By aborting on error,
841 debuggers break at the location the error occurred and can provide a stack
842 trace. Other tools that automatically provide stack traces on abort or that do
843 not want to continue execution after an error was triggered may also prefer to
846 The on error behavior of isl can be specified by calling
847 C<isl_options_set_on_error> or by setting the command line option
848 C<--isl-on-error>. Valid arguments for the function call are
849 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
850 choices for the command line option are C<warn>, C<continue> and C<abort>.
851 It is also possible to query the current error mode.
853 #include <isl/options.h>
854 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
855 int isl_options_get_on_error(isl_ctx *ctx);
859 Identifiers are used to identify both individual dimensions
860 and tuples of dimensions. They consist of an optional name and an optional
861 user pointer. The name and the user pointer cannot both be C<NULL>, however.
862 Identifiers with the same name but different pointer values
863 are considered to be distinct.
864 Similarly, identifiers with different names but the same pointer value
865 are also considered to be distinct.
866 Equal identifiers are represented using the same object.
867 Pairs of identifiers can therefore be tested for equality using the
869 Identifiers can be constructed, copied, freed, inspected and printed
870 using the following functions.
873 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
874 __isl_keep const char *name, void *user);
875 __isl_give isl_id *isl_id_set_free_user(
876 __isl_take isl_id *id,
877 void (*free_user)(void *user));
878 __isl_give isl_id *isl_id_copy(isl_id *id);
879 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
881 void *isl_id_get_user(__isl_keep isl_id *id);
882 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
884 __isl_give isl_printer *isl_printer_print_id(
885 __isl_take isl_printer *p, __isl_keep isl_id *id);
887 The callback set by C<isl_id_set_free_user> is called on the user
888 pointer when the last reference to the C<isl_id> is freed.
889 Note that C<isl_id_get_name> returns a pointer to some internal
890 data structure, so the result can only be used while the
891 corresponding C<isl_id> is alive.
895 Whenever a new set, relation or similar object is created from scratch,
896 the space in which it lives needs to be specified using an C<isl_space>.
897 Each space involves zero or more parameters and zero, one or two
898 tuples of set or input/output dimensions. The parameters and dimensions
899 are identified by an C<isl_dim_type> and a position.
900 The type C<isl_dim_param> refers to parameters,
901 the type C<isl_dim_set> refers to set dimensions (for spaces
902 with a single tuple of dimensions) and the types C<isl_dim_in>
903 and C<isl_dim_out> refer to input and output dimensions
904 (for spaces with two tuples of dimensions).
905 Local spaces (see L</"Local Spaces">) also contain dimensions
906 of type C<isl_dim_div>.
907 Note that parameters are only identified by their position within
908 a given object. Across different objects, parameters are (usually)
909 identified by their names or identifiers. Only unnamed parameters
910 are identified by their positions across objects. The use of unnamed
911 parameters is discouraged.
913 #include <isl/space.h>
914 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
915 unsigned nparam, unsigned n_in, unsigned n_out);
916 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
918 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
919 unsigned nparam, unsigned dim);
920 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
921 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
923 The space used for creating a parameter domain
924 needs to be created using C<isl_space_params_alloc>.
925 For other sets, the space
926 needs to be created using C<isl_space_set_alloc>, while
927 for a relation, the space
928 needs to be created using C<isl_space_alloc>.
930 To check whether a given space is that of a set or a map
931 or whether it is a parameter space, use these functions:
933 #include <isl/space.h>
934 isl_bool isl_space_is_params(__isl_keep isl_space *space);
935 isl_bool isl_space_is_set(__isl_keep isl_space *space);
936 isl_bool isl_space_is_map(__isl_keep isl_space *space);
938 Spaces can be compared using the following functions:
940 #include <isl/space.h>
941 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
942 __isl_keep isl_space *space2);
943 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
944 __isl_keep isl_space *space2);
945 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
946 __isl_keep isl_space *space2);
947 isl_bool isl_space_tuple_is_equal(
948 __isl_keep isl_space *space1,
949 enum isl_dim_type type1,
950 __isl_keep isl_space *space2,
951 enum isl_dim_type type2);
953 C<isl_space_is_domain> checks whether the first argument is equal
954 to the domain of the second argument. This requires in particular that
955 the first argument is a set space and that the second argument
956 is a map space. C<isl_space_tuple_is_equal> checks whether the given
957 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
958 spaces are the same. That is, it checks if they have the same
959 identifier (if any), the same dimension and the same internal structure
962 It is often useful to create objects that live in the
963 same space as some other object. This can be accomplished
964 by creating the new objects
965 (see L</"Creating New Sets and Relations"> or
966 L</"Functions">) based on the space
967 of the original object.
970 __isl_give isl_space *isl_basic_set_get_space(
971 __isl_keep isl_basic_set *bset);
972 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
974 #include <isl/union_set.h>
975 __isl_give isl_space *isl_union_set_get_space(
976 __isl_keep isl_union_set *uset);
979 __isl_give isl_space *isl_basic_map_get_space(
980 __isl_keep isl_basic_map *bmap);
981 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
983 #include <isl/union_map.h>
984 __isl_give isl_space *isl_union_map_get_space(
985 __isl_keep isl_union_map *umap);
987 #include <isl/constraint.h>
988 __isl_give isl_space *isl_constraint_get_space(
989 __isl_keep isl_constraint *constraint);
991 #include <isl/polynomial.h>
992 __isl_give isl_space *isl_qpolynomial_get_domain_space(
993 __isl_keep isl_qpolynomial *qp);
994 __isl_give isl_space *isl_qpolynomial_get_space(
995 __isl_keep isl_qpolynomial *qp);
996 __isl_give isl_space *
997 isl_qpolynomial_fold_get_domain_space(
998 __isl_keep isl_qpolynomial_fold *fold);
999 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1000 __isl_keep isl_qpolynomial_fold *fold);
1001 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1002 __isl_keep isl_pw_qpolynomial *pwqp);
1003 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1004 __isl_keep isl_pw_qpolynomial *pwqp);
1005 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1006 __isl_keep isl_pw_qpolynomial_fold *pwf);
1007 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1008 __isl_keep isl_pw_qpolynomial_fold *pwf);
1009 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1010 __isl_keep isl_union_pw_qpolynomial *upwqp);
1011 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1012 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1014 #include <isl/val.h>
1015 __isl_give isl_space *isl_multi_val_get_space(
1016 __isl_keep isl_multi_val *mv);
1018 #include <isl/aff.h>
1019 __isl_give isl_space *isl_aff_get_domain_space(
1020 __isl_keep isl_aff *aff);
1021 __isl_give isl_space *isl_aff_get_space(
1022 __isl_keep isl_aff *aff);
1023 __isl_give isl_space *isl_pw_aff_get_domain_space(
1024 __isl_keep isl_pw_aff *pwaff);
1025 __isl_give isl_space *isl_pw_aff_get_space(
1026 __isl_keep isl_pw_aff *pwaff);
1027 __isl_give isl_space *isl_multi_aff_get_domain_space(
1028 __isl_keep isl_multi_aff *maff);
1029 __isl_give isl_space *isl_multi_aff_get_space(
1030 __isl_keep isl_multi_aff *maff);
1031 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1032 __isl_keep isl_pw_multi_aff *pma);
1033 __isl_give isl_space *isl_pw_multi_aff_get_space(
1034 __isl_keep isl_pw_multi_aff *pma);
1035 __isl_give isl_space *isl_union_pw_aff_get_space(
1036 __isl_keep isl_union_pw_aff *upa);
1037 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1038 __isl_keep isl_union_pw_multi_aff *upma);
1039 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1040 __isl_keep isl_multi_pw_aff *mpa);
1041 __isl_give isl_space *isl_multi_pw_aff_get_space(
1042 __isl_keep isl_multi_pw_aff *mpa);
1043 __isl_give isl_space *
1044 isl_multi_union_pw_aff_get_domain_space(
1045 __isl_keep isl_multi_union_pw_aff *mupa);
1046 __isl_give isl_space *
1047 isl_multi_union_pw_aff_get_space(
1048 __isl_keep isl_multi_union_pw_aff *mupa);
1050 #include <isl/point.h>
1051 __isl_give isl_space *isl_point_get_space(
1052 __isl_keep isl_point *pnt);
1054 The number of dimensions of a given type of space
1055 may be read off from a space or an object that lives
1056 in a space using the following functions.
1057 In case of C<isl_space_dim>, type may be
1058 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1059 C<isl_dim_out> (only for relations), C<isl_dim_set>
1060 (only for sets) or C<isl_dim_all>.
1062 #include <isl/space.h>
1063 unsigned isl_space_dim(__isl_keep isl_space *space,
1064 enum isl_dim_type type);
1066 #include <isl/local_space.h>
1067 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1068 enum isl_dim_type type);
1070 #include <isl/set.h>
1071 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1072 enum isl_dim_type type);
1073 unsigned isl_set_dim(__isl_keep isl_set *set,
1074 enum isl_dim_type type);
1076 #include <isl/union_set.h>
1077 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1078 enum isl_dim_type type);
1080 #include <isl/map.h>
1081 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1082 enum isl_dim_type type);
1083 unsigned isl_map_dim(__isl_keep isl_map *map,
1084 enum isl_dim_type type);
1086 #include <isl/union_map.h>
1087 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1088 enum isl_dim_type type);
1090 #include <isl/val.h>
1091 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1092 enum isl_dim_type type);
1094 #include <isl/aff.h>
1095 int isl_aff_dim(__isl_keep isl_aff *aff,
1096 enum isl_dim_type type);
1097 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1098 enum isl_dim_type type);
1099 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1100 enum isl_dim_type type);
1101 unsigned isl_pw_multi_aff_dim(
1102 __isl_keep isl_pw_multi_aff *pma,
1103 enum isl_dim_type type);
1104 unsigned isl_multi_pw_aff_dim(
1105 __isl_keep isl_multi_pw_aff *mpa,
1106 enum isl_dim_type type);
1107 unsigned isl_union_pw_aff_dim(
1108 __isl_keep isl_union_pw_aff *upa,
1109 enum isl_dim_type type);
1110 unsigned isl_union_pw_multi_aff_dim(
1111 __isl_keep isl_union_pw_multi_aff *upma,
1112 enum isl_dim_type type);
1113 unsigned isl_multi_union_pw_aff_dim(
1114 __isl_keep isl_multi_union_pw_aff *mupa,
1115 enum isl_dim_type type);
1117 #include <isl/polynomial.h>
1118 unsigned isl_union_pw_qpolynomial_dim(
1119 __isl_keep isl_union_pw_qpolynomial *upwqp,
1120 enum isl_dim_type type);
1121 unsigned isl_union_pw_qpolynomial_fold_dim(
1122 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1123 enum isl_dim_type type);
1125 Note that an C<isl_union_set>, an C<isl_union_map>,
1126 an C<isl_union_pw_multi_aff>,
1127 an C<isl_union_pw_qpolynomial> and
1128 an C<isl_union_pw_qpolynomial_fold>
1129 only have parameters.
1131 The identifiers or names of the individual dimensions of spaces
1132 may be set or read off using the following functions on spaces
1133 or objects that live in spaces.
1134 These functions are mostly useful to obtain the identifiers, positions
1135 or names of the parameters. Identifiers of individual dimensions are
1136 essentially only useful for printing. They are ignored by all other
1137 operations and may not be preserved across those operations.
1139 #include <isl/space.h>
1140 __isl_give isl_space *isl_space_set_dim_id(
1141 __isl_take isl_space *space,
1142 enum isl_dim_type type, unsigned pos,
1143 __isl_take isl_id *id);
1144 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1145 enum isl_dim_type type, unsigned pos);
1146 __isl_give isl_id *isl_space_get_dim_id(
1147 __isl_keep isl_space *space,
1148 enum isl_dim_type type, unsigned pos);
1149 __isl_give isl_space *isl_space_set_dim_name(
1150 __isl_take isl_space *space,
1151 enum isl_dim_type type, unsigned pos,
1152 __isl_keep const char *name);
1153 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1154 enum isl_dim_type type, unsigned pos);
1155 __isl_keep const char *isl_space_get_dim_name(
1156 __isl_keep isl_space *space,
1157 enum isl_dim_type type, unsigned pos);
1159 #include <isl/local_space.h>
1160 __isl_give isl_local_space *isl_local_space_set_dim_id(
1161 __isl_take isl_local_space *ls,
1162 enum isl_dim_type type, unsigned pos,
1163 __isl_take isl_id *id);
1164 isl_bool isl_local_space_has_dim_id(
1165 __isl_keep isl_local_space *ls,
1166 enum isl_dim_type type, unsigned pos);
1167 __isl_give isl_id *isl_local_space_get_dim_id(
1168 __isl_keep isl_local_space *ls,
1169 enum isl_dim_type type, unsigned pos);
1170 __isl_give isl_local_space *isl_local_space_set_dim_name(
1171 __isl_take isl_local_space *ls,
1172 enum isl_dim_type type, unsigned pos, const char *s);
1173 isl_bool isl_local_space_has_dim_name(
1174 __isl_keep isl_local_space *ls,
1175 enum isl_dim_type type, unsigned pos)
1176 const char *isl_local_space_get_dim_name(
1177 __isl_keep isl_local_space *ls,
1178 enum isl_dim_type type, unsigned pos);
1180 #include <isl/constraint.h>
1181 const char *isl_constraint_get_dim_name(
1182 __isl_keep isl_constraint *constraint,
1183 enum isl_dim_type type, unsigned pos);
1185 #include <isl/set.h>
1186 __isl_give isl_id *isl_basic_set_get_dim_id(
1187 __isl_keep isl_basic_set *bset,
1188 enum isl_dim_type type, unsigned pos);
1189 __isl_give isl_set *isl_set_set_dim_id(
1190 __isl_take isl_set *set, enum isl_dim_type type,
1191 unsigned pos, __isl_take isl_id *id);
1192 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1193 enum isl_dim_type type, unsigned pos);
1194 __isl_give isl_id *isl_set_get_dim_id(
1195 __isl_keep isl_set *set, enum isl_dim_type type,
1197 const char *isl_basic_set_get_dim_name(
1198 __isl_keep isl_basic_set *bset,
1199 enum isl_dim_type type, unsigned pos);
1200 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1201 enum isl_dim_type type, unsigned pos);
1202 const char *isl_set_get_dim_name(
1203 __isl_keep isl_set *set,
1204 enum isl_dim_type type, unsigned pos);
1206 #include <isl/map.h>
1207 __isl_give isl_map *isl_map_set_dim_id(
1208 __isl_take isl_map *map, enum isl_dim_type type,
1209 unsigned pos, __isl_take isl_id *id);
1210 isl_bool isl_basic_map_has_dim_id(
1211 __isl_keep isl_basic_map *bmap,
1212 enum isl_dim_type type, unsigned pos);
1213 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1214 enum isl_dim_type type, unsigned pos);
1215 __isl_give isl_id *isl_map_get_dim_id(
1216 __isl_keep isl_map *map, enum isl_dim_type type,
1218 __isl_give isl_id *isl_union_map_get_dim_id(
1219 __isl_keep isl_union_map *umap,
1220 enum isl_dim_type type, unsigned pos);
1221 const char *isl_basic_map_get_dim_name(
1222 __isl_keep isl_basic_map *bmap,
1223 enum isl_dim_type type, unsigned pos);
1224 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1225 enum isl_dim_type type, unsigned pos);
1226 const char *isl_map_get_dim_name(
1227 __isl_keep isl_map *map,
1228 enum isl_dim_type type, unsigned pos);
1230 #include <isl/val.h>
1231 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1232 __isl_take isl_multi_val *mv,
1233 enum isl_dim_type type, unsigned pos,
1234 __isl_take isl_id *id);
1235 __isl_give isl_id *isl_multi_val_get_dim_id(
1236 __isl_keep isl_multi_val *mv,
1237 enum isl_dim_type type, unsigned pos);
1238 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1239 __isl_take isl_multi_val *mv,
1240 enum isl_dim_type type, unsigned pos, const char *s);
1242 #include <isl/aff.h>
1243 __isl_give isl_aff *isl_aff_set_dim_id(
1244 __isl_take isl_aff *aff, enum isl_dim_type type,
1245 unsigned pos, __isl_take isl_id *id);
1246 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1247 __isl_take isl_multi_aff *maff,
1248 enum isl_dim_type type, unsigned pos,
1249 __isl_take isl_id *id);
1250 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1251 __isl_take isl_pw_aff *pma,
1252 enum isl_dim_type type, unsigned pos,
1253 __isl_take isl_id *id);
1254 __isl_give isl_multi_pw_aff *
1255 isl_multi_pw_aff_set_dim_id(
1256 __isl_take isl_multi_pw_aff *mpa,
1257 enum isl_dim_type type, unsigned pos,
1258 __isl_take isl_id *id);
1259 __isl_give isl_multi_union_pw_aff *
1260 isl_multi_union_pw_aff_set_dim_id(
1261 __isl_take isl_multi_union_pw_aff *mupa,
1262 enum isl_dim_type type, unsigned pos,
1263 __isl_take isl_id *id);
1264 __isl_give isl_id *isl_multi_aff_get_dim_id(
1265 __isl_keep isl_multi_aff *ma,
1266 enum isl_dim_type type, unsigned pos);
1267 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1268 enum isl_dim_type type, unsigned pos);
1269 __isl_give isl_id *isl_pw_aff_get_dim_id(
1270 __isl_keep isl_pw_aff *pa,
1271 enum isl_dim_type type, unsigned pos);
1272 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1273 __isl_keep isl_pw_multi_aff *pma,
1274 enum isl_dim_type type, unsigned pos);
1275 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1276 __isl_keep isl_multi_pw_aff *mpa,
1277 enum isl_dim_type type, unsigned pos);
1278 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1279 __isl_keep isl_multi_union_pw_aff *mupa,
1280 enum isl_dim_type type, unsigned pos);
1281 __isl_give isl_aff *isl_aff_set_dim_name(
1282 __isl_take isl_aff *aff, enum isl_dim_type type,
1283 unsigned pos, const char *s);
1284 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1285 __isl_take isl_multi_aff *maff,
1286 enum isl_dim_type type, unsigned pos, const char *s);
1287 __isl_give isl_multi_pw_aff *
1288 isl_multi_pw_aff_set_dim_name(
1289 __isl_take isl_multi_pw_aff *mpa,
1290 enum isl_dim_type type, unsigned pos, const char *s);
1291 __isl_give isl_union_pw_aff *
1292 isl_union_pw_aff_set_dim_name(
1293 __isl_take isl_union_pw_aff *upa,
1294 enum isl_dim_type type, unsigned pos,
1296 __isl_give isl_union_pw_multi_aff *
1297 isl_union_pw_multi_aff_set_dim_name(
1298 __isl_take isl_union_pw_multi_aff *upma,
1299 enum isl_dim_type type, unsigned pos,
1301 __isl_give isl_multi_union_pw_aff *
1302 isl_multi_union_pw_aff_set_dim_name(
1303 __isl_take isl_multi_union_pw_aff *mupa,
1304 enum isl_dim_type type, unsigned pos,
1305 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1306 enum isl_dim_type type, unsigned pos);
1307 const char *isl_pw_aff_get_dim_name(
1308 __isl_keep isl_pw_aff *pa,
1309 enum isl_dim_type type, unsigned pos);
1310 const char *isl_pw_multi_aff_get_dim_name(
1311 __isl_keep isl_pw_multi_aff *pma,
1312 enum isl_dim_type type, unsigned pos);
1314 #include <isl/polynomial.h>
1315 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1316 __isl_take isl_qpolynomial *qp,
1317 enum isl_dim_type type, unsigned pos,
1319 __isl_give isl_pw_qpolynomial *
1320 isl_pw_qpolynomial_set_dim_name(
1321 __isl_take isl_pw_qpolynomial *pwqp,
1322 enum isl_dim_type type, unsigned pos,
1324 __isl_give isl_pw_qpolynomial_fold *
1325 isl_pw_qpolynomial_fold_set_dim_name(
1326 __isl_take isl_pw_qpolynomial_fold *pwf,
1327 enum isl_dim_type type, unsigned pos,
1329 __isl_give isl_union_pw_qpolynomial *
1330 isl_union_pw_qpolynomial_set_dim_name(
1331 __isl_take isl_union_pw_qpolynomial *upwqp,
1332 enum isl_dim_type type, unsigned pos,
1334 __isl_give isl_union_pw_qpolynomial_fold *
1335 isl_union_pw_qpolynomial_fold_set_dim_name(
1336 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1337 enum isl_dim_type type, unsigned pos,
1340 Note that C<isl_space_get_name> returns a pointer to some internal
1341 data structure, so the result can only be used while the
1342 corresponding C<isl_space> is alive.
1343 Also note that every function that operates on two sets or relations
1344 requires that both arguments have the same parameters. This also
1345 means that if one of the arguments has named parameters, then the
1346 other needs to have named parameters too and the names need to match.
1347 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1348 arguments may have different parameters (as long as they are named),
1349 in which case the result will have as parameters the union of the parameters of
1352 Given the identifier or name of a dimension (typically a parameter),
1353 its position can be obtained from the following functions.
1355 #include <isl/space.h>
1356 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1357 enum isl_dim_type type, __isl_keep isl_id *id);
1358 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1359 enum isl_dim_type type, const char *name);
1361 #include <isl/local_space.h>
1362 int isl_local_space_find_dim_by_name(
1363 __isl_keep isl_local_space *ls,
1364 enum isl_dim_type type, const char *name);
1366 #include <isl/val.h>
1367 int isl_multi_val_find_dim_by_id(
1368 __isl_keep isl_multi_val *mv,
1369 enum isl_dim_type type, __isl_keep isl_id *id);
1370 int isl_multi_val_find_dim_by_name(
1371 __isl_keep isl_multi_val *mv,
1372 enum isl_dim_type type, const char *name);
1374 #include <isl/set.h>
1375 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1376 enum isl_dim_type type, __isl_keep isl_id *id);
1377 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1378 enum isl_dim_type type, const char *name);
1380 #include <isl/map.h>
1381 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1382 enum isl_dim_type type, __isl_keep isl_id *id);
1383 int isl_basic_map_find_dim_by_name(
1384 __isl_keep isl_basic_map *bmap,
1385 enum isl_dim_type type, const char *name);
1386 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1387 enum isl_dim_type type, const char *name);
1388 int isl_union_map_find_dim_by_name(
1389 __isl_keep isl_union_map *umap,
1390 enum isl_dim_type type, const char *name);
1392 #include <isl/aff.h>
1393 int isl_multi_aff_find_dim_by_id(
1394 __isl_keep isl_multi_aff *ma,
1395 enum isl_dim_type type, __isl_keep isl_id *id);
1396 int isl_multi_pw_aff_find_dim_by_id(
1397 __isl_keep isl_multi_pw_aff *mpa,
1398 enum isl_dim_type type, __isl_keep isl_id *id);
1399 int isl_multi_union_pw_aff_find_dim_by_id(
1400 __isl_keep isl_union_multi_pw_aff *mupa,
1401 enum isl_dim_type type, __isl_keep isl_id *id);
1402 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1403 enum isl_dim_type type, const char *name);
1404 int isl_multi_aff_find_dim_by_name(
1405 __isl_keep isl_multi_aff *ma,
1406 enum isl_dim_type type, const char *name);
1407 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1408 enum isl_dim_type type, const char *name);
1409 int isl_multi_pw_aff_find_dim_by_name(
1410 __isl_keep isl_multi_pw_aff *mpa,
1411 enum isl_dim_type type, const char *name);
1412 int isl_pw_multi_aff_find_dim_by_name(
1413 __isl_keep isl_pw_multi_aff *pma,
1414 enum isl_dim_type type, const char *name);
1415 int isl_union_pw_aff_find_dim_by_name(
1416 __isl_keep isl_union_pw_aff *upa,
1417 enum isl_dim_type type, const char *name);
1418 int isl_union_pw_multi_aff_find_dim_by_name(
1419 __isl_keep isl_union_pw_multi_aff *upma,
1420 enum isl_dim_type type, const char *name);
1421 int isl_multi_union_pw_aff_find_dim_by_name(
1422 __isl_keep isl_multi_union_pw_aff *mupa,
1423 enum isl_dim_type type, const char *name);
1425 #include <isl/polynomial.h>
1426 int isl_pw_qpolynomial_find_dim_by_name(
1427 __isl_keep isl_pw_qpolynomial *pwqp,
1428 enum isl_dim_type type, const char *name);
1429 int isl_pw_qpolynomial_fold_find_dim_by_name(
1430 __isl_keep isl_pw_qpolynomial_fold *pwf,
1431 enum isl_dim_type type, const char *name);
1432 int isl_union_pw_qpolynomial_find_dim_by_name(
1433 __isl_keep isl_union_pw_qpolynomial *upwqp,
1434 enum isl_dim_type type, const char *name);
1435 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1436 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1437 enum isl_dim_type type, const char *name);
1439 The identifiers or names of entire spaces may be set or read off
1440 using the following functions.
1442 #include <isl/space.h>
1443 __isl_give isl_space *isl_space_set_tuple_id(
1444 __isl_take isl_space *space,
1445 enum isl_dim_type type, __isl_take isl_id *id);
1446 __isl_give isl_space *isl_space_reset_tuple_id(
1447 __isl_take isl_space *space, enum isl_dim_type type);
1448 isl_bool isl_space_has_tuple_id(
1449 __isl_keep isl_space *space,
1450 enum isl_dim_type type);
1451 __isl_give isl_id *isl_space_get_tuple_id(
1452 __isl_keep isl_space *space, enum isl_dim_type type);
1453 __isl_give isl_space *isl_space_set_tuple_name(
1454 __isl_take isl_space *space,
1455 enum isl_dim_type type, const char *s);
1456 isl_bool isl_space_has_tuple_name(
1457 __isl_keep isl_space *space,
1458 enum isl_dim_type type);
1459 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1460 enum isl_dim_type type);
1462 #include <isl/local_space.h>
1463 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1464 __isl_take isl_local_space *ls,
1465 enum isl_dim_type type, __isl_take isl_id *id);
1467 #include <isl/set.h>
1468 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1469 __isl_take isl_basic_set *bset,
1470 __isl_take isl_id *id);
1471 __isl_give isl_set *isl_set_set_tuple_id(
1472 __isl_take isl_set *set, __isl_take isl_id *id);
1473 __isl_give isl_set *isl_set_reset_tuple_id(
1474 __isl_take isl_set *set);
1475 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1476 __isl_give isl_id *isl_set_get_tuple_id(
1477 __isl_keep isl_set *set);
1478 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1479 __isl_take isl_basic_set *set, const char *s);
1480 __isl_give isl_set *isl_set_set_tuple_name(
1481 __isl_take isl_set *set, const char *s);
1482 const char *isl_basic_set_get_tuple_name(
1483 __isl_keep isl_basic_set *bset);
1484 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1485 const char *isl_set_get_tuple_name(
1486 __isl_keep isl_set *set);
1488 #include <isl/map.h>
1489 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1490 __isl_take isl_basic_map *bmap,
1491 enum isl_dim_type type, __isl_take isl_id *id);
1492 __isl_give isl_map *isl_map_set_tuple_id(
1493 __isl_take isl_map *map, enum isl_dim_type type,
1494 __isl_take isl_id *id);
1495 __isl_give isl_map *isl_map_reset_tuple_id(
1496 __isl_take isl_map *map, enum isl_dim_type type);
1497 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1498 enum isl_dim_type type);
1499 __isl_give isl_id *isl_map_get_tuple_id(
1500 __isl_keep isl_map *map, enum isl_dim_type type);
1501 __isl_give isl_map *isl_map_set_tuple_name(
1502 __isl_take isl_map *map,
1503 enum isl_dim_type type, const char *s);
1504 const char *isl_basic_map_get_tuple_name(
1505 __isl_keep isl_basic_map *bmap,
1506 enum isl_dim_type type);
1507 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1508 __isl_take isl_basic_map *bmap,
1509 enum isl_dim_type type, const char *s);
1510 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1511 enum isl_dim_type type);
1512 const char *isl_map_get_tuple_name(
1513 __isl_keep isl_map *map,
1514 enum isl_dim_type type);
1516 #include <isl/val.h>
1517 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1518 __isl_take isl_multi_val *mv,
1519 enum isl_dim_type type, __isl_take isl_id *id);
1520 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1521 __isl_take isl_multi_val *mv,
1522 enum isl_dim_type type);
1523 isl_bool isl_multi_val_has_tuple_id(
1524 __isl_keep isl_multi_val *mv,
1525 enum isl_dim_type type);
1526 __isl_give isl_id *isl_multi_val_get_tuple_id(
1527 __isl_keep isl_multi_val *mv,
1528 enum isl_dim_type type);
1529 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1530 __isl_take isl_multi_val *mv,
1531 enum isl_dim_type type, const char *s);
1532 const char *isl_multi_val_get_tuple_name(
1533 __isl_keep isl_multi_val *mv,
1534 enum isl_dim_type type);
1536 #include <isl/aff.h>
1537 __isl_give isl_aff *isl_aff_set_tuple_id(
1538 __isl_take isl_aff *aff,
1539 enum isl_dim_type type, __isl_take isl_id *id);
1540 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1541 __isl_take isl_multi_aff *maff,
1542 enum isl_dim_type type, __isl_take isl_id *id);
1543 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1544 __isl_take isl_pw_aff *pwaff,
1545 enum isl_dim_type type, __isl_take isl_id *id);
1546 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1547 __isl_take isl_pw_multi_aff *pma,
1548 enum isl_dim_type type, __isl_take isl_id *id);
1549 __isl_give isl_multi_union_pw_aff *
1550 isl_multi_union_pw_aff_set_tuple_id(
1551 __isl_take isl_multi_union_pw_aff *mupa,
1552 enum isl_dim_type type, __isl_take isl_id *id);
1553 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1554 __isl_take isl_multi_aff *ma,
1555 enum isl_dim_type type);
1556 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1557 __isl_take isl_pw_aff *pa,
1558 enum isl_dim_type type);
1559 __isl_give isl_multi_pw_aff *
1560 isl_multi_pw_aff_reset_tuple_id(
1561 __isl_take isl_multi_pw_aff *mpa,
1562 enum isl_dim_type type);
1563 __isl_give isl_pw_multi_aff *
1564 isl_pw_multi_aff_reset_tuple_id(
1565 __isl_take isl_pw_multi_aff *pma,
1566 enum isl_dim_type type);
1567 __isl_give isl_multi_union_pw_aff *
1568 isl_multi_union_pw_aff_reset_tuple_id(
1569 __isl_take isl_multi_union_pw_aff *mupa,
1570 enum isl_dim_type type);
1571 isl_bool isl_multi_aff_has_tuple_id(
1572 __isl_keep isl_multi_aff *ma,
1573 enum isl_dim_type type);
1574 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1575 __isl_keep isl_multi_aff *ma,
1576 enum isl_dim_type type);
1577 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1578 enum isl_dim_type type);
1579 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1580 __isl_keep isl_pw_aff *pa,
1581 enum isl_dim_type type);
1582 isl_bool isl_pw_multi_aff_has_tuple_id(
1583 __isl_keep isl_pw_multi_aff *pma,
1584 enum isl_dim_type type);
1585 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1586 __isl_keep isl_pw_multi_aff *pma,
1587 enum isl_dim_type type);
1588 isl_bool isl_multi_pw_aff_has_tuple_id(
1589 __isl_keep isl_multi_pw_aff *mpa,
1590 enum isl_dim_type type);
1591 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1592 __isl_keep isl_multi_pw_aff *mpa,
1593 enum isl_dim_type type);
1594 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1595 __isl_keep isl_multi_union_pw_aff *mupa,
1596 enum isl_dim_type type);
1597 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1598 __isl_keep isl_multi_union_pw_aff *mupa,
1599 enum isl_dim_type type);
1600 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1601 __isl_take isl_multi_aff *maff,
1602 enum isl_dim_type type, const char *s);
1603 __isl_give isl_multi_pw_aff *
1604 isl_multi_pw_aff_set_tuple_name(
1605 __isl_take isl_multi_pw_aff *mpa,
1606 enum isl_dim_type type, const char *s);
1607 __isl_give isl_multi_union_pw_aff *
1608 isl_multi_union_pw_aff_set_tuple_name(
1609 __isl_take isl_multi_union_pw_aff *mupa,
1610 enum isl_dim_type type, const char *s);
1611 const char *isl_multi_aff_get_tuple_name(
1612 __isl_keep isl_multi_aff *multi,
1613 enum isl_dim_type type);
1614 isl_bool isl_pw_multi_aff_has_tuple_name(
1615 __isl_keep isl_pw_multi_aff *pma,
1616 enum isl_dim_type type);
1617 const char *isl_pw_multi_aff_get_tuple_name(
1618 __isl_keep isl_pw_multi_aff *pma,
1619 enum isl_dim_type type);
1620 const char *isl_multi_union_pw_aff_get_tuple_name(
1621 __isl_keep isl_multi_union_pw_aff *mupa,
1622 enum isl_dim_type type);
1624 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1625 or C<isl_dim_set>. As with C<isl_space_get_name>,
1626 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1628 Binary operations require the corresponding spaces of their arguments
1629 to have the same name.
1631 To keep the names of all parameters and tuples, but reset the user pointers
1632 of all the corresponding identifiers, use the following function.
1634 #include <isl/space.h>
1635 __isl_give isl_space *isl_space_reset_user(
1636 __isl_take isl_space *space);
1638 #include <isl/set.h>
1639 __isl_give isl_set *isl_set_reset_user(
1640 __isl_take isl_set *set);
1642 #include <isl/map.h>
1643 __isl_give isl_map *isl_map_reset_user(
1644 __isl_take isl_map *map);
1646 #include <isl/union_set.h>
1647 __isl_give isl_union_set *isl_union_set_reset_user(
1648 __isl_take isl_union_set *uset);
1650 #include <isl/union_map.h>
1651 __isl_give isl_union_map *isl_union_map_reset_user(
1652 __isl_take isl_union_map *umap);
1654 #include <isl/val.h>
1655 __isl_give isl_multi_val *isl_multi_val_reset_user(
1656 __isl_take isl_multi_val *mv);
1658 #include <isl/aff.h>
1659 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1660 __isl_take isl_multi_aff *ma);
1661 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1662 __isl_take isl_pw_aff *pa);
1663 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1664 __isl_take isl_multi_pw_aff *mpa);
1665 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1666 __isl_take isl_pw_multi_aff *pma);
1667 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1668 __isl_take isl_union_pw_aff *upa);
1669 __isl_give isl_multi_union_pw_aff *
1670 isl_multi_union_pw_aff_reset_user(
1671 __isl_take isl_multi_union_pw_aff *mupa);
1672 __isl_give isl_union_pw_multi_aff *
1673 isl_union_pw_multi_aff_reset_user(
1674 __isl_take isl_union_pw_multi_aff *upma);
1676 #include <isl/polynomial.h>
1677 __isl_give isl_pw_qpolynomial *
1678 isl_pw_qpolynomial_reset_user(
1679 __isl_take isl_pw_qpolynomial *pwqp);
1680 __isl_give isl_union_pw_qpolynomial *
1681 isl_union_pw_qpolynomial_reset_user(
1682 __isl_take isl_union_pw_qpolynomial *upwqp);
1683 __isl_give isl_pw_qpolynomial_fold *
1684 isl_pw_qpolynomial_fold_reset_user(
1685 __isl_take isl_pw_qpolynomial_fold *pwf);
1686 __isl_give isl_union_pw_qpolynomial_fold *
1687 isl_union_pw_qpolynomial_fold_reset_user(
1688 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1690 Spaces can be nested. In particular, the domain of a set or
1691 the domain or range of a relation can be a nested relation.
1692 This process is also called I<wrapping>.
1693 The functions for detecting, constructing and deconstructing
1694 such nested spaces can be found in the wrapping properties
1695 of L</"Unary Properties">, the wrapping operations
1696 of L</"Unary Operations"> and the Cartesian product operations
1697 of L</"Basic Operations">.
1699 Spaces can be created from other spaces
1700 using the functions described in L</"Unary Operations">
1701 and L</"Binary Operations">.
1705 A local space is essentially a space with
1706 zero or more existentially quantified variables.
1707 The local space of various objects can be obtained
1708 using the following functions.
1710 #include <isl/constraint.h>
1711 __isl_give isl_local_space *isl_constraint_get_local_space(
1712 __isl_keep isl_constraint *constraint);
1714 #include <isl/set.h>
1715 __isl_give isl_local_space *isl_basic_set_get_local_space(
1716 __isl_keep isl_basic_set *bset);
1718 #include <isl/map.h>
1719 __isl_give isl_local_space *isl_basic_map_get_local_space(
1720 __isl_keep isl_basic_map *bmap);
1722 #include <isl/aff.h>
1723 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1724 __isl_keep isl_aff *aff);
1725 __isl_give isl_local_space *isl_aff_get_local_space(
1726 __isl_keep isl_aff *aff);
1728 A new local space can be created from a space using
1730 #include <isl/local_space.h>
1731 __isl_give isl_local_space *isl_local_space_from_space(
1732 __isl_take isl_space *space);
1734 They can be inspected, modified, copied and freed using the following functions.
1736 #include <isl/local_space.h>
1737 isl_bool isl_local_space_is_params(
1738 __isl_keep isl_local_space *ls);
1739 isl_bool isl_local_space_is_set(
1740 __isl_keep isl_local_space *ls);
1741 __isl_give isl_space *isl_local_space_get_space(
1742 __isl_keep isl_local_space *ls);
1743 __isl_give isl_aff *isl_local_space_get_div(
1744 __isl_keep isl_local_space *ls, int pos);
1745 __isl_give isl_local_space *isl_local_space_copy(
1746 __isl_keep isl_local_space *ls);
1747 __isl_null isl_local_space *isl_local_space_free(
1748 __isl_take isl_local_space *ls);
1750 Note that C<isl_local_space_get_div> can only be used on local spaces
1753 Two local spaces can be compared using
1755 isl_bool isl_local_space_is_equal(
1756 __isl_keep isl_local_space *ls1,
1757 __isl_keep isl_local_space *ls2);
1759 Local spaces can be created from other local spaces
1760 using the functions described in L</"Unary Operations">
1761 and L</"Binary Operations">.
1763 =head2 Creating New Sets and Relations
1765 C<isl> has functions for creating some standard sets and relations.
1769 =item * Empty sets and relations
1771 __isl_give isl_basic_set *isl_basic_set_empty(
1772 __isl_take isl_space *space);
1773 __isl_give isl_basic_map *isl_basic_map_empty(
1774 __isl_take isl_space *space);
1775 __isl_give isl_set *isl_set_empty(
1776 __isl_take isl_space *space);
1777 __isl_give isl_map *isl_map_empty(
1778 __isl_take isl_space *space);
1779 __isl_give isl_union_set *isl_union_set_empty(
1780 __isl_take isl_space *space);
1781 __isl_give isl_union_map *isl_union_map_empty(
1782 __isl_take isl_space *space);
1784 For C<isl_union_set>s and C<isl_union_map>s, the space
1785 is only used to specify the parameters.
1787 =item * Universe sets and relations
1789 __isl_give isl_basic_set *isl_basic_set_universe(
1790 __isl_take isl_space *space);
1791 __isl_give isl_basic_map *isl_basic_map_universe(
1792 __isl_take isl_space *space);
1793 __isl_give isl_set *isl_set_universe(
1794 __isl_take isl_space *space);
1795 __isl_give isl_map *isl_map_universe(
1796 __isl_take isl_space *space);
1797 __isl_give isl_union_set *isl_union_set_universe(
1798 __isl_take isl_union_set *uset);
1799 __isl_give isl_union_map *isl_union_map_universe(
1800 __isl_take isl_union_map *umap);
1802 The sets and relations constructed by the functions above
1803 contain all integer values, while those constructed by the
1804 functions below only contain non-negative values.
1806 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1807 __isl_take isl_space *space);
1808 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1809 __isl_take isl_space *space);
1810 __isl_give isl_set *isl_set_nat_universe(
1811 __isl_take isl_space *space);
1812 __isl_give isl_map *isl_map_nat_universe(
1813 __isl_take isl_space *space);
1815 =item * Identity relations
1817 __isl_give isl_basic_map *isl_basic_map_identity(
1818 __isl_take isl_space *space);
1819 __isl_give isl_map *isl_map_identity(
1820 __isl_take isl_space *space);
1822 The number of input and output dimensions in C<space> needs
1825 =item * Lexicographic order
1827 __isl_give isl_map *isl_map_lex_lt(
1828 __isl_take isl_space *set_space);
1829 __isl_give isl_map *isl_map_lex_le(
1830 __isl_take isl_space *set_space);
1831 __isl_give isl_map *isl_map_lex_gt(
1832 __isl_take isl_space *set_space);
1833 __isl_give isl_map *isl_map_lex_ge(
1834 __isl_take isl_space *set_space);
1835 __isl_give isl_map *isl_map_lex_lt_first(
1836 __isl_take isl_space *space, unsigned n);
1837 __isl_give isl_map *isl_map_lex_le_first(
1838 __isl_take isl_space *space, unsigned n);
1839 __isl_give isl_map *isl_map_lex_gt_first(
1840 __isl_take isl_space *space, unsigned n);
1841 __isl_give isl_map *isl_map_lex_ge_first(
1842 __isl_take isl_space *space, unsigned n);
1844 The first four functions take a space for a B<set>
1845 and return relations that express that the elements in the domain
1846 are lexicographically less
1847 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1848 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1849 than the elements in the range.
1850 The last four functions take a space for a map
1851 and return relations that express that the first C<n> dimensions
1852 in the domain are lexicographically less
1853 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1854 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1855 than the first C<n> dimensions in the range.
1859 A basic set or relation can be converted to a set or relation
1860 using the following functions.
1862 __isl_give isl_set *isl_set_from_basic_set(
1863 __isl_take isl_basic_set *bset);
1864 __isl_give isl_map *isl_map_from_basic_map(
1865 __isl_take isl_basic_map *bmap);
1867 Sets and relations can be converted to union sets and relations
1868 using the following functions.
1870 __isl_give isl_union_set *isl_union_set_from_basic_set(
1871 __isl_take isl_basic_set *bset);
1872 __isl_give isl_union_map *isl_union_map_from_basic_map(
1873 __isl_take isl_basic_map *bmap);
1874 __isl_give isl_union_set *isl_union_set_from_set(
1875 __isl_take isl_set *set);
1876 __isl_give isl_union_map *isl_union_map_from_map(
1877 __isl_take isl_map *map);
1879 The inverse conversions below can only be used if the input
1880 union set or relation is known to contain elements in exactly one
1883 __isl_give isl_set *isl_set_from_union_set(
1884 __isl_take isl_union_set *uset);
1885 __isl_give isl_map *isl_map_from_union_map(
1886 __isl_take isl_union_map *umap);
1888 Sets and relations can be copied and freed again using the following
1891 __isl_give isl_basic_set *isl_basic_set_copy(
1892 __isl_keep isl_basic_set *bset);
1893 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1894 __isl_give isl_union_set *isl_union_set_copy(
1895 __isl_keep isl_union_set *uset);
1896 __isl_give isl_basic_map *isl_basic_map_copy(
1897 __isl_keep isl_basic_map *bmap);
1898 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1899 __isl_give isl_union_map *isl_union_map_copy(
1900 __isl_keep isl_union_map *umap);
1901 __isl_null isl_basic_set *isl_basic_set_free(
1902 __isl_take isl_basic_set *bset);
1903 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1904 __isl_null isl_union_set *isl_union_set_free(
1905 __isl_take isl_union_set *uset);
1906 __isl_null isl_basic_map *isl_basic_map_free(
1907 __isl_take isl_basic_map *bmap);
1908 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1909 __isl_null isl_union_map *isl_union_map_free(
1910 __isl_take isl_union_map *umap);
1912 Other sets and relations can be constructed by starting
1913 from a universe set or relation, adding equality and/or
1914 inequality constraints and then projecting out the
1915 existentially quantified variables, if any.
1916 Constraints can be constructed, manipulated and
1917 added to (or removed from) (basic) sets and relations
1918 using the following functions.
1920 #include <isl/constraint.h>
1921 __isl_give isl_constraint *isl_constraint_alloc_equality(
1922 __isl_take isl_local_space *ls);
1923 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1924 __isl_take isl_local_space *ls);
1925 __isl_give isl_constraint *isl_constraint_set_constant_si(
1926 __isl_take isl_constraint *constraint, int v);
1927 __isl_give isl_constraint *isl_constraint_set_constant_val(
1928 __isl_take isl_constraint *constraint,
1929 __isl_take isl_val *v);
1930 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1931 __isl_take isl_constraint *constraint,
1932 enum isl_dim_type type, int pos, int v);
1933 __isl_give isl_constraint *
1934 isl_constraint_set_coefficient_val(
1935 __isl_take isl_constraint *constraint,
1936 enum isl_dim_type type, int pos,
1937 __isl_take isl_val *v);
1938 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1939 __isl_take isl_basic_map *bmap,
1940 __isl_take isl_constraint *constraint);
1941 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1942 __isl_take isl_basic_set *bset,
1943 __isl_take isl_constraint *constraint);
1944 __isl_give isl_map *isl_map_add_constraint(
1945 __isl_take isl_map *map,
1946 __isl_take isl_constraint *constraint);
1947 __isl_give isl_set *isl_set_add_constraint(
1948 __isl_take isl_set *set,
1949 __isl_take isl_constraint *constraint);
1951 For example, to create a set containing the even integers
1952 between 10 and 42, you would use the following code.
1955 isl_local_space *ls;
1957 isl_basic_set *bset;
1959 space = isl_space_set_alloc(ctx, 0, 2);
1960 bset = isl_basic_set_universe(isl_space_copy(space));
1961 ls = isl_local_space_from_space(space);
1963 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
1964 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1965 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1966 bset = isl_basic_set_add_constraint(bset, c);
1968 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
1969 c = isl_constraint_set_constant_si(c, -10);
1970 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1971 bset = isl_basic_set_add_constraint(bset, c);
1973 c = isl_constraint_alloc_inequality(ls);
1974 c = isl_constraint_set_constant_si(c, 42);
1975 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1976 bset = isl_basic_set_add_constraint(bset, c);
1978 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1982 isl_basic_set *bset;
1983 bset = isl_basic_set_read_from_str(ctx,
1984 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1986 A basic set or relation can also be constructed from two matrices
1987 describing the equalities and the inequalities.
1989 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1990 __isl_take isl_space *space,
1991 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1992 enum isl_dim_type c1,
1993 enum isl_dim_type c2, enum isl_dim_type c3,
1994 enum isl_dim_type c4);
1995 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1996 __isl_take isl_space *space,
1997 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1998 enum isl_dim_type c1,
1999 enum isl_dim_type c2, enum isl_dim_type c3,
2000 enum isl_dim_type c4, enum isl_dim_type c5);
2002 The C<isl_dim_type> arguments indicate the order in which
2003 different kinds of variables appear in the input matrices
2004 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2005 C<isl_dim_set> and C<isl_dim_div> for sets and
2006 of C<isl_dim_cst>, C<isl_dim_param>,
2007 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2009 A (basic or union) set or relation can also be constructed from a
2010 (union) (piecewise) (multiple) affine expression
2011 or a list of affine expressions
2012 (See L</"Functions">), provided these affine expressions do not
2015 __isl_give isl_basic_map *isl_basic_map_from_aff(
2016 __isl_take isl_aff *aff);
2017 __isl_give isl_map *isl_map_from_aff(
2018 __isl_take isl_aff *aff);
2019 __isl_give isl_set *isl_set_from_pw_aff(
2020 __isl_take isl_pw_aff *pwaff);
2021 __isl_give isl_map *isl_map_from_pw_aff(
2022 __isl_take isl_pw_aff *pwaff);
2023 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2024 __isl_take isl_space *domain_space,
2025 __isl_take isl_aff_list *list);
2026 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2027 __isl_take isl_multi_aff *maff)
2028 __isl_give isl_map *isl_map_from_multi_aff(
2029 __isl_take isl_multi_aff *maff)
2030 __isl_give isl_set *isl_set_from_pw_multi_aff(
2031 __isl_take isl_pw_multi_aff *pma);
2032 __isl_give isl_map *isl_map_from_pw_multi_aff(
2033 __isl_take isl_pw_multi_aff *pma);
2034 __isl_give isl_set *isl_set_from_multi_pw_aff(
2035 __isl_take isl_multi_pw_aff *mpa);
2036 __isl_give isl_map *isl_map_from_multi_pw_aff(
2037 __isl_take isl_multi_pw_aff *mpa);
2038 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2039 __isl_take isl_union_pw_aff *upa);
2040 __isl_give isl_union_map *
2041 isl_union_map_from_union_pw_multi_aff(
2042 __isl_take isl_union_pw_multi_aff *upma);
2043 __isl_give isl_union_map *
2044 isl_union_map_from_multi_union_pw_aff(
2045 __isl_take isl_multi_union_pw_aff *mupa);
2047 The C<domain_space> argument describes the domain of the resulting
2048 basic relation. It is required because the C<list> may consist
2049 of zero affine expressions.
2050 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2051 is not allowed to be zero-dimensional. The domain of the result
2052 is the shared domain of the union piecewise affine elements.
2054 =head2 Inspecting Sets and Relations
2056 Usually, the user should not have to care about the actual constraints
2057 of the sets and maps, but should instead apply the abstract operations
2058 explained in the following sections.
2059 Occasionally, however, it may be required to inspect the individual
2060 coefficients of the constraints. This section explains how to do so.
2061 In these cases, it may also be useful to have C<isl> compute
2062 an explicit representation of the existentially quantified variables.
2064 __isl_give isl_set *isl_set_compute_divs(
2065 __isl_take isl_set *set);
2066 __isl_give isl_map *isl_map_compute_divs(
2067 __isl_take isl_map *map);
2068 __isl_give isl_union_set *isl_union_set_compute_divs(
2069 __isl_take isl_union_set *uset);
2070 __isl_give isl_union_map *isl_union_map_compute_divs(
2071 __isl_take isl_union_map *umap);
2073 This explicit representation defines the existentially quantified
2074 variables as integer divisions of the other variables, possibly
2075 including earlier existentially quantified variables.
2076 An explicitly represented existentially quantified variable therefore
2077 has a unique value when the values of the other variables are known.
2078 If, furthermore, the same existentials, i.e., existentials
2079 with the same explicit representations, should appear in the
2080 same order in each of the disjuncts of a set or map, then the user should call
2081 either of the following functions.
2083 __isl_give isl_set *isl_set_align_divs(
2084 __isl_take isl_set *set);
2085 __isl_give isl_map *isl_map_align_divs(
2086 __isl_take isl_map *map);
2088 Alternatively, the existentially quantified variables can be removed
2089 using the following functions, which compute an overapproximation.
2091 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2092 __isl_take isl_basic_set *bset);
2093 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2094 __isl_take isl_basic_map *bmap);
2095 __isl_give isl_set *isl_set_remove_divs(
2096 __isl_take isl_set *set);
2097 __isl_give isl_map *isl_map_remove_divs(
2098 __isl_take isl_map *map);
2100 It is also possible to only remove those divs that are defined
2101 in terms of a given range of dimensions or only those for which
2102 no explicit representation is known.
2104 __isl_give isl_basic_set *
2105 isl_basic_set_remove_divs_involving_dims(
2106 __isl_take isl_basic_set *bset,
2107 enum isl_dim_type type,
2108 unsigned first, unsigned n);
2109 __isl_give isl_basic_map *
2110 isl_basic_map_remove_divs_involving_dims(
2111 __isl_take isl_basic_map *bmap,
2112 enum isl_dim_type type,
2113 unsigned first, unsigned n);
2114 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2115 __isl_take isl_set *set, enum isl_dim_type type,
2116 unsigned first, unsigned n);
2117 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2118 __isl_take isl_map *map, enum isl_dim_type type,
2119 unsigned first, unsigned n);
2121 __isl_give isl_basic_set *
2122 isl_basic_set_remove_unknown_divs(
2123 __isl_take isl_basic_set *bset);
2124 __isl_give isl_set *isl_set_remove_unknown_divs(
2125 __isl_take isl_set *set);
2126 __isl_give isl_map *isl_map_remove_unknown_divs(
2127 __isl_take isl_map *map);
2129 To iterate over all the sets or maps in a union set or map, use
2131 isl_stat isl_union_set_foreach_set(
2132 __isl_keep isl_union_set *uset,
2133 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2135 isl_stat isl_union_map_foreach_map(
2136 __isl_keep isl_union_map *umap,
2137 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2140 These functions call the callback function once for each
2141 (pair of) space(s) for which there are elements in the input.
2142 The argument to the callback contains all elements in the input
2143 with that (pair of) space(s).
2145 The number of sets or maps in a union set or map can be obtained
2148 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2149 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2151 To extract the set or map in a given space from a union, use
2153 __isl_give isl_set *isl_union_set_extract_set(
2154 __isl_keep isl_union_set *uset,
2155 __isl_take isl_space *space);
2156 __isl_give isl_map *isl_union_map_extract_map(
2157 __isl_keep isl_union_map *umap,
2158 __isl_take isl_space *space);
2160 To iterate over all the basic sets or maps in a set or map, use
2162 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2163 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2166 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2167 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2171 The callback function C<fn> should return 0 if successful and
2172 -1 if an error occurs. In the latter case, or if any other error
2173 occurs, the above functions will return -1.
2175 It should be noted that C<isl> does not guarantee that
2176 the basic sets or maps passed to C<fn> are disjoint.
2177 If this is required, then the user should call one of
2178 the following functions first.
2180 __isl_give isl_set *isl_set_make_disjoint(
2181 __isl_take isl_set *set);
2182 __isl_give isl_map *isl_map_make_disjoint(
2183 __isl_take isl_map *map);
2185 The number of basic sets in a set can be obtained
2186 or the number of basic maps in a map can be obtained
2189 #include <isl/set.h>
2190 int isl_set_n_basic_set(__isl_keep isl_set *set);
2192 #include <isl/map.h>
2193 int isl_map_n_basic_map(__isl_keep isl_map *map);
2195 It is also possible to obtain a list of basic sets from a set
2197 #include <isl/set.h>
2198 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2199 __isl_keep isl_set *set);
2201 The returned list can be manipulated using the functions in L<"Lists">.
2203 To iterate over the constraints of a basic set or map, use
2205 #include <isl/constraint.h>
2207 int isl_basic_set_n_constraint(
2208 __isl_keep isl_basic_set *bset);
2209 isl_stat isl_basic_set_foreach_constraint(
2210 __isl_keep isl_basic_set *bset,
2211 isl_stat (*fn)(__isl_take isl_constraint *c,
2214 int isl_basic_map_n_constraint(
2215 __isl_keep isl_basic_map *bmap);
2216 isl_stat isl_basic_map_foreach_constraint(
2217 __isl_keep isl_basic_map *bmap,
2218 isl_stat (*fn)(__isl_take isl_constraint *c,
2221 __isl_null isl_constraint *isl_constraint_free(
2222 __isl_take isl_constraint *c);
2224 Again, the callback function C<fn> should return 0 if successful and
2225 -1 if an error occurs. In the latter case, or if any other error
2226 occurs, the above functions will return -1.
2227 The constraint C<c> represents either an equality or an inequality.
2228 Use the following function to find out whether a constraint
2229 represents an equality. If not, it represents an inequality.
2231 isl_bool isl_constraint_is_equality(
2232 __isl_keep isl_constraint *constraint);
2234 It is also possible to obtain a list of constraints from a basic
2237 #include <isl/constraint.h>
2238 __isl_give isl_constraint_list *
2239 isl_basic_map_get_constraint_list(
2240 __isl_keep isl_basic_map *bmap);
2241 __isl_give isl_constraint_list *
2242 isl_basic_set_get_constraint_list(
2243 __isl_keep isl_basic_set *bset);
2245 These functions require that all existentially quantified variables
2246 have an explicit representation.
2247 The returned list can be manipulated using the functions in L<"Lists">.
2249 The coefficients of the constraints can be inspected using
2250 the following functions.
2252 isl_bool isl_constraint_is_lower_bound(
2253 __isl_keep isl_constraint *constraint,
2254 enum isl_dim_type type, unsigned pos);
2255 isl_bool isl_constraint_is_upper_bound(
2256 __isl_keep isl_constraint *constraint,
2257 enum isl_dim_type type, unsigned pos);
2258 __isl_give isl_val *isl_constraint_get_constant_val(
2259 __isl_keep isl_constraint *constraint);
2260 __isl_give isl_val *isl_constraint_get_coefficient_val(
2261 __isl_keep isl_constraint *constraint,
2262 enum isl_dim_type type, int pos);
2264 The explicit representations of the existentially quantified
2265 variables can be inspected using the following function.
2266 Note that the user is only allowed to use this function
2267 if the inspected set or map is the result of a call
2268 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2269 The existentially quantified variable is equal to the floor
2270 of the returned affine expression. The affine expression
2271 itself can be inspected using the functions in
2274 __isl_give isl_aff *isl_constraint_get_div(
2275 __isl_keep isl_constraint *constraint, int pos);
2277 To obtain the constraints of a basic set or map in matrix
2278 form, use the following functions.
2280 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2281 __isl_keep isl_basic_set *bset,
2282 enum isl_dim_type c1, enum isl_dim_type c2,
2283 enum isl_dim_type c3, enum isl_dim_type c4);
2284 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2285 __isl_keep isl_basic_set *bset,
2286 enum isl_dim_type c1, enum isl_dim_type c2,
2287 enum isl_dim_type c3, enum isl_dim_type c4);
2288 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2289 __isl_keep isl_basic_map *bmap,
2290 enum isl_dim_type c1,
2291 enum isl_dim_type c2, enum isl_dim_type c3,
2292 enum isl_dim_type c4, enum isl_dim_type c5);
2293 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2294 __isl_keep isl_basic_map *bmap,
2295 enum isl_dim_type c1,
2296 enum isl_dim_type c2, enum isl_dim_type c3,
2297 enum isl_dim_type c4, enum isl_dim_type c5);
2299 The C<isl_dim_type> arguments dictate the order in which
2300 different kinds of variables appear in the resulting matrix.
2301 For set inputs, they should be a permutation of
2302 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2303 For map inputs, they should be a permutation of
2304 C<isl_dim_cst>, C<isl_dim_param>,
2305 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2309 Points are elements of a set. They can be used to construct
2310 simple sets (boxes) or they can be used to represent the
2311 individual elements of a set.
2312 The zero point (the origin) can be created using
2314 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2316 The coordinates of a point can be inspected, set and changed
2319 __isl_give isl_val *isl_point_get_coordinate_val(
2320 __isl_keep isl_point *pnt,
2321 enum isl_dim_type type, int pos);
2322 __isl_give isl_point *isl_point_set_coordinate_val(
2323 __isl_take isl_point *pnt,
2324 enum isl_dim_type type, int pos,
2325 __isl_take isl_val *v);
2327 __isl_give isl_point *isl_point_add_ui(
2328 __isl_take isl_point *pnt,
2329 enum isl_dim_type type, int pos, unsigned val);
2330 __isl_give isl_point *isl_point_sub_ui(
2331 __isl_take isl_point *pnt,
2332 enum isl_dim_type type, int pos, unsigned val);
2334 Points can be copied or freed using
2336 __isl_give isl_point *isl_point_copy(
2337 __isl_keep isl_point *pnt);
2338 void isl_point_free(__isl_take isl_point *pnt);
2340 A singleton set can be created from a point using
2342 __isl_give isl_basic_set *isl_basic_set_from_point(
2343 __isl_take isl_point *pnt);
2344 __isl_give isl_set *isl_set_from_point(
2345 __isl_take isl_point *pnt);
2346 __isl_give isl_union_set *isl_union_set_from_point(
2347 __isl_take isl_point *pnt);
2349 and a box can be created from two opposite extremal points using
2351 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2352 __isl_take isl_point *pnt1,
2353 __isl_take isl_point *pnt2);
2354 __isl_give isl_set *isl_set_box_from_points(
2355 __isl_take isl_point *pnt1,
2356 __isl_take isl_point *pnt2);
2358 All elements of a B<bounded> (union) set can be enumerated using
2359 the following functions.
2361 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2362 isl_stat (*fn)(__isl_take isl_point *pnt,
2365 isl_stat isl_union_set_foreach_point(
2366 __isl_keep isl_union_set *uset,
2367 isl_stat (*fn)(__isl_take isl_point *pnt,
2371 The function C<fn> is called for each integer point in
2372 C<set> with as second argument the last argument of
2373 the C<isl_set_foreach_point> call. The function C<fn>
2374 should return C<0> on success and C<-1> on failure.
2375 In the latter case, C<isl_set_foreach_point> will stop
2376 enumerating and return C<-1> as well.
2377 If the enumeration is performed successfully and to completion,
2378 then C<isl_set_foreach_point> returns C<0>.
2380 To obtain a single point of a (basic or union) set, use
2382 __isl_give isl_point *isl_basic_set_sample_point(
2383 __isl_take isl_basic_set *bset);
2384 __isl_give isl_point *isl_set_sample_point(
2385 __isl_take isl_set *set);
2386 __isl_give isl_point *isl_union_set_sample_point(
2387 __isl_take isl_union_set *uset);
2389 If C<set> does not contain any (integer) points, then the
2390 resulting point will be ``void'', a property that can be
2393 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2397 Besides sets and relation, C<isl> also supports various types of functions.
2398 Each of these types is derived from the value type (see L</"Values">)
2399 or from one of two primitive function types
2400 through the application of zero or more type constructors.
2401 We first describe the primitive type and then we describe
2402 the types derived from these primitive types.
2404 =head3 Primitive Functions
2406 C<isl> support two primitive function types, quasi-affine
2407 expressions and quasipolynomials.
2408 A quasi-affine expression is defined either over a parameter
2409 space or over a set and is composed of integer constants,
2410 parameters and set variables, addition, subtraction and
2411 integer division by an integer constant.
2412 For example, the quasi-affine expression
2414 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2416 maps C<x> to C<2*floor((4 n + x)/9>.
2417 A quasipolynomial is a polynomial expression in quasi-affine
2418 expression. That is, it additionally allows for multiplication.
2419 Note, though, that it is not allowed to construct an integer
2420 division of an expression involving multiplications.
2421 Here is an example of a quasipolynomial that is not
2422 quasi-affine expression
2424 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2426 Note that the external representations of quasi-affine expressions
2427 and quasipolynomials are different. Quasi-affine expressions
2428 use a notation with square brackets just like binary relations,
2429 while quasipolynomials do not. This might change at some point.
2431 If a primitive function is defined over a parameter space,
2432 then the space of the function itself is that of a set.
2433 If it is defined over a set, then the space of the function
2434 is that of a relation. In both cases, the set space (or
2435 the output space) is single-dimensional, anonymous and unstructured.
2436 To create functions with multiple dimensions or with other kinds
2437 of set or output spaces, use multiple expressions
2438 (see L</"Multiple Expressions">).
2442 =item * Quasi-affine Expressions
2444 Besides the expressions described above, a quasi-affine
2445 expression can also be set to NaN. Such expressions
2446 typically represent a failure to represent a result
2447 as a quasi-affine expression.
2449 The zero quasi affine expression or the quasi affine expression
2450 that is equal to a given value or
2451 a specified dimension on a given domain can be created using
2453 #include <isl/aff.h>
2454 __isl_give isl_aff *isl_aff_zero_on_domain(
2455 __isl_take isl_local_space *ls);
2456 __isl_give isl_aff *isl_aff_val_on_domain(
2457 __isl_take isl_local_space *ls,
2458 __isl_take isl_val *val);
2459 __isl_give isl_aff *isl_aff_var_on_domain(
2460 __isl_take isl_local_space *ls,
2461 enum isl_dim_type type, unsigned pos);
2462 __isl_give isl_aff *isl_aff_nan_on_domain(
2463 __isl_take isl_local_space *ls);
2465 Quasi affine expressions can be copied and freed using
2467 #include <isl/aff.h>
2468 __isl_give isl_aff *isl_aff_copy(
2469 __isl_keep isl_aff *aff);
2470 __isl_null isl_aff *isl_aff_free(
2471 __isl_take isl_aff *aff);
2473 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2474 using the following function. The constraint is required to have
2475 a non-zero coefficient for the specified dimension.
2477 #include <isl/constraint.h>
2478 __isl_give isl_aff *isl_constraint_get_bound(
2479 __isl_keep isl_constraint *constraint,
2480 enum isl_dim_type type, int pos);
2482 The entire affine expression of the constraint can also be extracted
2483 using the following function.
2485 #include <isl/constraint.h>
2486 __isl_give isl_aff *isl_constraint_get_aff(
2487 __isl_keep isl_constraint *constraint);
2489 Conversely, an equality constraint equating
2490 the affine expression to zero or an inequality constraint enforcing
2491 the affine expression to be non-negative, can be constructed using
2493 __isl_give isl_constraint *isl_equality_from_aff(
2494 __isl_take isl_aff *aff);
2495 __isl_give isl_constraint *isl_inequality_from_aff(
2496 __isl_take isl_aff *aff);
2498 The coefficients and the integer divisions of an affine expression
2499 can be inspected using the following functions.
2501 #include <isl/aff.h>
2502 __isl_give isl_val *isl_aff_get_constant_val(
2503 __isl_keep isl_aff *aff);
2504 __isl_give isl_val *isl_aff_get_coefficient_val(
2505 __isl_keep isl_aff *aff,
2506 enum isl_dim_type type, int pos);
2507 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2508 enum isl_dim_type type, int pos);
2509 __isl_give isl_val *isl_aff_get_denominator_val(
2510 __isl_keep isl_aff *aff);
2511 __isl_give isl_aff *isl_aff_get_div(
2512 __isl_keep isl_aff *aff, int pos);
2514 They can be modified using the following functions.
2516 #include <isl/aff.h>
2517 __isl_give isl_aff *isl_aff_set_constant_si(
2518 __isl_take isl_aff *aff, int v);
2519 __isl_give isl_aff *isl_aff_set_constant_val(
2520 __isl_take isl_aff *aff, __isl_take isl_val *v);
2521 __isl_give isl_aff *isl_aff_set_coefficient_si(
2522 __isl_take isl_aff *aff,
2523 enum isl_dim_type type, int pos, int v);
2524 __isl_give isl_aff *isl_aff_set_coefficient_val(
2525 __isl_take isl_aff *aff,
2526 enum isl_dim_type type, int pos,
2527 __isl_take isl_val *v);
2529 __isl_give isl_aff *isl_aff_add_constant_si(
2530 __isl_take isl_aff *aff, int v);
2531 __isl_give isl_aff *isl_aff_add_constant_val(
2532 __isl_take isl_aff *aff, __isl_take isl_val *v);
2533 __isl_give isl_aff *isl_aff_add_constant_num_si(
2534 __isl_take isl_aff *aff, int v);
2535 __isl_give isl_aff *isl_aff_add_coefficient_si(
2536 __isl_take isl_aff *aff,
2537 enum isl_dim_type type, int pos, int v);
2538 __isl_give isl_aff *isl_aff_add_coefficient_val(
2539 __isl_take isl_aff *aff,
2540 enum isl_dim_type type, int pos,
2541 __isl_take isl_val *v);
2543 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2544 set the I<numerator> of the constant or coefficient, while
2545 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2546 the constant or coefficient as a whole.
2547 The C<add_constant> and C<add_coefficient> functions add an integer
2548 or rational value to
2549 the possibly rational constant or coefficient.
2550 The C<add_constant_num> functions add an integer value to
2553 =item * Quasipolynomials
2555 Some simple quasipolynomials can be created using the following functions.
2557 #include <isl/polynomial.h>
2558 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2559 __isl_take isl_space *domain);
2560 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2561 __isl_take isl_space *domain);
2562 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2563 __isl_take isl_space *domain);
2564 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2565 __isl_take isl_space *domain);
2566 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2567 __isl_take isl_space *domain);
2568 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2569 __isl_take isl_space *domain,
2570 __isl_take isl_val *val);
2571 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2572 __isl_take isl_space *domain,
2573 enum isl_dim_type type, unsigned pos);
2574 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2575 __isl_take isl_aff *aff);
2577 Recall that the space in which a quasipolynomial lives is a map space
2578 with a one-dimensional range. The C<domain> argument in some of
2579 the functions above corresponds to the domain of this map space.
2581 Quasipolynomials can be copied and freed again using the following
2584 #include <isl/polynomial.h>
2585 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2586 __isl_keep isl_qpolynomial *qp);
2587 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2588 __isl_take isl_qpolynomial *qp);
2590 The constant term of a quasipolynomial can be extracted using
2592 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2593 __isl_keep isl_qpolynomial *qp);
2595 To iterate over all terms in a quasipolynomial,
2598 isl_stat isl_qpolynomial_foreach_term(
2599 __isl_keep isl_qpolynomial *qp,
2600 isl_stat (*fn)(__isl_take isl_term *term,
2601 void *user), void *user);
2603 The terms themselves can be inspected and freed using
2606 unsigned isl_term_dim(__isl_keep isl_term *term,
2607 enum isl_dim_type type);
2608 __isl_give isl_val *isl_term_get_coefficient_val(
2609 __isl_keep isl_term *term);
2610 int isl_term_get_exp(__isl_keep isl_term *term,
2611 enum isl_dim_type type, unsigned pos);
2612 __isl_give isl_aff *isl_term_get_div(
2613 __isl_keep isl_term *term, unsigned pos);
2614 void isl_term_free(__isl_take isl_term *term);
2616 Each term is a product of parameters, set variables and
2617 integer divisions. The function C<isl_term_get_exp>
2618 returns the exponent of a given dimensions in the given term.
2624 A reduction represents a maximum or a minimum of its
2626 The only reduction type defined by C<isl> is
2627 C<isl_qpolynomial_fold>.
2629 There are currently no functions to directly create such
2630 objects, but they do appear in the piecewise quasipolynomial
2631 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2633 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2635 Reductions can be copied and freed using
2636 the following functions.
2638 #include <isl/polynomial.h>
2639 __isl_give isl_qpolynomial_fold *
2640 isl_qpolynomial_fold_copy(
2641 __isl_keep isl_qpolynomial_fold *fold);
2642 void isl_qpolynomial_fold_free(
2643 __isl_take isl_qpolynomial_fold *fold);
2645 To iterate over all quasipolynomials in a reduction, use
2647 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2648 __isl_keep isl_qpolynomial_fold *fold,
2649 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2650 void *user), void *user);
2652 =head3 Multiple Expressions
2654 A multiple expression represents a sequence of zero or
2655 more base expressions, all defined on the same domain space.
2656 The domain space of the multiple expression is the same
2657 as that of the base expressions, but the range space
2658 can be any space. In case the base expressions have
2659 a set space, the corresponding multiple expression
2660 also has a set space.
2661 Objects of the value type do not have an associated space.
2662 The space of a multiple value is therefore always a set space.
2663 Similarly, the space of a multiple union piecewise
2664 affine expression is always a set space.
2666 The multiple expression types defined by C<isl>
2667 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2668 C<isl_multi_union_pw_aff>.
2670 A multiple expression with the value zero for
2671 each output (or set) dimension can be created
2672 using the following functions.
2674 #include <isl/val.h>
2675 __isl_give isl_multi_val *isl_multi_val_zero(
2676 __isl_take isl_space *space);
2678 #include <isl/aff.h>
2679 __isl_give isl_multi_aff *isl_multi_aff_zero(
2680 __isl_take isl_space *space);
2681 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2682 __isl_take isl_space *space);
2683 __isl_give isl_multi_union_pw_aff *
2684 isl_multi_union_pw_aff_zero(
2685 __isl_take isl_space *space);
2687 Since there is no canonical way of representing a zero
2688 value of type C<isl_union_pw_aff>, the space passed
2689 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2691 An identity function can be created using the following
2692 functions. The space needs to be that of a relation
2693 with the same number of input and output dimensions.
2695 #include <isl/aff.h>
2696 __isl_give isl_multi_aff *isl_multi_aff_identity(
2697 __isl_take isl_space *space);
2698 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2699 __isl_take isl_space *space);
2701 A function that performs a projection on a universe
2702 relation or set can be created using the following functions.
2703 See also the corresponding
2704 projection operations in L</"Unary Operations">.
2706 #include <isl/aff.h>
2707 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2708 __isl_take isl_space *space);
2709 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2710 __isl_take isl_space *space);
2711 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2712 __isl_take isl_space *space,
2713 enum isl_dim_type type,
2714 unsigned first, unsigned n);
2716 A multiple expression can be created from a single
2717 base expression using the following functions.
2718 The space of the created multiple expression is the same
2719 as that of the base expression, except for
2720 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2721 lives in a parameter space and the output lives
2722 in a single-dimensional set space.
2724 #include <isl/aff.h>
2725 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2726 __isl_take isl_aff *aff);
2727 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2728 __isl_take isl_pw_aff *pa);
2729 __isl_give isl_multi_union_pw_aff *
2730 isl_multi_union_pw_aff_from_union_pw_aff(
2731 __isl_take isl_union_pw_aff *upa);
2733 A multiple expression can be created from a list
2734 of base expression in a specified space.
2735 The domain of this space needs to be the same
2736 as the domains of the base expressions in the list.
2737 If the base expressions have a set space (or no associated space),
2738 then this space also needs to be a set space.
2740 #include <isl/val.h>
2741 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2742 __isl_take isl_space *space,
2743 __isl_take isl_val_list *list);
2745 #include <isl/aff.h>
2746 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2747 __isl_take isl_space *space,
2748 __isl_take isl_aff_list *list);
2749 __isl_give isl_multi_pw_aff *
2750 isl_multi_pw_aff_from_pw_aff_list(
2751 __isl_take isl_space *space,
2752 __isl_take isl_pw_aff_list *list);
2753 __isl_give isl_multi_union_pw_aff *
2754 isl_multi_union_pw_aff_from_union_pw_aff_list(
2755 __isl_take isl_space *space,
2756 __isl_take isl_union_pw_aff_list *list);
2758 As a convenience, a multiple piecewise expression can
2759 also be created from a multiple expression.
2760 Each piecewise expression in the result has a single
2763 #include <isl/aff.h>
2764 __isl_give isl_multi_pw_aff *
2765 isl_multi_pw_aff_from_multi_aff(
2766 __isl_take isl_multi_aff *ma);
2768 Similarly, a multiple union expression can be
2769 created from a multiple expression.
2771 #include <isl/aff.h>
2772 __isl_give isl_multi_union_pw_aff *
2773 isl_multi_union_pw_aff_from_multi_aff(
2774 __isl_take isl_multi_aff *ma);
2775 __isl_give isl_multi_union_pw_aff *
2776 isl_multi_union_pw_aff_from_multi_pw_aff(
2777 __isl_take isl_multi_pw_aff *mpa);
2779 A multiple quasi-affine expression can be created from
2780 a multiple value with a given domain space using the following
2783 #include <isl/aff.h>
2784 __isl_give isl_multi_aff *
2785 isl_multi_aff_multi_val_on_space(
2786 __isl_take isl_space *space,
2787 __isl_take isl_multi_val *mv);
2790 a multiple union piecewise affine expression can be created from
2791 a multiple value with a given domain or
2792 a multiple affine expression with a given domain
2793 using the following functions.
2795 #include <isl/aff.h>
2796 __isl_give isl_multi_union_pw_aff *
2797 isl_multi_union_pw_aff_multi_val_on_domain(
2798 __isl_take isl_union_set *domain,
2799 __isl_take isl_multi_val *mv);
2800 __isl_give isl_multi_union_pw_aff *
2801 isl_multi_union_pw_aff_multi_aff_on_domain(
2802 __isl_take isl_union_set *domain,
2803 __isl_take isl_multi_aff *ma);
2805 Multiple expressions can be copied and freed using
2806 the following functions.
2808 #include <isl/val.h>
2809 __isl_give isl_multi_val *isl_multi_val_copy(
2810 __isl_keep isl_multi_val *mv);
2811 __isl_null isl_multi_val *isl_multi_val_free(
2812 __isl_take isl_multi_val *mv);
2814 #include <isl/aff.h>
2815 __isl_give isl_multi_aff *isl_multi_aff_copy(
2816 __isl_keep isl_multi_aff *maff);
2817 __isl_null isl_multi_aff *isl_multi_aff_free(
2818 __isl_take isl_multi_aff *maff);
2819 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2820 __isl_keep isl_multi_pw_aff *mpa);
2821 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2822 __isl_take isl_multi_pw_aff *mpa);
2823 __isl_give isl_multi_union_pw_aff *
2824 isl_multi_union_pw_aff_copy(
2825 __isl_keep isl_multi_union_pw_aff *mupa);
2826 __isl_null isl_multi_union_pw_aff *
2827 isl_multi_union_pw_aff_free(
2828 __isl_take isl_multi_union_pw_aff *mupa);
2830 The base expression at a given position of a multiple
2831 expression can be extracted using the following functions.
2833 #include <isl/val.h>
2834 __isl_give isl_val *isl_multi_val_get_val(
2835 __isl_keep isl_multi_val *mv, int pos);
2837 #include <isl/aff.h>
2838 __isl_give isl_aff *isl_multi_aff_get_aff(
2839 __isl_keep isl_multi_aff *multi, int pos);
2840 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2841 __isl_keep isl_multi_pw_aff *mpa, int pos);
2842 __isl_give isl_union_pw_aff *
2843 isl_multi_union_pw_aff_get_union_pw_aff(
2844 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2846 It can be replaced using the following functions.
2848 #include <isl/val.h>
2849 __isl_give isl_multi_val *isl_multi_val_set_val(
2850 __isl_take isl_multi_val *mv, int pos,
2851 __isl_take isl_val *val);
2853 #include <isl/aff.h>
2854 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2855 __isl_take isl_multi_aff *multi, int pos,
2856 __isl_take isl_aff *aff);
2857 __isl_give isl_multi_union_pw_aff *
2858 isl_multi_union_pw_aff_set_union_pw_aff(
2859 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2860 __isl_take isl_union_pw_aff *upa);
2862 As a convenience, a sequence of base expressions that have
2863 their domains in a given space can be extracted from a sequence
2864 of union expressions using the following function.
2866 #include <isl/aff.h>
2867 __isl_give isl_multi_pw_aff *
2868 isl_multi_union_pw_aff_extract_multi_pw_aff(
2869 __isl_keep isl_multi_union_pw_aff *mupa,
2870 __isl_take isl_space *space);
2872 Note that there is a difference between C<isl_multi_union_pw_aff>
2873 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2874 of unions of piecewise expressions, while the second is a union
2875 of piecewise sequences. In particular, multiple affine expressions
2876 in an C<isl_union_pw_multi_aff> may live in different spaces,
2877 while there is only a single multiple expression in
2878 an C<isl_multi_union_pw_aff>, which can therefore only live
2879 in a single space. This means that not every
2880 C<isl_union_pw_multi_aff> can be converted to
2881 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2882 C<isl_multi_union_pw_aff> carries no information
2883 about any possible domain and therefore cannot be converted
2884 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2885 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2886 while each multiple expression inside an C<isl_union_pw_multi_aff>
2887 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2888 of dimension greater than one may therefore not be exact.
2889 The following functions can
2890 be used to perform these conversions when they are possible.
2892 #include <isl/aff.h>
2893 __isl_give isl_multi_union_pw_aff *
2894 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2895 __isl_take isl_union_pw_multi_aff *upma);
2896 __isl_give isl_union_pw_multi_aff *
2897 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2898 __isl_take isl_multi_union_pw_aff *mupa);
2900 =head3 Piecewise Expressions
2902 A piecewise expression is an expression that is described
2903 using zero or more base expression defined over the same
2904 number of cells in the domain space of the base expressions.
2905 All base expressions are defined over the same
2906 domain space and the cells are disjoint.
2907 The space of a piecewise expression is the same as
2908 that of the base expressions.
2909 If the union of the cells is a strict subset of the domain
2910 space, then the value of the piecewise expression outside
2911 this union is different for types derived from quasi-affine
2912 expressions and those derived from quasipolynomials.
2913 Piecewise expressions derived from quasi-affine expressions
2914 are considered to be undefined outside the union of their cells.
2915 Piecewise expressions derived from quasipolynomials
2916 are considered to be zero outside the union of their cells.
2918 Piecewise quasipolynomials are mainly used by the C<barvinok>
2919 library for representing the number of elements in a parametric set or map.
2920 For example, the piecewise quasipolynomial
2922 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2924 represents the number of points in the map
2926 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2928 The piecewise expression types defined by C<isl>
2929 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2930 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2932 A piecewise expression with no cells can be created using
2933 the following functions.
2935 #include <isl/aff.h>
2936 __isl_give isl_pw_aff *isl_pw_aff_empty(
2937 __isl_take isl_space *space);
2938 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2939 __isl_take isl_space *space);
2941 A piecewise expression with a single universe cell can be
2942 created using the following functions.
2944 #include <isl/aff.h>
2945 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2946 __isl_take isl_aff *aff);
2947 __isl_give isl_pw_multi_aff *
2948 isl_pw_multi_aff_from_multi_aff(
2949 __isl_take isl_multi_aff *ma);
2951 #include <isl/polynomial.h>
2952 __isl_give isl_pw_qpolynomial *
2953 isl_pw_qpolynomial_from_qpolynomial(
2954 __isl_take isl_qpolynomial *qp);
2956 A piecewise expression with a single specified cell can be
2957 created using the following functions.
2959 #include <isl/aff.h>
2960 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2961 __isl_take isl_set *set, __isl_take isl_aff *aff);
2962 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2963 __isl_take isl_set *set,
2964 __isl_take isl_multi_aff *maff);
2966 #include <isl/polynomial.h>
2967 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2968 __isl_take isl_set *set,
2969 __isl_take isl_qpolynomial *qp);
2971 The following convenience functions first create a base expression and
2972 then create a piecewise expression over a universe domain.
2974 #include <isl/aff.h>
2975 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2976 __isl_take isl_local_space *ls);
2977 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2978 __isl_take isl_local_space *ls,
2979 enum isl_dim_type type, unsigned pos);
2980 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2981 __isl_take isl_local_space *ls);
2982 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2983 __isl_take isl_space *space);
2984 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2985 __isl_take isl_space *space);
2986 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2987 __isl_take isl_space *space);
2988 __isl_give isl_pw_multi_aff *
2989 isl_pw_multi_aff_project_out_map(
2990 __isl_take isl_space *space,
2991 enum isl_dim_type type,
2992 unsigned first, unsigned n);
2994 #include <isl/polynomial.h>
2995 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2996 __isl_take isl_space *space);
2998 The following convenience functions first create a base expression and
2999 then create a piecewise expression over a given domain.
3001 #include <isl/aff.h>
3002 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3003 __isl_take isl_set *domain,
3004 __isl_take isl_val *v);
3005 __isl_give isl_pw_multi_aff *
3006 isl_pw_multi_aff_multi_val_on_domain(
3007 __isl_take isl_set *domain,
3008 __isl_take isl_multi_val *mv);
3010 As a convenience, a piecewise multiple expression can
3011 also be created from a piecewise expression.
3012 Each multiple expression in the result is derived
3013 from the corresponding base expression.
3015 #include <isl/aff.h>
3016 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3017 __isl_take isl_pw_aff *pa);
3019 Similarly, a piecewise quasipolynomial can be
3020 created from a piecewise quasi-affine expression using
3021 the following function.
3023 #include <isl/polynomial.h>
3024 __isl_give isl_pw_qpolynomial *
3025 isl_pw_qpolynomial_from_pw_aff(
3026 __isl_take isl_pw_aff *pwaff);
3028 Piecewise expressions can be copied and freed using the following functions.
3030 #include <isl/aff.h>
3031 __isl_give isl_pw_aff *isl_pw_aff_copy(
3032 __isl_keep isl_pw_aff *pwaff);
3033 __isl_null isl_pw_aff *isl_pw_aff_free(
3034 __isl_take isl_pw_aff *pwaff);
3035 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3036 __isl_keep isl_pw_multi_aff *pma);
3037 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3038 __isl_take isl_pw_multi_aff *pma);
3040 #include <isl/polynomial.h>
3041 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3042 __isl_keep isl_pw_qpolynomial *pwqp);
3043 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3044 __isl_take isl_pw_qpolynomial *pwqp);
3045 __isl_give isl_pw_qpolynomial_fold *
3046 isl_pw_qpolynomial_fold_copy(
3047 __isl_keep isl_pw_qpolynomial_fold *pwf);
3048 __isl_null isl_pw_qpolynomial_fold *
3049 isl_pw_qpolynomial_fold_free(
3050 __isl_take isl_pw_qpolynomial_fold *pwf);
3052 To iterate over the different cells of a piecewise expression,
3053 use the following functions.
3055 #include <isl/aff.h>
3056 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3057 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3058 isl_stat isl_pw_aff_foreach_piece(
3059 __isl_keep isl_pw_aff *pwaff,
3060 isl_stat (*fn)(__isl_take isl_set *set,
3061 __isl_take isl_aff *aff,
3062 void *user), void *user);
3063 isl_stat isl_pw_multi_aff_foreach_piece(
3064 __isl_keep isl_pw_multi_aff *pma,
3065 isl_stat (*fn)(__isl_take isl_set *set,
3066 __isl_take isl_multi_aff *maff,
3067 void *user), void *user);
3069 #include <isl/polynomial.h>
3070 isl_stat isl_pw_qpolynomial_foreach_piece(
3071 __isl_keep isl_pw_qpolynomial *pwqp,
3072 isl_stat (*fn)(__isl_take isl_set *set,
3073 __isl_take isl_qpolynomial *qp,
3074 void *user), void *user);
3075 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3076 __isl_keep isl_pw_qpolynomial *pwqp,
3077 isl_stat (*fn)(__isl_take isl_set *set,
3078 __isl_take isl_qpolynomial *qp,
3079 void *user), void *user);
3080 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3081 __isl_keep isl_pw_qpolynomial_fold *pwf,
3082 isl_stat (*fn)(__isl_take isl_set *set,
3083 __isl_take isl_qpolynomial_fold *fold,
3084 void *user), void *user);
3085 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3086 __isl_keep isl_pw_qpolynomial_fold *pwf,
3087 isl_stat (*fn)(__isl_take isl_set *set,
3088 __isl_take isl_qpolynomial_fold *fold,
3089 void *user), void *user);
3091 As usual, the function C<fn> should return C<0> on success
3092 and C<-1> on failure. The difference between
3093 C<isl_pw_qpolynomial_foreach_piece> and
3094 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3095 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3096 compute unique representations for all existentially quantified
3097 variables and then turn these existentially quantified variables
3098 into extra set variables, adapting the associated quasipolynomial
3099 accordingly. This means that the C<set> passed to C<fn>
3100 will not have any existentially quantified variables, but that
3101 the dimensions of the sets may be different for different
3102 invocations of C<fn>.
3103 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3104 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3106 A piecewise expression consisting of the expressions at a given
3107 position of a piecewise multiple expression can be extracted
3108 using the following function.
3110 #include <isl/aff.h>
3111 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3112 __isl_keep isl_pw_multi_aff *pma, int pos);
3114 These expressions can be replaced using the following function.
3116 #include <isl/aff.h>
3117 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3118 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3119 __isl_take isl_pw_aff *pa);
3121 Note that there is a difference between C<isl_multi_pw_aff> and
3122 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3123 affine expressions, while the second is a piecewise sequence
3124 of affine expressions. In particular, each of the piecewise
3125 affine expressions in an C<isl_multi_pw_aff> may have a different
3126 domain, while all multiple expressions associated to a cell
3127 in an C<isl_pw_multi_aff> have the same domain.
3128 It is possible to convert between the two, but when converting
3129 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3130 of the result is the intersection of the domains of the input.
3131 The reverse conversion is exact.
3133 #include <isl/aff.h>
3134 __isl_give isl_pw_multi_aff *
3135 isl_pw_multi_aff_from_multi_pw_aff(
3136 __isl_take isl_multi_pw_aff *mpa);
3137 __isl_give isl_multi_pw_aff *
3138 isl_multi_pw_aff_from_pw_multi_aff(
3139 __isl_take isl_pw_multi_aff *pma);
3141 =head3 Union Expressions
3143 A union expression collects base expressions defined
3144 over different domains. The space of a union expression
3145 is that of the shared parameter space.
3147 The union expression types defined by C<isl>
3148 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3149 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3151 C<isl_union_pw_aff>,
3152 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3153 there can be at most one base expression for a given domain space.
3155 C<isl_union_pw_multi_aff>,
3156 there can be multiple such expressions for a given domain space,
3157 but the domains of these expressions need to be disjoint.
3159 An empty union expression can be created using the following functions.
3161 #include <isl/aff.h>
3162 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3163 __isl_take isl_space *space);
3164 __isl_give isl_union_pw_multi_aff *
3165 isl_union_pw_multi_aff_empty(
3166 __isl_take isl_space *space);
3168 #include <isl/polynomial.h>
3169 __isl_give isl_union_pw_qpolynomial *
3170 isl_union_pw_qpolynomial_zero(
3171 __isl_take isl_space *space);
3173 A union expression containing a single base expression
3174 can be created using the following functions.
3176 #include <isl/aff.h>
3177 __isl_give isl_union_pw_aff *
3178 isl_union_pw_aff_from_pw_aff(
3179 __isl_take isl_pw_aff *pa);
3180 __isl_give isl_union_pw_multi_aff *
3181 isl_union_pw_multi_aff_from_aff(
3182 __isl_take isl_aff *aff);
3183 __isl_give isl_union_pw_multi_aff *
3184 isl_union_pw_multi_aff_from_pw_multi_aff(
3185 __isl_take isl_pw_multi_aff *pma);
3187 #include <isl/polynomial.h>
3188 __isl_give isl_union_pw_qpolynomial *
3189 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3190 __isl_take isl_pw_qpolynomial *pwqp);
3192 The following functions create a base expression on each
3193 of the sets in the union set and collect the results.
3195 #include <isl/aff.h>
3196 __isl_give isl_union_pw_multi_aff *
3197 isl_union_pw_multi_aff_from_union_pw_aff(
3198 __isl_take isl_union_pw_aff *upa);
3199 __isl_give isl_union_pw_aff *
3200 isl_union_pw_multi_aff_get_union_pw_aff(
3201 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3202 __isl_give isl_union_pw_aff *
3203 isl_union_pw_aff_val_on_domain(
3204 __isl_take isl_union_set *domain,
3205 __isl_take isl_val *v);
3206 __isl_give isl_union_pw_multi_aff *
3207 isl_union_pw_multi_aff_multi_val_on_domain(
3208 __isl_take isl_union_set *domain,
3209 __isl_take isl_multi_val *mv);
3211 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3212 expression on a given domain can be created using the following
3215 #include <isl/aff.h>
3216 __isl_give isl_union_pw_aff *
3217 isl_union_pw_aff_aff_on_domain(
3218 __isl_take isl_union_set *domain,
3219 __isl_take isl_aff *aff);
3221 A base expression can be added to a union expression using
3222 the following functions.
3224 #include <isl/aff.h>
3225 __isl_give isl_union_pw_aff *
3226 isl_union_pw_aff_add_pw_aff(
3227 __isl_take isl_union_pw_aff *upa,
3228 __isl_take isl_pw_aff *pa);
3229 __isl_give isl_union_pw_multi_aff *
3230 isl_union_pw_multi_aff_add_pw_multi_aff(
3231 __isl_take isl_union_pw_multi_aff *upma,
3232 __isl_take isl_pw_multi_aff *pma);
3234 #include <isl/polynomial.h>
3235 __isl_give isl_union_pw_qpolynomial *
3236 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3237 __isl_take isl_union_pw_qpolynomial *upwqp,
3238 __isl_take isl_pw_qpolynomial *pwqp);
3240 Union expressions can be copied and freed using
3241 the following functions.
3243 #include <isl/aff.h>
3244 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3245 __isl_keep isl_union_pw_aff *upa);
3246 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3247 __isl_take isl_union_pw_aff *upa);
3248 __isl_give isl_union_pw_multi_aff *
3249 isl_union_pw_multi_aff_copy(
3250 __isl_keep isl_union_pw_multi_aff *upma);
3251 __isl_null isl_union_pw_multi_aff *
3252 isl_union_pw_multi_aff_free(
3253 __isl_take isl_union_pw_multi_aff *upma);
3255 #include <isl/polynomial.h>
3256 __isl_give isl_union_pw_qpolynomial *
3257 isl_union_pw_qpolynomial_copy(
3258 __isl_keep isl_union_pw_qpolynomial *upwqp);
3259 __isl_null isl_union_pw_qpolynomial *
3260 isl_union_pw_qpolynomial_free(
3261 __isl_take isl_union_pw_qpolynomial *upwqp);
3262 __isl_give isl_union_pw_qpolynomial_fold *
3263 isl_union_pw_qpolynomial_fold_copy(
3264 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3265 __isl_null isl_union_pw_qpolynomial_fold *
3266 isl_union_pw_qpolynomial_fold_free(
3267 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3269 To iterate over the base expressions in a union expression,
3270 use the following functions.
3272 #include <isl/aff.h>
3273 int isl_union_pw_aff_n_pw_aff(
3274 __isl_keep isl_union_pw_aff *upa);
3275 isl_stat isl_union_pw_aff_foreach_pw_aff(
3276 __isl_keep isl_union_pw_aff *upa,
3277 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3278 void *user), void *user);
3279 int isl_union_pw_multi_aff_n_pw_multi_aff(
3280 __isl_keep isl_union_pw_multi_aff *upma);
3281 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3282 __isl_keep isl_union_pw_multi_aff *upma,
3283 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3284 void *user), void *user);
3286 #include <isl/polynomial.h>
3287 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3288 __isl_keep isl_union_pw_qpolynomial *upwqp);
3289 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3290 __isl_keep isl_union_pw_qpolynomial *upwqp,
3291 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3292 void *user), void *user);
3293 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3294 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3295 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3296 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3297 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3298 void *user), void *user);
3300 To extract the base expression in a given space from a union, use
3301 the following functions.
3303 #include <isl/aff.h>
3304 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3305 __isl_keep isl_union_pw_aff *upa,
3306 __isl_take isl_space *space);
3307 __isl_give isl_pw_multi_aff *
3308 isl_union_pw_multi_aff_extract_pw_multi_aff(
3309 __isl_keep isl_union_pw_multi_aff *upma,
3310 __isl_take isl_space *space);
3312 #include <isl/polynomial.h>
3313 __isl_give isl_pw_qpolynomial *
3314 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3315 __isl_keep isl_union_pw_qpolynomial *upwqp,
3316 __isl_take isl_space *space);
3318 =head2 Input and Output
3320 For set and relation,
3321 C<isl> supports its own input/output format, which is similar
3322 to the C<Omega> format, but also supports the C<PolyLib> format
3324 For other object types, typically only an C<isl> format is supported.
3326 =head3 C<isl> format
3328 The C<isl> format is similar to that of C<Omega>, but has a different
3329 syntax for describing the parameters and allows for the definition
3330 of an existentially quantified variable as the integer division
3331 of an affine expression.
3332 For example, the set of integers C<i> between C<0> and C<n>
3333 such that C<i % 10 <= 6> can be described as
3335 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3338 A set or relation can have several disjuncts, separated
3339 by the keyword C<or>. Each disjunct is either a conjunction
3340 of constraints or a projection (C<exists>) of a conjunction
3341 of constraints. The constraints are separated by the keyword
3344 =head3 C<PolyLib> format
3346 If the represented set is a union, then the first line
3347 contains a single number representing the number of disjuncts.
3348 Otherwise, a line containing the number C<1> is optional.
3350 Each disjunct is represented by a matrix of constraints.
3351 The first line contains two numbers representing
3352 the number of rows and columns,
3353 where the number of rows is equal to the number of constraints
3354 and the number of columns is equal to two plus the number of variables.
3355 The following lines contain the actual rows of the constraint matrix.
3356 In each row, the first column indicates whether the constraint
3357 is an equality (C<0>) or inequality (C<1>). The final column
3358 corresponds to the constant term.
3360 If the set is parametric, then the coefficients of the parameters
3361 appear in the last columns before the constant column.
3362 The coefficients of any existentially quantified variables appear
3363 between those of the set variables and those of the parameters.
3365 =head3 Extended C<PolyLib> format
3367 The extended C<PolyLib> format is nearly identical to the
3368 C<PolyLib> format. The only difference is that the line
3369 containing the number of rows and columns of a constraint matrix
3370 also contains four additional numbers:
3371 the number of output dimensions, the number of input dimensions,
3372 the number of local dimensions (i.e., the number of existentially
3373 quantified variables) and the number of parameters.
3374 For sets, the number of ``output'' dimensions is equal
3375 to the number of set dimensions, while the number of ``input''
3380 Objects can be read from input using the following functions.
3382 #include <isl/val.h>
3383 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3385 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3386 isl_ctx *ctx, const char *str);
3388 #include <isl/set.h>
3389 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3390 isl_ctx *ctx, FILE *input);
3391 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3392 isl_ctx *ctx, const char *str);
3393 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3395 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3398 #include <isl/map.h>
3399 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3400 isl_ctx *ctx, FILE *input);
3401 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3402 isl_ctx *ctx, const char *str);
3403 __isl_give isl_map *isl_map_read_from_file(
3404 isl_ctx *ctx, FILE *input);
3405 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3408 #include <isl/union_set.h>
3409 __isl_give isl_union_set *isl_union_set_read_from_file(
3410 isl_ctx *ctx, FILE *input);
3411 __isl_give isl_union_set *isl_union_set_read_from_str(
3412 isl_ctx *ctx, const char *str);
3414 #include <isl/union_map.h>
3415 __isl_give isl_union_map *isl_union_map_read_from_file(
3416 isl_ctx *ctx, FILE *input);
3417 __isl_give isl_union_map *isl_union_map_read_from_str(
3418 isl_ctx *ctx, const char *str);
3420 #include <isl/aff.h>
3421 __isl_give isl_aff *isl_aff_read_from_str(
3422 isl_ctx *ctx, const char *str);
3423 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3424 isl_ctx *ctx, const char *str);
3425 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3426 isl_ctx *ctx, const char *str);
3427 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3428 isl_ctx *ctx, const char *str);
3429 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3430 isl_ctx *ctx, const char *str);
3431 __isl_give isl_union_pw_aff *
3432 isl_union_pw_aff_read_from_str(
3433 isl_ctx *ctx, const char *str);
3434 __isl_give isl_union_pw_multi_aff *
3435 isl_union_pw_multi_aff_read_from_str(
3436 isl_ctx *ctx, const char *str);
3437 __isl_give isl_multi_union_pw_aff *
3438 isl_multi_union_pw_aff_read_from_str(
3439 isl_ctx *ctx, const char *str);
3441 #include <isl/polynomial.h>
3442 __isl_give isl_union_pw_qpolynomial *
3443 isl_union_pw_qpolynomial_read_from_str(
3444 isl_ctx *ctx, const char *str);
3446 For sets and relations,
3447 the input format is autodetected and may be either the C<PolyLib> format
3448 or the C<isl> format.
3452 Before anything can be printed, an C<isl_printer> needs to
3455 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3457 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3458 __isl_null isl_printer *isl_printer_free(
3459 __isl_take isl_printer *printer);
3461 C<isl_printer_to_file> prints to the given file, while
3462 C<isl_printer_to_str> prints to a string that can be extracted
3463 using the following function.
3465 #include <isl/printer.h>
3466 __isl_give char *isl_printer_get_str(
3467 __isl_keep isl_printer *printer);
3469 The printer can be inspected using the following functions.
3471 FILE *isl_printer_get_file(
3472 __isl_keep isl_printer *printer);
3473 int isl_printer_get_output_format(
3474 __isl_keep isl_printer *p);
3475 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3477 The behavior of the printer can be modified in various ways
3479 __isl_give isl_printer *isl_printer_set_output_format(
3480 __isl_take isl_printer *p, int output_format);
3481 __isl_give isl_printer *isl_printer_set_indent(
3482 __isl_take isl_printer *p, int indent);
3483 __isl_give isl_printer *isl_printer_set_indent_prefix(
3484 __isl_take isl_printer *p, const char *prefix);
3485 __isl_give isl_printer *isl_printer_indent(
3486 __isl_take isl_printer *p, int indent);
3487 __isl_give isl_printer *isl_printer_set_prefix(
3488 __isl_take isl_printer *p, const char *prefix);
3489 __isl_give isl_printer *isl_printer_set_suffix(
3490 __isl_take isl_printer *p, const char *suffix);
3491 __isl_give isl_printer *isl_printer_set_yaml_style(
3492 __isl_take isl_printer *p, int yaml_style);
3494 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3495 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3496 and defaults to C<ISL_FORMAT_ISL>.
3497 Each line in the output is prefixed by C<indent_prefix>,
3498 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3499 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3500 In the C<PolyLib> format output,
3501 the coefficients of the existentially quantified variables
3502 appear between those of the set variables and those
3504 The function C<isl_printer_indent> increases the indentation
3505 by the specified amount (which may be negative).
3506 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3507 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3510 To actually print something, use
3512 #include <isl/printer.h>
3513 __isl_give isl_printer *isl_printer_print_double(
3514 __isl_take isl_printer *p, double d);
3516 #include <isl/val.h>
3517 __isl_give isl_printer *isl_printer_print_val(
3518 __isl_take isl_printer *p, __isl_keep isl_val *v);
3520 #include <isl/set.h>
3521 __isl_give isl_printer *isl_printer_print_basic_set(
3522 __isl_take isl_printer *printer,
3523 __isl_keep isl_basic_set *bset);
3524 __isl_give isl_printer *isl_printer_print_set(
3525 __isl_take isl_printer *printer,
3526 __isl_keep isl_set *set);
3528 #include <isl/map.h>
3529 __isl_give isl_printer *isl_printer_print_basic_map(
3530 __isl_take isl_printer *printer,
3531 __isl_keep isl_basic_map *bmap);
3532 __isl_give isl_printer *isl_printer_print_map(
3533 __isl_take isl_printer *printer,
3534 __isl_keep isl_map *map);
3536 #include <isl/union_set.h>
3537 __isl_give isl_printer *isl_printer_print_union_set(
3538 __isl_take isl_printer *p,
3539 __isl_keep isl_union_set *uset);
3541 #include <isl/union_map.h>
3542 __isl_give isl_printer *isl_printer_print_union_map(
3543 __isl_take isl_printer *p,
3544 __isl_keep isl_union_map *umap);
3546 #include <isl/val.h>
3547 __isl_give isl_printer *isl_printer_print_multi_val(
3548 __isl_take isl_printer *p,
3549 __isl_keep isl_multi_val *mv);
3551 #include <isl/aff.h>
3552 __isl_give isl_printer *isl_printer_print_aff(
3553 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3554 __isl_give isl_printer *isl_printer_print_multi_aff(
3555 __isl_take isl_printer *p,
3556 __isl_keep isl_multi_aff *maff);
3557 __isl_give isl_printer *isl_printer_print_pw_aff(
3558 __isl_take isl_printer *p,
3559 __isl_keep isl_pw_aff *pwaff);
3560 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3561 __isl_take isl_printer *p,
3562 __isl_keep isl_pw_multi_aff *pma);
3563 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3564 __isl_take isl_printer *p,
3565 __isl_keep isl_multi_pw_aff *mpa);
3566 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3567 __isl_take isl_printer *p,
3568 __isl_keep isl_union_pw_aff *upa);
3569 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3570 __isl_take isl_printer *p,
3571 __isl_keep isl_union_pw_multi_aff *upma);
3572 __isl_give isl_printer *
3573 isl_printer_print_multi_union_pw_aff(
3574 __isl_take isl_printer *p,
3575 __isl_keep isl_multi_union_pw_aff *mupa);
3577 #include <isl/polynomial.h>
3578 __isl_give isl_printer *isl_printer_print_qpolynomial(
3579 __isl_take isl_printer *p,
3580 __isl_keep isl_qpolynomial *qp);
3581 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3582 __isl_take isl_printer *p,
3583 __isl_keep isl_pw_qpolynomial *pwqp);
3584 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3585 __isl_take isl_printer *p,
3586 __isl_keep isl_union_pw_qpolynomial *upwqp);
3588 __isl_give isl_printer *
3589 isl_printer_print_pw_qpolynomial_fold(
3590 __isl_take isl_printer *p,
3591 __isl_keep isl_pw_qpolynomial_fold *pwf);
3592 __isl_give isl_printer *
3593 isl_printer_print_union_pw_qpolynomial_fold(
3594 __isl_take isl_printer *p,
3595 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3597 For C<isl_printer_print_qpolynomial>,
3598 C<isl_printer_print_pw_qpolynomial> and
3599 C<isl_printer_print_pw_qpolynomial_fold>,
3600 the output format of the printer
3601 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3602 For C<isl_printer_print_union_pw_qpolynomial> and
3603 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3605 In case of printing in C<ISL_FORMAT_C>, the user may want
3606 to set the names of all dimensions first.
3608 C<isl> also provides limited support for printing YAML documents,
3609 just enough for the internal use for printing such documents.
3611 #include <isl/printer.h>
3612 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3613 __isl_take isl_printer *p);
3614 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3615 __isl_take isl_printer *p);
3616 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3617 __isl_take isl_printer *p);
3618 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3619 __isl_take isl_printer *p);
3620 __isl_give isl_printer *isl_printer_yaml_next(
3621 __isl_take isl_printer *p);
3623 A document is started by a call to either
3624 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3625 Anything printed to the printer after such a call belong to the
3626 first key of the mapping or the first element in the sequence.
3627 The function C<isl_printer_yaml_next> moves to the value if
3628 we are currently printing a mapping key, the next key if we
3629 are printing a value or the next element if we are printing
3630 an element in a sequence.
3631 Nested mappings and sequences are initiated by the same
3632 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3633 Each call to these functions needs to have a corresponding call to
3634 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3636 When called on a file printer, the following function flushes
3637 the file. When called on a string printer, the buffer is cleared.
3639 __isl_give isl_printer *isl_printer_flush(
3640 __isl_take isl_printer *p);
3642 The following functions allow the user to attach
3643 notes to a printer in order to keep track of additional state.
3645 #include <isl/printer.h>
3646 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3647 __isl_keep isl_id *id);
3648 __isl_give isl_id *isl_printer_get_note(
3649 __isl_keep isl_printer *p, __isl_take isl_id *id);
3650 __isl_give isl_printer *isl_printer_set_note(
3651 __isl_take isl_printer *p,
3652 __isl_take isl_id *id, __isl_take isl_id *note);
3654 C<isl_printer_set_note> associates the given note to the given
3655 identifier in the printer.
3656 C<isl_printer_get_note> retrieves a note associated to an
3658 C<isl_printer_has_note> checks if there is such a note.
3659 C<isl_printer_get_note> fails if the requested note does not exist.
3661 Alternatively, a string representation can be obtained
3662 directly using the following functions, which always print
3665 #include <isl/space.h>
3666 __isl_give char *isl_space_to_str(
3667 __isl_keep isl_space *space);
3669 #include <isl/val.h>
3670 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3671 __isl_give char *isl_multi_val_to_str(
3672 __isl_keep isl_multi_val *mv);
3674 #include <isl/set.h>
3675 __isl_give char *isl_set_to_str(
3676 __isl_keep isl_set *set);
3678 #include <isl/union_set.h>
3679 __isl_give char *isl_union_set_to_str(
3680 __isl_keep isl_union_set *uset);
3682 #include <isl/map.h>
3683 __isl_give char *isl_map_to_str(
3684 __isl_keep isl_map *map);
3686 #include <isl/union_map.h>
3687 __isl_give char *isl_union_map_to_str(
3688 __isl_keep isl_union_map *umap);
3690 #include <isl/aff.h>
3691 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3692 __isl_give char *isl_pw_aff_to_str(
3693 __isl_keep isl_pw_aff *pa);
3694 __isl_give char *isl_multi_aff_to_str(
3695 __isl_keep isl_multi_aff *ma);
3696 __isl_give char *isl_pw_multi_aff_to_str(
3697 __isl_keep isl_pw_multi_aff *pma);
3698 __isl_give char *isl_multi_pw_aff_to_str(
3699 __isl_keep isl_multi_pw_aff *mpa);
3700 __isl_give char *isl_union_pw_aff_to_str(
3701 __isl_keep isl_union_pw_aff *upa);
3702 __isl_give char *isl_union_pw_multi_aff_to_str(
3703 __isl_keep isl_union_pw_multi_aff *upma);
3704 __isl_give char *isl_multi_union_pw_aff_to_str(
3705 __isl_keep isl_multi_union_pw_aff *mupa);
3709 =head3 Unary Properties
3715 The following functions test whether the given set or relation
3716 contains any integer points. The ``plain'' variants do not perform
3717 any computations, but simply check if the given set or relation
3718 is already known to be empty.
3720 isl_bool isl_basic_set_plain_is_empty(
3721 __isl_keep isl_basic_set *bset);
3722 isl_bool isl_basic_set_is_empty(
3723 __isl_keep isl_basic_set *bset);
3724 isl_bool isl_set_plain_is_empty(
3725 __isl_keep isl_set *set);
3726 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3727 isl_bool isl_union_set_is_empty(
3728 __isl_keep isl_union_set *uset);
3729 isl_bool isl_basic_map_plain_is_empty(
3730 __isl_keep isl_basic_map *bmap);
3731 isl_bool isl_basic_map_is_empty(
3732 __isl_keep isl_basic_map *bmap);
3733 isl_bool isl_map_plain_is_empty(
3734 __isl_keep isl_map *map);
3735 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3736 isl_bool isl_union_map_is_empty(
3737 __isl_keep isl_union_map *umap);
3739 =item * Universality
3741 isl_bool isl_basic_set_plain_is_universe(
3742 __isl_keep isl_basic_set *bset);
3743 isl_bool isl_basic_set_is_universe(
3744 __isl_keep isl_basic_set *bset);
3745 isl_bool isl_basic_map_plain_is_universe(
3746 __isl_keep isl_basic_map *bmap);
3747 isl_bool isl_basic_map_is_universe(
3748 __isl_keep isl_basic_map *bmap);
3749 isl_bool isl_set_plain_is_universe(
3750 __isl_keep isl_set *set);
3751 isl_bool isl_map_plain_is_universe(
3752 __isl_keep isl_map *map);
3754 =item * Single-valuedness
3756 #include <isl/set.h>
3757 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3759 #include <isl/map.h>
3760 isl_bool isl_basic_map_is_single_valued(
3761 __isl_keep isl_basic_map *bmap);
3762 isl_bool isl_map_plain_is_single_valued(
3763 __isl_keep isl_map *map);
3764 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3766 #include <isl/union_map.h>
3767 isl_bool isl_union_map_is_single_valued(
3768 __isl_keep isl_union_map *umap);
3772 isl_bool isl_map_plain_is_injective(
3773 __isl_keep isl_map *map);
3774 isl_bool isl_map_is_injective(
3775 __isl_keep isl_map *map);
3776 isl_bool isl_union_map_plain_is_injective(
3777 __isl_keep isl_union_map *umap);
3778 isl_bool isl_union_map_is_injective(
3779 __isl_keep isl_union_map *umap);
3783 isl_bool isl_map_is_bijective(
3784 __isl_keep isl_map *map);
3785 isl_bool isl_union_map_is_bijective(
3786 __isl_keep isl_union_map *umap);
3790 The following functions test whether the given relation
3791 only maps elements to themselves.
3793 #include <isl/map.h>
3794 isl_bool isl_map_is_identity(
3795 __isl_keep isl_map *map);
3797 #include <isl/union_map.h>
3798 isl_bool isl_union_map_is_identity(
3799 __isl_keep isl_union_map *umap);
3803 __isl_give isl_val *
3804 isl_basic_map_plain_get_val_if_fixed(
3805 __isl_keep isl_basic_map *bmap,
3806 enum isl_dim_type type, unsigned pos);
3807 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3808 __isl_keep isl_set *set,
3809 enum isl_dim_type type, unsigned pos);
3810 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3811 __isl_keep isl_map *map,
3812 enum isl_dim_type type, unsigned pos);
3814 If the set or relation obviously lies on a hyperplane where the given dimension
3815 has a fixed value, then return that value.
3816 Otherwise return NaN.
3820 isl_stat isl_set_dim_residue_class_val(
3821 __isl_keep isl_set *set,
3822 int pos, __isl_give isl_val **modulo,
3823 __isl_give isl_val **residue);
3825 Check if the values of the given set dimension are equal to a fixed
3826 value modulo some integer value. If so, assign the modulo to C<*modulo>
3827 and the fixed value to C<*residue>. If the given dimension attains only
3828 a single value, then assign C<0> to C<*modulo> and the fixed value to
3830 If the dimension does not attain only a single value and if no modulo
3831 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3835 To check whether the description of a set, relation or function depends
3836 on one or more given dimensions,
3837 the following functions can be used.
3839 #include <isl/constraint.h>
3840 isl_bool isl_constraint_involves_dims(
3841 __isl_keep isl_constraint *constraint,
3842 enum isl_dim_type type, unsigned first, unsigned n);
3844 #include <isl/set.h>
3845 isl_bool isl_basic_set_involves_dims(
3846 __isl_keep isl_basic_set *bset,
3847 enum isl_dim_type type, unsigned first, unsigned n);
3848 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3849 enum isl_dim_type type, unsigned first, unsigned n);
3851 #include <isl/map.h>
3852 isl_bool isl_basic_map_involves_dims(
3853 __isl_keep isl_basic_map *bmap,
3854 enum isl_dim_type type, unsigned first, unsigned n);
3855 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3856 enum isl_dim_type type, unsigned first, unsigned n);
3858 #include <isl/union_map.h>
3859 isl_bool isl_union_map_involves_dims(
3860 __isl_keep isl_union_map *umap,
3861 enum isl_dim_type type, unsigned first, unsigned n);
3863 #include <isl/aff.h>
3864 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3865 enum isl_dim_type type, unsigned first, unsigned n);
3866 isl_bool isl_pw_aff_involves_dims(
3867 __isl_keep isl_pw_aff *pwaff,
3868 enum isl_dim_type type, unsigned first, unsigned n);
3869 isl_bool isl_multi_aff_involves_dims(
3870 __isl_keep isl_multi_aff *ma,
3871 enum isl_dim_type type, unsigned first, unsigned n);
3872 isl_bool isl_multi_pw_aff_involves_dims(
3873 __isl_keep isl_multi_pw_aff *mpa,
3874 enum isl_dim_type type, unsigned first, unsigned n);
3876 #include <isl/polynomial.h>
3877 isl_bool isl_qpolynomial_involves_dims(
3878 __isl_keep isl_qpolynomial *qp,
3879 enum isl_dim_type type, unsigned first, unsigned n);
3881 Similarly, the following functions can be used to check whether
3882 a given dimension is involved in any lower or upper bound.
3884 #include <isl/set.h>
3885 isl_bool isl_set_dim_has_any_lower_bound(
3886 __isl_keep isl_set *set,
3887 enum isl_dim_type type, unsigned pos);
3888 isl_bool isl_set_dim_has_any_upper_bound(
3889 __isl_keep isl_set *set,
3890 enum isl_dim_type type, unsigned pos);
3892 Note that these functions return true even if there is a bound on
3893 the dimension on only some of the basic sets of C<set>.
3894 To check if they have a bound for all of the basic sets in C<set>,
3895 use the following functions instead.
3897 #include <isl/set.h>
3898 isl_bool isl_set_dim_has_lower_bound(
3899 __isl_keep isl_set *set,
3900 enum isl_dim_type type, unsigned pos);
3901 isl_bool isl_set_dim_has_upper_bound(
3902 __isl_keep isl_set *set,
3903 enum isl_dim_type type, unsigned pos);
3907 To check whether a set is a parameter domain, use this function:
3909 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3910 isl_bool isl_union_set_is_params(
3911 __isl_keep isl_union_set *uset);
3915 The following functions check whether the space of the given
3916 (basic) set or relation range is a wrapped relation.
3918 #include <isl/space.h>
3919 isl_bool isl_space_is_wrapping(
3920 __isl_keep isl_space *space);
3921 isl_bool isl_space_domain_is_wrapping(
3922 __isl_keep isl_space *space);
3923 isl_bool isl_space_range_is_wrapping(
3924 __isl_keep isl_space *space);
3926 #include <isl/set.h>
3927 isl_bool isl_basic_set_is_wrapping(
3928 __isl_keep isl_basic_set *bset);
3929 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3931 #include <isl/map.h>
3932 isl_bool isl_map_domain_is_wrapping(
3933 __isl_keep isl_map *map);
3934 isl_bool isl_map_range_is_wrapping(
3935 __isl_keep isl_map *map);
3937 #include <isl/val.h>
3938 isl_bool isl_multi_val_range_is_wrapping(
3939 __isl_keep isl_multi_val *mv);
3941 #include <isl/aff.h>
3942 isl_bool isl_multi_aff_range_is_wrapping(
3943 __isl_keep isl_multi_aff *ma);
3944 isl_bool isl_multi_pw_aff_range_is_wrapping(
3945 __isl_keep isl_multi_pw_aff *mpa);
3946 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3947 __isl_keep isl_multi_union_pw_aff *mupa);
3949 The input to C<isl_space_is_wrapping> should
3950 be the space of a set, while that of
3951 C<isl_space_domain_is_wrapping> and
3952 C<isl_space_range_is_wrapping> should be the space of a relation.
3954 =item * Internal Product
3956 isl_bool isl_basic_map_can_zip(
3957 __isl_keep isl_basic_map *bmap);
3958 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
3960 Check whether the product of domain and range of the given relation
3962 i.e., whether both domain and range are nested relations.
3966 #include <isl/space.h>
3967 isl_bool isl_space_can_curry(
3968 __isl_keep isl_space *space);
3970 #include <isl/map.h>
3971 isl_bool isl_basic_map_can_curry(
3972 __isl_keep isl_basic_map *bmap);
3973 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
3975 Check whether the domain of the (basic) relation is a wrapped relation.
3977 #include <isl/space.h>
3978 __isl_give isl_space *isl_space_uncurry(
3979 __isl_take isl_space *space);
3981 #include <isl/map.h>
3982 isl_bool isl_basic_map_can_uncurry(
3983 __isl_keep isl_basic_map *bmap);
3984 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
3986 Check whether the range of the (basic) relation is a wrapped relation.
3988 #include <isl/space.h>
3989 isl_bool isl_space_can_range_curry(
3990 __isl_keep isl_space *space);
3992 #include <isl/map.h>
3993 isl_bool isl_map_can_range_curry(
3994 __isl_keep isl_map *map);
3996 Check whether the domain of the relation wrapped in the range of
3997 the input is itself a wrapped relation.
3999 =item * Special Values
4001 #include <isl/aff.h>
4002 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4003 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4004 isl_bool isl_multi_pw_aff_is_cst(
4005 __isl_keep isl_multi_pw_aff *mpa);
4007 Check whether the given expression is a constant.
4009 #include <isl/aff.h>
4010 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4011 isl_bool isl_pw_aff_involves_nan(
4012 __isl_keep isl_pw_aff *pa);
4014 #include <isl/polynomial.h>
4015 isl_bool isl_qpolynomial_fold_is_nan(
4016 __isl_keep isl_qpolynomial_fold *fold);
4018 Check whether the given expression is equal to or involves NaN.
4020 #include <isl/aff.h>
4021 isl_bool isl_aff_plain_is_zero(
4022 __isl_keep isl_aff *aff);
4024 Check whether the affine expression is obviously zero.
4028 =head3 Binary Properties
4034 The following functions check whether two objects
4035 represent the same set, relation or function.
4036 The C<plain> variants only return true if the objects
4037 are obviously the same. That is, they may return false
4038 even if the objects are the same, but they will never
4039 return true if the objects are not the same.
4041 #include <isl/set.h>
4042 isl_bool isl_basic_set_plain_is_equal(
4043 __isl_keep isl_basic_set *bset1,
4044 __isl_keep isl_basic_set *bset2);
4045 isl_bool isl_basic_set_is_equal(
4046 __isl_keep isl_basic_set *bset1,
4047 __isl_keep isl_basic_set *bset2);
4048 isl_bool isl_set_plain_is_equal(
4049 __isl_keep isl_set *set1,
4050 __isl_keep isl_set *set2);
4051 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4052 __isl_keep isl_set *set2);
4054 #include <isl/map.h>
4055 isl_bool isl_basic_map_is_equal(
4056 __isl_keep isl_basic_map *bmap1,
4057 __isl_keep isl_basic_map *bmap2);
4058 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4059 __isl_keep isl_map *map2);
4060 isl_bool isl_map_plain_is_equal(
4061 __isl_keep isl_map *map1,
4062 __isl_keep isl_map *map2);
4064 #include <isl/union_set.h>
4065 isl_bool isl_union_set_is_equal(
4066 __isl_keep isl_union_set *uset1,
4067 __isl_keep isl_union_set *uset2);
4069 #include <isl/union_map.h>
4070 isl_bool isl_union_map_is_equal(
4071 __isl_keep isl_union_map *umap1,
4072 __isl_keep isl_union_map *umap2);
4074 #include <isl/aff.h>
4075 isl_bool isl_aff_plain_is_equal(
4076 __isl_keep isl_aff *aff1,
4077 __isl_keep isl_aff *aff2);
4078 isl_bool isl_multi_aff_plain_is_equal(
4079 __isl_keep isl_multi_aff *maff1,
4080 __isl_keep isl_multi_aff *maff2);
4081 isl_bool isl_pw_aff_plain_is_equal(
4082 __isl_keep isl_pw_aff *pwaff1,
4083 __isl_keep isl_pw_aff *pwaff2);
4084 isl_bool isl_pw_multi_aff_plain_is_equal(
4085 __isl_keep isl_pw_multi_aff *pma1,
4086 __isl_keep isl_pw_multi_aff *pma2);
4087 isl_bool isl_multi_pw_aff_plain_is_equal(
4088 __isl_keep isl_multi_pw_aff *mpa1,
4089 __isl_keep isl_multi_pw_aff *mpa2);
4090 isl_bool isl_multi_pw_aff_is_equal(
4091 __isl_keep isl_multi_pw_aff *mpa1,
4092 __isl_keep isl_multi_pw_aff *mpa2);
4093 isl_bool isl_union_pw_aff_plain_is_equal(
4094 __isl_keep isl_union_pw_aff *upa1,
4095 __isl_keep isl_union_pw_aff *upa2);
4096 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4097 __isl_keep isl_union_pw_multi_aff *upma1,
4098 __isl_keep isl_union_pw_multi_aff *upma2);
4099 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4100 __isl_keep isl_multi_union_pw_aff *mupa1,
4101 __isl_keep isl_multi_union_pw_aff *mupa2);
4103 #include <isl/polynomial.h>
4104 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4105 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4106 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4107 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4108 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4109 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4111 =item * Disjointness
4113 #include <isl/set.h>
4114 isl_bool isl_basic_set_is_disjoint(
4115 __isl_keep isl_basic_set *bset1,
4116 __isl_keep isl_basic_set *bset2);
4117 isl_bool isl_set_plain_is_disjoint(
4118 __isl_keep isl_set *set1,
4119 __isl_keep isl_set *set2);
4120 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4121 __isl_keep isl_set *set2);
4123 #include <isl/map.h>
4124 isl_bool isl_basic_map_is_disjoint(
4125 __isl_keep isl_basic_map *bmap1,
4126 __isl_keep isl_basic_map *bmap2);
4127 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4128 __isl_keep isl_map *map2);
4130 #include <isl/union_set.h>
4131 isl_bool isl_union_set_is_disjoint(
4132 __isl_keep isl_union_set *uset1,
4133 __isl_keep isl_union_set *uset2);
4135 #include <isl/union_map.h>
4136 isl_bool isl_union_map_is_disjoint(
4137 __isl_keep isl_union_map *umap1,
4138 __isl_keep isl_union_map *umap2);
4142 isl_bool isl_basic_set_is_subset(
4143 __isl_keep isl_basic_set *bset1,
4144 __isl_keep isl_basic_set *bset2);
4145 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4146 __isl_keep isl_set *set2);
4147 isl_bool isl_set_is_strict_subset(
4148 __isl_keep isl_set *set1,
4149 __isl_keep isl_set *set2);
4150 isl_bool isl_union_set_is_subset(
4151 __isl_keep isl_union_set *uset1,
4152 __isl_keep isl_union_set *uset2);
4153 isl_bool isl_union_set_is_strict_subset(
4154 __isl_keep isl_union_set *uset1,
4155 __isl_keep isl_union_set *uset2);
4156 isl_bool isl_basic_map_is_subset(
4157 __isl_keep isl_basic_map *bmap1,
4158 __isl_keep isl_basic_map *bmap2);
4159 isl_bool isl_basic_map_is_strict_subset(
4160 __isl_keep isl_basic_map *bmap1,
4161 __isl_keep isl_basic_map *bmap2);
4162 isl_bool isl_map_is_subset(
4163 __isl_keep isl_map *map1,
4164 __isl_keep isl_map *map2);
4165 isl_bool isl_map_is_strict_subset(
4166 __isl_keep isl_map *map1,
4167 __isl_keep isl_map *map2);
4168 isl_bool isl_union_map_is_subset(
4169 __isl_keep isl_union_map *umap1,
4170 __isl_keep isl_union_map *umap2);
4171 isl_bool isl_union_map_is_strict_subset(
4172 __isl_keep isl_union_map *umap1,
4173 __isl_keep isl_union_map *umap2);
4175 Check whether the first argument is a (strict) subset of the
4180 Every comparison function returns a negative value if the first
4181 argument is considered smaller than the second, a positive value
4182 if the first argument is considered greater and zero if the two
4183 constraints are considered the same by the comparison criterion.
4185 #include <isl/constraint.h>
4186 int isl_constraint_plain_cmp(
4187 __isl_keep isl_constraint *c1,
4188 __isl_keep isl_constraint *c2);
4190 This function is useful for sorting C<isl_constraint>s.
4191 The order depends on the internal representation of the inputs.
4192 The order is fixed over different calls to the function (assuming
4193 the internal representation of the inputs has not changed), but may
4194 change over different versions of C<isl>.
4196 #include <isl/constraint.h>
4197 int isl_constraint_cmp_last_non_zero(
4198 __isl_keep isl_constraint *c1,
4199 __isl_keep isl_constraint *c2);
4201 This function can be used to sort constraints that live in the same
4202 local space. Constraints that involve ``earlier'' dimensions or
4203 that have a smaller coefficient for the shared latest dimension
4204 are considered smaller than other constraints.
4205 This function only defines a B<partial> order.
4207 #include <isl/set.h>
4208 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4209 __isl_keep isl_set *set2);
4211 This function is useful for sorting C<isl_set>s.
4212 The order depends on the internal representation of the inputs.
4213 The order is fixed over different calls to the function (assuming
4214 the internal representation of the inputs has not changed), but may
4215 change over different versions of C<isl>.
4217 #include <isl/aff.h>
4218 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4219 __isl_keep isl_pw_aff *pa2);
4221 The function C<isl_pw_aff_plain_cmp> can be used to sort
4222 C<isl_pw_aff>s. The order is not strictly defined.
4223 The current order sorts expressions that only involve
4224 earlier dimensions before those that involve later dimensions.
4228 =head2 Unary Operations
4234 __isl_give isl_set *isl_set_complement(
4235 __isl_take isl_set *set);
4236 __isl_give isl_map *isl_map_complement(
4237 __isl_take isl_map *map);
4241 #include <isl/space.h>
4242 __isl_give isl_space *isl_space_reverse(
4243 __isl_take isl_space *space);
4245 #include <isl/map.h>
4246 __isl_give isl_basic_map *isl_basic_map_reverse(
4247 __isl_take isl_basic_map *bmap);
4248 __isl_give isl_map *isl_map_reverse(
4249 __isl_take isl_map *map);
4251 #include <isl/union_map.h>
4252 __isl_give isl_union_map *isl_union_map_reverse(
4253 __isl_take isl_union_map *umap);
4257 #include <isl/space.h>
4258 __isl_give isl_space *isl_space_domain(
4259 __isl_take isl_space *space);
4260 __isl_give isl_space *isl_space_range(
4261 __isl_take isl_space *space);
4262 __isl_give isl_space *isl_space_params(
4263 __isl_take isl_space *space);
4265 #include <isl/local_space.h>
4266 __isl_give isl_local_space *isl_local_space_domain(
4267 __isl_take isl_local_space *ls);
4268 __isl_give isl_local_space *isl_local_space_range(
4269 __isl_take isl_local_space *ls);
4271 #include <isl/set.h>
4272 __isl_give isl_basic_set *isl_basic_set_project_out(
4273 __isl_take isl_basic_set *bset,
4274 enum isl_dim_type type, unsigned first, unsigned n);
4275 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4276 enum isl_dim_type type, unsigned first, unsigned n);
4277 __isl_give isl_map *isl_set_project_onto_map(
4278 __isl_take isl_set *set,
4279 enum isl_dim_type type, unsigned first,
4281 __isl_give isl_basic_set *isl_basic_set_params(
4282 __isl_take isl_basic_set *bset);
4283 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4285 The function C<isl_set_project_onto_map> returns a relation
4286 that projects the input set onto the given set dimensions.
4288 #include <isl/map.h>
4289 __isl_give isl_basic_map *isl_basic_map_project_out(
4290 __isl_take isl_basic_map *bmap,
4291 enum isl_dim_type type, unsigned first, unsigned n);
4292 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4293 enum isl_dim_type type, unsigned first, unsigned n);
4294 __isl_give isl_basic_set *isl_basic_map_domain(
4295 __isl_take isl_basic_map *bmap);
4296 __isl_give isl_basic_set *isl_basic_map_range(
4297 __isl_take isl_basic_map *bmap);
4298 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4299 __isl_give isl_set *isl_map_domain(
4300 __isl_take isl_map *bmap);
4301 __isl_give isl_set *isl_map_range(
4302 __isl_take isl_map *map);
4304 #include <isl/union_set.h>
4305 __isl_give isl_union_set *isl_union_set_project_out(
4306 __isl_take isl_union_set *uset,
4307 enum isl_dim_type type,
4308 unsigned first, unsigned n);
4309 __isl_give isl_set *isl_union_set_params(
4310 __isl_take isl_union_set *uset);
4312 The function C<isl_union_set_project_out> can only project out
4315 #include <isl/union_map.h>
4316 __isl_give isl_union_map *isl_union_map_project_out(
4317 __isl_take isl_union_map *umap,
4318 enum isl_dim_type type, unsigned first, unsigned n);
4319 __isl_give isl_set *isl_union_map_params(
4320 __isl_take isl_union_map *umap);
4321 __isl_give isl_union_set *isl_union_map_domain(
4322 __isl_take isl_union_map *umap);
4323 __isl_give isl_union_set *isl_union_map_range(
4324 __isl_take isl_union_map *umap);
4326 The function C<isl_union_map_project_out> can only project out
4329 #include <isl/aff.h>
4330 __isl_give isl_aff *isl_aff_project_domain_on_params(
4331 __isl_take isl_aff *aff);
4332 __isl_give isl_pw_multi_aff *
4333 isl_pw_multi_aff_project_domain_on_params(
4334 __isl_take isl_pw_multi_aff *pma);
4335 __isl_give isl_set *isl_pw_aff_domain(
4336 __isl_take isl_pw_aff *pwaff);
4337 __isl_give isl_set *isl_pw_multi_aff_domain(
4338 __isl_take isl_pw_multi_aff *pma);
4339 __isl_give isl_set *isl_multi_pw_aff_domain(
4340 __isl_take isl_multi_pw_aff *mpa);
4341 __isl_give isl_union_set *isl_union_pw_aff_domain(
4342 __isl_take isl_union_pw_aff *upa);
4343 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4344 __isl_take isl_union_pw_multi_aff *upma);
4345 __isl_give isl_union_set *
4346 isl_multi_union_pw_aff_domain(
4347 __isl_take isl_multi_union_pw_aff *mupa);
4348 __isl_give isl_set *isl_pw_aff_params(
4349 __isl_take isl_pw_aff *pwa);
4351 The function C<isl_multi_union_pw_aff_domain> requires its
4352 input to have at least one set dimension.
4354 #include <isl/polynomial.h>
4355 __isl_give isl_qpolynomial *
4356 isl_qpolynomial_project_domain_on_params(
4357 __isl_take isl_qpolynomial *qp);
4358 __isl_give isl_pw_qpolynomial *
4359 isl_pw_qpolynomial_project_domain_on_params(
4360 __isl_take isl_pw_qpolynomial *pwqp);
4361 __isl_give isl_pw_qpolynomial_fold *
4362 isl_pw_qpolynomial_fold_project_domain_on_params(
4363 __isl_take isl_pw_qpolynomial_fold *pwf);
4364 __isl_give isl_set *isl_pw_qpolynomial_domain(
4365 __isl_take isl_pw_qpolynomial *pwqp);
4366 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4367 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4368 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4369 __isl_take isl_union_pw_qpolynomial *upwqp);
4371 #include <isl/space.h>
4372 __isl_give isl_space *isl_space_domain_map(
4373 __isl_take isl_space *space);
4374 __isl_give isl_space *isl_space_range_map(
4375 __isl_take isl_space *space);
4377 #include <isl/map.h>
4378 __isl_give isl_map *isl_set_wrapped_domain_map(
4379 __isl_take isl_set *set);
4380 __isl_give isl_basic_map *isl_basic_map_domain_map(
4381 __isl_take isl_basic_map *bmap);
4382 __isl_give isl_basic_map *isl_basic_map_range_map(
4383 __isl_take isl_basic_map *bmap);
4384 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4385 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4387 #include <isl/union_map.h>
4388 __isl_give isl_union_map *isl_union_map_domain_map(
4389 __isl_take isl_union_map *umap);
4390 __isl_give isl_union_pw_multi_aff *
4391 isl_union_map_domain_map_union_pw_multi_aff(
4392 __isl_take isl_union_map *umap);
4393 __isl_give isl_union_map *isl_union_map_range_map(
4394 __isl_take isl_union_map *umap);
4395 __isl_give isl_union_map *
4396 isl_union_set_wrapped_domain_map(
4397 __isl_take isl_union_set *uset);
4399 The functions above construct a (basic, regular or union) relation
4400 that maps (a wrapped version of) the input relation to its domain or range.
4401 C<isl_set_wrapped_domain_map> maps the input set to the domain
4402 of its wrapped relation.
4406 __isl_give isl_basic_set *isl_basic_set_eliminate(
4407 __isl_take isl_basic_set *bset,
4408 enum isl_dim_type type,
4409 unsigned first, unsigned n);
4410 __isl_give isl_set *isl_set_eliminate(
4411 __isl_take isl_set *set, enum isl_dim_type type,
4412 unsigned first, unsigned n);
4413 __isl_give isl_basic_map *isl_basic_map_eliminate(
4414 __isl_take isl_basic_map *bmap,
4415 enum isl_dim_type type,
4416 unsigned first, unsigned n);
4417 __isl_give isl_map *isl_map_eliminate(
4418 __isl_take isl_map *map, enum isl_dim_type type,
4419 unsigned first, unsigned n);
4421 Eliminate the coefficients for the given dimensions from the constraints,
4422 without removing the dimensions.
4424 =item * Constructing a set from a parameter domain
4426 A zero-dimensional space or (basic) set can be constructed
4427 on a given parameter domain using the following functions.
4429 #include <isl/space.h>
4430 __isl_give isl_space *isl_space_set_from_params(
4431 __isl_take isl_space *space);
4433 #include <isl/set.h>
4434 __isl_give isl_basic_set *isl_basic_set_from_params(
4435 __isl_take isl_basic_set *bset);
4436 __isl_give isl_set *isl_set_from_params(
4437 __isl_take isl_set *set);
4439 =item * Constructing a relation from one or two sets
4441 Create a relation with the given set(s) as domain and/or range.
4442 If only the domain or the range is specified, then
4443 the range or domain of the created relation is a zero-dimensional
4444 flat anonymous space.
4446 #include <isl/space.h>
4447 __isl_give isl_space *isl_space_from_domain(
4448 __isl_take isl_space *space);
4449 __isl_give isl_space *isl_space_from_range(
4450 __isl_take isl_space *space);
4451 __isl_give isl_space *isl_space_map_from_set(
4452 __isl_take isl_space *space);
4453 __isl_give isl_space *isl_space_map_from_domain_and_range(
4454 __isl_take isl_space *domain,
4455 __isl_take isl_space *range);
4457 #include <isl/local_space.h>
4458 __isl_give isl_local_space *isl_local_space_from_domain(
4459 __isl_take isl_local_space *ls);
4461 #include <isl/map.h>
4462 __isl_give isl_map *isl_map_from_domain(
4463 __isl_take isl_set *set);
4464 __isl_give isl_map *isl_map_from_range(
4465 __isl_take isl_set *set);
4467 #include <isl/union_map.h>
4468 __isl_give isl_union_map *
4469 isl_union_map_from_domain_and_range(
4470 __isl_take isl_union_set *domain,
4471 __isl_take isl_union_set *range);
4473 #include <isl/val.h>
4474 __isl_give isl_multi_val *isl_multi_val_from_range(
4475 __isl_take isl_multi_val *mv);
4477 #include <isl/aff.h>
4478 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4479 __isl_take isl_multi_aff *ma);
4480 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4481 __isl_take isl_pw_aff *pwa);
4482 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4483 __isl_take isl_multi_pw_aff *mpa);
4484 __isl_give isl_multi_union_pw_aff *
4485 isl_multi_union_pw_aff_from_range(
4486 __isl_take isl_multi_union_pw_aff *mupa);
4487 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4488 __isl_take isl_set *set);
4489 __isl_give isl_union_pw_multi_aff *
4490 isl_union_pw_multi_aff_from_domain(
4491 __isl_take isl_union_set *uset);
4495 #include <isl/set.h>
4496 __isl_give isl_basic_set *isl_basic_set_fix_si(
4497 __isl_take isl_basic_set *bset,
4498 enum isl_dim_type type, unsigned pos, int value);
4499 __isl_give isl_basic_set *isl_basic_set_fix_val(
4500 __isl_take isl_basic_set *bset,
4501 enum isl_dim_type type, unsigned pos,
4502 __isl_take isl_val *v);
4503 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4504 enum isl_dim_type type, unsigned pos, int value);
4505 __isl_give isl_set *isl_set_fix_val(
4506 __isl_take isl_set *set,
4507 enum isl_dim_type type, unsigned pos,
4508 __isl_take isl_val *v);
4510 #include <isl/map.h>
4511 __isl_give isl_basic_map *isl_basic_map_fix_si(
4512 __isl_take isl_basic_map *bmap,
4513 enum isl_dim_type type, unsigned pos, int value);
4514 __isl_give isl_basic_map *isl_basic_map_fix_val(
4515 __isl_take isl_basic_map *bmap,
4516 enum isl_dim_type type, unsigned pos,
4517 __isl_take isl_val *v);
4518 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4519 enum isl_dim_type type, unsigned pos, int value);
4520 __isl_give isl_map *isl_map_fix_val(
4521 __isl_take isl_map *map,
4522 enum isl_dim_type type, unsigned pos,
4523 __isl_take isl_val *v);
4525 #include <isl/aff.h>
4526 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4527 __isl_take isl_pw_multi_aff *pma,
4528 enum isl_dim_type type, unsigned pos, int value);
4530 #include <isl/polynomial.h>
4531 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4532 __isl_take isl_pw_qpolynomial *pwqp,
4533 enum isl_dim_type type, unsigned n,
4534 __isl_take isl_val *v);
4536 Intersect the set, relation or function domain
4537 with the hyperplane where the given
4538 dimension has the fixed given value.
4540 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4541 __isl_take isl_basic_map *bmap,
4542 enum isl_dim_type type, unsigned pos, int value);
4543 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4544 __isl_take isl_basic_map *bmap,
4545 enum isl_dim_type type, unsigned pos, int value);
4546 __isl_give isl_set *isl_set_lower_bound_si(
4547 __isl_take isl_set *set,
4548 enum isl_dim_type type, unsigned pos, int value);
4549 __isl_give isl_set *isl_set_lower_bound_val(
4550 __isl_take isl_set *set,
4551 enum isl_dim_type type, unsigned pos,
4552 __isl_take isl_val *value);
4553 __isl_give isl_map *isl_map_lower_bound_si(
4554 __isl_take isl_map *map,
4555 enum isl_dim_type type, unsigned pos, int value);
4556 __isl_give isl_set *isl_set_upper_bound_si(
4557 __isl_take isl_set *set,
4558 enum isl_dim_type type, unsigned pos, int value);
4559 __isl_give isl_set *isl_set_upper_bound_val(
4560 __isl_take isl_set *set,
4561 enum isl_dim_type type, unsigned pos,
4562 __isl_take isl_val *value);
4563 __isl_give isl_map *isl_map_upper_bound_si(
4564 __isl_take isl_map *map,
4565 enum isl_dim_type type, unsigned pos, int value);
4567 Intersect the set or relation with the half-space where the given
4568 dimension has a value bounded by the fixed given integer value.
4570 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4571 enum isl_dim_type type1, int pos1,
4572 enum isl_dim_type type2, int pos2);
4573 __isl_give isl_basic_map *isl_basic_map_equate(
4574 __isl_take isl_basic_map *bmap,
4575 enum isl_dim_type type1, int pos1,
4576 enum isl_dim_type type2, int pos2);
4577 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4578 enum isl_dim_type type1, int pos1,
4579 enum isl_dim_type type2, int pos2);
4581 Intersect the set or relation with the hyperplane where the given
4582 dimensions are equal to each other.
4584 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4585 enum isl_dim_type type1, int pos1,
4586 enum isl_dim_type type2, int pos2);
4588 Intersect the relation with the hyperplane where the given
4589 dimensions have opposite values.
4591 __isl_give isl_map *isl_map_order_le(
4592 __isl_take isl_map *map,
4593 enum isl_dim_type type1, int pos1,
4594 enum isl_dim_type type2, int pos2);
4595 __isl_give isl_basic_map *isl_basic_map_order_ge(
4596 __isl_take isl_basic_map *bmap,
4597 enum isl_dim_type type1, int pos1,
4598 enum isl_dim_type type2, int pos2);
4599 __isl_give isl_map *isl_map_order_ge(
4600 __isl_take isl_map *map,
4601 enum isl_dim_type type1, int pos1,
4602 enum isl_dim_type type2, int pos2);
4603 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4604 enum isl_dim_type type1, int pos1,
4605 enum isl_dim_type type2, int pos2);
4606 __isl_give isl_basic_map *isl_basic_map_order_gt(
4607 __isl_take isl_basic_map *bmap,
4608 enum isl_dim_type type1, int pos1,
4609 enum isl_dim_type type2, int pos2);
4610 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4611 enum isl_dim_type type1, int pos1,
4612 enum isl_dim_type type2, int pos2);
4614 Intersect the relation with the half-space where the given
4615 dimensions satisfy the given ordering.
4619 #include <isl/aff.h>
4620 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4621 __isl_take isl_aff *aff);
4622 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4623 __isl_take isl_aff *aff);
4624 __isl_give isl_set *isl_pw_aff_pos_set(
4625 __isl_take isl_pw_aff *pa);
4626 __isl_give isl_set *isl_pw_aff_nonneg_set(
4627 __isl_take isl_pw_aff *pwaff);
4628 __isl_give isl_set *isl_pw_aff_zero_set(
4629 __isl_take isl_pw_aff *pwaff);
4630 __isl_give isl_set *isl_pw_aff_non_zero_set(
4631 __isl_take isl_pw_aff *pwaff);
4632 __isl_give isl_union_set *
4633 isl_union_pw_aff_zero_union_set(
4634 __isl_take isl_union_pw_aff *upa);
4635 __isl_give isl_union_set *
4636 isl_multi_union_pw_aff_zero_union_set(
4637 __isl_take isl_multi_union_pw_aff *mupa);
4639 The function C<isl_aff_neg_basic_set> returns a basic set
4640 containing those elements in the domain space
4641 of C<aff> where C<aff> is negative.
4642 The function C<isl_pw_aff_nonneg_set> returns a set
4643 containing those elements in the domain
4644 of C<pwaff> where C<pwaff> is non-negative.
4645 The function C<isl_multi_union_pw_aff_zero_union_set>
4646 returns a union set containing those elements
4647 in the domains of its elements where they are all zero.
4651 __isl_give isl_map *isl_set_identity(
4652 __isl_take isl_set *set);
4653 __isl_give isl_union_map *isl_union_set_identity(
4654 __isl_take isl_union_set *uset);
4655 __isl_give isl_union_pw_multi_aff *
4656 isl_union_set_identity_union_pw_multi_aff(
4657 __isl_take isl_union_set *uset);
4659 Construct an identity relation on the given (union) set.
4661 =item * Function Extraction
4663 A piecewise quasi affine expression that is equal to 1 on a set
4664 and 0 outside the set can be created using the following function.
4666 #include <isl/aff.h>
4667 __isl_give isl_pw_aff *isl_set_indicator_function(
4668 __isl_take isl_set *set);
4670 A piecewise multiple quasi affine expression can be extracted
4671 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4672 and the C<isl_map> is single-valued.
4673 In case of a conversion from an C<isl_union_map>
4674 to an C<isl_union_pw_multi_aff>, these properties need to hold
4675 in each domain space.
4676 A conversion to a C<isl_multi_union_pw_aff> additionally
4677 requires that the input is non-empty and involves only a single
4680 #include <isl/aff.h>
4681 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4682 __isl_take isl_set *set);
4683 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4684 __isl_take isl_map *map);
4686 __isl_give isl_union_pw_multi_aff *
4687 isl_union_pw_multi_aff_from_union_set(
4688 __isl_take isl_union_set *uset);
4689 __isl_give isl_union_pw_multi_aff *
4690 isl_union_pw_multi_aff_from_union_map(
4691 __isl_take isl_union_map *umap);
4693 __isl_give isl_multi_union_pw_aff *
4694 isl_multi_union_pw_aff_from_union_map(
4695 __isl_take isl_union_map *umap);
4699 __isl_give isl_basic_set *isl_basic_map_deltas(
4700 __isl_take isl_basic_map *bmap);
4701 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4702 __isl_give isl_union_set *isl_union_map_deltas(
4703 __isl_take isl_union_map *umap);
4705 These functions return a (basic) set containing the differences
4706 between image elements and corresponding domain elements in the input.
4708 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4709 __isl_take isl_basic_map *bmap);
4710 __isl_give isl_map *isl_map_deltas_map(
4711 __isl_take isl_map *map);
4712 __isl_give isl_union_map *isl_union_map_deltas_map(
4713 __isl_take isl_union_map *umap);
4715 The functions above construct a (basic, regular or union) relation
4716 that maps (a wrapped version of) the input relation to its delta set.
4720 Simplify the representation of a set, relation or functions by trying
4721 to combine pairs of basic sets or relations into a single
4722 basic set or relation.
4724 #include <isl/set.h>
4725 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4727 #include <isl/map.h>
4728 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4730 #include <isl/union_set.h>
4731 __isl_give isl_union_set *isl_union_set_coalesce(
4732 __isl_take isl_union_set *uset);
4734 #include <isl/union_map.h>
4735 __isl_give isl_union_map *isl_union_map_coalesce(
4736 __isl_take isl_union_map *umap);
4738 #include <isl/aff.h>
4739 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4740 __isl_take isl_pw_aff *pwqp);
4741 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4742 __isl_take isl_pw_multi_aff *pma);
4743 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4744 __isl_take isl_multi_pw_aff *mpa);
4745 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4746 __isl_take isl_union_pw_aff *upa);
4747 __isl_give isl_union_pw_multi_aff *
4748 isl_union_pw_multi_aff_coalesce(
4749 __isl_take isl_union_pw_multi_aff *upma);
4750 __isl_give isl_multi_union_pw_aff *
4751 isl_multi_union_pw_aff_coalesce(
4752 __isl_take isl_multi_union_pw_aff *aff);
4754 #include <isl/polynomial.h>
4755 __isl_give isl_pw_qpolynomial_fold *
4756 isl_pw_qpolynomial_fold_coalesce(
4757 __isl_take isl_pw_qpolynomial_fold *pwf);
4758 __isl_give isl_union_pw_qpolynomial *
4759 isl_union_pw_qpolynomial_coalesce(
4760 __isl_take isl_union_pw_qpolynomial *upwqp);
4761 __isl_give isl_union_pw_qpolynomial_fold *
4762 isl_union_pw_qpolynomial_fold_coalesce(
4763 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4765 One of the methods for combining pairs of basic sets or relations
4766 can result in coefficients that are much larger than those that appear
4767 in the constraints of the input. By default, the coefficients are
4768 not allowed to grow larger, but this can be changed by unsetting
4769 the following option.
4771 isl_stat isl_options_set_coalesce_bounded_wrapping(
4772 isl_ctx *ctx, int val);
4773 int isl_options_get_coalesce_bounded_wrapping(
4776 =item * Detecting equalities
4778 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4779 __isl_take isl_basic_set *bset);
4780 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4781 __isl_take isl_basic_map *bmap);
4782 __isl_give isl_set *isl_set_detect_equalities(
4783 __isl_take isl_set *set);
4784 __isl_give isl_map *isl_map_detect_equalities(
4785 __isl_take isl_map *map);
4786 __isl_give isl_union_set *isl_union_set_detect_equalities(
4787 __isl_take isl_union_set *uset);
4788 __isl_give isl_union_map *isl_union_map_detect_equalities(
4789 __isl_take isl_union_map *umap);
4791 Simplify the representation of a set or relation by detecting implicit
4794 =item * Removing redundant constraints
4796 #include <isl/set.h>
4797 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4798 __isl_take isl_basic_set *bset);
4799 __isl_give isl_set *isl_set_remove_redundancies(
4800 __isl_take isl_set *set);
4802 #include <isl/union_set.h>
4803 __isl_give isl_union_set *
4804 isl_union_set_remove_redundancies(
4805 __isl_take isl_union_set *uset);
4807 #include <isl/map.h>
4808 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4809 __isl_take isl_basic_map *bmap);
4810 __isl_give isl_map *isl_map_remove_redundancies(
4811 __isl_take isl_map *map);
4813 #include <isl/union_map.h>
4814 __isl_give isl_union_map *
4815 isl_union_map_remove_redundancies(
4816 __isl_take isl_union_map *umap);
4820 __isl_give isl_basic_set *isl_set_convex_hull(
4821 __isl_take isl_set *set);
4822 __isl_give isl_basic_map *isl_map_convex_hull(
4823 __isl_take isl_map *map);
4825 If the input set or relation has any existentially quantified
4826 variables, then the result of these operations is currently undefined.
4830 #include <isl/set.h>
4831 __isl_give isl_basic_set *
4832 isl_set_unshifted_simple_hull(
4833 __isl_take isl_set *set);
4834 __isl_give isl_basic_set *isl_set_simple_hull(
4835 __isl_take isl_set *set);
4836 __isl_give isl_basic_set *
4837 isl_set_plain_unshifted_simple_hull(
4838 __isl_take isl_set *set);
4839 __isl_give isl_basic_set *
4840 isl_set_unshifted_simple_hull_from_set_list(
4841 __isl_take isl_set *set,
4842 __isl_take isl_set_list *list);
4844 #include <isl/map.h>
4845 __isl_give isl_basic_map *
4846 isl_map_unshifted_simple_hull(
4847 __isl_take isl_map *map);
4848 __isl_give isl_basic_map *isl_map_simple_hull(
4849 __isl_take isl_map *map);
4850 __isl_give isl_basic_map *
4851 isl_map_plain_unshifted_simple_hull(
4852 __isl_take isl_map *map);
4853 __isl_give isl_basic_map *
4854 isl_map_unshifted_simple_hull_from_map_list(
4855 __isl_take isl_map *map,
4856 __isl_take isl_map_list *list);
4858 #include <isl/union_map.h>
4859 __isl_give isl_union_map *isl_union_map_simple_hull(
4860 __isl_take isl_union_map *umap);
4862 These functions compute a single basic set or relation
4863 that contains the whole input set or relation.
4864 In particular, the output is described by translates
4865 of the constraints describing the basic sets or relations in the input.
4866 In case of C<isl_set_unshifted_simple_hull>, only the original
4867 constraints are used, without any translation.
4868 In case of C<isl_set_plain_unshifted_simple_hull> and
4869 C<isl_map_plain_unshifted_simple_hull>, the result is described
4870 by original constraints that are obviously satisfied
4871 by the entire input set or relation.
4872 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4873 C<isl_map_unshifted_simple_hull_from_map_list>, the
4874 constraints are taken from the elements of the second argument.
4878 (See \autoref{s:simple hull}.)
4884 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4885 __isl_take isl_basic_set *bset);
4886 __isl_give isl_basic_set *isl_set_affine_hull(
4887 __isl_take isl_set *set);
4888 __isl_give isl_union_set *isl_union_set_affine_hull(
4889 __isl_take isl_union_set *uset);
4890 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4891 __isl_take isl_basic_map *bmap);
4892 __isl_give isl_basic_map *isl_map_affine_hull(
4893 __isl_take isl_map *map);
4894 __isl_give isl_union_map *isl_union_map_affine_hull(
4895 __isl_take isl_union_map *umap);
4897 In case of union sets and relations, the affine hull is computed
4900 =item * Polyhedral hull
4902 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4903 __isl_take isl_set *set);
4904 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4905 __isl_take isl_map *map);
4906 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4907 __isl_take isl_union_set *uset);
4908 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4909 __isl_take isl_union_map *umap);
4911 These functions compute a single basic set or relation
4912 not involving any existentially quantified variables
4913 that contains the whole input set or relation.
4914 In case of union sets and relations, the polyhedral hull is computed
4917 =item * Other approximations
4919 #include <isl/set.h>
4920 __isl_give isl_basic_set *
4921 isl_basic_set_drop_constraints_involving_dims(
4922 __isl_take isl_basic_set *bset,
4923 enum isl_dim_type type,
4924 unsigned first, unsigned n);
4925 __isl_give isl_basic_set *
4926 isl_basic_set_drop_constraints_not_involving_dims(
4927 __isl_take isl_basic_set *bset,
4928 enum isl_dim_type type,
4929 unsigned first, unsigned n);
4930 __isl_give isl_set *
4931 isl_set_drop_constraints_involving_dims(
4932 __isl_take isl_set *set,
4933 enum isl_dim_type type,
4934 unsigned first, unsigned n);
4935 __isl_give isl_set *
4936 isl_set_drop_constraints_not_involving_dims(
4937 __isl_take isl_set *set,
4938 enum isl_dim_type type,
4939 unsigned first, unsigned n);
4941 #include <isl/map.h>
4942 __isl_give isl_basic_map *
4943 isl_basic_map_drop_constraints_involving_dims(
4944 __isl_take isl_basic_map *bmap,
4945 enum isl_dim_type type,
4946 unsigned first, unsigned n);
4947 __isl_give isl_basic_map *
4948 isl_basic_map_drop_constraints_not_involving_dims(
4949 __isl_take isl_basic_map *bmap,
4950 enum isl_dim_type type,
4951 unsigned first, unsigned n);
4952 __isl_give isl_map *
4953 isl_map_drop_constraints_involving_dims(
4954 __isl_take isl_map *map,
4955 enum isl_dim_type type,
4956 unsigned first, unsigned n);
4957 __isl_give isl_map *
4958 isl_map_drop_constraints_not_involving_dims(
4959 __isl_take isl_map *map,
4960 enum isl_dim_type type,
4961 unsigned first, unsigned n);
4963 These functions drop any constraints (not) involving the specified dimensions.
4964 Note that the result depends on the representation of the input.
4966 #include <isl/polynomial.h>
4967 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4968 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4969 __isl_give isl_union_pw_qpolynomial *
4970 isl_union_pw_qpolynomial_to_polynomial(
4971 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4973 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4974 the polynomial will be an overapproximation. If C<sign> is negative,
4975 it will be an underapproximation. If C<sign> is zero, the approximation
4976 will lie somewhere in between.
4980 __isl_give isl_basic_set *isl_basic_set_sample(
4981 __isl_take isl_basic_set *bset);
4982 __isl_give isl_basic_set *isl_set_sample(
4983 __isl_take isl_set *set);
4984 __isl_give isl_basic_map *isl_basic_map_sample(
4985 __isl_take isl_basic_map *bmap);
4986 __isl_give isl_basic_map *isl_map_sample(
4987 __isl_take isl_map *map);
4989 If the input (basic) set or relation is non-empty, then return
4990 a singleton subset of the input. Otherwise, return an empty set.
4992 =item * Optimization
4994 #include <isl/ilp.h>
4995 __isl_give isl_val *isl_basic_set_max_val(
4996 __isl_keep isl_basic_set *bset,
4997 __isl_keep isl_aff *obj);
4998 __isl_give isl_val *isl_set_min_val(
4999 __isl_keep isl_set *set,
5000 __isl_keep isl_aff *obj);
5001 __isl_give isl_val *isl_set_max_val(
5002 __isl_keep isl_set *set,
5003 __isl_keep isl_aff *obj);
5004 __isl_give isl_multi_val *
5005 isl_union_set_min_multi_union_pw_aff(
5006 __isl_keep isl_union_set *set,
5007 __isl_keep isl_multi_union_pw_aff *obj);
5009 Compute the minimum or maximum of the integer affine expression C<obj>
5010 over the points in C<set>, returning the result in C<opt>.
5011 The result is C<NULL> in case of an error, the optimal value in case
5012 there is one, negative infinity or infinity if the problem is unbounded and
5013 NaN if the problem is empty.
5015 =item * Parametric optimization
5017 __isl_give isl_pw_aff *isl_set_dim_min(
5018 __isl_take isl_set *set, int pos);
5019 __isl_give isl_pw_aff *isl_set_dim_max(
5020 __isl_take isl_set *set, int pos);
5021 __isl_give isl_pw_aff *isl_map_dim_max(
5022 __isl_take isl_map *map, int pos);
5024 Compute the minimum or maximum of the given set or output dimension
5025 as a function of the parameters (and input dimensions), but independently
5026 of the other set or output dimensions.
5027 For lexicographic optimization, see L<"Lexicographic Optimization">.
5031 The following functions compute either the set of (rational) coefficient
5032 values of valid constraints for the given set or the set of (rational)
5033 values satisfying the constraints with coefficients from the given set.
5034 Internally, these two sets of functions perform essentially the
5035 same operations, except that the set of coefficients is assumed to
5036 be a cone, while the set of values may be any polyhedron.
5037 The current implementation is based on the Farkas lemma and
5038 Fourier-Motzkin elimination, but this may change or be made optional
5039 in future. In particular, future implementations may use different
5040 dualization algorithms or skip the elimination step.
5042 __isl_give isl_basic_set *isl_basic_set_coefficients(
5043 __isl_take isl_basic_set *bset);
5044 __isl_give isl_basic_set *isl_set_coefficients(
5045 __isl_take isl_set *set);
5046 __isl_give isl_union_set *isl_union_set_coefficients(
5047 __isl_take isl_union_set *bset);
5048 __isl_give isl_basic_set *isl_basic_set_solutions(
5049 __isl_take isl_basic_set *bset);
5050 __isl_give isl_basic_set *isl_set_solutions(
5051 __isl_take isl_set *set);
5052 __isl_give isl_union_set *isl_union_set_solutions(
5053 __isl_take isl_union_set *bset);
5057 __isl_give isl_map *isl_map_fixed_power_val(
5058 __isl_take isl_map *map,
5059 __isl_take isl_val *exp);
5060 __isl_give isl_union_map *
5061 isl_union_map_fixed_power_val(
5062 __isl_take isl_union_map *umap,
5063 __isl_take isl_val *exp);
5065 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5066 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5067 of C<map> is computed.
5069 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5071 __isl_give isl_union_map *isl_union_map_power(
5072 __isl_take isl_union_map *umap, int *exact);
5074 Compute a parametric representation for all positive powers I<k> of C<map>.
5075 The result maps I<k> to a nested relation corresponding to the
5076 I<k>th power of C<map>.
5077 The result may be an overapproximation. If the result is known to be exact,
5078 then C<*exact> is set to C<1>.
5080 =item * Transitive closure
5082 __isl_give isl_map *isl_map_transitive_closure(
5083 __isl_take isl_map *map, int *exact);
5084 __isl_give isl_union_map *isl_union_map_transitive_closure(
5085 __isl_take isl_union_map *umap, int *exact);
5087 Compute the transitive closure of C<map>.
5088 The result may be an overapproximation. If the result is known to be exact,
5089 then C<*exact> is set to C<1>.
5091 =item * Reaching path lengths
5093 __isl_give isl_map *isl_map_reaching_path_lengths(
5094 __isl_take isl_map *map, int *exact);
5096 Compute a relation that maps each element in the range of C<map>
5097 to the lengths of all paths composed of edges in C<map> that
5098 end up in the given element.
5099 The result may be an overapproximation. If the result is known to be exact,
5100 then C<*exact> is set to C<1>.
5101 To compute the I<maximal> path length, the resulting relation
5102 should be postprocessed by C<isl_map_lexmax>.
5103 In particular, if the input relation is a dependence relation
5104 (mapping sources to sinks), then the maximal path length corresponds
5105 to the free schedule.
5106 Note, however, that C<isl_map_lexmax> expects the maximum to be
5107 finite, so if the path lengths are unbounded (possibly due to
5108 the overapproximation), then you will get an error message.
5112 #include <isl/space.h>
5113 __isl_give isl_space *isl_space_wrap(
5114 __isl_take isl_space *space);
5115 __isl_give isl_space *isl_space_unwrap(
5116 __isl_take isl_space *space);
5118 #include <isl/local_space.h>
5119 __isl_give isl_local_space *isl_local_space_wrap(
5120 __isl_take isl_local_space *ls);
5122 #include <isl/set.h>
5123 __isl_give isl_basic_map *isl_basic_set_unwrap(
5124 __isl_take isl_basic_set *bset);
5125 __isl_give isl_map *isl_set_unwrap(
5126 __isl_take isl_set *set);
5128 #include <isl/map.h>
5129 __isl_give isl_basic_set *isl_basic_map_wrap(
5130 __isl_take isl_basic_map *bmap);
5131 __isl_give isl_set *isl_map_wrap(
5132 __isl_take isl_map *map);
5134 #include <isl/union_set.h>
5135 __isl_give isl_union_map *isl_union_set_unwrap(
5136 __isl_take isl_union_set *uset);
5138 #include <isl/union_map.h>
5139 __isl_give isl_union_set *isl_union_map_wrap(
5140 __isl_take isl_union_map *umap);
5142 The input to C<isl_space_unwrap> should
5143 be the space of a set, while that of
5144 C<isl_space_wrap> should be the space of a relation.
5145 Conversely, the output of C<isl_space_unwrap> is the space
5146 of a relation, while that of C<isl_space_wrap> is the space of a set.
5150 Remove any internal structure of domain (and range) of the given
5151 set or relation. If there is any such internal structure in the input,
5152 then the name of the space is also removed.
5154 #include <isl/local_space.h>
5155 __isl_give isl_local_space *
5156 isl_local_space_flatten_domain(
5157 __isl_take isl_local_space *ls);
5158 __isl_give isl_local_space *
5159 isl_local_space_flatten_range(
5160 __isl_take isl_local_space *ls);
5162 #include <isl/set.h>
5163 __isl_give isl_basic_set *isl_basic_set_flatten(
5164 __isl_take isl_basic_set *bset);
5165 __isl_give isl_set *isl_set_flatten(
5166 __isl_take isl_set *set);
5168 #include <isl/map.h>
5169 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5170 __isl_take isl_basic_map *bmap);
5171 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5172 __isl_take isl_basic_map *bmap);
5173 __isl_give isl_map *isl_map_flatten_range(
5174 __isl_take isl_map *map);
5175 __isl_give isl_map *isl_map_flatten_domain(
5176 __isl_take isl_map *map);
5177 __isl_give isl_basic_map *isl_basic_map_flatten(
5178 __isl_take isl_basic_map *bmap);
5179 __isl_give isl_map *isl_map_flatten(
5180 __isl_take isl_map *map);
5182 #include <isl/val.h>
5183 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5184 __isl_take isl_multi_val *mv);
5186 #include <isl/aff.h>
5187 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5188 __isl_take isl_multi_aff *ma);
5189 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5190 __isl_take isl_multi_aff *ma);
5191 __isl_give isl_multi_pw_aff *
5192 isl_multi_pw_aff_flatten_range(
5193 __isl_take isl_multi_pw_aff *mpa);
5194 __isl_give isl_multi_union_pw_aff *
5195 isl_multi_union_pw_aff_flatten_range(
5196 __isl_take isl_multi_union_pw_aff *mupa);
5198 #include <isl/map.h>
5199 __isl_give isl_map *isl_set_flatten_map(
5200 __isl_take isl_set *set);
5202 The function above constructs a relation
5203 that maps the input set to a flattened version of the set.
5207 Lift the input set to a space with extra dimensions corresponding
5208 to the existentially quantified variables in the input.
5209 In particular, the result lives in a wrapped map where the domain
5210 is the original space and the range corresponds to the original
5211 existentially quantified variables.
5213 #include <isl/set.h>
5214 __isl_give isl_basic_set *isl_basic_set_lift(
5215 __isl_take isl_basic_set *bset);
5216 __isl_give isl_set *isl_set_lift(
5217 __isl_take isl_set *set);
5218 __isl_give isl_union_set *isl_union_set_lift(
5219 __isl_take isl_union_set *uset);
5221 Given a local space that contains the existentially quantified
5222 variables of a set, a basic relation that, when applied to
5223 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5224 can be constructed using the following function.
5226 #include <isl/local_space.h>
5227 __isl_give isl_basic_map *isl_local_space_lifting(
5228 __isl_take isl_local_space *ls);
5230 #include <isl/aff.h>
5231 __isl_give isl_multi_aff *isl_multi_aff_lift(
5232 __isl_take isl_multi_aff *maff,
5233 __isl_give isl_local_space **ls);
5235 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5236 then it is assigned the local space that lies at the basis of
5237 the lifting applied.
5239 =item * Internal Product
5241 #include <isl/space.h>
5242 __isl_give isl_space *isl_space_zip(
5243 __isl_take isl_space *space);
5245 #include <isl/map.h>
5246 __isl_give isl_basic_map *isl_basic_map_zip(
5247 __isl_take isl_basic_map *bmap);
5248 __isl_give isl_map *isl_map_zip(
5249 __isl_take isl_map *map);
5251 #include <isl/union_map.h>
5252 __isl_give isl_union_map *isl_union_map_zip(
5253 __isl_take isl_union_map *umap);
5255 Given a relation with nested relations for domain and range,
5256 interchange the range of the domain with the domain of the range.
5260 #include <isl/space.h>
5261 __isl_give isl_space *isl_space_curry(
5262 __isl_take isl_space *space);
5263 __isl_give isl_space *isl_space_uncurry(
5264 __isl_take isl_space *space);
5266 #include <isl/map.h>
5267 __isl_give isl_basic_map *isl_basic_map_curry(
5268 __isl_take isl_basic_map *bmap);
5269 __isl_give isl_basic_map *isl_basic_map_uncurry(
5270 __isl_take isl_basic_map *bmap);
5271 __isl_give isl_map *isl_map_curry(
5272 __isl_take isl_map *map);
5273 __isl_give isl_map *isl_map_uncurry(
5274 __isl_take isl_map *map);
5276 #include <isl/union_map.h>
5277 __isl_give isl_union_map *isl_union_map_curry(
5278 __isl_take isl_union_map *umap);
5279 __isl_give isl_union_map *isl_union_map_uncurry(
5280 __isl_take isl_union_map *umap);
5282 Given a relation with a nested relation for domain,
5283 the C<curry> functions
5284 move the range of the nested relation out of the domain
5285 and use it as the domain of a nested relation in the range,
5286 with the original range as range of this nested relation.
5287 The C<uncurry> functions perform the inverse operation.
5289 #include <isl/space.h>
5290 __isl_give isl_space *isl_space_range_curry(
5291 __isl_take isl_space *space);
5293 #include <isl/map.h>
5294 __isl_give isl_map *isl_map_range_curry(
5295 __isl_take isl_map *map);
5297 #include <isl/union_map.h>
5298 __isl_give isl_union_map *isl_union_map_range_curry(
5299 __isl_take isl_union_map *umap);
5301 These functions apply the currying to the relation that
5302 is nested inside the range of the input.
5304 =item * Aligning parameters
5306 Change the order of the parameters of the given set, relation
5308 such that the first parameters match those of C<model>.
5309 This may involve the introduction of extra parameters.
5310 All parameters need to be named.
5312 #include <isl/space.h>
5313 __isl_give isl_space *isl_space_align_params(
5314 __isl_take isl_space *space1,
5315 __isl_take isl_space *space2)
5317 #include <isl/set.h>
5318 __isl_give isl_basic_set *isl_basic_set_align_params(
5319 __isl_take isl_basic_set *bset,
5320 __isl_take isl_space *model);
5321 __isl_give isl_set *isl_set_align_params(
5322 __isl_take isl_set *set,
5323 __isl_take isl_space *model);
5325 #include <isl/map.h>
5326 __isl_give isl_basic_map *isl_basic_map_align_params(
5327 __isl_take isl_basic_map *bmap,
5328 __isl_take isl_space *model);
5329 __isl_give isl_map *isl_map_align_params(
5330 __isl_take isl_map *map,
5331 __isl_take isl_space *model);
5333 #include <isl/val.h>
5334 __isl_give isl_multi_val *isl_multi_val_align_params(
5335 __isl_take isl_multi_val *mv,
5336 __isl_take isl_space *model);
5338 #include <isl/aff.h>
5339 __isl_give isl_aff *isl_aff_align_params(
5340 __isl_take isl_aff *aff,
5341 __isl_take isl_space *model);
5342 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5343 __isl_take isl_multi_aff *multi,
5344 __isl_take isl_space *model);
5345 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5346 __isl_take isl_pw_aff *pwaff,
5347 __isl_take isl_space *model);
5348 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5349 __isl_take isl_pw_multi_aff *pma,
5350 __isl_take isl_space *model);
5351 __isl_give isl_union_pw_aff *
5352 isl_union_pw_aff_align_params(
5353 __isl_take isl_union_pw_aff *upa,
5354 __isl_take isl_space *model);
5355 __isl_give isl_union_pw_multi_aff *
5356 isl_union_pw_multi_aff_align_params(
5357 __isl_take isl_union_pw_multi_aff *upma,
5358 __isl_take isl_space *model);
5359 __isl_give isl_multi_union_pw_aff *
5360 isl_multi_union_pw_aff_align_params(
5361 __isl_take isl_multi_union_pw_aff *mupa,
5362 __isl_take isl_space *model);
5364 #include <isl/polynomial.h>
5365 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5366 __isl_take isl_qpolynomial *qp,
5367 __isl_take isl_space *model);
5369 =item * Unary Arithmetic Operations
5371 #include <isl/set.h>
5372 __isl_give isl_set *isl_set_neg(
5373 __isl_take isl_set *set);
5374 #include <isl/map.h>
5375 __isl_give isl_map *isl_map_neg(
5376 __isl_take isl_map *map);
5378 C<isl_set_neg> constructs a set containing the opposites of
5379 the elements in its argument.
5380 The domain of the result of C<isl_map_neg> is the same
5381 as the domain of its argument. The corresponding range
5382 elements are the opposites of the corresponding range
5383 elements in the argument.
5385 #include <isl/val.h>
5386 __isl_give isl_multi_val *isl_multi_val_neg(
5387 __isl_take isl_multi_val *mv);
5389 #include <isl/aff.h>
5390 __isl_give isl_aff *isl_aff_neg(
5391 __isl_take isl_aff *aff);
5392 __isl_give isl_multi_aff *isl_multi_aff_neg(
5393 __isl_take isl_multi_aff *ma);
5394 __isl_give isl_pw_aff *isl_pw_aff_neg(
5395 __isl_take isl_pw_aff *pwaff);
5396 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5397 __isl_take isl_pw_multi_aff *pma);
5398 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5399 __isl_take isl_multi_pw_aff *mpa);
5400 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5401 __isl_take isl_union_pw_aff *upa);
5402 __isl_give isl_union_pw_multi_aff *
5403 isl_union_pw_multi_aff_neg(
5404 __isl_take isl_union_pw_multi_aff *upma);
5405 __isl_give isl_multi_union_pw_aff *
5406 isl_multi_union_pw_aff_neg(
5407 __isl_take isl_multi_union_pw_aff *mupa);
5408 __isl_give isl_aff *isl_aff_ceil(
5409 __isl_take isl_aff *aff);
5410 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5411 __isl_take isl_pw_aff *pwaff);
5412 __isl_give isl_aff *isl_aff_floor(
5413 __isl_take isl_aff *aff);
5414 __isl_give isl_multi_aff *isl_multi_aff_floor(
5415 __isl_take isl_multi_aff *ma);
5416 __isl_give isl_pw_aff *isl_pw_aff_floor(
5417 __isl_take isl_pw_aff *pwaff);
5418 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5419 __isl_take isl_union_pw_aff *upa);
5420 __isl_give isl_multi_union_pw_aff *
5421 isl_multi_union_pw_aff_floor(
5422 __isl_take isl_multi_union_pw_aff *mupa);
5424 #include <isl/aff.h>
5425 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5426 __isl_take isl_pw_aff_list *list);
5427 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5428 __isl_take isl_pw_aff_list *list);
5430 #include <isl/polynomial.h>
5431 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5432 __isl_take isl_qpolynomial *qp);
5433 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5434 __isl_take isl_pw_qpolynomial *pwqp);
5435 __isl_give isl_union_pw_qpolynomial *
5436 isl_union_pw_qpolynomial_neg(
5437 __isl_take isl_union_pw_qpolynomial *upwqp);
5438 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5439 __isl_take isl_qpolynomial *qp,
5441 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5442 __isl_take isl_pw_qpolynomial *pwqp,
5447 The following functions evaluate a function in a point.
5449 #include <isl/polynomial.h>
5450 __isl_give isl_val *isl_pw_qpolynomial_eval(
5451 __isl_take isl_pw_qpolynomial *pwqp,
5452 __isl_take isl_point *pnt);
5453 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5454 __isl_take isl_pw_qpolynomial_fold *pwf,
5455 __isl_take isl_point *pnt);
5456 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5457 __isl_take isl_union_pw_qpolynomial *upwqp,
5458 __isl_take isl_point *pnt);
5459 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5460 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5461 __isl_take isl_point *pnt);
5463 =item * Dimension manipulation
5465 It is usually not advisable to directly change the (input or output)
5466 space of a set or a relation as this removes the name and the internal
5467 structure of the space. However, the functions below can be useful
5468 to add new parameters, assuming
5469 C<isl_set_align_params> and C<isl_map_align_params>
5472 #include <isl/space.h>
5473 __isl_give isl_space *isl_space_add_dims(
5474 __isl_take isl_space *space,
5475 enum isl_dim_type type, unsigned n);
5476 __isl_give isl_space *isl_space_insert_dims(
5477 __isl_take isl_space *space,
5478 enum isl_dim_type type, unsigned pos, unsigned n);
5479 __isl_give isl_space *isl_space_drop_dims(
5480 __isl_take isl_space *space,
5481 enum isl_dim_type type, unsigned first, unsigned n);
5482 __isl_give isl_space *isl_space_move_dims(
5483 __isl_take isl_space *space,
5484 enum isl_dim_type dst_type, unsigned dst_pos,
5485 enum isl_dim_type src_type, unsigned src_pos,
5488 #include <isl/local_space.h>
5489 __isl_give isl_local_space *isl_local_space_add_dims(
5490 __isl_take isl_local_space *ls,
5491 enum isl_dim_type type, unsigned n);
5492 __isl_give isl_local_space *isl_local_space_insert_dims(
5493 __isl_take isl_local_space *ls,
5494 enum isl_dim_type type, unsigned first, unsigned n);
5495 __isl_give isl_local_space *isl_local_space_drop_dims(
5496 __isl_take isl_local_space *ls,
5497 enum isl_dim_type type, unsigned first, unsigned n);
5499 #include <isl/set.h>
5500 __isl_give isl_basic_set *isl_basic_set_add_dims(
5501 __isl_take isl_basic_set *bset,
5502 enum isl_dim_type type, unsigned n);
5503 __isl_give isl_set *isl_set_add_dims(
5504 __isl_take isl_set *set,
5505 enum isl_dim_type type, unsigned n);
5506 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5507 __isl_take isl_basic_set *bset,
5508 enum isl_dim_type type, unsigned pos,
5510 __isl_give isl_set *isl_set_insert_dims(
5511 __isl_take isl_set *set,
5512 enum isl_dim_type type, unsigned pos, unsigned n);
5513 __isl_give isl_basic_set *isl_basic_set_move_dims(
5514 __isl_take isl_basic_set *bset,
5515 enum isl_dim_type dst_type, unsigned dst_pos,
5516 enum isl_dim_type src_type, unsigned src_pos,
5518 __isl_give isl_set *isl_set_move_dims(
5519 __isl_take isl_set *set,
5520 enum isl_dim_type dst_type, unsigned dst_pos,
5521 enum isl_dim_type src_type, unsigned src_pos,
5524 #include <isl/map.h>
5525 __isl_give isl_basic_map *isl_basic_map_add_dims(
5526 __isl_take isl_basic_map *bmap,
5527 enum isl_dim_type type, unsigned n);
5528 __isl_give isl_map *isl_map_add_dims(
5529 __isl_take isl_map *map,
5530 enum isl_dim_type type, unsigned n);
5531 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5532 __isl_take isl_basic_map *bmap,
5533 enum isl_dim_type type, unsigned pos,
5535 __isl_give isl_map *isl_map_insert_dims(
5536 __isl_take isl_map *map,
5537 enum isl_dim_type type, unsigned pos, unsigned n);
5538 __isl_give isl_basic_map *isl_basic_map_move_dims(
5539 __isl_take isl_basic_map *bmap,
5540 enum isl_dim_type dst_type, unsigned dst_pos,
5541 enum isl_dim_type src_type, unsigned src_pos,
5543 __isl_give isl_map *isl_map_move_dims(
5544 __isl_take isl_map *map,
5545 enum isl_dim_type dst_type, unsigned dst_pos,
5546 enum isl_dim_type src_type, unsigned src_pos,
5549 #include <isl/val.h>
5550 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5551 __isl_take isl_multi_val *mv,
5552 enum isl_dim_type type, unsigned first, unsigned n);
5553 __isl_give isl_multi_val *isl_multi_val_add_dims(
5554 __isl_take isl_multi_val *mv,
5555 enum isl_dim_type type, unsigned n);
5556 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5557 __isl_take isl_multi_val *mv,
5558 enum isl_dim_type type, unsigned first, unsigned n);
5560 #include <isl/aff.h>
5561 __isl_give isl_aff *isl_aff_insert_dims(
5562 __isl_take isl_aff *aff,
5563 enum isl_dim_type type, unsigned first, unsigned n);
5564 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5565 __isl_take isl_multi_aff *ma,
5566 enum isl_dim_type type, unsigned first, unsigned n);
5567 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5568 __isl_take isl_pw_aff *pwaff,
5569 enum isl_dim_type type, unsigned first, unsigned n);
5570 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5571 __isl_take isl_multi_pw_aff *mpa,
5572 enum isl_dim_type type, unsigned first, unsigned n);
5573 __isl_give isl_aff *isl_aff_add_dims(
5574 __isl_take isl_aff *aff,
5575 enum isl_dim_type type, unsigned n);
5576 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5577 __isl_take isl_multi_aff *ma,
5578 enum isl_dim_type type, unsigned n);
5579 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5580 __isl_take isl_pw_aff *pwaff,
5581 enum isl_dim_type type, unsigned n);
5582 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5583 __isl_take isl_multi_pw_aff *mpa,
5584 enum isl_dim_type type, unsigned n);
5585 __isl_give isl_aff *isl_aff_drop_dims(
5586 __isl_take isl_aff *aff,
5587 enum isl_dim_type type, unsigned first, unsigned n);
5588 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5589 __isl_take isl_multi_aff *maff,
5590 enum isl_dim_type type, unsigned first, unsigned n);
5591 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5592 __isl_take isl_pw_aff *pwaff,
5593 enum isl_dim_type type, unsigned first, unsigned n);
5594 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5595 __isl_take isl_pw_multi_aff *pma,
5596 enum isl_dim_type type, unsigned first, unsigned n);
5597 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5598 __isl_take isl_union_pw_aff *upa,
5599 enum isl_dim_type type, unsigned first, unsigned n);
5600 __isl_give isl_union_pw_multi_aff *
5601 isl_union_pw_multi_aff_drop_dims(
5602 __isl_take isl_union_pw_multi_aff *upma,
5603 enum isl_dim_type type,
5604 unsigned first, unsigned n);
5605 __isl_give isl_multi_union_pw_aff *
5606 isl_multi_union_pw_aff_drop_dims(
5607 __isl_take isl_multi_union_pw_aff *mupa,
5608 enum isl_dim_type type, unsigned first,
5610 __isl_give isl_aff *isl_aff_move_dims(
5611 __isl_take isl_aff *aff,
5612 enum isl_dim_type dst_type, unsigned dst_pos,
5613 enum isl_dim_type src_type, unsigned src_pos,
5615 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5616 __isl_take isl_multi_aff *ma,
5617 enum isl_dim_type dst_type, unsigned dst_pos,
5618 enum isl_dim_type src_type, unsigned src_pos,
5620 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5621 __isl_take isl_pw_aff *pa,
5622 enum isl_dim_type dst_type, unsigned dst_pos,
5623 enum isl_dim_type src_type, unsigned src_pos,
5625 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5626 __isl_take isl_multi_pw_aff *pma,
5627 enum isl_dim_type dst_type, unsigned dst_pos,
5628 enum isl_dim_type src_type, unsigned src_pos,
5631 #include <isl/polynomial.h>
5632 __isl_give isl_union_pw_qpolynomial *
5633 isl_union_pw_qpolynomial_drop_dims(
5634 __isl_take isl_union_pw_qpolynomial *upwqp,
5635 enum isl_dim_type type,
5636 unsigned first, unsigned n);
5637 __isl_give isl_union_pw_qpolynomial_fold *
5638 isl_union_pw_qpolynomial_fold_drop_dims(
5639 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5640 enum isl_dim_type type,
5641 unsigned first, unsigned n);
5643 The operations on union expressions can only manipulate parameters.
5647 =head2 Binary Operations
5649 The two arguments of a binary operation not only need to live
5650 in the same C<isl_ctx>, they currently also need to have
5651 the same (number of) parameters.
5653 =head3 Basic Operations
5657 =item * Intersection
5659 #include <isl/local_space.h>
5660 __isl_give isl_local_space *isl_local_space_intersect(
5661 __isl_take isl_local_space *ls1,
5662 __isl_take isl_local_space *ls2);
5664 #include <isl/set.h>
5665 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5666 __isl_take isl_basic_set *bset1,
5667 __isl_take isl_basic_set *bset2);
5668 __isl_give isl_basic_set *isl_basic_set_intersect(
5669 __isl_take isl_basic_set *bset1,
5670 __isl_take isl_basic_set *bset2);
5671 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5672 __isl_take struct isl_basic_set_list *list);
5673 __isl_give isl_set *isl_set_intersect_params(
5674 __isl_take isl_set *set,
5675 __isl_take isl_set *params);
5676 __isl_give isl_set *isl_set_intersect(
5677 __isl_take isl_set *set1,
5678 __isl_take isl_set *set2);
5680 #include <isl/map.h>
5681 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5682 __isl_take isl_basic_map *bmap,
5683 __isl_take isl_basic_set *bset);
5684 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5685 __isl_take isl_basic_map *bmap,
5686 __isl_take isl_basic_set *bset);
5687 __isl_give isl_basic_map *isl_basic_map_intersect(
5688 __isl_take isl_basic_map *bmap1,
5689 __isl_take isl_basic_map *bmap2);
5690 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5691 __isl_take isl_basic_map_list *list);
5692 __isl_give isl_map *isl_map_intersect_params(
5693 __isl_take isl_map *map,
5694 __isl_take isl_set *params);
5695 __isl_give isl_map *isl_map_intersect_domain(
5696 __isl_take isl_map *map,
5697 __isl_take isl_set *set);
5698 __isl_give isl_map *isl_map_intersect_range(
5699 __isl_take isl_map *map,
5700 __isl_take isl_set *set);
5701 __isl_give isl_map *isl_map_intersect(
5702 __isl_take isl_map *map1,
5703 __isl_take isl_map *map2);
5705 #include <isl/union_set.h>
5706 __isl_give isl_union_set *isl_union_set_intersect_params(
5707 __isl_take isl_union_set *uset,
5708 __isl_take isl_set *set);
5709 __isl_give isl_union_set *isl_union_set_intersect(
5710 __isl_take isl_union_set *uset1,
5711 __isl_take isl_union_set *uset2);
5713 #include <isl/union_map.h>
5714 __isl_give isl_union_map *isl_union_map_intersect_params(
5715 __isl_take isl_union_map *umap,
5716 __isl_take isl_set *set);
5717 __isl_give isl_union_map *isl_union_map_intersect_domain(
5718 __isl_take isl_union_map *umap,
5719 __isl_take isl_union_set *uset);
5720 __isl_give isl_union_map *isl_union_map_intersect_range(
5721 __isl_take isl_union_map *umap,
5722 __isl_take isl_union_set *uset);
5723 __isl_give isl_union_map *isl_union_map_intersect(
5724 __isl_take isl_union_map *umap1,
5725 __isl_take isl_union_map *umap2);
5727 #include <isl/aff.h>
5728 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5729 __isl_take isl_pw_aff *pa,
5730 __isl_take isl_set *set);
5731 __isl_give isl_multi_pw_aff *
5732 isl_multi_pw_aff_intersect_domain(
5733 __isl_take isl_multi_pw_aff *mpa,
5734 __isl_take isl_set *domain);
5735 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5736 __isl_take isl_pw_multi_aff *pma,
5737 __isl_take isl_set *set);
5738 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5739 __isl_take isl_union_pw_aff *upa,
5740 __isl_take isl_union_set *uset);
5741 __isl_give isl_union_pw_multi_aff *
5742 isl_union_pw_multi_aff_intersect_domain(
5743 __isl_take isl_union_pw_multi_aff *upma,
5744 __isl_take isl_union_set *uset);
5745 __isl_give isl_multi_union_pw_aff *
5746 isl_multi_union_pw_aff_intersect_domain(
5747 __isl_take isl_multi_union_pw_aff *mupa,
5748 __isl_take isl_union_set *uset);
5749 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5750 __isl_take isl_pw_aff *pa,
5751 __isl_take isl_set *set);
5752 __isl_give isl_multi_pw_aff *
5753 isl_multi_pw_aff_intersect_params(
5754 __isl_take isl_multi_pw_aff *mpa,
5755 __isl_take isl_set *set);
5756 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5757 __isl_take isl_pw_multi_aff *pma,
5758 __isl_take isl_set *set);
5759 __isl_give isl_union_pw_aff *
5760 isl_union_pw_aff_intersect_params(
5761 __isl_take isl_union_pw_aff *upa,
5762 __isl_give isl_union_pw_multi_aff *
5763 isl_union_pw_multi_aff_intersect_params(
5764 __isl_take isl_union_pw_multi_aff *upma,
5765 __isl_take isl_set *set);
5766 __isl_give isl_multi_union_pw_aff *
5767 isl_multi_union_pw_aff_intersect_params(
5768 __isl_take isl_multi_union_pw_aff *mupa,
5769 __isl_take isl_set *params);
5770 isl_multi_union_pw_aff_intersect_range(
5771 __isl_take isl_multi_union_pw_aff *mupa,
5772 __isl_take isl_set *set);
5774 #include <isl/polynomial.h>
5775 __isl_give isl_pw_qpolynomial *
5776 isl_pw_qpolynomial_intersect_domain(
5777 __isl_take isl_pw_qpolynomial *pwpq,
5778 __isl_take isl_set *set);
5779 __isl_give isl_union_pw_qpolynomial *
5780 isl_union_pw_qpolynomial_intersect_domain(
5781 __isl_take isl_union_pw_qpolynomial *upwpq,
5782 __isl_take isl_union_set *uset);
5783 __isl_give isl_union_pw_qpolynomial_fold *
5784 isl_union_pw_qpolynomial_fold_intersect_domain(
5785 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5786 __isl_take isl_union_set *uset);
5787 __isl_give isl_pw_qpolynomial *
5788 isl_pw_qpolynomial_intersect_params(
5789 __isl_take isl_pw_qpolynomial *pwpq,
5790 __isl_take isl_set *set);
5791 __isl_give isl_pw_qpolynomial_fold *
5792 isl_pw_qpolynomial_fold_intersect_params(
5793 __isl_take isl_pw_qpolynomial_fold *pwf,
5794 __isl_take isl_set *set);
5795 __isl_give isl_union_pw_qpolynomial *
5796 isl_union_pw_qpolynomial_intersect_params(
5797 __isl_take isl_union_pw_qpolynomial *upwpq,
5798 __isl_take isl_set *set);
5799 __isl_give isl_union_pw_qpolynomial_fold *
5800 isl_union_pw_qpolynomial_fold_intersect_params(
5801 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5802 __isl_take isl_set *set);
5804 The second argument to the C<_params> functions needs to be
5805 a parametric (basic) set. For the other functions, a parametric set
5806 for either argument is only allowed if the other argument is
5807 a parametric set as well.
5808 The list passed to C<isl_basic_set_list_intersect> needs to have
5809 at least one element and all elements need to live in the same space.
5810 The function C<isl_multi_union_pw_aff_intersect_range>
5811 restricts the input function to those shared domain elements
5812 that map to the specified range.
5816 #include <isl/set.h>
5817 __isl_give isl_set *isl_basic_set_union(
5818 __isl_take isl_basic_set *bset1,
5819 __isl_take isl_basic_set *bset2);
5820 __isl_give isl_set *isl_set_union(
5821 __isl_take isl_set *set1,
5822 __isl_take isl_set *set2);
5823 __isl_give isl_set *isl_set_list_union(
5824 __isl_take isl_set_list *list);
5826 #include <isl/map.h>
5827 __isl_give isl_map *isl_basic_map_union(
5828 __isl_take isl_basic_map *bmap1,
5829 __isl_take isl_basic_map *bmap2);
5830 __isl_give isl_map *isl_map_union(
5831 __isl_take isl_map *map1,
5832 __isl_take isl_map *map2);
5834 #include <isl/union_set.h>
5835 __isl_give isl_union_set *isl_union_set_union(
5836 __isl_take isl_union_set *uset1,
5837 __isl_take isl_union_set *uset2);
5838 __isl_give isl_union_set *isl_union_set_list_union(
5839 __isl_take isl_union_set_list *list);
5841 #include <isl/union_map.h>
5842 __isl_give isl_union_map *isl_union_map_union(
5843 __isl_take isl_union_map *umap1,
5844 __isl_take isl_union_map *umap2);
5846 The list passed to C<isl_set_list_union> needs to have
5847 at least one element and all elements need to live in the same space.
5849 =item * Set difference
5851 #include <isl/set.h>
5852 __isl_give isl_set *isl_set_subtract(
5853 __isl_take isl_set *set1,
5854 __isl_take isl_set *set2);
5856 #include <isl/map.h>
5857 __isl_give isl_map *isl_map_subtract(
5858 __isl_take isl_map *map1,
5859 __isl_take isl_map *map2);
5860 __isl_give isl_map *isl_map_subtract_domain(
5861 __isl_take isl_map *map,
5862 __isl_take isl_set *dom);
5863 __isl_give isl_map *isl_map_subtract_range(
5864 __isl_take isl_map *map,
5865 __isl_take isl_set *dom);
5867 #include <isl/union_set.h>
5868 __isl_give isl_union_set *isl_union_set_subtract(
5869 __isl_take isl_union_set *uset1,
5870 __isl_take isl_union_set *uset2);
5872 #include <isl/union_map.h>
5873 __isl_give isl_union_map *isl_union_map_subtract(
5874 __isl_take isl_union_map *umap1,
5875 __isl_take isl_union_map *umap2);
5876 __isl_give isl_union_map *isl_union_map_subtract_domain(
5877 __isl_take isl_union_map *umap,
5878 __isl_take isl_union_set *dom);
5879 __isl_give isl_union_map *isl_union_map_subtract_range(
5880 __isl_take isl_union_map *umap,
5881 __isl_take isl_union_set *dom);
5883 #include <isl/aff.h>
5884 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5885 __isl_take isl_pw_aff *pa,
5886 __isl_take isl_set *set);
5887 __isl_give isl_pw_multi_aff *
5888 isl_pw_multi_aff_subtract_domain(
5889 __isl_take isl_pw_multi_aff *pma,
5890 __isl_take isl_set *set);
5891 __isl_give isl_union_pw_aff *
5892 isl_union_pw_aff_subtract_domain(
5893 __isl_take isl_union_pw_aff *upa,
5894 __isl_take isl_union_set *uset);
5895 __isl_give isl_union_pw_multi_aff *
5896 isl_union_pw_multi_aff_subtract_domain(
5897 __isl_take isl_union_pw_multi_aff *upma,
5898 __isl_take isl_set *set);
5900 #include <isl/polynomial.h>
5901 __isl_give isl_pw_qpolynomial *
5902 isl_pw_qpolynomial_subtract_domain(
5903 __isl_take isl_pw_qpolynomial *pwpq,
5904 __isl_take isl_set *set);
5905 __isl_give isl_pw_qpolynomial_fold *
5906 isl_pw_qpolynomial_fold_subtract_domain(
5907 __isl_take isl_pw_qpolynomial_fold *pwf,
5908 __isl_take isl_set *set);
5909 __isl_give isl_union_pw_qpolynomial *
5910 isl_union_pw_qpolynomial_subtract_domain(
5911 __isl_take isl_union_pw_qpolynomial *upwpq,
5912 __isl_take isl_union_set *uset);
5913 __isl_give isl_union_pw_qpolynomial_fold *
5914 isl_union_pw_qpolynomial_fold_subtract_domain(
5915 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5916 __isl_take isl_union_set *uset);
5920 #include <isl/space.h>
5921 __isl_give isl_space *isl_space_join(
5922 __isl_take isl_space *left,
5923 __isl_take isl_space *right);
5925 #include <isl/map.h>
5926 __isl_give isl_basic_set *isl_basic_set_apply(
5927 __isl_take isl_basic_set *bset,
5928 __isl_take isl_basic_map *bmap);
5929 __isl_give isl_set *isl_set_apply(
5930 __isl_take isl_set *set,
5931 __isl_take isl_map *map);
5932 __isl_give isl_union_set *isl_union_set_apply(
5933 __isl_take isl_union_set *uset,
5934 __isl_take isl_union_map *umap);
5935 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5936 __isl_take isl_basic_map *bmap1,
5937 __isl_take isl_basic_map *bmap2);
5938 __isl_give isl_basic_map *isl_basic_map_apply_range(
5939 __isl_take isl_basic_map *bmap1,
5940 __isl_take isl_basic_map *bmap2);
5941 __isl_give isl_map *isl_map_apply_domain(
5942 __isl_take isl_map *map1,
5943 __isl_take isl_map *map2);
5944 __isl_give isl_map *isl_map_apply_range(
5945 __isl_take isl_map *map1,
5946 __isl_take isl_map *map2);
5948 #include <isl/union_map.h>
5949 __isl_give isl_union_map *isl_union_map_apply_domain(
5950 __isl_take isl_union_map *umap1,
5951 __isl_take isl_union_map *umap2);
5952 __isl_give isl_union_map *isl_union_map_apply_range(
5953 __isl_take isl_union_map *umap1,
5954 __isl_take isl_union_map *umap2);
5956 #include <isl/aff.h>
5957 __isl_give isl_union_pw_aff *
5958 isl_multi_union_pw_aff_apply_aff(
5959 __isl_take isl_multi_union_pw_aff *mupa,
5960 __isl_take isl_aff *aff);
5961 __isl_give isl_union_pw_aff *
5962 isl_multi_union_pw_aff_apply_pw_aff(
5963 __isl_take isl_multi_union_pw_aff *mupa,
5964 __isl_take isl_pw_aff *pa);
5965 __isl_give isl_multi_union_pw_aff *
5966 isl_multi_union_pw_aff_apply_multi_aff(
5967 __isl_take isl_multi_union_pw_aff *mupa,
5968 __isl_take isl_multi_aff *ma);
5969 __isl_give isl_multi_union_pw_aff *
5970 isl_multi_union_pw_aff_apply_pw_multi_aff(
5971 __isl_take isl_multi_union_pw_aff *mupa,
5972 __isl_take isl_pw_multi_aff *pma);
5974 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5975 over the shared domain of the elements of the input. The dimension is
5976 required to be greater than zero.
5977 The C<isl_multi_union_pw_aff> argument of
5978 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5979 but only if the range of the C<isl_multi_aff> argument
5980 is also zero-dimensional.
5981 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5983 #include <isl/polynomial.h>
5984 __isl_give isl_pw_qpolynomial_fold *
5985 isl_set_apply_pw_qpolynomial_fold(
5986 __isl_take isl_set *set,
5987 __isl_take isl_pw_qpolynomial_fold *pwf,
5989 __isl_give isl_pw_qpolynomial_fold *
5990 isl_map_apply_pw_qpolynomial_fold(
5991 __isl_take isl_map *map,
5992 __isl_take isl_pw_qpolynomial_fold *pwf,
5994 __isl_give isl_union_pw_qpolynomial_fold *
5995 isl_union_set_apply_union_pw_qpolynomial_fold(
5996 __isl_take isl_union_set *uset,
5997 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5999 __isl_give isl_union_pw_qpolynomial_fold *
6000 isl_union_map_apply_union_pw_qpolynomial_fold(
6001 __isl_take isl_union_map *umap,
6002 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6005 The functions taking a map
6006 compose the given map with the given piecewise quasipolynomial reduction.
6007 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6008 over all elements in the intersection of the range of the map
6009 and the domain of the piecewise quasipolynomial reduction
6010 as a function of an element in the domain of the map.
6011 The functions taking a set compute a bound over all elements in the
6012 intersection of the set and the domain of the
6013 piecewise quasipolynomial reduction.
6017 #include <isl/set.h>
6018 __isl_give isl_basic_set *
6019 isl_basic_set_preimage_multi_aff(
6020 __isl_take isl_basic_set *bset,
6021 __isl_take isl_multi_aff *ma);
6022 __isl_give isl_set *isl_set_preimage_multi_aff(
6023 __isl_take isl_set *set,
6024 __isl_take isl_multi_aff *ma);
6025 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6026 __isl_take isl_set *set,
6027 __isl_take isl_pw_multi_aff *pma);
6028 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6029 __isl_take isl_set *set,
6030 __isl_take isl_multi_pw_aff *mpa);
6032 #include <isl/union_set.h>
6033 __isl_give isl_union_set *
6034 isl_union_set_preimage_multi_aff(
6035 __isl_take isl_union_set *uset,
6036 __isl_take isl_multi_aff *ma);
6037 __isl_give isl_union_set *
6038 isl_union_set_preimage_pw_multi_aff(
6039 __isl_take isl_union_set *uset,
6040 __isl_take isl_pw_multi_aff *pma);
6041 __isl_give isl_union_set *
6042 isl_union_set_preimage_union_pw_multi_aff(
6043 __isl_take isl_union_set *uset,
6044 __isl_take isl_union_pw_multi_aff *upma);
6046 #include <isl/map.h>
6047 __isl_give isl_basic_map *
6048 isl_basic_map_preimage_domain_multi_aff(
6049 __isl_take isl_basic_map *bmap,
6050 __isl_take isl_multi_aff *ma);
6051 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6052 __isl_take isl_map *map,
6053 __isl_take isl_multi_aff *ma);
6054 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6055 __isl_take isl_map *map,
6056 __isl_take isl_multi_aff *ma);
6057 __isl_give isl_map *
6058 isl_map_preimage_domain_pw_multi_aff(
6059 __isl_take isl_map *map,
6060 __isl_take isl_pw_multi_aff *pma);
6061 __isl_give isl_map *
6062 isl_map_preimage_range_pw_multi_aff(
6063 __isl_take isl_map *map,
6064 __isl_take isl_pw_multi_aff *pma);
6065 __isl_give isl_map *
6066 isl_map_preimage_domain_multi_pw_aff(
6067 __isl_take isl_map *map,
6068 __isl_take isl_multi_pw_aff *mpa);
6069 __isl_give isl_basic_map *
6070 isl_basic_map_preimage_range_multi_aff(
6071 __isl_take isl_basic_map *bmap,
6072 __isl_take isl_multi_aff *ma);
6074 #include <isl/union_map.h>
6075 __isl_give isl_union_map *
6076 isl_union_map_preimage_domain_multi_aff(
6077 __isl_take isl_union_map *umap,
6078 __isl_take isl_multi_aff *ma);
6079 __isl_give isl_union_map *
6080 isl_union_map_preimage_range_multi_aff(
6081 __isl_take isl_union_map *umap,
6082 __isl_take isl_multi_aff *ma);
6083 __isl_give isl_union_map *
6084 isl_union_map_preimage_domain_pw_multi_aff(
6085 __isl_take isl_union_map *umap,
6086 __isl_take isl_pw_multi_aff *pma);
6087 __isl_give isl_union_map *
6088 isl_union_map_preimage_range_pw_multi_aff(
6089 __isl_take isl_union_map *umap,
6090 __isl_take isl_pw_multi_aff *pma);
6091 __isl_give isl_union_map *
6092 isl_union_map_preimage_domain_union_pw_multi_aff(
6093 __isl_take isl_union_map *umap,
6094 __isl_take isl_union_pw_multi_aff *upma);
6095 __isl_give isl_union_map *
6096 isl_union_map_preimage_range_union_pw_multi_aff(
6097 __isl_take isl_union_map *umap,
6098 __isl_take isl_union_pw_multi_aff *upma);
6100 These functions compute the preimage of the given set or map domain/range under
6101 the given function. In other words, the expression is plugged
6102 into the set description or into the domain/range of the map.
6106 #include <isl/aff.h>
6107 __isl_give isl_aff *isl_aff_pullback_aff(
6108 __isl_take isl_aff *aff1,
6109 __isl_take isl_aff *aff2);
6110 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6111 __isl_take isl_aff *aff,
6112 __isl_take isl_multi_aff *ma);
6113 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6114 __isl_take isl_pw_aff *pa,
6115 __isl_take isl_multi_aff *ma);
6116 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6117 __isl_take isl_pw_aff *pa,
6118 __isl_take isl_pw_multi_aff *pma);
6119 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6120 __isl_take isl_pw_aff *pa,
6121 __isl_take isl_multi_pw_aff *mpa);
6122 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6123 __isl_take isl_multi_aff *ma1,
6124 __isl_take isl_multi_aff *ma2);
6125 __isl_give isl_pw_multi_aff *
6126 isl_pw_multi_aff_pullback_multi_aff(
6127 __isl_take isl_pw_multi_aff *pma,
6128 __isl_take isl_multi_aff *ma);
6129 __isl_give isl_multi_pw_aff *
6130 isl_multi_pw_aff_pullback_multi_aff(
6131 __isl_take isl_multi_pw_aff *mpa,
6132 __isl_take isl_multi_aff *ma);
6133 __isl_give isl_pw_multi_aff *
6134 isl_pw_multi_aff_pullback_pw_multi_aff(
6135 __isl_take isl_pw_multi_aff *pma1,
6136 __isl_take isl_pw_multi_aff *pma2);
6137 __isl_give isl_multi_pw_aff *
6138 isl_multi_pw_aff_pullback_pw_multi_aff(
6139 __isl_take isl_multi_pw_aff *mpa,
6140 __isl_take isl_pw_multi_aff *pma);
6141 __isl_give isl_multi_pw_aff *
6142 isl_multi_pw_aff_pullback_multi_pw_aff(
6143 __isl_take isl_multi_pw_aff *mpa1,
6144 __isl_take isl_multi_pw_aff *mpa2);
6145 __isl_give isl_union_pw_aff *
6146 isl_union_pw_aff_pullback_union_pw_multi_aff(
6147 __isl_take isl_union_pw_aff *upa,
6148 __isl_take isl_union_pw_multi_aff *upma);
6149 __isl_give isl_union_pw_multi_aff *
6150 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6151 __isl_take isl_union_pw_multi_aff *upma1,
6152 __isl_take isl_union_pw_multi_aff *upma2);
6153 __isl_give isl_multi_union_pw_aff *
6154 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6155 __isl_take isl_multi_union_pw_aff *mupa,
6156 __isl_take isl_union_pw_multi_aff *upma);
6158 These functions precompose the first expression by the second function.
6159 In other words, the second function is plugged
6160 into the first expression.
6164 #include <isl/aff.h>
6165 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6166 __isl_take isl_aff *aff1,
6167 __isl_take isl_aff *aff2);
6168 __isl_give isl_set *isl_aff_eq_set(
6169 __isl_take isl_aff *aff1,
6170 __isl_take isl_aff *aff2);
6171 __isl_give isl_basic_set *isl_aff_le_basic_set(
6172 __isl_take isl_aff *aff1,
6173 __isl_take isl_aff *aff2);
6174 __isl_give isl_set *isl_aff_le_set(
6175 __isl_take isl_aff *aff1,
6176 __isl_take isl_aff *aff2);
6177 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6178 __isl_take isl_aff *aff1,
6179 __isl_take isl_aff *aff2);
6180 __isl_give isl_set *isl_aff_ge_set(
6181 __isl_take isl_aff *aff1,
6182 __isl_take isl_aff *aff2);
6183 __isl_give isl_set *isl_pw_aff_eq_set(
6184 __isl_take isl_pw_aff *pwaff1,
6185 __isl_take isl_pw_aff *pwaff2);
6186 __isl_give isl_set *isl_pw_aff_ne_set(
6187 __isl_take isl_pw_aff *pwaff1,
6188 __isl_take isl_pw_aff *pwaff2);
6189 __isl_give isl_set *isl_pw_aff_le_set(
6190 __isl_take isl_pw_aff *pwaff1,
6191 __isl_take isl_pw_aff *pwaff2);
6192 __isl_give isl_set *isl_pw_aff_lt_set(
6193 __isl_take isl_pw_aff *pwaff1,
6194 __isl_take isl_pw_aff *pwaff2);
6195 __isl_give isl_set *isl_pw_aff_ge_set(
6196 __isl_take isl_pw_aff *pwaff1,
6197 __isl_take isl_pw_aff *pwaff2);
6198 __isl_give isl_set *isl_pw_aff_gt_set(
6199 __isl_take isl_pw_aff *pwaff1,
6200 __isl_take isl_pw_aff *pwaff2);
6202 __isl_give isl_set *isl_multi_aff_lex_le_set(
6203 __isl_take isl_multi_aff *ma1,
6204 __isl_take isl_multi_aff *ma2);
6205 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6206 __isl_take isl_multi_aff *ma1,
6207 __isl_take isl_multi_aff *ma2);
6208 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6209 __isl_take isl_multi_aff *ma1,
6210 __isl_take isl_multi_aff *ma2);
6211 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6212 __isl_take isl_multi_aff *ma1,
6213 __isl_take isl_multi_aff *ma2);
6215 __isl_give isl_set *isl_pw_aff_list_eq_set(
6216 __isl_take isl_pw_aff_list *list1,
6217 __isl_take isl_pw_aff_list *list2);
6218 __isl_give isl_set *isl_pw_aff_list_ne_set(
6219 __isl_take isl_pw_aff_list *list1,
6220 __isl_take isl_pw_aff_list *list2);
6221 __isl_give isl_set *isl_pw_aff_list_le_set(
6222 __isl_take isl_pw_aff_list *list1,
6223 __isl_take isl_pw_aff_list *list2);
6224 __isl_give isl_set *isl_pw_aff_list_lt_set(
6225 __isl_take isl_pw_aff_list *list1,
6226 __isl_take isl_pw_aff_list *list2);
6227 __isl_give isl_set *isl_pw_aff_list_ge_set(
6228 __isl_take isl_pw_aff_list *list1,
6229 __isl_take isl_pw_aff_list *list2);
6230 __isl_give isl_set *isl_pw_aff_list_gt_set(
6231 __isl_take isl_pw_aff_list *list1,
6232 __isl_take isl_pw_aff_list *list2);
6234 The function C<isl_aff_ge_basic_set> returns a basic set
6235 containing those elements in the shared space
6236 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6237 The function C<isl_pw_aff_ge_set> returns a set
6238 containing those elements in the shared domain
6239 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6240 greater than or equal to C<pwaff2>.
6241 The function C<isl_multi_aff_lex_le_set> returns a set
6242 containing those elements in the shared domain space
6243 where C<ma1> is lexicographically smaller than or
6245 The functions operating on C<isl_pw_aff_list> apply the corresponding
6246 C<isl_pw_aff> function to each pair of elements in the two lists.
6248 #include <isl/aff.h>
6249 __isl_give isl_map *isl_pw_aff_eq_map(
6250 __isl_take isl_pw_aff *pa1,
6251 __isl_take isl_pw_aff *pa2);
6252 __isl_give isl_map *isl_pw_aff_lt_map(
6253 __isl_take isl_pw_aff *pa1,
6254 __isl_take isl_pw_aff *pa2);
6255 __isl_give isl_map *isl_pw_aff_gt_map(
6256 __isl_take isl_pw_aff *pa1,
6257 __isl_take isl_pw_aff *pa2);
6259 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6260 __isl_take isl_multi_pw_aff *mpa1,
6261 __isl_take isl_multi_pw_aff *mpa2);
6262 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6263 __isl_take isl_multi_pw_aff *mpa1,
6264 __isl_take isl_multi_pw_aff *mpa2);
6265 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6266 __isl_take isl_multi_pw_aff *mpa1,
6267 __isl_take isl_multi_pw_aff *mpa2);
6269 These functions return a map between domain elements of the arguments
6270 where the function values satisfy the given relation.
6272 #include <isl/union_map.h>
6273 __isl_give isl_union_map *
6274 isl_union_map_eq_at_multi_union_pw_aff(
6275 __isl_take isl_union_map *umap,
6276 __isl_take isl_multi_union_pw_aff *mupa);
6277 __isl_give isl_union_map *
6278 isl_union_map_lex_lt_at_multi_union_pw_aff(
6279 __isl_take isl_union_map *umap,
6280 __isl_take isl_multi_union_pw_aff *mupa);
6281 __isl_give isl_union_map *
6282 isl_union_map_lex_gt_at_multi_union_pw_aff(
6283 __isl_take isl_union_map *umap,
6284 __isl_take isl_multi_union_pw_aff *mupa);
6286 These functions select the subset of elements in the union map
6287 that have an equal or lexicographically smaller function value.
6289 =item * Cartesian Product
6291 #include <isl/space.h>
6292 __isl_give isl_space *isl_space_product(
6293 __isl_take isl_space *space1,
6294 __isl_take isl_space *space2);
6295 __isl_give isl_space *isl_space_domain_product(
6296 __isl_take isl_space *space1,
6297 __isl_take isl_space *space2);
6298 __isl_give isl_space *isl_space_range_product(
6299 __isl_take isl_space *space1,
6300 __isl_take isl_space *space2);
6303 C<isl_space_product>, C<isl_space_domain_product>
6304 and C<isl_space_range_product> take pairs or relation spaces and
6305 produce a single relations space, where either the domain, the range
6306 or both domain and range are wrapped spaces of relations between
6307 the domains and/or ranges of the input spaces.
6308 If the product is only constructed over the domain or the range
6309 then the ranges or the domains of the inputs should be the same.
6310 The function C<isl_space_product> also accepts a pair of set spaces,
6311 in which case it returns a wrapped space of a relation between the
6314 #include <isl/set.h>
6315 __isl_give isl_set *isl_set_product(
6316 __isl_take isl_set *set1,
6317 __isl_take isl_set *set2);
6319 #include <isl/map.h>
6320 __isl_give isl_basic_map *isl_basic_map_domain_product(
6321 __isl_take isl_basic_map *bmap1,
6322 __isl_take isl_basic_map *bmap2);
6323 __isl_give isl_basic_map *isl_basic_map_range_product(
6324 __isl_take isl_basic_map *bmap1,
6325 __isl_take isl_basic_map *bmap2);
6326 __isl_give isl_basic_map *isl_basic_map_product(
6327 __isl_take isl_basic_map *bmap1,
6328 __isl_take isl_basic_map *bmap2);
6329 __isl_give isl_map *isl_map_domain_product(
6330 __isl_take isl_map *map1,
6331 __isl_take isl_map *map2);
6332 __isl_give isl_map *isl_map_range_product(
6333 __isl_take isl_map *map1,
6334 __isl_take isl_map *map2);
6335 __isl_give isl_map *isl_map_product(
6336 __isl_take isl_map *map1,
6337 __isl_take isl_map *map2);
6339 #include <isl/union_set.h>
6340 __isl_give isl_union_set *isl_union_set_product(
6341 __isl_take isl_union_set *uset1,
6342 __isl_take isl_union_set *uset2);
6344 #include <isl/union_map.h>
6345 __isl_give isl_union_map *isl_union_map_domain_product(
6346 __isl_take isl_union_map *umap1,
6347 __isl_take isl_union_map *umap2);
6348 __isl_give isl_union_map *isl_union_map_range_product(
6349 __isl_take isl_union_map *umap1,
6350 __isl_take isl_union_map *umap2);
6351 __isl_give isl_union_map *isl_union_map_product(
6352 __isl_take isl_union_map *umap1,
6353 __isl_take isl_union_map *umap2);
6355 #include <isl/val.h>
6356 __isl_give isl_multi_val *isl_multi_val_range_product(
6357 __isl_take isl_multi_val *mv1,
6358 __isl_take isl_multi_val *mv2);
6359 __isl_give isl_multi_val *isl_multi_val_product(
6360 __isl_take isl_multi_val *mv1,
6361 __isl_take isl_multi_val *mv2);
6363 #include <isl/aff.h>
6364 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6365 __isl_take isl_multi_aff *ma1,
6366 __isl_take isl_multi_aff *ma2);
6367 __isl_give isl_multi_aff *isl_multi_aff_product(
6368 __isl_take isl_multi_aff *ma1,
6369 __isl_take isl_multi_aff *ma2);
6370 __isl_give isl_multi_pw_aff *
6371 isl_multi_pw_aff_range_product(
6372 __isl_take isl_multi_pw_aff *mpa1,
6373 __isl_take isl_multi_pw_aff *mpa2);
6374 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6375 __isl_take isl_multi_pw_aff *mpa1,
6376 __isl_take isl_multi_pw_aff *mpa2);
6377 __isl_give isl_pw_multi_aff *
6378 isl_pw_multi_aff_range_product(
6379 __isl_take isl_pw_multi_aff *pma1,
6380 __isl_take isl_pw_multi_aff *pma2);
6381 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6382 __isl_take isl_pw_multi_aff *pma1,
6383 __isl_take isl_pw_multi_aff *pma2);
6384 __isl_give isl_multi_union_pw_aff *
6385 isl_multi_union_pw_aff_range_product(
6386 __isl_take isl_multi_union_pw_aff *mupa1,
6387 __isl_take isl_multi_union_pw_aff *mupa2);
6389 The above functions compute the cross product of the given
6390 sets, relations or functions. The domains and ranges of the results
6391 are wrapped maps between domains and ranges of the inputs.
6392 To obtain a ``flat'' product, use the following functions
6395 #include <isl/set.h>
6396 __isl_give isl_basic_set *isl_basic_set_flat_product(
6397 __isl_take isl_basic_set *bset1,
6398 __isl_take isl_basic_set *bset2);
6399 __isl_give isl_set *isl_set_flat_product(
6400 __isl_take isl_set *set1,
6401 __isl_take isl_set *set2);
6403 #include <isl/map.h>
6404 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6405 __isl_take isl_basic_map *bmap1,
6406 __isl_take isl_basic_map *bmap2);
6407 __isl_give isl_map *isl_map_flat_domain_product(
6408 __isl_take isl_map *map1,
6409 __isl_take isl_map *map2);
6410 __isl_give isl_map *isl_map_flat_range_product(
6411 __isl_take isl_map *map1,
6412 __isl_take isl_map *map2);
6413 __isl_give isl_basic_map *isl_basic_map_flat_product(
6414 __isl_take isl_basic_map *bmap1,
6415 __isl_take isl_basic_map *bmap2);
6416 __isl_give isl_map *isl_map_flat_product(
6417 __isl_take isl_map *map1,
6418 __isl_take isl_map *map2);
6420 #include <isl/union_map.h>
6421 __isl_give isl_union_map *
6422 isl_union_map_flat_domain_product(
6423 __isl_take isl_union_map *umap1,
6424 __isl_take isl_union_map *umap2);
6425 __isl_give isl_union_map *
6426 isl_union_map_flat_range_product(
6427 __isl_take isl_union_map *umap1,
6428 __isl_take isl_union_map *umap2);
6430 #include <isl/val.h>
6431 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6432 __isl_take isl_multi_val *mv1,
6433 __isl_take isl_multi_aff *mv2);
6435 #include <isl/aff.h>
6436 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6437 __isl_take isl_multi_aff *ma1,
6438 __isl_take isl_multi_aff *ma2);
6439 __isl_give isl_pw_multi_aff *
6440 isl_pw_multi_aff_flat_range_product(
6441 __isl_take isl_pw_multi_aff *pma1,
6442 __isl_take isl_pw_multi_aff *pma2);
6443 __isl_give isl_multi_pw_aff *
6444 isl_multi_pw_aff_flat_range_product(
6445 __isl_take isl_multi_pw_aff *mpa1,
6446 __isl_take isl_multi_pw_aff *mpa2);
6447 __isl_give isl_union_pw_multi_aff *
6448 isl_union_pw_multi_aff_flat_range_product(
6449 __isl_take isl_union_pw_multi_aff *upma1,
6450 __isl_take isl_union_pw_multi_aff *upma2);
6451 __isl_give isl_multi_union_pw_aff *
6452 isl_multi_union_pw_aff_flat_range_product(
6453 __isl_take isl_multi_union_pw_aff *mupa1,
6454 __isl_take isl_multi_union_pw_aff *mupa2);
6456 #include <isl/space.h>
6457 __isl_give isl_space *isl_space_factor_domain(
6458 __isl_take isl_space *space);
6459 __isl_give isl_space *isl_space_factor_range(
6460 __isl_take isl_space *space);
6461 __isl_give isl_space *isl_space_domain_factor_domain(
6462 __isl_take isl_space *space);
6463 __isl_give isl_space *isl_space_domain_factor_range(
6464 __isl_take isl_space *space);
6465 __isl_give isl_space *isl_space_range_factor_domain(
6466 __isl_take isl_space *space);
6467 __isl_give isl_space *isl_space_range_factor_range(
6468 __isl_take isl_space *space);
6470 The functions C<isl_space_range_factor_domain> and
6471 C<isl_space_range_factor_range> extract the two arguments from
6472 the result of a call to C<isl_space_range_product>.
6474 The arguments of a call to a product can be extracted
6475 from the result using the following functions.
6477 #include <isl/map.h>
6478 __isl_give isl_map *isl_map_factor_domain(
6479 __isl_take isl_map *map);
6480 __isl_give isl_map *isl_map_factor_range(
6481 __isl_take isl_map *map);
6482 __isl_give isl_map *isl_map_domain_factor_domain(
6483 __isl_take isl_map *map);
6484 __isl_give isl_map *isl_map_domain_factor_range(
6485 __isl_take isl_map *map);
6486 __isl_give isl_map *isl_map_range_factor_domain(
6487 __isl_take isl_map *map);
6488 __isl_give isl_map *isl_map_range_factor_range(
6489 __isl_take isl_map *map);
6491 #include <isl/union_map.h>
6492 __isl_give isl_union_map *isl_union_map_factor_domain(
6493 __isl_take isl_union_map *umap);
6494 __isl_give isl_union_map *isl_union_map_factor_range(
6495 __isl_take isl_union_map *umap);
6496 __isl_give isl_union_map *
6497 isl_union_map_domain_factor_domain(
6498 __isl_take isl_union_map *umap);
6499 __isl_give isl_union_map *
6500 isl_union_map_domain_factor_range(
6501 __isl_take isl_union_map *umap);
6502 __isl_give isl_union_map *
6503 isl_union_map_range_factor_domain(
6504 __isl_take isl_union_map *umap);
6505 __isl_give isl_union_map *
6506 isl_union_map_range_factor_range(
6507 __isl_take isl_union_map *umap);
6509 #include <isl/val.h>
6510 __isl_give isl_multi_val *isl_multi_val_factor_range(
6511 __isl_take isl_multi_val *mv);
6512 __isl_give isl_multi_val *
6513 isl_multi_val_range_factor_domain(
6514 __isl_take isl_multi_val *mv);
6515 __isl_give isl_multi_val *
6516 isl_multi_val_range_factor_range(
6517 __isl_take isl_multi_val *mv);
6519 #include <isl/aff.h>
6520 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6521 __isl_take isl_multi_aff *ma);
6522 __isl_give isl_multi_aff *
6523 isl_multi_aff_range_factor_domain(
6524 __isl_take isl_multi_aff *ma);
6525 __isl_give isl_multi_aff *
6526 isl_multi_aff_range_factor_range(
6527 __isl_take isl_multi_aff *ma);
6528 __isl_give isl_multi_pw_aff *
6529 isl_multi_pw_aff_factor_range(
6530 __isl_take isl_multi_pw_aff *mpa);
6531 __isl_give isl_multi_pw_aff *
6532 isl_multi_pw_aff_range_factor_domain(
6533 __isl_take isl_multi_pw_aff *mpa);
6534 __isl_give isl_multi_pw_aff *
6535 isl_multi_pw_aff_range_factor_range(
6536 __isl_take isl_multi_pw_aff *mpa);
6537 __isl_give isl_multi_union_pw_aff *
6538 isl_multi_union_pw_aff_factor_range(
6539 __isl_take isl_multi_union_pw_aff *mupa);
6540 __isl_give isl_multi_union_pw_aff *
6541 isl_multi_union_pw_aff_range_factor_domain(
6542 __isl_take isl_multi_union_pw_aff *mupa);
6543 __isl_give isl_multi_union_pw_aff *
6544 isl_multi_union_pw_aff_range_factor_range(
6545 __isl_take isl_multi_union_pw_aff *mupa);
6547 The splice functions are a generalization of the flat product functions,
6548 where the second argument may be inserted at any position inside
6549 the first argument rather than being placed at the end.
6550 The functions C<isl_multi_val_factor_range>,
6551 C<isl_multi_aff_factor_range>,
6552 C<isl_multi_pw_aff_factor_range> and
6553 C<isl_multi_union_pw_aff_factor_range>
6554 take functions that live in a set space.
6556 #include <isl/val.h>
6557 __isl_give isl_multi_val *isl_multi_val_range_splice(
6558 __isl_take isl_multi_val *mv1, unsigned pos,
6559 __isl_take isl_multi_val *mv2);
6561 #include <isl/aff.h>
6562 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6563 __isl_take isl_multi_aff *ma1, unsigned pos,
6564 __isl_take isl_multi_aff *ma2);
6565 __isl_give isl_multi_aff *isl_multi_aff_splice(
6566 __isl_take isl_multi_aff *ma1,
6567 unsigned in_pos, unsigned out_pos,
6568 __isl_take isl_multi_aff *ma2);
6569 __isl_give isl_multi_pw_aff *
6570 isl_multi_pw_aff_range_splice(
6571 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6572 __isl_take isl_multi_pw_aff *mpa2);
6573 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6574 __isl_take isl_multi_pw_aff *mpa1,
6575 unsigned in_pos, unsigned out_pos,
6576 __isl_take isl_multi_pw_aff *mpa2);
6577 __isl_give isl_multi_union_pw_aff *
6578 isl_multi_union_pw_aff_range_splice(
6579 __isl_take isl_multi_union_pw_aff *mupa1,
6581 __isl_take isl_multi_union_pw_aff *mupa2);
6583 =item * Simplification
6585 When applied to a set or relation,
6586 the gist operation returns a set or relation that has the
6587 same intersection with the context as the input set or relation.
6588 Any implicit equality in the intersection is made explicit in the result,
6589 while all inequalities that are redundant with respect to the intersection
6591 In case of union sets and relations, the gist operation is performed
6594 When applied to a function,
6595 the gist operation applies the set gist operation to each of
6596 the cells in the domain of the input piecewise expression.
6597 The context is also exploited
6598 to simplify the expression associated to each cell.
6600 #include <isl/set.h>
6601 __isl_give isl_basic_set *isl_basic_set_gist(
6602 __isl_take isl_basic_set *bset,
6603 __isl_take isl_basic_set *context);
6604 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6605 __isl_take isl_set *context);
6606 __isl_give isl_set *isl_set_gist_params(
6607 __isl_take isl_set *set,
6608 __isl_take isl_set *context);
6610 #include <isl/map.h>
6611 __isl_give isl_basic_map *isl_basic_map_gist(
6612 __isl_take isl_basic_map *bmap,
6613 __isl_take isl_basic_map *context);
6614 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6615 __isl_take isl_basic_map *bmap,
6616 __isl_take isl_basic_set *context);
6617 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6618 __isl_take isl_map *context);
6619 __isl_give isl_map *isl_map_gist_params(
6620 __isl_take isl_map *map,
6621 __isl_take isl_set *context);
6622 __isl_give isl_map *isl_map_gist_domain(
6623 __isl_take isl_map *map,
6624 __isl_take isl_set *context);
6625 __isl_give isl_map *isl_map_gist_range(
6626 __isl_take isl_map *map,
6627 __isl_take isl_set *context);
6629 #include <isl/union_set.h>
6630 __isl_give isl_union_set *isl_union_set_gist(
6631 __isl_take isl_union_set *uset,
6632 __isl_take isl_union_set *context);
6633 __isl_give isl_union_set *isl_union_set_gist_params(
6634 __isl_take isl_union_set *uset,
6635 __isl_take isl_set *set);
6637 #include <isl/union_map.h>
6638 __isl_give isl_union_map *isl_union_map_gist(
6639 __isl_take isl_union_map *umap,
6640 __isl_take isl_union_map *context);
6641 __isl_give isl_union_map *isl_union_map_gist_params(
6642 __isl_take isl_union_map *umap,
6643 __isl_take isl_set *set);
6644 __isl_give isl_union_map *isl_union_map_gist_domain(
6645 __isl_take isl_union_map *umap,
6646 __isl_take isl_union_set *uset);
6647 __isl_give isl_union_map *isl_union_map_gist_range(
6648 __isl_take isl_union_map *umap,
6649 __isl_take isl_union_set *uset);
6651 #include <isl/aff.h>
6652 __isl_give isl_aff *isl_aff_gist_params(
6653 __isl_take isl_aff *aff,
6654 __isl_take isl_set *context);
6655 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6656 __isl_take isl_set *context);
6657 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6658 __isl_take isl_multi_aff *maff,
6659 __isl_take isl_set *context);
6660 __isl_give isl_multi_aff *isl_multi_aff_gist(
6661 __isl_take isl_multi_aff *maff,
6662 __isl_take isl_set *context);
6663 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6664 __isl_take isl_pw_aff *pwaff,
6665 __isl_take isl_set *context);
6666 __isl_give isl_pw_aff *isl_pw_aff_gist(
6667 __isl_take isl_pw_aff *pwaff,
6668 __isl_take isl_set *context);
6669 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6670 __isl_take isl_pw_multi_aff *pma,
6671 __isl_take isl_set *set);
6672 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6673 __isl_take isl_pw_multi_aff *pma,
6674 __isl_take isl_set *set);
6675 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6676 __isl_take isl_multi_pw_aff *mpa,
6677 __isl_take isl_set *set);
6678 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6679 __isl_take isl_multi_pw_aff *mpa,
6680 __isl_take isl_set *set);
6681 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6682 __isl_take isl_union_pw_aff *upa,
6683 __isl_take isl_union_set *context);
6684 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6685 __isl_take isl_union_pw_aff *upa,
6686 __isl_take isl_set *context);
6687 __isl_give isl_union_pw_multi_aff *
6688 isl_union_pw_multi_aff_gist_params(
6689 __isl_take isl_union_pw_multi_aff *upma,
6690 __isl_take isl_set *context);
6691 __isl_give isl_union_pw_multi_aff *
6692 isl_union_pw_multi_aff_gist(
6693 __isl_take isl_union_pw_multi_aff *upma,
6694 __isl_take isl_union_set *context);
6695 __isl_give isl_multi_union_pw_aff *
6696 isl_multi_union_pw_aff_gist_params(
6697 __isl_take isl_multi_union_pw_aff *aff,
6698 __isl_take isl_set *context);
6699 __isl_give isl_multi_union_pw_aff *
6700 isl_multi_union_pw_aff_gist(
6701 __isl_take isl_multi_union_pw_aff *aff,
6702 __isl_take isl_union_set *context);
6704 #include <isl/polynomial.h>
6705 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6706 __isl_take isl_qpolynomial *qp,
6707 __isl_take isl_set *context);
6708 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6709 __isl_take isl_qpolynomial *qp,
6710 __isl_take isl_set *context);
6711 __isl_give isl_qpolynomial_fold *
6712 isl_qpolynomial_fold_gist_params(
6713 __isl_take isl_qpolynomial_fold *fold,
6714 __isl_take isl_set *context);
6715 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6716 __isl_take isl_qpolynomial_fold *fold,
6717 __isl_take isl_set *context);
6718 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6719 __isl_take isl_pw_qpolynomial *pwqp,
6720 __isl_take isl_set *context);
6721 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6722 __isl_take isl_pw_qpolynomial *pwqp,
6723 __isl_take isl_set *context);
6724 __isl_give isl_pw_qpolynomial_fold *
6725 isl_pw_qpolynomial_fold_gist(
6726 __isl_take isl_pw_qpolynomial_fold *pwf,
6727 __isl_take isl_set *context);
6728 __isl_give isl_pw_qpolynomial_fold *
6729 isl_pw_qpolynomial_fold_gist_params(
6730 __isl_take isl_pw_qpolynomial_fold *pwf,
6731 __isl_take isl_set *context);
6732 __isl_give isl_union_pw_qpolynomial *
6733 isl_union_pw_qpolynomial_gist_params(
6734 __isl_take isl_union_pw_qpolynomial *upwqp,
6735 __isl_take isl_set *context);
6736 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6737 __isl_take isl_union_pw_qpolynomial *upwqp,
6738 __isl_take isl_union_set *context);
6739 __isl_give isl_union_pw_qpolynomial_fold *
6740 isl_union_pw_qpolynomial_fold_gist(
6741 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6742 __isl_take isl_union_set *context);
6743 __isl_give isl_union_pw_qpolynomial_fold *
6744 isl_union_pw_qpolynomial_fold_gist_params(
6745 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6746 __isl_take isl_set *context);
6748 =item * Binary Arithmetic Operations
6750 #include <isl/set.h>
6751 __isl_give isl_set *isl_set_sum(
6752 __isl_take isl_set *set1,
6753 __isl_take isl_set *set2);
6754 #include <isl/map.h>
6755 __isl_give isl_map *isl_map_sum(
6756 __isl_take isl_map *map1,
6757 __isl_take isl_map *map2);
6759 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6760 i.e., the set containing the sums of pairs of elements from
6761 C<set1> and C<set2>.
6762 The domain of the result of C<isl_map_sum> is the intersection
6763 of the domains of its two arguments. The corresponding range
6764 elements are the sums of the corresponding range elements
6765 in the two arguments.
6767 #include <isl/val.h>
6768 __isl_give isl_multi_val *isl_multi_val_add(
6769 __isl_take isl_multi_val *mv1,
6770 __isl_take isl_multi_val *mv2);
6771 __isl_give isl_multi_val *isl_multi_val_sub(
6772 __isl_take isl_multi_val *mv1,
6773 __isl_take isl_multi_val *mv2);
6775 #include <isl/aff.h>
6776 __isl_give isl_aff *isl_aff_add(
6777 __isl_take isl_aff *aff1,
6778 __isl_take isl_aff *aff2);
6779 __isl_give isl_multi_aff *isl_multi_aff_add(
6780 __isl_take isl_multi_aff *maff1,
6781 __isl_take isl_multi_aff *maff2);
6782 __isl_give isl_pw_aff *isl_pw_aff_add(
6783 __isl_take isl_pw_aff *pwaff1,
6784 __isl_take isl_pw_aff *pwaff2);
6785 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6786 __isl_take isl_multi_pw_aff *mpa1,
6787 __isl_take isl_multi_pw_aff *mpa2);
6788 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6789 __isl_take isl_pw_multi_aff *pma1,
6790 __isl_take isl_pw_multi_aff *pma2);
6791 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6792 __isl_take isl_union_pw_aff *upa1,
6793 __isl_take isl_union_pw_aff *upa2);
6794 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6795 __isl_take isl_union_pw_multi_aff *upma1,
6796 __isl_take isl_union_pw_multi_aff *upma2);
6797 __isl_give isl_multi_union_pw_aff *
6798 isl_multi_union_pw_aff_add(
6799 __isl_take isl_multi_union_pw_aff *mupa1,
6800 __isl_take isl_multi_union_pw_aff *mupa2);
6801 __isl_give isl_pw_aff *isl_pw_aff_min(
6802 __isl_take isl_pw_aff *pwaff1,
6803 __isl_take isl_pw_aff *pwaff2);
6804 __isl_give isl_pw_aff *isl_pw_aff_max(
6805 __isl_take isl_pw_aff *pwaff1,
6806 __isl_take isl_pw_aff *pwaff2);
6807 __isl_give isl_aff *isl_aff_sub(
6808 __isl_take isl_aff *aff1,
6809 __isl_take isl_aff *aff2);
6810 __isl_give isl_multi_aff *isl_multi_aff_sub(
6811 __isl_take isl_multi_aff *ma1,
6812 __isl_take isl_multi_aff *ma2);
6813 __isl_give isl_pw_aff *isl_pw_aff_sub(
6814 __isl_take isl_pw_aff *pwaff1,
6815 __isl_take isl_pw_aff *pwaff2);
6816 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6817 __isl_take isl_multi_pw_aff *mpa1,
6818 __isl_take isl_multi_pw_aff *mpa2);
6819 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6820 __isl_take isl_pw_multi_aff *pma1,
6821 __isl_take isl_pw_multi_aff *pma2);
6822 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6823 __isl_take isl_union_pw_aff *upa1,
6824 __isl_take isl_union_pw_aff *upa2);
6825 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6826 __isl_take isl_union_pw_multi_aff *upma1,
6827 __isl_take isl_union_pw_multi_aff *upma2);
6828 __isl_give isl_multi_union_pw_aff *
6829 isl_multi_union_pw_aff_sub(
6830 __isl_take isl_multi_union_pw_aff *mupa1,
6831 __isl_take isl_multi_union_pw_aff *mupa2);
6833 C<isl_aff_sub> subtracts the second argument from the first.
6835 #include <isl/polynomial.h>
6836 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6837 __isl_take isl_qpolynomial *qp1,
6838 __isl_take isl_qpolynomial *qp2);
6839 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6840 __isl_take isl_pw_qpolynomial *pwqp1,
6841 __isl_take isl_pw_qpolynomial *pwqp2);
6842 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6843 __isl_take isl_pw_qpolynomial *pwqp1,
6844 __isl_take isl_pw_qpolynomial *pwqp2);
6845 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6846 __isl_take isl_pw_qpolynomial_fold *pwf1,
6847 __isl_take isl_pw_qpolynomial_fold *pwf2);
6848 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6849 __isl_take isl_union_pw_qpolynomial *upwqp1,
6850 __isl_take isl_union_pw_qpolynomial *upwqp2);
6851 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6852 __isl_take isl_qpolynomial *qp1,
6853 __isl_take isl_qpolynomial *qp2);
6854 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6855 __isl_take isl_pw_qpolynomial *pwqp1,
6856 __isl_take isl_pw_qpolynomial *pwqp2);
6857 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6858 __isl_take isl_union_pw_qpolynomial *upwqp1,
6859 __isl_take isl_union_pw_qpolynomial *upwqp2);
6860 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6861 __isl_take isl_pw_qpolynomial_fold *pwf1,
6862 __isl_take isl_pw_qpolynomial_fold *pwf2);
6863 __isl_give isl_union_pw_qpolynomial_fold *
6864 isl_union_pw_qpolynomial_fold_fold(
6865 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6866 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6868 #include <isl/aff.h>
6869 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6870 __isl_take isl_pw_aff *pwaff1,
6871 __isl_take isl_pw_aff *pwaff2);
6872 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6873 __isl_take isl_pw_multi_aff *pma1,
6874 __isl_take isl_pw_multi_aff *pma2);
6875 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6876 __isl_take isl_union_pw_aff *upa1,
6877 __isl_take isl_union_pw_aff *upa2);
6878 __isl_give isl_union_pw_multi_aff *
6879 isl_union_pw_multi_aff_union_add(
6880 __isl_take isl_union_pw_multi_aff *upma1,
6881 __isl_take isl_union_pw_multi_aff *upma2);
6882 __isl_give isl_multi_union_pw_aff *
6883 isl_multi_union_pw_aff_union_add(
6884 __isl_take isl_multi_union_pw_aff *mupa1,
6885 __isl_take isl_multi_union_pw_aff *mupa2);
6886 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6887 __isl_take isl_pw_aff *pwaff1,
6888 __isl_take isl_pw_aff *pwaff2);
6889 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6890 __isl_take isl_pw_aff *pwaff1,
6891 __isl_take isl_pw_aff *pwaff2);
6893 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6894 expression with a domain that is the union of those of C<pwaff1> and
6895 C<pwaff2> and such that on each cell, the quasi-affine expression is
6896 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6897 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6898 associated expression is the defined one.
6899 This in contrast to the C<isl_pw_aff_max> function, which is
6900 only defined on the shared definition domain of the arguments.
6902 #include <isl/val.h>
6903 __isl_give isl_multi_val *isl_multi_val_add_val(
6904 __isl_take isl_multi_val *mv,
6905 __isl_take isl_val *v);
6906 __isl_give isl_multi_val *isl_multi_val_mod_val(
6907 __isl_take isl_multi_val *mv,
6908 __isl_take isl_val *v);
6909 __isl_give isl_multi_val *isl_multi_val_scale_val(
6910 __isl_take isl_multi_val *mv,
6911 __isl_take isl_val *v);
6912 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6913 __isl_take isl_multi_val *mv,
6914 __isl_take isl_val *v);
6916 #include <isl/aff.h>
6917 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6918 __isl_take isl_val *mod);
6919 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6920 __isl_take isl_pw_aff *pa,
6921 __isl_take isl_val *mod);
6922 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6923 __isl_take isl_union_pw_aff *upa,
6924 __isl_take isl_val *f);
6925 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6926 __isl_take isl_val *v);
6927 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6928 __isl_take isl_multi_aff *ma,
6929 __isl_take isl_val *v);
6930 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6931 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6932 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6933 __isl_take isl_multi_pw_aff *mpa,
6934 __isl_take isl_val *v);
6935 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6936 __isl_take isl_pw_multi_aff *pma,
6937 __isl_take isl_val *v);
6938 __isl_give isl_union_pw_multi_aff *
6939 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6940 __isl_take isl_union_pw_aff *upa,
6941 __isl_take isl_val *f);
6942 isl_union_pw_multi_aff_scale_val(
6943 __isl_take isl_union_pw_multi_aff *upma,
6944 __isl_take isl_val *val);
6945 __isl_give isl_multi_union_pw_aff *
6946 isl_multi_union_pw_aff_scale_val(
6947 __isl_take isl_multi_union_pw_aff *mupa,
6948 __isl_take isl_val *v);
6949 __isl_give isl_aff *isl_aff_scale_down_ui(
6950 __isl_take isl_aff *aff, unsigned f);
6951 __isl_give isl_aff *isl_aff_scale_down_val(
6952 __isl_take isl_aff *aff, __isl_take isl_val *v);
6953 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6954 __isl_take isl_multi_aff *ma,
6955 __isl_take isl_val *v);
6956 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6957 __isl_take isl_pw_aff *pa,
6958 __isl_take isl_val *f);
6959 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6960 __isl_take isl_multi_pw_aff *mpa,
6961 __isl_take isl_val *v);
6962 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6963 __isl_take isl_pw_multi_aff *pma,
6964 __isl_take isl_val *v);
6965 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6966 __isl_take isl_union_pw_aff *upa,
6967 __isl_take isl_val *v);
6968 __isl_give isl_union_pw_multi_aff *
6969 isl_union_pw_multi_aff_scale_down_val(
6970 __isl_take isl_union_pw_multi_aff *upma,
6971 __isl_take isl_val *val);
6972 __isl_give isl_multi_union_pw_aff *
6973 isl_multi_union_pw_aff_scale_down_val(
6974 __isl_take isl_multi_union_pw_aff *mupa,
6975 __isl_take isl_val *v);
6977 #include <isl/polynomial.h>
6978 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6979 __isl_take isl_qpolynomial *qp,
6980 __isl_take isl_val *v);
6981 __isl_give isl_qpolynomial_fold *
6982 isl_qpolynomial_fold_scale_val(
6983 __isl_take isl_qpolynomial_fold *fold,
6984 __isl_take isl_val *v);
6985 __isl_give isl_pw_qpolynomial *
6986 isl_pw_qpolynomial_scale_val(
6987 __isl_take isl_pw_qpolynomial *pwqp,
6988 __isl_take isl_val *v);
6989 __isl_give isl_pw_qpolynomial_fold *
6990 isl_pw_qpolynomial_fold_scale_val(
6991 __isl_take isl_pw_qpolynomial_fold *pwf,
6992 __isl_take isl_val *v);
6993 __isl_give isl_union_pw_qpolynomial *
6994 isl_union_pw_qpolynomial_scale_val(
6995 __isl_take isl_union_pw_qpolynomial *upwqp,
6996 __isl_take isl_val *v);
6997 __isl_give isl_union_pw_qpolynomial_fold *
6998 isl_union_pw_qpolynomial_fold_scale_val(
6999 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7000 __isl_take isl_val *v);
7001 __isl_give isl_qpolynomial *
7002 isl_qpolynomial_scale_down_val(
7003 __isl_take isl_qpolynomial *qp,
7004 __isl_take isl_val *v);
7005 __isl_give isl_qpolynomial_fold *
7006 isl_qpolynomial_fold_scale_down_val(
7007 __isl_take isl_qpolynomial_fold *fold,
7008 __isl_take isl_val *v);
7009 __isl_give isl_pw_qpolynomial *
7010 isl_pw_qpolynomial_scale_down_val(
7011 __isl_take isl_pw_qpolynomial *pwqp,
7012 __isl_take isl_val *v);
7013 __isl_give isl_pw_qpolynomial_fold *
7014 isl_pw_qpolynomial_fold_scale_down_val(
7015 __isl_take isl_pw_qpolynomial_fold *pwf,
7016 __isl_take isl_val *v);
7017 __isl_give isl_union_pw_qpolynomial *
7018 isl_union_pw_qpolynomial_scale_down_val(
7019 __isl_take isl_union_pw_qpolynomial *upwqp,
7020 __isl_take isl_val *v);
7021 __isl_give isl_union_pw_qpolynomial_fold *
7022 isl_union_pw_qpolynomial_fold_scale_down_val(
7023 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7024 __isl_take isl_val *v);
7026 #include <isl/val.h>
7027 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7028 __isl_take isl_multi_val *mv1,
7029 __isl_take isl_multi_val *mv2);
7030 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7031 __isl_take isl_multi_val *mv1,
7032 __isl_take isl_multi_val *mv2);
7033 __isl_give isl_multi_val *
7034 isl_multi_val_scale_down_multi_val(
7035 __isl_take isl_multi_val *mv1,
7036 __isl_take isl_multi_val *mv2);
7038 #include <isl/aff.h>
7039 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7040 __isl_take isl_multi_aff *ma,
7041 __isl_take isl_multi_val *mv);
7042 __isl_give isl_multi_union_pw_aff *
7043 isl_multi_union_pw_aff_mod_multi_val(
7044 __isl_take isl_multi_union_pw_aff *upma,
7045 __isl_take isl_multi_val *mv);
7046 __isl_give isl_multi_pw_aff *
7047 isl_multi_pw_aff_mod_multi_val(
7048 __isl_take isl_multi_pw_aff *mpa,
7049 __isl_take isl_multi_val *mv);
7050 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7051 __isl_take isl_multi_aff *ma,
7052 __isl_take isl_multi_val *mv);
7053 __isl_give isl_pw_multi_aff *
7054 isl_pw_multi_aff_scale_multi_val(
7055 __isl_take isl_pw_multi_aff *pma,
7056 __isl_take isl_multi_val *mv);
7057 __isl_give isl_multi_pw_aff *
7058 isl_multi_pw_aff_scale_multi_val(
7059 __isl_take isl_multi_pw_aff *mpa,
7060 __isl_take isl_multi_val *mv);
7061 __isl_give isl_multi_union_pw_aff *
7062 isl_multi_union_pw_aff_scale_multi_val(
7063 __isl_take isl_multi_union_pw_aff *mupa,
7064 __isl_take isl_multi_val *mv);
7065 __isl_give isl_union_pw_multi_aff *
7066 isl_union_pw_multi_aff_scale_multi_val(
7067 __isl_take isl_union_pw_multi_aff *upma,
7068 __isl_take isl_multi_val *mv);
7069 __isl_give isl_multi_aff *
7070 isl_multi_aff_scale_down_multi_val(
7071 __isl_take isl_multi_aff *ma,
7072 __isl_take isl_multi_val *mv);
7073 __isl_give isl_multi_pw_aff *
7074 isl_multi_pw_aff_scale_down_multi_val(
7075 __isl_take isl_multi_pw_aff *mpa,
7076 __isl_take isl_multi_val *mv);
7077 __isl_give isl_multi_union_pw_aff *
7078 isl_multi_union_pw_aff_scale_down_multi_val(
7079 __isl_take isl_multi_union_pw_aff *mupa,
7080 __isl_take isl_multi_val *mv);
7082 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7083 by the corresponding elements of C<mv>.
7085 #include <isl/aff.h>
7086 __isl_give isl_aff *isl_aff_mul(
7087 __isl_take isl_aff *aff1,
7088 __isl_take isl_aff *aff2);
7089 __isl_give isl_aff *isl_aff_div(
7090 __isl_take isl_aff *aff1,
7091 __isl_take isl_aff *aff2);
7092 __isl_give isl_pw_aff *isl_pw_aff_mul(
7093 __isl_take isl_pw_aff *pwaff1,
7094 __isl_take isl_pw_aff *pwaff2);
7095 __isl_give isl_pw_aff *isl_pw_aff_div(
7096 __isl_take isl_pw_aff *pa1,
7097 __isl_take isl_pw_aff *pa2);
7098 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7099 __isl_take isl_pw_aff *pa1,
7100 __isl_take isl_pw_aff *pa2);
7101 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7102 __isl_take isl_pw_aff *pa1,
7103 __isl_take isl_pw_aff *pa2);
7105 When multiplying two affine expressions, at least one of the two needs
7106 to be a constant. Similarly, when dividing an affine expression by another,
7107 the second expression needs to be a constant.
7108 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7109 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7112 #include <isl/polynomial.h>
7113 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7114 __isl_take isl_qpolynomial *qp1,
7115 __isl_take isl_qpolynomial *qp2);
7116 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7117 __isl_take isl_pw_qpolynomial *pwqp1,
7118 __isl_take isl_pw_qpolynomial *pwqp2);
7119 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7120 __isl_take isl_union_pw_qpolynomial *upwqp1,
7121 __isl_take isl_union_pw_qpolynomial *upwqp2);
7125 =head3 Lexicographic Optimization
7127 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7128 the following functions
7129 compute a set that contains the lexicographic minimum or maximum
7130 of the elements in C<set> (or C<bset>) for those values of the parameters
7131 that satisfy C<dom>.
7132 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7133 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7135 In other words, the union of the parameter values
7136 for which the result is non-empty and of C<*empty>
7139 #include <isl/set.h>
7140 __isl_give isl_set *isl_basic_set_partial_lexmin(
7141 __isl_take isl_basic_set *bset,
7142 __isl_take isl_basic_set *dom,
7143 __isl_give isl_set **empty);
7144 __isl_give isl_set *isl_basic_set_partial_lexmax(
7145 __isl_take isl_basic_set *bset,
7146 __isl_take isl_basic_set *dom,
7147 __isl_give isl_set **empty);
7148 __isl_give isl_set *isl_set_partial_lexmin(
7149 __isl_take isl_set *set, __isl_take isl_set *dom,
7150 __isl_give isl_set **empty);
7151 __isl_give isl_set *isl_set_partial_lexmax(
7152 __isl_take isl_set *set, __isl_take isl_set *dom,
7153 __isl_give isl_set **empty);
7155 Given a (basic) set C<set> (or C<bset>), the following functions simply
7156 return a set containing the lexicographic minimum or maximum
7157 of the elements in C<set> (or C<bset>).
7158 In case of union sets, the optimum is computed per space.
7160 #include <isl/set.h>
7161 __isl_give isl_set *isl_basic_set_lexmin(
7162 __isl_take isl_basic_set *bset);
7163 __isl_give isl_set *isl_basic_set_lexmax(
7164 __isl_take isl_basic_set *bset);
7165 __isl_give isl_set *isl_set_lexmin(
7166 __isl_take isl_set *set);
7167 __isl_give isl_set *isl_set_lexmax(
7168 __isl_take isl_set *set);
7169 __isl_give isl_union_set *isl_union_set_lexmin(
7170 __isl_take isl_union_set *uset);
7171 __isl_give isl_union_set *isl_union_set_lexmax(
7172 __isl_take isl_union_set *uset);
7174 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7175 the following functions
7176 compute a relation that maps each element of C<dom>
7177 to the single lexicographic minimum or maximum
7178 of the elements that are associated to that same
7179 element in C<map> (or C<bmap>).
7180 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7181 that contains the elements in C<dom> that do not map
7182 to any elements in C<map> (or C<bmap>).
7183 In other words, the union of the domain of the result and of C<*empty>
7186 #include <isl/map.h>
7187 __isl_give isl_map *isl_basic_map_partial_lexmax(
7188 __isl_take isl_basic_map *bmap,
7189 __isl_take isl_basic_set *dom,
7190 __isl_give isl_set **empty);
7191 __isl_give isl_map *isl_basic_map_partial_lexmin(
7192 __isl_take isl_basic_map *bmap,
7193 __isl_take isl_basic_set *dom,
7194 __isl_give isl_set **empty);
7195 __isl_give isl_map *isl_map_partial_lexmax(
7196 __isl_take isl_map *map, __isl_take isl_set *dom,
7197 __isl_give isl_set **empty);
7198 __isl_give isl_map *isl_map_partial_lexmin(
7199 __isl_take isl_map *map, __isl_take isl_set *dom,
7200 __isl_give isl_set **empty);
7202 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7203 return a map mapping each element in the domain of
7204 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7205 of all elements associated to that element.
7206 In case of union relations, the optimum is computed per space.
7208 #include <isl/map.h>
7209 __isl_give isl_map *isl_basic_map_lexmin(
7210 __isl_take isl_basic_map *bmap);
7211 __isl_give isl_map *isl_basic_map_lexmax(
7212 __isl_take isl_basic_map *bmap);
7213 __isl_give isl_map *isl_map_lexmin(
7214 __isl_take isl_map *map);
7215 __isl_give isl_map *isl_map_lexmax(
7216 __isl_take isl_map *map);
7217 __isl_give isl_union_map *isl_union_map_lexmin(
7218 __isl_take isl_union_map *umap);
7219 __isl_give isl_union_map *isl_union_map_lexmax(
7220 __isl_take isl_union_map *umap);
7222 The following functions return their result in the form of
7223 a piecewise multi-affine expression,
7224 but are otherwise equivalent to the corresponding functions
7225 returning a basic set or relation.
7227 #include <isl/set.h>
7228 __isl_give isl_pw_multi_aff *
7229 isl_basic_set_partial_lexmin_pw_multi_aff(
7230 __isl_take isl_basic_set *bset,
7231 __isl_take isl_basic_set *dom,
7232 __isl_give isl_set **empty);
7233 __isl_give isl_pw_multi_aff *
7234 isl_basic_set_partial_lexmax_pw_multi_aff(
7235 __isl_take isl_basic_set *bset,
7236 __isl_take isl_basic_set *dom,
7237 __isl_give isl_set **empty);
7238 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7239 __isl_take isl_set *set);
7240 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7241 __isl_take isl_set *set);
7243 #include <isl/map.h>
7244 __isl_give isl_pw_multi_aff *
7245 isl_basic_map_lexmin_pw_multi_aff(
7246 __isl_take isl_basic_map *bmap);
7247 __isl_give isl_pw_multi_aff *
7248 isl_basic_map_partial_lexmin_pw_multi_aff(
7249 __isl_take isl_basic_map *bmap,
7250 __isl_take isl_basic_set *dom,
7251 __isl_give isl_set **empty);
7252 __isl_give isl_pw_multi_aff *
7253 isl_basic_map_partial_lexmax_pw_multi_aff(
7254 __isl_take isl_basic_map *bmap,
7255 __isl_take isl_basic_set *dom,
7256 __isl_give isl_set **empty);
7257 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7258 __isl_take isl_map *map);
7259 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7260 __isl_take isl_map *map);
7262 The following functions return the lexicographic minimum or maximum
7263 on the shared domain of the inputs and the single defined function
7264 on those parts of the domain where only a single function is defined.
7266 #include <isl/aff.h>
7267 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7268 __isl_take isl_pw_multi_aff *pma1,
7269 __isl_take isl_pw_multi_aff *pma2);
7270 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7271 __isl_take isl_pw_multi_aff *pma1,
7272 __isl_take isl_pw_multi_aff *pma2);
7274 If the input to a lexicographic optimization problem has
7275 multiple constraints with the same coefficients for the optimized
7276 variables, then, by default, this symmetry is exploited by
7277 replacing those constraints by a single constraint with
7278 an abstract bound, which is in turn bounded by the corresponding terms
7279 in the original constraints.
7280 Without this optimization, the solver would typically consider
7281 all possible orderings of those original bounds, resulting in a needless
7282 decomposition of the domain.
7283 However, the optimization can also result in slowdowns since
7284 an extra parameter is introduced that may get used in additional
7286 The following option determines whether symmetry detection is applied
7287 during lexicographic optimization.
7289 #include <isl/options.h>
7290 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7292 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7296 See also \autoref{s:offline}.
7300 =head2 Ternary Operations
7302 #include <isl/aff.h>
7303 __isl_give isl_pw_aff *isl_pw_aff_cond(
7304 __isl_take isl_pw_aff *cond,
7305 __isl_take isl_pw_aff *pwaff_true,
7306 __isl_take isl_pw_aff *pwaff_false);
7308 The function C<isl_pw_aff_cond> performs a conditional operator
7309 and returns an expression that is equal to C<pwaff_true>
7310 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7311 where C<cond> is zero.
7315 Lists are defined over several element types, including
7316 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7317 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7318 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7319 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7320 Here we take lists of C<isl_set>s as an example.
7321 Lists can be created, copied, modified and freed using the following functions.
7323 #include <isl/set.h>
7324 __isl_give isl_set_list *isl_set_list_from_set(
7325 __isl_take isl_set *el);
7326 __isl_give isl_set_list *isl_set_list_alloc(
7327 isl_ctx *ctx, int n);
7328 __isl_give isl_set_list *isl_set_list_copy(
7329 __isl_keep isl_set_list *list);
7330 __isl_give isl_set_list *isl_set_list_insert(
7331 __isl_take isl_set_list *list, unsigned pos,
7332 __isl_take isl_set *el);
7333 __isl_give isl_set_list *isl_set_list_add(
7334 __isl_take isl_set_list *list,
7335 __isl_take isl_set *el);
7336 __isl_give isl_set_list *isl_set_list_drop(
7337 __isl_take isl_set_list *list,
7338 unsigned first, unsigned n);
7339 __isl_give isl_set_list *isl_set_list_set_set(
7340 __isl_take isl_set_list *list, int index,
7341 __isl_take isl_set *set);
7342 __isl_give isl_set_list *isl_set_list_concat(
7343 __isl_take isl_set_list *list1,
7344 __isl_take isl_set_list *list2);
7345 __isl_give isl_set_list *isl_set_list_sort(
7346 __isl_take isl_set_list *list,
7347 int (*cmp)(__isl_keep isl_set *a,
7348 __isl_keep isl_set *b, void *user),
7350 __isl_null isl_set_list *isl_set_list_free(
7351 __isl_take isl_set_list *list);
7353 C<isl_set_list_alloc> creates an empty list with an initial capacity
7354 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7355 add elements to a list, increasing its capacity as needed.
7356 C<isl_set_list_from_set> creates a list with a single element.
7358 Lists can be inspected using the following functions.
7360 #include <isl/set.h>
7361 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7362 __isl_give isl_set *isl_set_list_get_set(
7363 __isl_keep isl_set_list *list, int index);
7364 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7365 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7367 isl_stat isl_set_list_foreach_scc(
7368 __isl_keep isl_set_list *list,
7369 isl_bool (*follows)(__isl_keep isl_set *a,
7370 __isl_keep isl_set *b, void *user),
7372 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7375 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7376 strongly connected components of the graph with as vertices the elements
7377 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7378 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7379 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7381 Lists can be printed using
7383 #include <isl/set.h>
7384 __isl_give isl_printer *isl_printer_print_set_list(
7385 __isl_take isl_printer *p,
7386 __isl_keep isl_set_list *list);
7388 =head2 Associative arrays
7390 Associative arrays map isl objects of a specific type to isl objects
7391 of some (other) specific type. They are defined for several pairs
7392 of types, including (C<isl_map>, C<isl_basic_set>),
7393 (C<isl_id>, C<isl_ast_expr>),
7394 (C<isl_id>, C<isl_id>) and
7395 (C<isl_id>, C<isl_pw_aff>).
7396 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7399 Associative arrays can be created, copied and freed using
7400 the following functions.
7402 #include <isl/id_to_ast_expr.h>
7403 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7404 isl_ctx *ctx, int min_size);
7405 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7406 __isl_keep isl_id_to_ast_expr *id2expr);
7407 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7408 __isl_take isl_id_to_ast_expr *id2expr);
7410 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7411 to specify the expected size of the associative array.
7412 The associative array will be grown automatically as needed.
7414 Associative arrays can be inspected using the following functions.
7416 #include <isl/id_to_ast_expr.h>
7417 __isl_give isl_maybe_isl_ast_expr
7418 isl_id_to_ast_expr_try_get(
7419 __isl_keep isl_id_to_ast_expr *id2expr,
7420 __isl_keep isl_id *key);
7421 isl_bool isl_id_to_ast_expr_has(
7422 __isl_keep isl_id_to_ast_expr *id2expr,
7423 __isl_keep isl_id *key);
7424 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7425 __isl_keep isl_id_to_ast_expr *id2expr,
7426 __isl_take isl_id *key);
7427 isl_stat isl_id_to_ast_expr_foreach(
7428 __isl_keep isl_id_to_ast_expr *id2expr,
7429 isl_stat (*fn)(__isl_take isl_id *key,
7430 __isl_take isl_ast_expr *val, void *user),
7433 The function C<isl_id_to_ast_expr_try_get> returns a structure
7434 containing two elements, C<valid> and C<value>.
7435 If there is a value associated to the key, then C<valid>
7436 is set to C<isl_bool_true> and C<value> contains a copy of
7437 the associated value. Otherwise C<value> is C<NULL> and
7438 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7439 on whether some error has occurred or there simply is no associated value.
7440 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7441 in the structure and
7442 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7444 Associative arrays can be modified using the following functions.
7446 #include <isl/id_to_ast_expr.h>
7447 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7448 __isl_take isl_id_to_ast_expr *id2expr,
7449 __isl_take isl_id *key,
7450 __isl_take isl_ast_expr *val);
7451 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7452 __isl_take isl_id_to_ast_expr *id2expr,
7453 __isl_take isl_id *key);
7455 Associative arrays can be printed using the following function.
7457 #include <isl/id_to_ast_expr.h>
7458 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7459 __isl_take isl_printer *p,
7460 __isl_keep isl_id_to_ast_expr *id2expr);
7464 Vectors can be created, copied and freed using the following functions.
7466 #include <isl/vec.h>
7467 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7469 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7470 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7472 Note that the elements of a newly created vector may have arbitrary values.
7473 The elements can be changed and inspected using the following functions.
7475 int isl_vec_size(__isl_keep isl_vec *vec);
7476 __isl_give isl_val *isl_vec_get_element_val(
7477 __isl_keep isl_vec *vec, int pos);
7478 __isl_give isl_vec *isl_vec_set_element_si(
7479 __isl_take isl_vec *vec, int pos, int v);
7480 __isl_give isl_vec *isl_vec_set_element_val(
7481 __isl_take isl_vec *vec, int pos,
7482 __isl_take isl_val *v);
7483 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7485 __isl_give isl_vec *isl_vec_set_val(
7486 __isl_take isl_vec *vec, __isl_take isl_val *v);
7487 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7488 __isl_keep isl_vec *vec2, int pos);
7490 C<isl_vec_get_element> will return a negative value if anything went wrong.
7491 In that case, the value of C<*v> is undefined.
7493 The following function can be used to concatenate two vectors.
7495 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7496 __isl_take isl_vec *vec2);
7500 Matrices can be created, copied and freed using the following functions.
7502 #include <isl/mat.h>
7503 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7504 unsigned n_row, unsigned n_col);
7505 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7506 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7508 Note that the elements of a newly created matrix may have arbitrary values.
7509 The elements can be changed and inspected using the following functions.
7511 int isl_mat_rows(__isl_keep isl_mat *mat);
7512 int isl_mat_cols(__isl_keep isl_mat *mat);
7513 __isl_give isl_val *isl_mat_get_element_val(
7514 __isl_keep isl_mat *mat, int row, int col);
7515 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7516 int row, int col, int v);
7517 __isl_give isl_mat *isl_mat_set_element_val(
7518 __isl_take isl_mat *mat, int row, int col,
7519 __isl_take isl_val *v);
7521 C<isl_mat_get_element> will return a negative value if anything went wrong.
7522 In that case, the value of C<*v> is undefined.
7524 The following function can be used to compute the (right) inverse
7525 of a matrix, i.e., a matrix such that the product of the original
7526 and the inverse (in that order) is a multiple of the identity matrix.
7527 The input matrix is assumed to be of full row-rank.
7529 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7531 The following function can be used to compute the (right) kernel
7532 (or null space) of a matrix, i.e., a matrix such that the product of
7533 the original and the kernel (in that order) is the zero matrix.
7535 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7537 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7539 The following functions determine
7540 an upper or lower bound on a quasipolynomial over its domain.
7542 __isl_give isl_pw_qpolynomial_fold *
7543 isl_pw_qpolynomial_bound(
7544 __isl_take isl_pw_qpolynomial *pwqp,
7545 enum isl_fold type, int *tight);
7547 __isl_give isl_union_pw_qpolynomial_fold *
7548 isl_union_pw_qpolynomial_bound(
7549 __isl_take isl_union_pw_qpolynomial *upwqp,
7550 enum isl_fold type, int *tight);
7552 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7553 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7554 is the returned bound is known be tight, i.e., for each value
7555 of the parameters there is at least
7556 one element in the domain that reaches the bound.
7557 If the domain of C<pwqp> is not wrapping, then the bound is computed
7558 over all elements in that domain and the result has a purely parametric
7559 domain. If the domain of C<pwqp> is wrapping, then the bound is
7560 computed over the range of the wrapped relation. The domain of the
7561 wrapped relation becomes the domain of the result.
7563 =head2 Parametric Vertex Enumeration
7565 The parametric vertex enumeration described in this section
7566 is mainly intended to be used internally and by the C<barvinok>
7569 #include <isl/vertices.h>
7570 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7571 __isl_keep isl_basic_set *bset);
7573 The function C<isl_basic_set_compute_vertices> performs the
7574 actual computation of the parametric vertices and the chamber
7575 decomposition and store the result in an C<isl_vertices> object.
7576 This information can be queried by either iterating over all
7577 the vertices or iterating over all the chambers or cells
7578 and then iterating over all vertices that are active on the chamber.
7580 isl_stat isl_vertices_foreach_vertex(
7581 __isl_keep isl_vertices *vertices,
7582 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7583 void *user), void *user);
7585 isl_stat isl_vertices_foreach_cell(
7586 __isl_keep isl_vertices *vertices,
7587 isl_stat (*fn)(__isl_take isl_cell *cell,
7588 void *user), void *user);
7589 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7590 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7591 void *user), void *user);
7593 Other operations that can be performed on an C<isl_vertices> object are
7596 int isl_vertices_get_n_vertices(
7597 __isl_keep isl_vertices *vertices);
7598 void isl_vertices_free(__isl_take isl_vertices *vertices);
7600 Vertices can be inspected and destroyed using the following functions.
7602 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7603 __isl_give isl_basic_set *isl_vertex_get_domain(
7604 __isl_keep isl_vertex *vertex);
7605 __isl_give isl_multi_aff *isl_vertex_get_expr(
7606 __isl_keep isl_vertex *vertex);
7607 void isl_vertex_free(__isl_take isl_vertex *vertex);
7609 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7610 describing the vertex in terms of the parameters,
7611 while C<isl_vertex_get_domain> returns the activity domain
7614 Chambers can be inspected and destroyed using the following functions.
7616 __isl_give isl_basic_set *isl_cell_get_domain(
7617 __isl_keep isl_cell *cell);
7618 void isl_cell_free(__isl_take isl_cell *cell);
7620 =head1 Polyhedral Compilation Library
7622 This section collects functionality in C<isl> that has been specifically
7623 designed for use during polyhedral compilation.
7625 =head2 Schedule Trees
7627 A schedule tree is a structured representation of a schedule,
7628 assigning a relative order to a set of domain elements.
7629 The relative order expressed by the schedule tree is
7630 defined recursively. In particular, the order between
7631 two domain elements is determined by the node that is closest
7632 to the root that refers to both elements and that orders them apart.
7633 Each node in the tree is of one of several types.
7634 The root node is always of type C<isl_schedule_node_domain>
7635 (or C<isl_schedule_node_extension>)
7636 and it describes the (extra) domain elements to which the schedule applies.
7637 The other types of nodes are as follows.
7641 =item C<isl_schedule_node_band>
7643 A band of schedule dimensions. Each schedule dimension is represented
7644 by a union piecewise quasi-affine expression. If this expression
7645 assigns a different value to two domain elements, while all previous
7646 schedule dimensions in the same band assign them the same value,
7647 then the two domain elements are ordered according to these two
7649 Each expression is required to be total in the domain elements
7650 that reach the band node.
7652 =item C<isl_schedule_node_expansion>
7654 An expansion node maps each of the domain elements that reach the node
7655 to one or more domain elements. The image of this mapping forms
7656 the set of domain elements that reach the child of the expansion node.
7657 The function that maps each of the expanded domain elements
7658 to the original domain element from which it was expanded
7659 is called the contraction.
7661 =item C<isl_schedule_node_filter>
7663 A filter node does not impose any ordering, but rather intersects
7664 the set of domain elements that the current subtree refers to
7665 with a given union set. The subtree of the filter node only
7666 refers to domain elements in the intersection.
7667 A filter node is typically only used a child of a sequence or
7670 =item C<isl_schedule_node_leaf>
7672 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7674 =item C<isl_schedule_node_mark>
7676 A mark node can be used to attach any kind of information to a subtree
7677 of the schedule tree.
7679 =item C<isl_schedule_node_sequence>
7681 A sequence node has one or more children, each of which is a filter node.
7682 The filters on these filter nodes form a partition of
7683 the domain elements that the current subtree refers to.
7684 If two domain elements appear in distinct filters then the sequence
7685 node orders them according to the child positions of the corresponding
7688 =item C<isl_schedule_node_set>
7690 A set node is similar to a sequence node, except that
7691 it expresses that domain elements appearing in distinct filters
7692 may have any order. The order of the children of a set node
7693 is therefore also immaterial.
7697 The following node types are only supported by the AST generator.
7701 =item C<isl_schedule_node_context>
7703 The context describes constraints on the parameters and
7704 the schedule dimensions of outer
7705 bands that the AST generator may assume to hold. It is also the only
7706 kind of node that may introduce additional parameters.
7707 The space of the context is that of the flat product of the outer
7708 band nodes. In particular, if there are no outer band nodes, then
7709 this space is the unnamed zero-dimensional space.
7710 Since a context node references the outer band nodes, any tree
7711 containing a context node is considered to be anchored.
7713 =item C<isl_schedule_node_extension>
7715 An extension node instructs the AST generator to add additional
7716 domain elements that need to be scheduled.
7717 The additional domain elements are described by the range of
7718 the extension map in terms of the outer schedule dimensions,
7719 i.e., the flat product of the outer band nodes.
7720 Note that domain elements are added whenever the AST generator
7721 reaches the extension node, meaning that there are still some
7722 active domain elements for which an AST needs to be generated.
7723 The conditions under which some domain elements are still active
7724 may however not be completely described by the outer AST nodes
7725 generated at that point.
7727 An extension node may also appear as the root of a schedule tree,
7728 when it is intended to be inserted into another tree
7729 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7730 In this case, the domain of the extension node should
7731 correspond to the flat product of the outer band nodes
7732 in this other schedule tree at the point where the extension tree
7735 =item C<isl_schedule_node_guard>
7737 The guard describes constraints on the parameters and
7738 the schedule dimensions of outer
7739 bands that need to be enforced by the outer nodes
7740 in the generated AST.
7741 The space of the guard is that of the flat product of the outer
7742 band nodes. In particular, if there are no outer band nodes, then
7743 this space is the unnamed zero-dimensional space.
7744 Since a guard node references the outer band nodes, any tree
7745 containing a guard node is considered to be anchored.
7749 Except for the C<isl_schedule_node_context> nodes,
7750 none of the nodes may introduce any parameters that were not
7751 already present in the root domain node.
7753 A schedule tree is encapsulated in an C<isl_schedule> object.
7754 The simplest such objects, those with a tree consisting of single domain node,
7755 can be created using the following functions with either an empty
7756 domain or a given domain.
7758 #include <isl/schedule.h>
7759 __isl_give isl_schedule *isl_schedule_empty(
7760 __isl_take isl_space *space);
7761 __isl_give isl_schedule *isl_schedule_from_domain(
7762 __isl_take isl_union_set *domain);
7764 The function C<isl_schedule_constraints_compute_schedule> described
7765 in L</"Scheduling"> can also be used to construct schedules.
7767 C<isl_schedule> objects may be copied and freed using the following functions.
7769 #include <isl/schedule.h>
7770 __isl_give isl_schedule *isl_schedule_copy(
7771 __isl_keep isl_schedule *sched);
7772 __isl_null isl_schedule *isl_schedule_free(
7773 __isl_take isl_schedule *sched);
7775 The following functions checks whether two C<isl_schedule> objects
7776 are obviously the same.
7778 #include <isl/schedule.h>
7779 isl_bool isl_schedule_plain_is_equal(
7780 __isl_keep isl_schedule *schedule1,
7781 __isl_keep isl_schedule *schedule2);
7783 The domain of the schedule, i.e., the domain described by the root node,
7784 can be obtained using the following function.
7786 #include <isl/schedule.h>
7787 __isl_give isl_union_set *isl_schedule_get_domain(
7788 __isl_keep isl_schedule *schedule);
7790 An extra top-level band node (right underneath the domain node) can
7791 be introduced into the schedule using the following function.
7792 The schedule tree is assumed not to have any anchored nodes.
7794 #include <isl/schedule.h>
7795 __isl_give isl_schedule *
7796 isl_schedule_insert_partial_schedule(
7797 __isl_take isl_schedule *schedule,
7798 __isl_take isl_multi_union_pw_aff *partial);
7800 A top-level context node (right underneath the domain node) can
7801 be introduced into the schedule using the following function.
7803 #include <isl/schedule.h>
7804 __isl_give isl_schedule *isl_schedule_insert_context(
7805 __isl_take isl_schedule *schedule,
7806 __isl_take isl_set *context)
7808 A top-level guard node (right underneath the domain node) can
7809 be introduced into the schedule using the following function.
7811 #include <isl/schedule.h>
7812 __isl_give isl_schedule *isl_schedule_insert_guard(
7813 __isl_take isl_schedule *schedule,
7814 __isl_take isl_set *guard)
7816 A schedule that combines two schedules either in the given
7817 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7818 or an C<isl_schedule_node_set> node,
7819 can be created using the following functions.
7821 #include <isl/schedule.h>
7822 __isl_give isl_schedule *isl_schedule_sequence(
7823 __isl_take isl_schedule *schedule1,
7824 __isl_take isl_schedule *schedule2);
7825 __isl_give isl_schedule *isl_schedule_set(
7826 __isl_take isl_schedule *schedule1,
7827 __isl_take isl_schedule *schedule2);
7829 The domains of the two input schedules need to be disjoint.
7831 The following function can be used to restrict the domain
7832 of a schedule with a domain node as root to be a subset of the given union set.
7833 This operation may remove nodes in the tree that have become
7836 #include <isl/schedule.h>
7837 __isl_give isl_schedule *isl_schedule_intersect_domain(
7838 __isl_take isl_schedule *schedule,
7839 __isl_take isl_union_set *domain);
7841 The following function can be used to simplify the domain
7842 of a schedule with a domain node as root with respect to the given
7845 #include <isl/schedule.h>
7846 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7847 __isl_take isl_schedule *schedule,
7848 __isl_take isl_set *context);
7850 The following function resets the user pointers on all parameter
7851 and tuple identifiers referenced by the nodes of the given schedule.
7853 #include <isl/schedule.h>
7854 __isl_give isl_schedule *isl_schedule_reset_user(
7855 __isl_take isl_schedule *schedule);
7857 The following function aligns the parameters of all nodes
7858 in the given schedule to the given space.
7860 #include <isl/schedule.h>
7861 __isl_give isl_schedule *isl_schedule_align_params(
7862 __isl_take isl_schedule *schedule,
7863 __isl_take isl_space *space);
7865 The following function allows the user to plug in a given function
7866 in the iteration domains. The input schedule is not allowed to contain
7867 any expansion nodes.
7869 #include <isl/schedule.h>
7870 __isl_give isl_schedule *
7871 isl_schedule_pullback_union_pw_multi_aff(
7872 __isl_take isl_schedule *schedule,
7873 __isl_take isl_union_pw_multi_aff *upma);
7875 The following function can be used to plug in the schedule C<expansion>
7876 in the leaves of C<schedule>, where C<contraction> describes how
7877 the domain elements of C<expansion> map to the domain elements
7878 at the original leaves of C<schedule>.
7879 The resulting schedule will contain expansion nodes, unless
7880 C<contraction> is an identity function.
7882 #include <isl/schedule.h>
7883 __isl_give isl_schedule *isl_schedule_expand(
7884 __isl_take isl_schedule *schedule,
7885 __isl_take isl_union_pw_multi_aff *contraction,
7886 __isl_take isl_schedule *expansion);
7888 An C<isl_union_map> representation of the schedule can be obtained
7889 from an C<isl_schedule> using the following function.
7891 #include <isl/schedule.h>
7892 __isl_give isl_union_map *isl_schedule_get_map(
7893 __isl_keep isl_schedule *sched);
7895 The resulting relation encodes the same relative ordering as
7896 the schedule by mapping the domain elements to a common schedule space.
7897 If the schedule_separate_components option is set, then the order
7898 of the children of a set node is explicitly encoded in the result.
7899 If the tree contains any expansion nodes, then the relation
7900 is formulated in terms of the expanded domain elements.
7902 Schedules can be read from input using the following functions.
7904 #include <isl/schedule.h>
7905 __isl_give isl_schedule *isl_schedule_read_from_file(
7906 isl_ctx *ctx, FILE *input);
7907 __isl_give isl_schedule *isl_schedule_read_from_str(
7908 isl_ctx *ctx, const char *str);
7910 A representation of the schedule can be printed using
7912 #include <isl/schedule.h>
7913 __isl_give isl_printer *isl_printer_print_schedule(
7914 __isl_take isl_printer *p,
7915 __isl_keep isl_schedule *schedule);
7916 __isl_give char *isl_schedule_to_str(
7917 __isl_keep isl_schedule *schedule);
7919 C<isl_schedule_to_str> prints the schedule in flow format.
7921 The schedule tree can be traversed through the use of
7922 C<isl_schedule_node> objects that point to a particular
7923 position in the schedule tree. Whenever a C<isl_schedule_node>
7924 is use to modify a node in the schedule tree, the original schedule
7925 tree is left untouched and the modifications are performed to a copy
7926 of the tree. The returned C<isl_schedule_node> then points to
7927 this modified copy of the tree.
7929 The root of the schedule tree can be obtained using the following function.
7931 #include <isl/schedule.h>
7932 __isl_give isl_schedule_node *isl_schedule_get_root(
7933 __isl_keep isl_schedule *schedule);
7935 A pointer to a newly created schedule tree with a single domain
7936 node can be created using the following functions.
7938 #include <isl/schedule_node.h>
7939 __isl_give isl_schedule_node *
7940 isl_schedule_node_from_domain(
7941 __isl_take isl_union_set *domain);
7942 __isl_give isl_schedule_node *
7943 isl_schedule_node_from_extension(
7944 __isl_take isl_union_map *extension);
7946 C<isl_schedule_node_from_extension> creates a tree with an extension
7949 Schedule nodes can be copied and freed using the following functions.
7951 #include <isl/schedule_node.h>
7952 __isl_give isl_schedule_node *isl_schedule_node_copy(
7953 __isl_keep isl_schedule_node *node);
7954 __isl_null isl_schedule_node *isl_schedule_node_free(
7955 __isl_take isl_schedule_node *node);
7957 The following functions can be used to check if two schedule
7958 nodes point to the same position in the same schedule.
7960 #include <isl/schedule_node.h>
7961 isl_bool isl_schedule_node_is_equal(
7962 __isl_keep isl_schedule_node *node1,
7963 __isl_keep isl_schedule_node *node2);
7965 The following properties can be obtained from a schedule node.
7967 #include <isl/schedule_node.h>
7968 enum isl_schedule_node_type isl_schedule_node_get_type(
7969 __isl_keep isl_schedule_node *node);
7970 enum isl_schedule_node_type
7971 isl_schedule_node_get_parent_type(
7972 __isl_keep isl_schedule_node *node);
7973 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7974 __isl_keep isl_schedule_node *node);
7976 The function C<isl_schedule_node_get_type> returns the type of
7977 the node, while C<isl_schedule_node_get_parent_type> returns
7978 type of the parent of the node, which is required to exist.
7979 The function C<isl_schedule_node_get_schedule> returns a copy
7980 to the schedule to which the node belongs.
7982 The following functions can be used to move the schedule node
7983 to a different position in the tree or to check if such a position
7986 #include <isl/schedule_node.h>
7987 isl_bool isl_schedule_node_has_parent(
7988 __isl_keep isl_schedule_node *node);
7989 __isl_give isl_schedule_node *isl_schedule_node_parent(
7990 __isl_take isl_schedule_node *node);
7991 __isl_give isl_schedule_node *isl_schedule_node_root(
7992 __isl_take isl_schedule_node *node);
7993 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
7994 __isl_take isl_schedule_node *node,
7996 int isl_schedule_node_n_children(
7997 __isl_keep isl_schedule_node *node);
7998 __isl_give isl_schedule_node *isl_schedule_node_child(
7999 __isl_take isl_schedule_node *node, int pos);
8000 isl_bool isl_schedule_node_has_children(
8001 __isl_keep isl_schedule_node *node);
8002 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8003 __isl_take isl_schedule_node *node);
8004 isl_bool isl_schedule_node_has_previous_sibling(
8005 __isl_keep isl_schedule_node *node);
8006 __isl_give isl_schedule_node *
8007 isl_schedule_node_previous_sibling(
8008 __isl_take isl_schedule_node *node);
8009 isl_bool isl_schedule_node_has_next_sibling(
8010 __isl_keep isl_schedule_node *node);
8011 __isl_give isl_schedule_node *
8012 isl_schedule_node_next_sibling(
8013 __isl_take isl_schedule_node *node);
8015 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8016 is the node itself, the ancestor of generation 1 is its parent and so on.
8018 It is also possible to query the number of ancestors of a node,
8019 the position of the current node
8020 within the children of its parent, the position of the subtree
8021 containing a node within the children of an ancestor
8022 or to obtain a copy of a given
8023 child without destroying the current node.
8024 Given two nodes that point to the same schedule, their closest
8025 shared ancestor can be obtained using
8026 C<isl_schedule_node_get_shared_ancestor>.
8028 #include <isl/schedule_node.h>
8029 int isl_schedule_node_get_tree_depth(
8030 __isl_keep isl_schedule_node *node);
8031 int isl_schedule_node_get_child_position(
8032 __isl_keep isl_schedule_node *node);
8033 int isl_schedule_node_get_ancestor_child_position(
8034 __isl_keep isl_schedule_node *node,
8035 __isl_keep isl_schedule_node *ancestor);
8036 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8037 __isl_keep isl_schedule_node *node, int pos);
8038 __isl_give isl_schedule_node *
8039 isl_schedule_node_get_shared_ancestor(
8040 __isl_keep isl_schedule_node *node1,
8041 __isl_keep isl_schedule_node *node2);
8043 All nodes in a schedule tree or
8044 all descendants of a specific node (including the node) can be visited
8045 in depth-first pre-order using the following functions.
8047 #include <isl/schedule.h>
8048 isl_stat isl_schedule_foreach_schedule_node_top_down(
8049 __isl_keep isl_schedule *sched,
8050 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8051 void *user), void *user);
8053 #include <isl/schedule_node.h>
8054 isl_stat isl_schedule_node_foreach_descendant_top_down(
8055 __isl_keep isl_schedule_node *node,
8056 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8057 void *user), void *user);
8059 The callback function is slightly different from the usual
8060 callbacks in that it not only indicates success (non-negative result)
8061 or failure (negative result), but also indicates whether the children
8062 of the given node should be visited. In particular, if the callback
8063 returns a positive value, then the children are visited, but if
8064 the callback returns zero, then the children are not visited.
8066 The ancestors of a node in a schedule tree can be visited from
8067 the root down to and including the parent of the node using
8068 the following function.
8070 #include <isl/schedule_node.h>
8071 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8072 __isl_keep isl_schedule_node *node,
8073 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8074 void *user), void *user);
8076 The following functions allows for a depth-first post-order
8077 traversal of the nodes in a schedule tree or
8078 of the descendants of a specific node (including the node
8079 itself), where the user callback is allowed to modify the
8082 #include <isl/schedule.h>
8083 __isl_give isl_schedule *
8084 isl_schedule_map_schedule_node_bottom_up(
8085 __isl_take isl_schedule *schedule,
8086 __isl_give isl_schedule_node *(*fn)(
8087 __isl_take isl_schedule_node *node,
8088 void *user), void *user);
8090 #include <isl/schedule_node.h>
8091 __isl_give isl_schedule_node *
8092 isl_schedule_node_map_descendant_bottom_up(
8093 __isl_take isl_schedule_node *node,
8094 __isl_give isl_schedule_node *(*fn)(
8095 __isl_take isl_schedule_node *node,
8096 void *user), void *user);
8098 The traversal continues from the node returned by the callback function.
8099 It is the responsibility of the user to ensure that this does not
8100 lead to an infinite loop. It is safest to always return a pointer
8101 to the same position (same ancestors and child positions) as the input node.
8103 The following function removes a node (along with its descendants)
8104 from a schedule tree and returns a pointer to the leaf at the
8105 same position in the updated tree.
8106 It is not allowed to remove the root of a schedule tree or
8107 a child of a set or sequence node.
8109 #include <isl/schedule_node.h>
8110 __isl_give isl_schedule_node *isl_schedule_node_cut(
8111 __isl_take isl_schedule_node *node);
8113 The following function removes a single node
8114 from a schedule tree and returns a pointer to the child
8115 of the node, now located at the position of the original node
8116 or to a leaf node at that position if there was no child.
8117 It is not allowed to remove the root of a schedule tree,
8118 a set or sequence node, a child of a set or sequence node or
8119 a band node with an anchored subtree.
8121 #include <isl/schedule_node.h>
8122 __isl_give isl_schedule_node *isl_schedule_node_delete(
8123 __isl_take isl_schedule_node *node);
8125 Most nodes in a schedule tree only contain local information.
8126 In some cases, however, a node may also refer to outer band nodes.
8127 This means that the position of the node within the tree should
8128 not be changed, or at least that no changes are performed to the
8129 outer band nodes. The following function can be used to test
8130 whether the subtree rooted at a given node contains any such nodes.
8132 #include <isl/schedule_node.h>
8133 isl_bool isl_schedule_node_is_subtree_anchored(
8134 __isl_keep isl_schedule_node *node);
8136 The following function resets the user pointers on all parameter
8137 and tuple identifiers referenced by the given schedule node.
8139 #include <isl/schedule_node.h>
8140 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8141 __isl_take isl_schedule_node *node);
8143 The following function aligns the parameters of the given schedule
8144 node to the given space.
8146 #include <isl/schedule_node.h>
8147 __isl_give isl_schedule_node *
8148 isl_schedule_node_align_params(
8149 __isl_take isl_schedule_node *node,
8150 __isl_take isl_space *space);
8152 Several node types have their own functions for querying
8153 (and in some cases setting) some node type specific properties.
8155 #include <isl/schedule_node.h>
8156 __isl_give isl_space *isl_schedule_node_band_get_space(
8157 __isl_keep isl_schedule_node *node);
8158 __isl_give isl_multi_union_pw_aff *
8159 isl_schedule_node_band_get_partial_schedule(
8160 __isl_keep isl_schedule_node *node);
8161 __isl_give isl_union_map *
8162 isl_schedule_node_band_get_partial_schedule_union_map(
8163 __isl_keep isl_schedule_node *node);
8164 unsigned isl_schedule_node_band_n_member(
8165 __isl_keep isl_schedule_node *node);
8166 isl_bool isl_schedule_node_band_member_get_coincident(
8167 __isl_keep isl_schedule_node *node, int pos);
8168 __isl_give isl_schedule_node *
8169 isl_schedule_node_band_member_set_coincident(
8170 __isl_take isl_schedule_node *node, int pos,
8172 isl_bool isl_schedule_node_band_get_permutable(
8173 __isl_keep isl_schedule_node *node);
8174 __isl_give isl_schedule_node *
8175 isl_schedule_node_band_set_permutable(
8176 __isl_take isl_schedule_node *node, int permutable);
8177 enum isl_ast_loop_type
8178 isl_schedule_node_band_member_get_ast_loop_type(
8179 __isl_keep isl_schedule_node *node, int pos);
8180 __isl_give isl_schedule_node *
8181 isl_schedule_node_band_member_set_ast_loop_type(
8182 __isl_take isl_schedule_node *node, int pos,
8183 enum isl_ast_loop_type type);
8184 __isl_give isl_union_set *
8185 enum isl_ast_loop_type
8186 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8187 __isl_keep isl_schedule_node *node, int pos);
8188 __isl_give isl_schedule_node *
8189 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8190 __isl_take isl_schedule_node *node, int pos,
8191 enum isl_ast_loop_type type);
8192 isl_schedule_node_band_get_ast_build_options(
8193 __isl_keep isl_schedule_node *node);
8194 __isl_give isl_schedule_node *
8195 isl_schedule_node_band_set_ast_build_options(
8196 __isl_take isl_schedule_node *node,
8197 __isl_take isl_union_set *options);
8198 __isl_give isl_set *
8199 isl_schedule_node_band_get_ast_isolate_option(
8200 __isl_keep isl_schedule_node *node);
8202 The function C<isl_schedule_node_band_get_space> returns the space
8203 of the partial schedule of the band.
8204 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8205 returns a representation of the partial schedule of the band node
8206 in the form of an C<isl_union_map>.
8207 The coincident and permutable properties are set by
8208 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8210 A scheduling dimension is considered to be ``coincident''
8211 if it satisfies the coincidence constraints within its band.
8212 That is, if the dependence distances of the coincidence
8213 constraints are all zero in that direction (for fixed
8214 iterations of outer bands).
8215 A band is marked permutable if it was produced using the Pluto-like scheduler.
8216 Note that the scheduler may have to resort to a Feautrier style scheduling
8217 step even if the default scheduler is used.
8218 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8219 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8220 For the meaning of these loop AST generation types and the difference
8221 between the regular loop AST generation type and the isolate
8222 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8223 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8224 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8225 may return C<isl_ast_loop_error> if an error occurs.
8226 The AST build options govern how an AST is generated for
8227 the individual schedule dimensions during AST generation.
8228 See L</"AST Generation Options (Schedule Tree)">.
8229 The isolate option for the given node can be extracted from these
8230 AST build options using the function
8231 C<isl_schedule_node_band_get_ast_isolate_option>.
8233 #include <isl/schedule_node.h>
8234 __isl_give isl_set *
8235 isl_schedule_node_context_get_context(
8236 __isl_keep isl_schedule_node *node);
8238 #include <isl/schedule_node.h>
8239 __isl_give isl_union_set *
8240 isl_schedule_node_domain_get_domain(
8241 __isl_keep isl_schedule_node *node);
8243 #include <isl/schedule_node.h>
8244 __isl_give isl_union_map *
8245 isl_schedule_node_expansion_get_expansion(
8246 __isl_keep isl_schedule_node *node);
8247 __isl_give isl_union_pw_multi_aff *
8248 isl_schedule_node_expansion_get_contraction(
8249 __isl_keep isl_schedule_node *node);
8251 #include <isl/schedule_node.h>
8252 __isl_give isl_union_map *
8253 isl_schedule_node_extension_get_extension(
8254 __isl_keep isl_schedule_node *node);
8256 #include <isl/schedule_node.h>
8257 __isl_give isl_union_set *
8258 isl_schedule_node_filter_get_filter(
8259 __isl_keep isl_schedule_node *node);
8261 #include <isl/schedule_node.h>
8262 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8263 __isl_keep isl_schedule_node *node);
8265 #include <isl/schedule_node.h>
8266 __isl_give isl_id *isl_schedule_node_mark_get_id(
8267 __isl_keep isl_schedule_node *node);
8269 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8270 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8271 partial schedules related to the node.
8273 #include <isl/schedule_node.h>
8274 __isl_give isl_multi_union_pw_aff *
8275 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8276 __isl_keep isl_schedule_node *node);
8277 __isl_give isl_union_pw_multi_aff *
8278 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8279 __isl_keep isl_schedule_node *node);
8280 __isl_give isl_union_map *
8281 isl_schedule_node_get_prefix_schedule_union_map(
8282 __isl_keep isl_schedule_node *node);
8283 __isl_give isl_union_map *
8284 isl_schedule_node_get_prefix_schedule_relation(
8285 __isl_keep isl_schedule_node *node);
8286 __isl_give isl_union_map *
8287 isl_schedule_node_get_subtree_schedule_union_map(
8288 __isl_keep isl_schedule_node *node);
8290 In particular, the functions
8291 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8292 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8293 and C<isl_schedule_node_get_prefix_schedule_union_map>
8294 return a relative ordering on the domain elements that reach the given
8295 node determined by its ancestors.
8296 The function C<isl_schedule_node_get_prefix_schedule_relation>
8297 additionally includes the domain constraints in the result.
8298 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8299 returns a representation of the partial schedule defined by the
8300 subtree rooted at the given node.
8301 If the tree contains any expansion nodes, then the subtree schedule
8302 is formulated in terms of the expanded domain elements.
8303 The tree passed to functions returning a prefix schedule
8304 may only contain extension nodes if these would not affect
8305 the result of these functions. That is, if one of the ancestors
8306 is an extension node, then all of the domain elements that were
8307 added by the extension node need to have been filtered out
8308 by filter nodes between the extension node and the input node.
8309 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8310 may not contain in extension nodes in the selected subtree.
8312 The expansion/contraction defined by an entire subtree, combining
8313 the expansions/contractions
8314 on the expansion nodes in the subtree, can be obtained using
8315 the following functions.
8317 #include <isl/schedule_node.h>
8318 __isl_give isl_union_map *
8319 isl_schedule_node_get_subtree_expansion(
8320 __isl_keep isl_schedule_node *node);
8321 __isl_give isl_union_pw_multi_aff *
8322 isl_schedule_node_get_subtree_contraction(
8323 __isl_keep isl_schedule_node *node);
8325 The total number of outer band members of given node, i.e.,
8326 the shared output dimension of the maps in the result
8327 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8328 using the following function.
8330 #include <isl/schedule_node.h>
8331 int isl_schedule_node_get_schedule_depth(
8332 __isl_keep isl_schedule_node *node);
8334 The following functions return the elements that reach the given node
8335 or the union of universes in the spaces that contain these elements.
8337 #include <isl/schedule_node.h>
8338 __isl_give isl_union_set *
8339 isl_schedule_node_get_domain(
8340 __isl_keep isl_schedule_node *node);
8341 __isl_give isl_union_set *
8342 isl_schedule_node_get_universe_domain(
8343 __isl_keep isl_schedule_node *node);
8345 The input tree of C<isl_schedule_node_get_domain>
8346 may only contain extension nodes if these would not affect
8347 the result of this function. That is, if one of the ancestors
8348 is an extension node, then all of the domain elements that were
8349 added by the extension node need to have been filtered out
8350 by filter nodes between the extension node and the input node.
8352 The following functions can be used to introduce additional nodes
8353 in the schedule tree. The new node is introduced at the point
8354 in the tree where the C<isl_schedule_node> points to and
8355 the results points to the new node.
8357 #include <isl/schedule_node.h>
8358 __isl_give isl_schedule_node *
8359 isl_schedule_node_insert_partial_schedule(
8360 __isl_take isl_schedule_node *node,
8361 __isl_take isl_multi_union_pw_aff *schedule);
8363 This function inserts a new band node with (the greatest integer
8364 part of) the given partial schedule.
8365 The subtree rooted at the given node is assumed not to have
8368 #include <isl/schedule_node.h>
8369 __isl_give isl_schedule_node *
8370 isl_schedule_node_insert_context(
8371 __isl_take isl_schedule_node *node,
8372 __isl_take isl_set *context);
8374 This function inserts a new context node with the given context constraints.
8376 #include <isl/schedule_node.h>
8377 __isl_give isl_schedule_node *
8378 isl_schedule_node_insert_filter(
8379 __isl_take isl_schedule_node *node,
8380 __isl_take isl_union_set *filter);
8382 This function inserts a new filter node with the given filter.
8383 If the original node already pointed to a filter node, then the
8384 two filter nodes are merged into one.
8386 #include <isl/schedule_node.h>
8387 __isl_give isl_schedule_node *
8388 isl_schedule_node_insert_guard(
8389 __isl_take isl_schedule_node *node,
8390 __isl_take isl_set *guard);
8392 This function inserts a new guard node with the given guard constraints.
8394 #include <isl/schedule_node.h>
8395 __isl_give isl_schedule_node *
8396 isl_schedule_node_insert_mark(
8397 __isl_take isl_schedule_node *node,
8398 __isl_take isl_id *mark);
8400 This function inserts a new mark node with the give mark identifier.
8402 #include <isl/schedule_node.h>
8403 __isl_give isl_schedule_node *
8404 isl_schedule_node_insert_sequence(
8405 __isl_take isl_schedule_node *node,
8406 __isl_take isl_union_set_list *filters);
8407 __isl_give isl_schedule_node *
8408 isl_schedule_node_insert_set(
8409 __isl_take isl_schedule_node *node,
8410 __isl_take isl_union_set_list *filters);
8412 These functions insert a new sequence or set node with the given
8413 filters as children.
8415 #include <isl/schedule_node.h>
8416 __isl_give isl_schedule_node *isl_schedule_node_group(
8417 __isl_take isl_schedule_node *node,
8418 __isl_take isl_id *group_id);
8420 This function introduces an expansion node in between the current
8421 node and its parent that expands instances of a space with tuple
8422 identifier C<group_id> to the original domain elements that reach
8423 the node. The group instances are identified by the prefix schedule
8424 of those domain elements. The ancestors of the node are adjusted
8425 to refer to the group instances instead of the original domain
8426 elements. The return value points to the same node in the updated
8427 schedule tree as the input node, i.e., to the child of the newly
8428 introduced expansion node. Grouping instances of different statements
8429 ensures that they will be treated as a single statement by the
8430 AST generator up to the point of the expansion node.
8432 The following function can be used to flatten a nested
8435 #include <isl/schedule_node.h>
8436 __isl_give isl_schedule_node *
8437 isl_schedule_node_sequence_splice_child(
8438 __isl_take isl_schedule_node *node, int pos);
8440 That is, given a sequence node C<node> that has another sequence node
8441 in its child at position C<pos> (in particular, the child of that filter
8442 node is a sequence node), attach the children of that other sequence
8443 node as children of C<node>, replacing the original child at position
8446 The partial schedule of a band node can be scaled (down) or reduced using
8447 the following functions.
8449 #include <isl/schedule_node.h>
8450 __isl_give isl_schedule_node *
8451 isl_schedule_node_band_scale(
8452 __isl_take isl_schedule_node *node,
8453 __isl_take isl_multi_val *mv);
8454 __isl_give isl_schedule_node *
8455 isl_schedule_node_band_scale_down(
8456 __isl_take isl_schedule_node *node,
8457 __isl_take isl_multi_val *mv);
8458 __isl_give isl_schedule_node *
8459 isl_schedule_node_band_mod(
8460 __isl_take isl_schedule_node *node,
8461 __isl_take isl_multi_val *mv);
8463 The spaces of the two arguments need to match.
8464 After scaling, the partial schedule is replaced by its greatest
8465 integer part to ensure that the schedule remains integral.
8467 The partial schedule of a band node can be shifted by an
8468 C<isl_multi_union_pw_aff> with a domain that is a superset
8469 of the domain of the partial schedule using
8470 the following function.
8472 #include <isl/schedule_node.h>
8473 __isl_give isl_schedule_node *
8474 isl_schedule_node_band_shift(
8475 __isl_take isl_schedule_node *node,
8476 __isl_take isl_multi_union_pw_aff *shift);
8478 A band node can be tiled using the following function.
8480 #include <isl/schedule_node.h>
8481 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8482 __isl_take isl_schedule_node *node,
8483 __isl_take isl_multi_val *sizes);
8485 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8487 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8488 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8490 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8492 The C<isl_schedule_node_band_tile> function tiles
8493 the band using the given tile sizes inside its schedule.
8494 A new child band node is created to represent the point loops and it is
8495 inserted between the modified band and its children.
8496 The subtree rooted at the given node is assumed not to have
8498 The C<tile_scale_tile_loops> option specifies whether the tile
8499 loops iterators should be scaled by the tile sizes.
8500 If the C<tile_shift_point_loops> option is set, then the point loops
8501 are shifted to start at zero.
8503 A band node can be split into two nested band nodes
8504 using the following function.
8506 #include <isl/schedule_node.h>
8507 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8508 __isl_take isl_schedule_node *node, int pos);
8510 The resulting outer band node contains the first C<pos> dimensions of
8511 the schedule of C<node> while the inner band contains the remaining dimensions.
8512 The schedules of the two band nodes live in anonymous spaces.
8513 The loop AST generation type options and the isolate option
8514 are split over the the two band nodes.
8516 A band node can be moved down to the leaves of the subtree rooted
8517 at the band node using the following function.
8519 #include <isl/schedule_node.h>
8520 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8521 __isl_take isl_schedule_node *node);
8523 The subtree rooted at the given node is assumed not to have
8525 The result points to the node in the resulting tree that is in the same
8526 position as the node pointed to by C<node> in the original tree.
8528 #include <isl/schedule_node.h>
8529 __isl_give isl_schedule_node *
8530 isl_schedule_node_order_before(
8531 __isl_take isl_schedule_node *node,
8532 __isl_take isl_union_set *filter);
8533 __isl_give isl_schedule_node *
8534 isl_schedule_node_order_after(
8535 __isl_take isl_schedule_node *node,
8536 __isl_take isl_union_set *filter);
8538 These functions split the domain elements that reach C<node>
8539 into those that satisfy C<filter> and those that do not and
8540 arranges for the elements that do satisfy the filter to be
8541 executed before (in case of C<isl_schedule_node_order_before>)
8542 or after (in case of C<isl_schedule_node_order_after>)
8543 those that do not. The order is imposed by
8544 a sequence node, possibly reusing the grandparent of C<node>
8545 on two copies of the subtree attached to the original C<node>.
8546 Both copies are simplified with respect to their filter.
8548 Return a pointer to the copy of the subtree that does not
8549 satisfy C<filter>. If there is no such copy (because all
8550 reaching domain elements satisfy the filter), then return
8551 the original pointer.
8553 #include <isl/schedule_node.h>
8554 __isl_give isl_schedule_node *
8555 isl_schedule_node_graft_before(
8556 __isl_take isl_schedule_node *node,
8557 __isl_take isl_schedule_node *graft);
8558 __isl_give isl_schedule_node *
8559 isl_schedule_node_graft_after(
8560 __isl_take isl_schedule_node *node,
8561 __isl_take isl_schedule_node *graft);
8563 This function inserts the C<graft> tree into the tree containing C<node>
8564 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8565 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8566 The root node of C<graft>
8567 should be an extension node where the domain of the extension
8568 is the flat product of all outer band nodes of C<node>.
8569 The root node may also be a domain node.
8570 The elements of the domain or the range of the extension may not
8571 intersect with the domain elements that reach "node".
8572 The schedule tree of C<graft> may not be anchored.
8574 The schedule tree of C<node> is modified to include an extension node
8575 corresponding to the root node of C<graft> as a child of the original
8576 parent of C<node>. The original node that C<node> points to and the
8577 child of the root node of C<graft> are attached to this extension node
8578 through a sequence, with appropriate filters and with the child
8579 of C<graft> appearing before or after the original C<node>.
8581 If C<node> already appears inside a sequence that is the child of
8582 an extension node and if the spaces of the new domain elements
8583 do not overlap with those of the original domain elements,
8584 then that extension node is extended with the new extension
8585 rather than introducing a new segment of extension and sequence nodes.
8587 Return a pointer to the same node in the modified tree that
8588 C<node> pointed to in the original tree.
8590 A representation of the schedule node can be printed using
8592 #include <isl/schedule_node.h>
8593 __isl_give isl_printer *isl_printer_print_schedule_node(
8594 __isl_take isl_printer *p,
8595 __isl_keep isl_schedule_node *node);
8596 __isl_give char *isl_schedule_node_to_str(
8597 __isl_keep isl_schedule_node *node);
8599 C<isl_schedule_node_to_str> prints the schedule node in block format.
8601 =head2 Dependence Analysis
8603 C<isl> contains specialized functionality for performing
8604 array dataflow analysis. That is, given a I<sink> access relation
8605 and a collection of possible I<source> access relations,
8606 C<isl> can compute relations that describe
8607 for each iteration of the sink access, which iteration
8608 of which of the source access relations was the last
8609 to access the same data element before the given iteration
8611 The resulting dependence relations map source iterations
8612 to either the corresponding sink iterations or
8613 pairs of corresponding sink iterations and accessed data elements.
8614 To compute standard flow dependences, the sink should be
8615 a read, while the sources should be writes.
8616 If any of the source accesses are marked as being I<may>
8617 accesses, then there will be a dependence from the last
8618 I<must> access B<and> from any I<may> access that follows
8619 this last I<must> access.
8620 In particular, if I<all> sources are I<may> accesses,
8621 then memory based dependence analysis is performed.
8622 If, on the other hand, all sources are I<must> accesses,
8623 then value based dependence analysis is performed.
8625 =head3 High-level Interface
8627 A high-level interface to dependence analysis is provided
8628 by the following function.
8630 #include <isl/flow.h>
8631 __isl_give isl_union_flow *
8632 isl_union_access_info_compute_flow(
8633 __isl_take isl_union_access_info *access);
8635 The input C<isl_union_access_info> object describes the sink
8636 access relations, the source access relations and a schedule,
8637 while the output C<isl_union_flow> object describes
8638 the resulting dependence relations and the subsets of the
8639 sink relations for which no source was found.
8641 An C<isl_union_access_info> is created, modified, copied and freed using
8642 the following functions.
8644 #include <isl/flow.h>
8645 __isl_give isl_union_access_info *
8646 isl_union_access_info_from_sink(
8647 __isl_take isl_union_map *sink);
8648 __isl_give isl_union_access_info *
8649 isl_union_access_info_set_must_source(
8650 __isl_take isl_union_access_info *access,
8651 __isl_take isl_union_map *must_source);
8652 __isl_give isl_union_access_info *
8653 isl_union_access_info_set_may_source(
8654 __isl_take isl_union_access_info *access,
8655 __isl_take isl_union_map *may_source);
8656 __isl_give isl_union_access_info *
8657 isl_union_access_info_set_schedule(
8658 __isl_take isl_union_access_info *access,
8659 __isl_take isl_schedule *schedule);
8660 __isl_give isl_union_access_info *
8661 isl_union_access_info_set_schedule_map(
8662 __isl_take isl_union_access_info *access,
8663 __isl_take isl_union_map *schedule_map);
8664 __isl_give isl_union_access_info *
8665 isl_union_access_info_copy(
8666 __isl_keep isl_union_access_info *access);
8667 __isl_null isl_union_access_info *
8668 isl_union_access_info_free(
8669 __isl_take isl_union_access_info *access);
8671 The may sources set by C<isl_union_access_info_set_may_source>
8672 do not need to include the must sources set by
8673 C<isl_union_access_info_set_must_source> as a subset.
8674 The user is free not to call one (or both) of these functions,
8675 in which case the corresponding set is kept to its empty default.
8676 Similarly, the default schedule initialized by
8677 C<isl_union_access_info_from_sink> is empty.
8678 The current schedule is determined by the last call to either
8679 C<isl_union_access_info_set_schedule> or
8680 C<isl_union_access_info_set_schedule_map>.
8681 The domain of the schedule corresponds to the domains of
8682 the access relations. In particular, the domains of the access
8683 relations are effectively intersected with the domain of the schedule
8684 and only the resulting accesses are considered by the dependence analysis.
8686 A representation of the information contained in an object
8687 of type C<isl_union_access_info> can be obtained using
8689 #include <isl/flow.h>
8690 __isl_give isl_printer *
8691 isl_printer_print_union_access_info(
8692 __isl_take isl_printer *p,
8693 __isl_keep isl_union_access_info *access);
8694 __isl_give char *isl_union_access_info_to_str(
8695 __isl_keep isl_union_access_info *access);
8697 C<isl_union_access_info_to_str> prints the information in flow format.
8699 The output of C<isl_union_access_info_compute_flow> can be examined
8700 and freed using the following functions.
8702 #include <isl/flow.h>
8703 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8704 __isl_keep isl_union_flow *flow);
8705 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8706 __isl_keep isl_union_flow *flow);
8707 __isl_give isl_union_map *
8708 isl_union_flow_get_full_must_dependence(
8709 __isl_keep isl_union_flow *flow);
8710 __isl_give isl_union_map *
8711 isl_union_flow_get_full_may_dependence(
8712 __isl_keep isl_union_flow *flow);
8713 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8714 __isl_keep isl_union_flow *flow);
8715 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8716 __isl_keep isl_union_flow *flow);
8717 __isl_null isl_union_flow *isl_union_flow_free(
8718 __isl_take isl_union_flow *flow);
8720 The relation returned by C<isl_union_flow_get_must_dependence>
8721 relates domain elements of must sources to domain elements of the sink.
8722 The relation returned by C<isl_union_flow_get_may_dependence>
8723 relates domain elements of must or may sources to domain elements of the sink
8724 and includes the previous relation as a subset.
8725 The relation returned by C<isl_union_flow_get_full_must_dependence>
8726 relates domain elements of must sources to pairs of domain elements of the sink
8727 and accessed data elements.
8728 The relation returned by C<isl_union_flow_get_full_may_dependence>
8729 relates domain elements of must or may sources to pairs of
8730 domain elements of the sink and accessed data elements.
8731 This relation includes the previous relation as a subset.
8732 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8733 of the sink relation for which no dependences have been found.
8734 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8735 of the sink relation for which no definite dependences have been found.
8736 That is, it contains those sink access that do not contribute to any
8737 of the elements in the relation returned
8738 by C<isl_union_flow_get_must_dependence>.
8740 A representation of the information contained in an object
8741 of type C<isl_union_flow> can be obtained using
8743 #include <isl/flow.h>
8744 __isl_give isl_printer *isl_printer_print_union_flow(
8745 __isl_take isl_printer *p,
8746 __isl_keep isl_union_flow *flow);
8747 __isl_give char *isl_union_flow_to_str(
8748 __isl_keep isl_union_flow *flow);
8750 C<isl_union_flow_to_str> prints the information in flow format.
8752 =head3 Low-level Interface
8754 A lower-level interface is provided by the following functions.
8756 #include <isl/flow.h>
8758 typedef int (*isl_access_level_before)(void *first, void *second);
8760 __isl_give isl_access_info *isl_access_info_alloc(
8761 __isl_take isl_map *sink,
8762 void *sink_user, isl_access_level_before fn,
8764 __isl_give isl_access_info *isl_access_info_add_source(
8765 __isl_take isl_access_info *acc,
8766 __isl_take isl_map *source, int must,
8768 __isl_null isl_access_info *isl_access_info_free(
8769 __isl_take isl_access_info *acc);
8771 __isl_give isl_flow *isl_access_info_compute_flow(
8772 __isl_take isl_access_info *acc);
8774 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8775 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8776 void *dep_user, void *user),
8778 __isl_give isl_map *isl_flow_get_no_source(
8779 __isl_keep isl_flow *deps, int must);
8780 void isl_flow_free(__isl_take isl_flow *deps);
8782 The function C<isl_access_info_compute_flow> performs the actual
8783 dependence analysis. The other functions are used to construct
8784 the input for this function or to read off the output.
8786 The input is collected in an C<isl_access_info>, which can
8787 be created through a call to C<isl_access_info_alloc>.
8788 The arguments to this functions are the sink access relation
8789 C<sink>, a token C<sink_user> used to identify the sink
8790 access to the user, a callback function for specifying the
8791 relative order of source and sink accesses, and the number
8792 of source access relations that will be added.
8793 The callback function has type C<int (*)(void *first, void *second)>.
8794 The function is called with two user supplied tokens identifying
8795 either a source or the sink and it should return the shared nesting
8796 level and the relative order of the two accesses.
8797 In particular, let I<n> be the number of loops shared by
8798 the two accesses. If C<first> precedes C<second> textually,
8799 then the function should return I<2 * n + 1>; otherwise,
8800 it should return I<2 * n>.
8801 The sources can be added to the C<isl_access_info> by performing
8802 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8803 C<must> indicates whether the source is a I<must> access
8804 or a I<may> access. Note that a multi-valued access relation
8805 should only be marked I<must> if every iteration in the domain
8806 of the relation accesses I<all> elements in its image.
8807 The C<source_user> token is again used to identify
8808 the source access. The range of the source access relation
8809 C<source> should have the same dimension as the range
8810 of the sink access relation.
8811 The C<isl_access_info_free> function should usually not be
8812 called explicitly, because it is called implicitly by
8813 C<isl_access_info_compute_flow>.
8815 The result of the dependence analysis is collected in an
8816 C<isl_flow>. There may be elements of
8817 the sink access for which no preceding source access could be
8818 found or for which all preceding sources are I<may> accesses.
8819 The relations containing these elements can be obtained through
8820 calls to C<isl_flow_get_no_source>, the first with C<must> set
8821 and the second with C<must> unset.
8822 In the case of standard flow dependence analysis,
8823 with the sink a read and the sources I<must> writes,
8824 the first relation corresponds to the reads from uninitialized
8825 array elements and the second relation is empty.
8826 The actual flow dependences can be extracted using
8827 C<isl_flow_foreach>. This function will call the user-specified
8828 callback function C<fn> for each B<non-empty> dependence between
8829 a source and the sink. The callback function is called
8830 with four arguments, the actual flow dependence relation
8831 mapping source iterations to sink iterations, a boolean that
8832 indicates whether it is a I<must> or I<may> dependence, a token
8833 identifying the source and an additional C<void *> with value
8834 equal to the third argument of the C<isl_flow_foreach> call.
8835 A dependence is marked I<must> if it originates from a I<must>
8836 source and if it is not followed by any I<may> sources.
8838 After finishing with an C<isl_flow>, the user should call
8839 C<isl_flow_free> to free all associated memory.
8841 =head3 Interaction with the Low-level Interface
8843 During the dependence analysis, we frequently need to perform
8844 the following operation. Given a relation between sink iterations
8845 and potential source iterations from a particular source domain,
8846 what is the last potential source iteration corresponding to each
8847 sink iteration. It can sometimes be convenient to adjust
8848 the set of potential source iterations before or after each such operation.
8849 The prototypical example is fuzzy array dataflow analysis,
8850 where we need to analyze if, based on data-dependent constraints,
8851 the sink iteration can ever be executed without one or more of
8852 the corresponding potential source iterations being executed.
8853 If so, we can introduce extra parameters and select an unknown
8854 but fixed source iteration from the potential source iterations.
8855 To be able to perform such manipulations, C<isl> provides the following
8858 #include <isl/flow.h>
8860 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8861 __isl_keep isl_map *source_map,
8862 __isl_keep isl_set *sink, void *source_user,
8864 __isl_give isl_access_info *isl_access_info_set_restrict(
8865 __isl_take isl_access_info *acc,
8866 isl_access_restrict fn, void *user);
8868 The function C<isl_access_info_set_restrict> should be called
8869 before calling C<isl_access_info_compute_flow> and registers a callback function
8870 that will be called any time C<isl> is about to compute the last
8871 potential source. The first argument is the (reverse) proto-dependence,
8872 mapping sink iterations to potential source iterations.
8873 The second argument represents the sink iterations for which
8874 we want to compute the last source iteration.
8875 The third argument is the token corresponding to the source
8876 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8877 The callback is expected to return a restriction on either the input or
8878 the output of the operation computing the last potential source.
8879 If the input needs to be restricted then restrictions are needed
8880 for both the source and the sink iterations. The sink iterations
8881 and the potential source iterations will be intersected with these sets.
8882 If the output needs to be restricted then only a restriction on the source
8883 iterations is required.
8884 If any error occurs, the callback should return C<NULL>.
8885 An C<isl_restriction> object can be created, freed and inspected
8886 using the following functions.
8888 #include <isl/flow.h>
8890 __isl_give isl_restriction *isl_restriction_input(
8891 __isl_take isl_set *source_restr,
8892 __isl_take isl_set *sink_restr);
8893 __isl_give isl_restriction *isl_restriction_output(
8894 __isl_take isl_set *source_restr);
8895 __isl_give isl_restriction *isl_restriction_none(
8896 __isl_take isl_map *source_map);
8897 __isl_give isl_restriction *isl_restriction_empty(
8898 __isl_take isl_map *source_map);
8899 __isl_null isl_restriction *isl_restriction_free(
8900 __isl_take isl_restriction *restr);
8902 C<isl_restriction_none> and C<isl_restriction_empty> are special
8903 cases of C<isl_restriction_input>. C<isl_restriction_none>
8904 is essentially equivalent to
8906 isl_restriction_input(isl_set_universe(
8907 isl_space_range(isl_map_get_space(source_map))),
8909 isl_space_domain(isl_map_get_space(source_map))));
8911 whereas C<isl_restriction_empty> is essentially equivalent to
8913 isl_restriction_input(isl_set_empty(
8914 isl_space_range(isl_map_get_space(source_map))),
8916 isl_space_domain(isl_map_get_space(source_map))));
8920 #include <isl/schedule.h>
8921 __isl_give isl_schedule *
8922 isl_schedule_constraints_compute_schedule(
8923 __isl_take isl_schedule_constraints *sc);
8925 The function C<isl_schedule_constraints_compute_schedule> can be
8926 used to compute a schedule that satisfies the given schedule constraints.
8927 These schedule constraints include the iteration domain for which
8928 a schedule should be computed and dependences between pairs of
8929 iterations. In particular, these dependences include
8930 I<validity> dependences and I<proximity> dependences.
8931 By default, the algorithm used to construct the schedule is similar
8932 to that of C<Pluto>.
8933 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8935 The generated schedule respects all validity dependences.
8936 That is, all dependence distances over these dependences in the
8937 scheduled space are lexicographically positive.
8939 The default algorithm tries to ensure that the dependence distances
8940 over coincidence constraints are zero and to minimize the
8941 dependence distances over proximity dependences.
8942 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8943 for groups of domains where the dependence distances over validity
8944 dependences have only non-negative values.
8945 Note that when minimizing the maximal dependence distance
8946 over proximity dependences, a single affine expression in the parameters
8947 is constructed that bounds all dependence distances. If no such expression
8948 exists, then the algorithm will fail and resort to an alternative
8949 scheduling algorithm. In particular, this means that adding proximity
8950 dependences may eliminate valid solutions. A typical example where this
8951 phenomenon may occur is when some subset of the proximity dependences
8952 has no restriction on some parameter, forcing the coefficient of that
8953 parameter to be zero, while some other subset forces the dependence
8954 distance to depend on that parameter, requiring the same coefficient
8956 When using Feautrier's algorithm, the coincidence and proximity constraints
8957 are only taken into account during the extension to a
8958 full-dimensional schedule.
8960 An C<isl_schedule_constraints> object can be constructed
8961 and manipulated using the following functions.
8963 #include <isl/schedule.h>
8964 __isl_give isl_schedule_constraints *
8965 isl_schedule_constraints_copy(
8966 __isl_keep isl_schedule_constraints *sc);
8967 __isl_give isl_schedule_constraints *
8968 isl_schedule_constraints_on_domain(
8969 __isl_take isl_union_set *domain);
8970 __isl_give isl_schedule_constraints *
8971 isl_schedule_constraints_set_context(
8972 __isl_take isl_schedule_constraints *sc,
8973 __isl_take isl_set *context);
8974 __isl_give isl_schedule_constraints *
8975 isl_schedule_constraints_set_validity(
8976 __isl_take isl_schedule_constraints *sc,
8977 __isl_take isl_union_map *validity);
8978 __isl_give isl_schedule_constraints *
8979 isl_schedule_constraints_set_coincidence(
8980 __isl_take isl_schedule_constraints *sc,
8981 __isl_take isl_union_map *coincidence);
8982 __isl_give isl_schedule_constraints *
8983 isl_schedule_constraints_set_proximity(
8984 __isl_take isl_schedule_constraints *sc,
8985 __isl_take isl_union_map *proximity);
8986 __isl_give isl_schedule_constraints *
8987 isl_schedule_constraints_set_conditional_validity(
8988 __isl_take isl_schedule_constraints *sc,
8989 __isl_take isl_union_map *condition,
8990 __isl_take isl_union_map *validity);
8991 __isl_give isl_schedule_constraints *
8992 isl_schedule_constraints_apply(
8993 __isl_take isl_schedule_constraints *sc,
8994 __isl_take isl_union_map *umap);
8995 __isl_null isl_schedule_constraints *
8996 isl_schedule_constraints_free(
8997 __isl_take isl_schedule_constraints *sc);
8999 The initial C<isl_schedule_constraints> object created by
9000 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9001 That is, it has an empty set of dependences.
9002 The function C<isl_schedule_constraints_set_context> allows the user
9003 to specify additional constraints on the parameters that may
9004 be assumed to hold during the construction of the schedule.
9005 The function C<isl_schedule_constraints_set_validity> replaces the
9006 validity dependences, mapping domain elements I<i> to domain
9007 elements that should be scheduled after I<i>.
9008 The function C<isl_schedule_constraints_set_coincidence> replaces the
9009 coincidence dependences, mapping domain elements I<i> to domain
9010 elements that should be scheduled together with I<I>, if possible.
9011 The function C<isl_schedule_constraints_set_proximity> replaces the
9012 proximity dependences, mapping domain elements I<i> to domain
9013 elements that should be scheduled either before I<I>
9014 or as early as possible after I<i>.
9016 The function C<isl_schedule_constraints_set_conditional_validity>
9017 replaces the conditional validity constraints.
9018 A conditional validity constraint is only imposed when any of the corresponding
9019 conditions is satisfied, i.e., when any of them is non-zero.
9020 That is, the scheduler ensures that within each band if the dependence
9021 distances over the condition constraints are not all zero
9022 then all corresponding conditional validity constraints are respected.
9023 A conditional validity constraint corresponds to a condition
9024 if the two are adjacent, i.e., if the domain of one relation intersect
9025 the range of the other relation.
9026 The typical use case of conditional validity constraints is
9027 to allow order constraints between live ranges to be violated
9028 as long as the live ranges themselves are local to the band.
9029 To allow more fine-grained control over which conditions correspond
9030 to which conditional validity constraints, the domains and ranges
9031 of these relations may include I<tags>. That is, the domains and
9032 ranges of those relation may themselves be wrapped relations
9033 where the iteration domain appears in the domain of those wrapped relations
9034 and the range of the wrapped relations can be arbitrarily chosen
9035 by the user. Conditions and conditional validity constraints are only
9036 considered adjacent to each other if the entire wrapped relation matches.
9037 In particular, a relation with a tag will never be considered adjacent
9038 to a relation without a tag.
9040 The function C<isl_schedule_constraints_compute_schedule> takes
9041 schedule constraints that are defined on some set of domain elements
9042 and transforms them to schedule constraints on the elements
9043 to which these domain elements are mapped by the given transformation.
9045 An C<isl_schedule_constraints> object can be inspected
9046 using the following functions.
9048 #include <isl/schedule.h>
9049 __isl_give isl_union_set *
9050 isl_schedule_constraints_get_domain(
9051 __isl_keep isl_schedule_constraints *sc);
9052 __isl_give isl_union_map *
9053 isl_schedule_constraints_get_validity(
9054 __isl_keep isl_schedule_constraints *sc);
9055 __isl_give isl_union_map *
9056 isl_schedule_constraints_get_coincidence(
9057 __isl_keep isl_schedule_constraints *sc);
9058 __isl_give isl_union_map *
9059 isl_schedule_constraints_get_proximity(
9060 __isl_keep isl_schedule_constraints *sc);
9061 __isl_give isl_union_map *
9062 isl_schedule_constraints_get_conditional_validity(
9063 __isl_keep isl_schedule_constraints *sc);
9064 __isl_give isl_union_map *
9065 isl_schedule_constraints_get_conditional_validity_condition(
9066 __isl_keep isl_schedule_constraints *sc);
9068 The following function computes a schedule directly from
9069 an iteration domain and validity and proximity dependences
9070 and is implemented in terms of the functions described above.
9071 The use of C<isl_union_set_compute_schedule> is discouraged.
9073 #include <isl/schedule.h>
9074 __isl_give isl_schedule *isl_union_set_compute_schedule(
9075 __isl_take isl_union_set *domain,
9076 __isl_take isl_union_map *validity,
9077 __isl_take isl_union_map *proximity);
9079 The generated schedule represents a schedule tree.
9080 For more information on schedule trees, see
9081 L</"Schedule Trees">.
9085 #include <isl/schedule.h>
9086 isl_stat isl_options_set_schedule_max_coefficient(
9087 isl_ctx *ctx, int val);
9088 int isl_options_get_schedule_max_coefficient(
9090 isl_stat isl_options_set_schedule_max_constant_term(
9091 isl_ctx *ctx, int val);
9092 int isl_options_get_schedule_max_constant_term(
9094 isl_stat isl_options_set_schedule_serialize_sccs(
9095 isl_ctx *ctx, int val);
9096 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9097 isl_stat isl_options_set_schedule_whole_component(
9098 isl_ctx *ctx, int val);
9099 int isl_options_get_schedule_whole_component(
9101 isl_stat isl_options_set_schedule_maximize_band_depth(
9102 isl_ctx *ctx, int val);
9103 int isl_options_get_schedule_maximize_band_depth(
9105 isl_stat isl_options_set_schedule_maximize_coincidence(
9106 isl_ctx *ctx, int val);
9107 int isl_options_get_schedule_maximize_coincidence(
9109 isl_stat isl_options_set_schedule_outer_coincidence(
9110 isl_ctx *ctx, int val);
9111 int isl_options_get_schedule_outer_coincidence(
9113 isl_stat isl_options_set_schedule_split_scaled(
9114 isl_ctx *ctx, int val);
9115 int isl_options_get_schedule_split_scaled(
9117 isl_stat isl_options_set_schedule_treat_coalescing(
9118 isl_ctx *ctx, int val);
9119 int isl_options_get_schedule_treat_coalescing(
9121 isl_stat isl_options_set_schedule_algorithm(
9122 isl_ctx *ctx, int val);
9123 int isl_options_get_schedule_algorithm(
9125 isl_stat isl_options_set_schedule_separate_components(
9126 isl_ctx *ctx, int val);
9127 int isl_options_get_schedule_separate_components(
9132 =item * schedule_max_coefficient
9134 This option enforces that the coefficients for variable and parameter
9135 dimensions in the calculated schedule are not larger than the specified value.
9136 This option can significantly increase the speed of the scheduling calculation
9137 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9138 this option does not introduce bounds on the variable or parameter
9141 =item * schedule_max_constant_term
9143 This option enforces that the constant coefficients in the calculated schedule
9144 are not larger than the maximal constant term. This option can significantly
9145 increase the speed of the scheduling calculation and may also prevent fusing of
9146 unrelated dimensions. A value of -1 means that this option does not introduce
9147 bounds on the constant coefficients.
9149 =item * schedule_serialize_sccs
9151 If this option is set, then all strongly connected components
9152 in the dependence graph are serialized as soon as they are detected.
9153 This means in particular that instances of statements will only
9154 appear in the same band node if these statements belong
9155 to the same strongly connected component at the point where
9156 the band node is constructed.
9158 =item * schedule_whole_component
9160 If this option is set, then entire (weakly) connected
9161 components in the dependence graph are scheduled together
9163 Otherwise, each strongly connected component within
9164 such a weakly connected component is first scheduled separately
9165 and then combined with other strongly connected components.
9166 This option has no effect if C<schedule_serialize_sccs> is set.
9168 =item * schedule_maximize_band_depth
9170 If this option is set, then the scheduler tries to maximize
9171 the width of the bands. Wider bands give more possibilities for tiling.
9172 In particular, if the C<schedule_whole_component> option is set,
9173 then bands are split if this might result in wider bands.
9174 Otherwise, the effect of this option is to only allow
9175 strongly connected components to be combined if this does
9176 not reduce the width of the bands.
9177 Note that if the C<schedule_serialize_sccs> options is set, then
9178 the C<schedule_maximize_band_depth> option therefore has no effect.
9180 =item * schedule_maximize_coincidence
9182 This option is only effective if the C<schedule_whole_component>
9183 option is turned off.
9184 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9185 strongly connected components are only combined with each other
9186 if this does not reduce the number of coincident band members.
9188 =item * schedule_outer_coincidence
9190 If this option is set, then we try to construct schedules
9191 where the outermost scheduling dimension in each band
9192 satisfies the coincidence constraints.
9194 =item * schedule_algorithm
9196 Selects the scheduling algorithm to be used.
9197 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9198 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9200 =item * schedule_split_scaled
9202 If this option is set, then we try to construct schedules in which the
9203 constant term is split off from the linear part if the linear parts of
9204 the scheduling rows for all nodes in the graphs have a common non-trivial
9206 The constant term is then placed in a separate band and the linear
9208 This option is only effective when the Feautrier style scheduler is
9209 being used, either as the main scheduler or as a fallback for the
9210 Pluto-like scheduler.
9212 =item * schedule_treat_coalescing
9214 If this option is set, then the scheduler will try and avoid
9215 producing schedules that perform loop coalescing.
9216 In particular, for the Pluto-like scheduler, this option places
9217 bounds on the schedule coefficients based on the sizes of the instance sets.
9218 For the Feautrier style scheduler, this option detects potentially
9219 coalescing schedules and then tries to adjust the schedule to avoid
9222 =item * schedule_separate_components
9224 If this option is set then the function C<isl_schedule_get_map>
9225 will treat set nodes in the same way as sequence nodes.
9229 =head2 AST Generation
9231 This section describes the C<isl> functionality for generating
9232 ASTs that visit all the elements
9233 in a domain in an order specified by a schedule tree or
9235 In case the schedule given as a C<isl_union_map>, an AST is generated
9236 that visits all the elements in the domain of the C<isl_union_map>
9237 according to the lexicographic order of the corresponding image
9238 element(s). If the range of the C<isl_union_map> consists of
9239 elements in more than one space, then each of these spaces is handled
9240 separately in an arbitrary order.
9241 It should be noted that the schedule tree or the image elements
9242 in a schedule map only specify the I<order>
9243 in which the corresponding domain elements should be visited.
9244 No direct relation between the partial schedule values
9245 or the image elements on the one hand and the loop iterators
9246 in the generated AST on the other hand should be assumed.
9248 Each AST is generated within a build. The initial build
9249 simply specifies the constraints on the parameters (if any)
9250 and can be created, inspected, copied and freed using the following functions.
9252 #include <isl/ast_build.h>
9253 __isl_give isl_ast_build *isl_ast_build_alloc(
9255 __isl_give isl_ast_build *isl_ast_build_from_context(
9256 __isl_take isl_set *set);
9257 __isl_give isl_ast_build *isl_ast_build_copy(
9258 __isl_keep isl_ast_build *build);
9259 __isl_null isl_ast_build *isl_ast_build_free(
9260 __isl_take isl_ast_build *build);
9262 The C<set> argument is usually a parameter set with zero or more parameters.
9263 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9264 this set is required to be a parameter set.
9265 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9266 specify any parameter constraints.
9267 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9268 and L</"Fine-grained Control over AST Generation">.
9269 Finally, the AST itself can be constructed using one of the following
9272 #include <isl/ast_build.h>
9273 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9274 __isl_keep isl_ast_build *build,
9275 __isl_take isl_schedule *schedule);
9276 __isl_give isl_ast_node *
9277 isl_ast_build_node_from_schedule_map(
9278 __isl_keep isl_ast_build *build,
9279 __isl_take isl_union_map *schedule);
9281 =head3 Inspecting the AST
9283 The basic properties of an AST node can be obtained as follows.
9285 #include <isl/ast.h>
9286 enum isl_ast_node_type isl_ast_node_get_type(
9287 __isl_keep isl_ast_node *node);
9289 The type of an AST node is one of
9290 C<isl_ast_node_for>,
9292 C<isl_ast_node_block>,
9293 C<isl_ast_node_mark> or
9294 C<isl_ast_node_user>.
9295 An C<isl_ast_node_for> represents a for node.
9296 An C<isl_ast_node_if> represents an if node.
9297 An C<isl_ast_node_block> represents a compound node.
9298 An C<isl_ast_node_mark> introduces a mark in the AST.
9299 An C<isl_ast_node_user> represents an expression statement.
9300 An expression statement typically corresponds to a domain element, i.e.,
9301 one of the elements that is visited by the AST.
9303 Each type of node has its own additional properties.
9305 #include <isl/ast.h>
9306 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9307 __isl_keep isl_ast_node *node);
9308 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9309 __isl_keep isl_ast_node *node);
9310 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9311 __isl_keep isl_ast_node *node);
9312 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9313 __isl_keep isl_ast_node *node);
9314 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9315 __isl_keep isl_ast_node *node);
9316 isl_bool isl_ast_node_for_is_degenerate(
9317 __isl_keep isl_ast_node *node);
9319 An C<isl_ast_for> is considered degenerate if it is known to execute
9322 #include <isl/ast.h>
9323 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9324 __isl_keep isl_ast_node *node);
9325 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9326 __isl_keep isl_ast_node *node);
9327 isl_bool isl_ast_node_if_has_else(
9328 __isl_keep isl_ast_node *node);
9329 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9330 __isl_keep isl_ast_node *node);
9332 __isl_give isl_ast_node_list *
9333 isl_ast_node_block_get_children(
9334 __isl_keep isl_ast_node *node);
9336 __isl_give isl_id *isl_ast_node_mark_get_id(
9337 __isl_keep isl_ast_node *node);
9338 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9339 __isl_keep isl_ast_node *node);
9341 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9342 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9344 #include <isl/ast.h>
9345 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9346 __isl_keep isl_ast_node *node);
9348 All descendants of a specific node in the AST (including the node itself)
9350 in depth-first pre-order using the following function.
9352 #include <isl/ast.h>
9353 isl_stat isl_ast_node_foreach_descendant_top_down(
9354 __isl_keep isl_ast_node *node,
9355 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9356 void *user), void *user);
9358 The callback function should return C<isl_bool_true> if the children
9359 of the given node should be visited and C<isl_bool_false> if they should not.
9360 It should return C<isl_bool_error> in case of failure, in which case
9361 the entire traversal is aborted.
9363 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9364 the following functions.
9366 #include <isl/ast.h>
9367 enum isl_ast_expr_type isl_ast_expr_get_type(
9368 __isl_keep isl_ast_expr *expr);
9370 The type of an AST expression is one of
9372 C<isl_ast_expr_id> or
9373 C<isl_ast_expr_int>.
9374 An C<isl_ast_expr_op> represents the result of an operation.
9375 An C<isl_ast_expr_id> represents an identifier.
9376 An C<isl_ast_expr_int> represents an integer value.
9378 Each type of expression has its own additional properties.
9380 #include <isl/ast.h>
9381 enum isl_ast_op_type isl_ast_expr_get_op_type(
9382 __isl_keep isl_ast_expr *expr);
9383 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9384 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9385 __isl_keep isl_ast_expr *expr, int pos);
9386 isl_stat isl_ast_expr_foreach_ast_op_type(
9387 __isl_keep isl_ast_expr *expr,
9388 isl_stat (*fn)(enum isl_ast_op_type type,
9389 void *user), void *user);
9390 isl_stat isl_ast_node_foreach_ast_op_type(
9391 __isl_keep isl_ast_node *node,
9392 isl_stat (*fn)(enum isl_ast_op_type type,
9393 void *user), void *user);
9395 C<isl_ast_expr_get_op_type> returns the type of the operation
9396 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9397 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9399 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9400 C<isl_ast_op_type> that appears in C<expr>.
9401 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9402 C<isl_ast_op_type> that appears in C<node>.
9403 The operation type is one of the following.
9407 =item C<isl_ast_op_and>
9409 Logical I<and> of two arguments.
9410 Both arguments can be evaluated.
9412 =item C<isl_ast_op_and_then>
9414 Logical I<and> of two arguments.
9415 The second argument can only be evaluated if the first evaluates to true.
9417 =item C<isl_ast_op_or>
9419 Logical I<or> of two arguments.
9420 Both arguments can be evaluated.
9422 =item C<isl_ast_op_or_else>
9424 Logical I<or> of two arguments.
9425 The second argument can only be evaluated if the first evaluates to false.
9427 =item C<isl_ast_op_max>
9429 Maximum of two or more arguments.
9431 =item C<isl_ast_op_min>
9433 Minimum of two or more arguments.
9435 =item C<isl_ast_op_minus>
9439 =item C<isl_ast_op_add>
9441 Sum of two arguments.
9443 =item C<isl_ast_op_sub>
9445 Difference of two arguments.
9447 =item C<isl_ast_op_mul>
9449 Product of two arguments.
9451 =item C<isl_ast_op_div>
9453 Exact division. That is, the result is known to be an integer.
9455 =item C<isl_ast_op_fdiv_q>
9457 Result of integer division, rounded towards negative
9460 =item C<isl_ast_op_pdiv_q>
9462 Result of integer division, where dividend is known to be non-negative.
9464 =item C<isl_ast_op_pdiv_r>
9466 Remainder of integer division, where dividend is known to be non-negative.
9468 =item C<isl_ast_op_zdiv_r>
9470 Equal to zero iff the remainder on integer division is zero.
9472 =item C<isl_ast_op_cond>
9474 Conditional operator defined on three arguments.
9475 If the first argument evaluates to true, then the result
9476 is equal to the second argument. Otherwise, the result
9477 is equal to the third argument.
9478 The second and third argument may only be evaluated if
9479 the first argument evaluates to true and false, respectively.
9480 Corresponds to C<a ? b : c> in C.
9482 =item C<isl_ast_op_select>
9484 Conditional operator defined on three arguments.
9485 If the first argument evaluates to true, then the result
9486 is equal to the second argument. Otherwise, the result
9487 is equal to the third argument.
9488 The second and third argument may be evaluated independently
9489 of the value of the first argument.
9490 Corresponds to C<a * b + (1 - a) * c> in C.
9492 =item C<isl_ast_op_eq>
9496 =item C<isl_ast_op_le>
9498 Less than or equal relation.
9500 =item C<isl_ast_op_lt>
9504 =item C<isl_ast_op_ge>
9506 Greater than or equal relation.
9508 =item C<isl_ast_op_gt>
9510 Greater than relation.
9512 =item C<isl_ast_op_call>
9515 The number of arguments of the C<isl_ast_expr> is one more than
9516 the number of arguments in the function call, the first argument
9517 representing the function being called.
9519 =item C<isl_ast_op_access>
9522 The number of arguments of the C<isl_ast_expr> is one more than
9523 the number of index expressions in the array access, the first argument
9524 representing the array being accessed.
9526 =item C<isl_ast_op_member>
9529 This operation has two arguments, a structure and the name of
9530 the member of the structure being accessed.
9534 #include <isl/ast.h>
9535 __isl_give isl_id *isl_ast_expr_get_id(
9536 __isl_keep isl_ast_expr *expr);
9538 Return the identifier represented by the AST expression.
9540 #include <isl/ast.h>
9541 __isl_give isl_val *isl_ast_expr_get_val(
9542 __isl_keep isl_ast_expr *expr);
9544 Return the integer represented by the AST expression.
9546 =head3 Properties of ASTs
9548 #include <isl/ast.h>
9549 isl_bool isl_ast_expr_is_equal(
9550 __isl_keep isl_ast_expr *expr1,
9551 __isl_keep isl_ast_expr *expr2);
9553 Check if two C<isl_ast_expr>s are equal to each other.
9555 =head3 Manipulating and printing the AST
9557 AST nodes can be copied and freed using the following functions.
9559 #include <isl/ast.h>
9560 __isl_give isl_ast_node *isl_ast_node_copy(
9561 __isl_keep isl_ast_node *node);
9562 __isl_null isl_ast_node *isl_ast_node_free(
9563 __isl_take isl_ast_node *node);
9565 AST expressions can be copied and freed using the following functions.
9567 #include <isl/ast.h>
9568 __isl_give isl_ast_expr *isl_ast_expr_copy(
9569 __isl_keep isl_ast_expr *expr);
9570 __isl_null isl_ast_expr *isl_ast_expr_free(
9571 __isl_take isl_ast_expr *expr);
9573 New AST expressions can be created either directly or within
9574 the context of an C<isl_ast_build>.
9576 #include <isl/ast.h>
9577 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9578 __isl_take isl_val *v);
9579 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9580 __isl_take isl_id *id);
9581 __isl_give isl_ast_expr *isl_ast_expr_neg(
9582 __isl_take isl_ast_expr *expr);
9583 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9584 __isl_take isl_ast_expr *expr);
9585 __isl_give isl_ast_expr *isl_ast_expr_add(
9586 __isl_take isl_ast_expr *expr1,
9587 __isl_take isl_ast_expr *expr2);
9588 __isl_give isl_ast_expr *isl_ast_expr_sub(
9589 __isl_take isl_ast_expr *expr1,
9590 __isl_take isl_ast_expr *expr2);
9591 __isl_give isl_ast_expr *isl_ast_expr_mul(
9592 __isl_take isl_ast_expr *expr1,
9593 __isl_take isl_ast_expr *expr2);
9594 __isl_give isl_ast_expr *isl_ast_expr_div(
9595 __isl_take isl_ast_expr *expr1,
9596 __isl_take isl_ast_expr *expr2);
9597 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9598 __isl_take isl_ast_expr *expr1,
9599 __isl_take isl_ast_expr *expr2);
9600 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9601 __isl_take isl_ast_expr *expr1,
9602 __isl_take isl_ast_expr *expr2);
9603 __isl_give isl_ast_expr *isl_ast_expr_and(
9604 __isl_take isl_ast_expr *expr1,
9605 __isl_take isl_ast_expr *expr2)
9606 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9607 __isl_take isl_ast_expr *expr1,
9608 __isl_take isl_ast_expr *expr2)
9609 __isl_give isl_ast_expr *isl_ast_expr_or(
9610 __isl_take isl_ast_expr *expr1,
9611 __isl_take isl_ast_expr *expr2)
9612 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9613 __isl_take isl_ast_expr *expr1,
9614 __isl_take isl_ast_expr *expr2)
9615 __isl_give isl_ast_expr *isl_ast_expr_eq(
9616 __isl_take isl_ast_expr *expr1,
9617 __isl_take isl_ast_expr *expr2);
9618 __isl_give isl_ast_expr *isl_ast_expr_le(
9619 __isl_take isl_ast_expr *expr1,
9620 __isl_take isl_ast_expr *expr2);
9621 __isl_give isl_ast_expr *isl_ast_expr_lt(
9622 __isl_take isl_ast_expr *expr1,
9623 __isl_take isl_ast_expr *expr2);
9624 __isl_give isl_ast_expr *isl_ast_expr_ge(
9625 __isl_take isl_ast_expr *expr1,
9626 __isl_take isl_ast_expr *expr2);
9627 __isl_give isl_ast_expr *isl_ast_expr_gt(
9628 __isl_take isl_ast_expr *expr1,
9629 __isl_take isl_ast_expr *expr2);
9630 __isl_give isl_ast_expr *isl_ast_expr_access(
9631 __isl_take isl_ast_expr *array,
9632 __isl_take isl_ast_expr_list *indices);
9633 __isl_give isl_ast_expr *isl_ast_expr_call(
9634 __isl_take isl_ast_expr *function,
9635 __isl_take isl_ast_expr_list *arguments);
9637 The function C<isl_ast_expr_address_of> can be applied to an
9638 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9639 to represent the address of the C<isl_ast_expr_access>. The function
9640 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9641 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9643 #include <isl/ast_build.h>
9644 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9645 __isl_keep isl_ast_build *build,
9646 __isl_take isl_set *set);
9647 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9648 __isl_keep isl_ast_build *build,
9649 __isl_take isl_pw_aff *pa);
9650 __isl_give isl_ast_expr *
9651 isl_ast_build_access_from_pw_multi_aff(
9652 __isl_keep isl_ast_build *build,
9653 __isl_take isl_pw_multi_aff *pma);
9654 __isl_give isl_ast_expr *
9655 isl_ast_build_access_from_multi_pw_aff(
9656 __isl_keep isl_ast_build *build,
9657 __isl_take isl_multi_pw_aff *mpa);
9658 __isl_give isl_ast_expr *
9659 isl_ast_build_call_from_pw_multi_aff(
9660 __isl_keep isl_ast_build *build,
9661 __isl_take isl_pw_multi_aff *pma);
9662 __isl_give isl_ast_expr *
9663 isl_ast_build_call_from_multi_pw_aff(
9664 __isl_keep isl_ast_build *build,
9665 __isl_take isl_multi_pw_aff *mpa);
9668 the domains of C<pa>, C<mpa> and C<pma> should correspond
9669 to the schedule space of C<build>.
9670 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9671 the function being called.
9672 If the accessed space is a nested relation, then it is taken
9673 to represent an access of the member specified by the range
9674 of this nested relation of the structure specified by the domain
9675 of the nested relation.
9677 The following functions can be used to modify an C<isl_ast_expr>.
9679 #include <isl/ast.h>
9680 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9681 __isl_take isl_ast_expr *expr, int pos,
9682 __isl_take isl_ast_expr *arg);
9684 Replace the argument of C<expr> at position C<pos> by C<arg>.
9686 #include <isl/ast.h>
9687 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9688 __isl_take isl_ast_expr *expr,
9689 __isl_take isl_id_to_ast_expr *id2expr);
9691 The function C<isl_ast_expr_substitute_ids> replaces the
9692 subexpressions of C<expr> of type C<isl_ast_expr_id>
9693 by the corresponding expression in C<id2expr>, if there is any.
9696 User specified data can be attached to an C<isl_ast_node> and obtained
9697 from the same C<isl_ast_node> using the following functions.
9699 #include <isl/ast.h>
9700 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9701 __isl_take isl_ast_node *node,
9702 __isl_take isl_id *annotation);
9703 __isl_give isl_id *isl_ast_node_get_annotation(
9704 __isl_keep isl_ast_node *node);
9706 Basic printing can be performed using the following functions.
9708 #include <isl/ast.h>
9709 __isl_give isl_printer *isl_printer_print_ast_expr(
9710 __isl_take isl_printer *p,
9711 __isl_keep isl_ast_expr *expr);
9712 __isl_give isl_printer *isl_printer_print_ast_node(
9713 __isl_take isl_printer *p,
9714 __isl_keep isl_ast_node *node);
9715 __isl_give char *isl_ast_expr_to_str(
9716 __isl_keep isl_ast_expr *expr);
9717 __isl_give char *isl_ast_expr_to_C_str(
9718 __isl_keep isl_ast_expr *expr);
9719 __isl_give char *isl_ast_node_to_C_str(
9720 __isl_keep isl_ast_node *node);
9722 The functions C<isl_ast_expr_to_C_str> and
9723 C<isl_ast_node_to_C_str> are convenience functions
9724 that return a string representation of the input in C format.
9726 More advanced printing can be performed using the following functions.
9728 #include <isl/ast.h>
9729 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9730 __isl_take isl_printer *p,
9731 enum isl_ast_op_type type,
9732 __isl_keep const char *name);
9733 isl_stat isl_options_set_ast_print_macro_once(
9734 isl_ctx *ctx, int val);
9735 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9736 __isl_give isl_printer *isl_ast_op_type_print_macro(
9737 enum isl_ast_op_type type,
9738 __isl_take isl_printer *p);
9739 __isl_give isl_printer *isl_ast_expr_print_macros(
9740 __isl_keep isl_ast_expr *expr,
9741 __isl_take isl_printer *p);
9742 __isl_give isl_printer *isl_ast_node_print_macros(
9743 __isl_keep isl_ast_node *node,
9744 __isl_take isl_printer *p);
9745 __isl_give isl_printer *isl_ast_node_print(
9746 __isl_keep isl_ast_node *node,
9747 __isl_take isl_printer *p,
9748 __isl_take isl_ast_print_options *options);
9749 __isl_give isl_printer *isl_ast_node_for_print(
9750 __isl_keep isl_ast_node *node,
9751 __isl_take isl_printer *p,
9752 __isl_take isl_ast_print_options *options);
9753 __isl_give isl_printer *isl_ast_node_if_print(
9754 __isl_keep isl_ast_node *node,
9755 __isl_take isl_printer *p,
9756 __isl_take isl_ast_print_options *options);
9758 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9759 C<isl> may print out an AST that makes use of macros such
9760 as C<floord>, C<min> and C<max>.
9761 The names of these macros may be modified by a call
9762 to C<isl_ast_op_type_set_print_name>. The user-specified
9763 names are associated to the printer object.
9764 C<isl_ast_op_type_print_macro> prints out the macro
9765 corresponding to a specific C<isl_ast_op_type>.
9766 If the print-macro-once option is set, then a given macro definition
9767 is only printed once to any given printer object.
9768 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9769 for subexpressions where these macros would be used and prints
9770 out the required macro definitions.
9771 Essentially, C<isl_ast_expr_print_macros> calls
9772 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9773 as function argument.
9774 C<isl_ast_node_print_macros> does the same
9775 for expressions in its C<isl_ast_node> argument.
9776 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9777 C<isl_ast_node_if_print> print an C<isl_ast_node>
9778 in C<ISL_FORMAT_C>, but allow for some extra control
9779 through an C<isl_ast_print_options> object.
9780 This object can be created using the following functions.
9782 #include <isl/ast.h>
9783 __isl_give isl_ast_print_options *
9784 isl_ast_print_options_alloc(isl_ctx *ctx);
9785 __isl_give isl_ast_print_options *
9786 isl_ast_print_options_copy(
9787 __isl_keep isl_ast_print_options *options);
9788 __isl_null isl_ast_print_options *
9789 isl_ast_print_options_free(
9790 __isl_take isl_ast_print_options *options);
9792 __isl_give isl_ast_print_options *
9793 isl_ast_print_options_set_print_user(
9794 __isl_take isl_ast_print_options *options,
9795 __isl_give isl_printer *(*print_user)(
9796 __isl_take isl_printer *p,
9797 __isl_take isl_ast_print_options *options,
9798 __isl_keep isl_ast_node *node, void *user),
9800 __isl_give isl_ast_print_options *
9801 isl_ast_print_options_set_print_for(
9802 __isl_take isl_ast_print_options *options,
9803 __isl_give isl_printer *(*print_for)(
9804 __isl_take isl_printer *p,
9805 __isl_take isl_ast_print_options *options,
9806 __isl_keep isl_ast_node *node, void *user),
9809 The callback set by C<isl_ast_print_options_set_print_user>
9810 is called whenever a node of type C<isl_ast_node_user> needs to
9812 The callback set by C<isl_ast_print_options_set_print_for>
9813 is called whenever a node of type C<isl_ast_node_for> needs to
9815 Note that C<isl_ast_node_for_print> will I<not> call the
9816 callback set by C<isl_ast_print_options_set_print_for> on the node
9817 on which C<isl_ast_node_for_print> is called, but only on nested
9818 nodes of type C<isl_ast_node_for>. It is therefore safe to
9819 call C<isl_ast_node_for_print> from within the callback set by
9820 C<isl_ast_print_options_set_print_for>.
9822 The following option determines the type to be used for iterators
9823 while printing the AST.
9825 isl_stat isl_options_set_ast_iterator_type(
9826 isl_ctx *ctx, const char *val);
9827 const char *isl_options_get_ast_iterator_type(
9830 The AST printer only prints body nodes as blocks if these
9831 blocks cannot be safely omitted.
9832 For example, a C<for> node with one body node will not be
9833 surrounded with braces in C<ISL_FORMAT_C>.
9834 A block will always be printed by setting the following option.
9836 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9838 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9842 #include <isl/ast_build.h>
9843 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9844 isl_ctx *ctx, int val);
9845 int isl_options_get_ast_build_atomic_upper_bound(
9847 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9849 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9850 isl_stat isl_options_set_ast_build_detect_min_max(
9851 isl_ctx *ctx, int val);
9852 int isl_options_get_ast_build_detect_min_max(
9854 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9855 isl_ctx *ctx, int val);
9856 int isl_options_get_ast_build_exploit_nested_bounds(
9858 isl_stat isl_options_set_ast_build_group_coscheduled(
9859 isl_ctx *ctx, int val);
9860 int isl_options_get_ast_build_group_coscheduled(
9862 isl_stat isl_options_set_ast_build_scale_strides(
9863 isl_ctx *ctx, int val);
9864 int isl_options_get_ast_build_scale_strides(
9866 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9868 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9869 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9871 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9875 =item * ast_build_atomic_upper_bound
9877 Generate loop upper bounds that consist of the current loop iterator,
9878 an operator and an expression not involving the iterator.
9879 If this option is not set, then the current loop iterator may appear
9880 several times in the upper bound.
9881 For example, when this option is turned off, AST generation
9884 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9888 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9891 When the option is turned on, the following AST is generated
9893 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9896 =item * ast_build_prefer_pdiv
9898 If this option is turned off, then the AST generation will
9899 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9900 operators, but no C<isl_ast_op_pdiv_q> or
9901 C<isl_ast_op_pdiv_r> operators.
9902 If this option is turned on, then C<isl> will try to convert
9903 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9904 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9906 =item * ast_build_detect_min_max
9908 If this option is turned on, then C<isl> will try and detect
9909 min or max-expressions when building AST expressions from
9910 piecewise affine expressions.
9912 =item * ast_build_exploit_nested_bounds
9914 Simplify conditions based on bounds of nested for loops.
9915 In particular, remove conditions that are implied by the fact
9916 that one or more nested loops have at least one iteration,
9917 meaning that the upper bound is at least as large as the lower bound.
9918 For example, when this option is turned off, AST generation
9921 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
9927 for (int c0 = 0; c0 <= N; c0 += 1)
9928 for (int c1 = 0; c1 <= M; c1 += 1)
9931 When the option is turned on, the following AST is generated
9933 for (int c0 = 0; c0 <= N; c0 += 1)
9934 for (int c1 = 0; c1 <= M; c1 += 1)
9937 =item * ast_build_group_coscheduled
9939 If two domain elements are assigned the same schedule point, then
9940 they may be executed in any order and they may even appear in different
9941 loops. If this options is set, then the AST generator will make
9942 sure that coscheduled domain elements do not appear in separate parts
9943 of the AST. This is useful in case of nested AST generation
9944 if the outer AST generation is given only part of a schedule
9945 and the inner AST generation should handle the domains that are
9946 coscheduled by this initial part of the schedule together.
9947 For example if an AST is generated for a schedule
9949 { A[i] -> [0]; B[i] -> [0] }
9951 then the C<isl_ast_build_set_create_leaf> callback described
9952 below may get called twice, once for each domain.
9953 Setting this option ensures that the callback is only called once
9954 on both domains together.
9956 =item * ast_build_separation_bounds
9958 This option specifies which bounds to use during separation.
9959 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
9960 then all (possibly implicit) bounds on the current dimension will
9961 be used during separation.
9962 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
9963 then only those bounds that are explicitly available will
9964 be used during separation.
9966 =item * ast_build_scale_strides
9968 This option specifies whether the AST generator is allowed
9969 to scale down iterators of strided loops.
9971 =item * ast_build_allow_else
9973 This option specifies whether the AST generator is allowed
9974 to construct if statements with else branches.
9976 =item * ast_build_allow_or
9978 This option specifies whether the AST generator is allowed
9979 to construct if conditions with disjunctions.
9983 =head3 AST Generation Options (Schedule Tree)
9985 In case of AST construction from a schedule tree, the options
9986 that control how an AST is created from the individual schedule
9987 dimensions are stored in the band nodes of the tree
9988 (see L</"Schedule Trees">).
9990 In particular, a schedule dimension can be handled in four
9991 different ways, atomic, separate, unroll or the default.
9992 This loop AST generation type can be set using
9993 C<isl_schedule_node_band_member_set_ast_loop_type>.
9995 the first three can be selected by including a one-dimensional
9996 element with as value the position of the schedule dimension
9997 within the band and as name one of C<atomic>, C<separate>
9998 or C<unroll> in the options
9999 set by C<isl_schedule_node_band_set_ast_build_options>.
10000 Only one of these three may be specified for
10001 any given schedule dimension within a band node.
10002 If none of these is specified, then the default
10003 is used. The meaning of the options is as follows.
10009 When this option is specified, the AST generator will make
10010 sure that a given domains space only appears in a single
10011 loop at the specified level.
10013 For example, for the schedule tree
10015 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10017 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10018 options: "{ atomic[x] }"
10020 the following AST will be generated
10022 for (int c0 = 0; c0 <= 10; c0 += 1) {
10029 On the other hand, for the schedule tree
10031 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10033 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10034 options: "{ separate[x] }"
10036 the following AST will be generated
10040 for (int c0 = 1; c0 <= 9; c0 += 1) {
10047 If neither C<atomic> nor C<separate> is specified, then the AST generator
10048 may produce either of these two results or some intermediate form.
10052 When this option is specified, the AST generator will
10053 split the domain of the specified schedule dimension
10054 into pieces with a fixed set of statements for which
10055 instances need to be executed by the iterations in
10056 the schedule domain part. This option tends to avoid
10057 the generation of guards inside the corresponding loops.
10058 See also the C<atomic> option.
10062 When this option is specified, the AST generator will
10063 I<completely> unroll the corresponding schedule dimension.
10064 It is the responsibility of the user to ensure that such
10065 unrolling is possible.
10066 To obtain a partial unrolling, the user should apply an additional
10067 strip-mining to the schedule and fully unroll the inner schedule
10072 The C<isolate> option is a bit more involved. It allows the user
10073 to isolate a range of schedule dimension values from smaller and
10074 greater values. Additionally, the user may specify a different
10075 atomic/separate/unroll choice for the isolated part and the remaining
10076 parts. The typical use case of the C<isolate> option is to isolate
10077 full tiles from partial tiles.
10078 The part that needs to be isolated may depend on outer schedule dimensions.
10079 The option therefore needs to be able to reference those outer schedule
10080 dimensions. In particular, the space of the C<isolate> option is that
10081 of a wrapped map with as domain the flat product of all outer band nodes
10082 and as range the space of the current band node.
10083 The atomic/separate/unroll choice for the isolated part is determined
10084 by an option that lives in an unnamed wrapped space with as domain
10085 a zero-dimensional C<isolate> space and as range the regular
10086 C<atomic>, C<separate> or C<unroll> space.
10087 This option may also be set directly using
10088 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10089 The atomic/separate/unroll choice for the remaining part is determined
10090 by the regular C<atomic>, C<separate> or C<unroll> option.
10091 Since the C<isolate> option references outer schedule dimensions,
10092 its use in a band node causes any tree containing the node
10093 to be considered anchored.
10095 As an example, consider the isolation of full tiles from partial tiles
10096 in a tiling of a triangular domain. The original schedule is as follows.
10098 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10100 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10101 { A[i,j] -> [floor(j/10)] }, \
10102 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10106 for (int c0 = 0; c0 <= 10; c0 += 1)
10107 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10108 for (int c2 = 10 * c0;
10109 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10110 for (int c3 = 10 * c1;
10111 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10114 Isolating the full tiles, we have the following input
10116 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10118 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10119 { A[i,j] -> [floor(j/10)] }, \
10120 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10121 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10122 10a+9+10b+9 <= 100 }"
10127 for (int c0 = 0; c0 <= 8; c0 += 1) {
10128 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10129 for (int c2 = 10 * c0;
10130 c2 <= 10 * c0 + 9; c2 += 1)
10131 for (int c3 = 10 * c1;
10132 c3 <= 10 * c1 + 9; c3 += 1)
10134 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10135 for (int c2 = 10 * c0;
10136 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10137 for (int c3 = 10 * c1;
10138 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10141 for (int c0 = 9; c0 <= 10; c0 += 1)
10142 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10143 for (int c2 = 10 * c0;
10144 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10145 for (int c3 = 10 * c1;
10146 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10150 We may then additionally unroll the innermost loop of the isolated part
10152 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10154 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10155 { A[i,j] -> [floor(j/10)] }, \
10156 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10157 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10158 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10163 for (int c0 = 0; c0 <= 8; c0 += 1) {
10164 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10165 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10167 A(c2, 10 * c1 + 1);
10168 A(c2, 10 * c1 + 2);
10169 A(c2, 10 * c1 + 3);
10170 A(c2, 10 * c1 + 4);
10171 A(c2, 10 * c1 + 5);
10172 A(c2, 10 * c1 + 6);
10173 A(c2, 10 * c1 + 7);
10174 A(c2, 10 * c1 + 8);
10175 A(c2, 10 * c1 + 9);
10177 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10178 for (int c2 = 10 * c0;
10179 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10180 for (int c3 = 10 * c1;
10181 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10184 for (int c0 = 9; c0 <= 10; c0 += 1)
10185 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10186 for (int c2 = 10 * c0;
10187 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10188 for (int c3 = 10 * c1;
10189 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10194 =head3 AST Generation Options (Schedule Map)
10196 In case of AST construction using
10197 C<isl_ast_build_node_from_schedule_map>, the options
10198 that control how an AST is created from the individual schedule
10199 dimensions are stored in the C<isl_ast_build>.
10200 They can be set using the following function.
10202 #include <isl/ast_build.h>
10203 __isl_give isl_ast_build *
10204 isl_ast_build_set_options(
10205 __isl_take isl_ast_build *control,
10206 __isl_take isl_union_map *options);
10208 The options are encoded in an C<isl_union_map>.
10209 The domain of this union relation refers to the schedule domain,
10210 i.e., the range of the schedule passed
10211 to C<isl_ast_build_node_from_schedule_map>.
10212 In the case of nested AST generation (see L</"Nested AST Generation">),
10213 the domain of C<options> should refer to the extra piece of the schedule.
10214 That is, it should be equal to the range of the wrapped relation in the
10215 range of the schedule.
10216 The range of the options can consist of elements in one or more spaces,
10217 the names of which determine the effect of the option.
10218 The values of the range typically also refer to the schedule dimension
10219 to which the option applies. In case of nested AST generation
10220 (see L</"Nested AST Generation">), these values refer to the position
10221 of the schedule dimension within the innermost AST generation.
10222 The constraints on the domain elements of
10223 the option should only refer to this dimension and earlier dimensions.
10224 We consider the following spaces.
10228 =item C<separation_class>
10230 B<This option has been deprecated. Use the isolate option on
10231 schedule trees instead.>
10233 This space is a wrapped relation between two one dimensional spaces.
10234 The input space represents the schedule dimension to which the option
10235 applies and the output space represents the separation class.
10236 While constructing a loop corresponding to the specified schedule
10237 dimension(s), the AST generator will try to generate separate loops
10238 for domain elements that are assigned different classes.
10239 If only some of the elements are assigned a class, then those elements
10240 that are not assigned any class will be treated as belonging to a class
10241 that is separate from the explicitly assigned classes.
10242 The typical use case for this option is to separate full tiles from
10244 The other options, described below, are applied after the separation
10247 As an example, consider the separation into full and partial tiles
10248 of a tiling of a triangular domain.
10249 Take, for example, the domain
10251 { A[i,j] : 0 <= i,j and i + j <= 100 }
10253 and a tiling into tiles of 10 by 10. The input to the AST generator
10254 is then the schedule
10256 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10259 Without any options, the following AST is generated
10261 for (int c0 = 0; c0 <= 10; c0 += 1)
10262 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10263 for (int c2 = 10 * c0;
10264 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10266 for (int c3 = 10 * c1;
10267 c3 <= min(10 * c1 + 9, -c2 + 100);
10271 Separation into full and partial tiles can be obtained by assigning
10272 a class, say C<0>, to the full tiles. The full tiles are represented by those
10273 values of the first and second schedule dimensions for which there are
10274 values of the third and fourth dimensions to cover an entire tile.
10275 That is, we need to specify the following option
10277 { [a,b,c,d] -> separation_class[[0]->[0]] :
10278 exists b': 0 <= 10a,10b' and
10279 10a+9+10b'+9 <= 100;
10280 [a,b,c,d] -> separation_class[[1]->[0]] :
10281 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10283 which simplifies to
10285 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10286 a >= 0 and b >= 0 and b <= 8 - a;
10287 [a, b, c, d] -> separation_class[[0] -> [0]] :
10288 a >= 0 and a <= 8 }
10290 With this option, the generated AST is as follows
10293 for (int c0 = 0; c0 <= 8; c0 += 1) {
10294 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10295 for (int c2 = 10 * c0;
10296 c2 <= 10 * c0 + 9; c2 += 1)
10297 for (int c3 = 10 * c1;
10298 c3 <= 10 * c1 + 9; c3 += 1)
10300 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10301 for (int c2 = 10 * c0;
10302 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10304 for (int c3 = 10 * c1;
10305 c3 <= min(-c2 + 100, 10 * c1 + 9);
10309 for (int c0 = 9; c0 <= 10; c0 += 1)
10310 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10311 for (int c2 = 10 * c0;
10312 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10314 for (int c3 = 10 * c1;
10315 c3 <= min(10 * c1 + 9, -c2 + 100);
10322 This is a single-dimensional space representing the schedule dimension(s)
10323 to which ``separation'' should be applied. Separation tries to split
10324 a loop into several pieces if this can avoid the generation of guards
10326 See also the C<atomic> option.
10330 This is a single-dimensional space representing the schedule dimension(s)
10331 for which the domains should be considered ``atomic''. That is, the
10332 AST generator will make sure that any given domain space will only appear
10333 in a single loop at the specified level.
10335 Consider the following schedule
10337 { a[i] -> [i] : 0 <= i < 10;
10338 b[i] -> [i+1] : 0 <= i < 10 }
10340 If the following option is specified
10342 { [i] -> separate[x] }
10344 then the following AST will be generated
10348 for (int c0 = 1; c0 <= 9; c0 += 1) {
10355 If, on the other hand, the following option is specified
10357 { [i] -> atomic[x] }
10359 then the following AST will be generated
10361 for (int c0 = 0; c0 <= 10; c0 += 1) {
10368 If neither C<atomic> nor C<separate> is specified, then the AST generator
10369 may produce either of these two results or some intermediate form.
10373 This is a single-dimensional space representing the schedule dimension(s)
10374 that should be I<completely> unrolled.
10375 To obtain a partial unrolling, the user should apply an additional
10376 strip-mining to the schedule and fully unroll the inner loop.
10380 =head3 Fine-grained Control over AST Generation
10382 Besides specifying the constraints on the parameters,
10383 an C<isl_ast_build> object can be used to control
10384 various aspects of the AST generation process.
10385 In case of AST construction using
10386 C<isl_ast_build_node_from_schedule_map>,
10387 the most prominent way of control is through ``options'',
10388 as explained above.
10390 Additional control is available through the following functions.
10392 #include <isl/ast_build.h>
10393 __isl_give isl_ast_build *
10394 isl_ast_build_set_iterators(
10395 __isl_take isl_ast_build *control,
10396 __isl_take isl_id_list *iterators);
10398 The function C<isl_ast_build_set_iterators> allows the user to
10399 specify a list of iterator C<isl_id>s to be used as iterators.
10400 If the input schedule is injective, then
10401 the number of elements in this list should be as large as the dimension
10402 of the schedule space, but no direct correspondence should be assumed
10403 between dimensions and elements.
10404 If the input schedule is not injective, then an additional number
10405 of C<isl_id>s equal to the largest dimension of the input domains
10407 If the number of provided C<isl_id>s is insufficient, then additional
10408 names are automatically generated.
10410 #include <isl/ast_build.h>
10411 __isl_give isl_ast_build *
10412 isl_ast_build_set_create_leaf(
10413 __isl_take isl_ast_build *control,
10414 __isl_give isl_ast_node *(*fn)(
10415 __isl_take isl_ast_build *build,
10416 void *user), void *user);
10419 C<isl_ast_build_set_create_leaf> function allows for the
10420 specification of a callback that should be called whenever the AST
10421 generator arrives at an element of the schedule domain.
10422 The callback should return an AST node that should be inserted
10423 at the corresponding position of the AST. The default action (when
10424 the callback is not set) is to continue generating parts of the AST to scan
10425 all the domain elements associated to the schedule domain element
10426 and to insert user nodes, ``calling'' the domain element, for each of them.
10427 The C<build> argument contains the current state of the C<isl_ast_build>.
10428 To ease nested AST generation (see L</"Nested AST Generation">),
10429 all control information that is
10430 specific to the current AST generation such as the options and
10431 the callbacks has been removed from this C<isl_ast_build>.
10432 The callback would typically return the result of a nested
10433 AST generation or a
10434 user defined node created using the following function.
10436 #include <isl/ast.h>
10437 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10438 __isl_take isl_ast_expr *expr);
10440 #include <isl/ast_build.h>
10441 __isl_give isl_ast_build *
10442 isl_ast_build_set_at_each_domain(
10443 __isl_take isl_ast_build *build,
10444 __isl_give isl_ast_node *(*fn)(
10445 __isl_take isl_ast_node *node,
10446 __isl_keep isl_ast_build *build,
10447 void *user), void *user);
10448 __isl_give isl_ast_build *
10449 isl_ast_build_set_before_each_for(
10450 __isl_take isl_ast_build *build,
10451 __isl_give isl_id *(*fn)(
10452 __isl_keep isl_ast_build *build,
10453 void *user), void *user);
10454 __isl_give isl_ast_build *
10455 isl_ast_build_set_after_each_for(
10456 __isl_take isl_ast_build *build,
10457 __isl_give isl_ast_node *(*fn)(
10458 __isl_take isl_ast_node *node,
10459 __isl_keep isl_ast_build *build,
10460 void *user), void *user);
10461 __isl_give isl_ast_build *
10462 isl_ast_build_set_before_each_mark(
10463 __isl_take isl_ast_build *build,
10464 isl_stat (*fn)(__isl_keep isl_id *mark,
10465 __isl_keep isl_ast_build *build,
10466 void *user), void *user);
10467 __isl_give isl_ast_build *
10468 isl_ast_build_set_after_each_mark(
10469 __isl_take isl_ast_build *build,
10470 __isl_give isl_ast_node *(*fn)(
10471 __isl_take isl_ast_node *node,
10472 __isl_keep isl_ast_build *build,
10473 void *user), void *user);
10475 The callback set by C<isl_ast_build_set_at_each_domain> will
10476 be called for each domain AST node.
10477 The callbacks set by C<isl_ast_build_set_before_each_for>
10478 and C<isl_ast_build_set_after_each_for> will be called
10479 for each for AST node. The first will be called in depth-first
10480 pre-order, while the second will be called in depth-first post-order.
10481 Since C<isl_ast_build_set_before_each_for> is called before the for
10482 node is actually constructed, it is only passed an C<isl_ast_build>.
10483 The returned C<isl_id> will be added as an annotation (using
10484 C<isl_ast_node_set_annotation>) to the constructed for node.
10485 In particular, if the user has also specified an C<after_each_for>
10486 callback, then the annotation can be retrieved from the node passed to
10487 that callback using C<isl_ast_node_get_annotation>.
10488 The callbacks set by C<isl_ast_build_set_before_each_mark>
10489 and C<isl_ast_build_set_after_each_mark> will be called for each
10490 mark AST node that is created, i.e., for each mark schedule node
10491 in the input schedule tree. The first will be called in depth-first
10492 pre-order, while the second will be called in depth-first post-order.
10493 Since the callback set by C<isl_ast_build_set_before_each_mark>
10494 is called before the mark AST node is actually constructed, it is passed
10495 the identifier of the mark node.
10496 All callbacks should C<NULL> (or -1) on failure.
10497 The given C<isl_ast_build> can be used to create new
10498 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10499 or C<isl_ast_build_call_from_pw_multi_aff>.
10501 =head3 Nested AST Generation
10503 C<isl> allows the user to create an AST within the context
10504 of another AST. These nested ASTs are created using the
10505 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10506 the outer AST. The C<build> argument should be an C<isl_ast_build>
10507 passed to a callback set by
10508 C<isl_ast_build_set_create_leaf>.
10509 The space of the range of the C<schedule> argument should refer
10510 to this build. In particular, the space should be a wrapped
10511 relation and the domain of this wrapped relation should be the
10512 same as that of the range of the schedule returned by
10513 C<isl_ast_build_get_schedule> below.
10514 In practice, the new schedule is typically
10515 created by calling C<isl_union_map_range_product> on the old schedule
10516 and some extra piece of the schedule.
10517 The space of the schedule domain is also available from
10518 the C<isl_ast_build>.
10520 #include <isl/ast_build.h>
10521 __isl_give isl_union_map *isl_ast_build_get_schedule(
10522 __isl_keep isl_ast_build *build);
10523 __isl_give isl_space *isl_ast_build_get_schedule_space(
10524 __isl_keep isl_ast_build *build);
10525 __isl_give isl_ast_build *isl_ast_build_restrict(
10526 __isl_take isl_ast_build *build,
10527 __isl_take isl_set *set);
10529 The C<isl_ast_build_get_schedule> function returns a (partial)
10530 schedule for the domains elements for which part of the AST still needs to
10531 be generated in the current build.
10532 In particular, the domain elements are mapped to those iterations of the loops
10533 enclosing the current point of the AST generation inside which
10534 the domain elements are executed.
10535 No direct correspondence between
10536 the input schedule and this schedule should be assumed.
10537 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10538 to create a set for C<isl_ast_build_restrict> to intersect
10539 with the current build. In particular, the set passed to
10540 C<isl_ast_build_restrict> can have additional parameters.
10541 The ids of the set dimensions in the space returned by
10542 C<isl_ast_build_get_schedule_space> correspond to the
10543 iterators of the already generated loops.
10544 The user should not rely on the ids of the output dimensions
10545 of the relations in the union relation returned by
10546 C<isl_ast_build_get_schedule> having any particular value.
10548 =head1 Applications
10550 Although C<isl> is mainly meant to be used as a library,
10551 it also contains some basic applications that use some
10552 of the functionality of C<isl>.
10553 The input may be specified in either the L<isl format>
10554 or the L<PolyLib format>.
10556 =head2 C<isl_polyhedron_sample>
10558 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10559 an integer element of the polyhedron, if there is any.
10560 The first column in the output is the denominator and is always
10561 equal to 1. If the polyhedron contains no integer points,
10562 then a vector of length zero is printed.
10566 C<isl_pip> takes the same input as the C<example> program
10567 from the C<piplib> distribution, i.e., a set of constraints
10568 on the parameters, a line containing only -1 and finally a set
10569 of constraints on a parametric polyhedron.
10570 The coefficients of the parameters appear in the last columns
10571 (but before the final constant column).
10572 The output is the lexicographic minimum of the parametric polyhedron.
10573 As C<isl> currently does not have its own output format, the output
10574 is just a dump of the internal state.
10576 =head2 C<isl_polyhedron_minimize>
10578 C<isl_polyhedron_minimize> computes the minimum of some linear
10579 or affine objective function over the integer points in a polyhedron.
10580 If an affine objective function
10581 is given, then the constant should appear in the last column.
10583 =head2 C<isl_polytope_scan>
10585 Given a polytope, C<isl_polytope_scan> prints
10586 all integer points in the polytope.
10588 =head2 C<isl_codegen>
10590 Given a schedule, a context set and an options relation,
10591 C<isl_codegen> prints out an AST that scans the domain elements
10592 of the schedule in the order of their image(s) taking into account
10593 the constraints in the context set.