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);
3460 __isl_give char *isl_printer_get_str(
3461 __isl_keep isl_printer *printer);
3463 The printer can be inspected using the following functions.
3465 FILE *isl_printer_get_file(
3466 __isl_keep isl_printer *printer);
3467 int isl_printer_get_output_format(
3468 __isl_keep isl_printer *p);
3469 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3471 The behavior of the printer can be modified in various ways
3473 __isl_give isl_printer *isl_printer_set_output_format(
3474 __isl_take isl_printer *p, int output_format);
3475 __isl_give isl_printer *isl_printer_set_indent(
3476 __isl_take isl_printer *p, int indent);
3477 __isl_give isl_printer *isl_printer_set_indent_prefix(
3478 __isl_take isl_printer *p, const char *prefix);
3479 __isl_give isl_printer *isl_printer_indent(
3480 __isl_take isl_printer *p, int indent);
3481 __isl_give isl_printer *isl_printer_set_prefix(
3482 __isl_take isl_printer *p, const char *prefix);
3483 __isl_give isl_printer *isl_printer_set_suffix(
3484 __isl_take isl_printer *p, const char *suffix);
3485 __isl_give isl_printer *isl_printer_set_yaml_style(
3486 __isl_take isl_printer *p, int yaml_style);
3488 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3489 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3490 and defaults to C<ISL_FORMAT_ISL>.
3491 Each line in the output is prefixed by C<indent_prefix>,
3492 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3493 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3494 In the C<PolyLib> format output,
3495 the coefficients of the existentially quantified variables
3496 appear between those of the set variables and those
3498 The function C<isl_printer_indent> increases the indentation
3499 by the specified amount (which may be negative).
3500 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3501 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3504 To actually print something, use
3506 #include <isl/printer.h>
3507 __isl_give isl_printer *isl_printer_print_double(
3508 __isl_take isl_printer *p, double d);
3510 #include <isl/val.h>
3511 __isl_give isl_printer *isl_printer_print_val(
3512 __isl_take isl_printer *p, __isl_keep isl_val *v);
3514 #include <isl/set.h>
3515 __isl_give isl_printer *isl_printer_print_basic_set(
3516 __isl_take isl_printer *printer,
3517 __isl_keep isl_basic_set *bset);
3518 __isl_give isl_printer *isl_printer_print_set(
3519 __isl_take isl_printer *printer,
3520 __isl_keep isl_set *set);
3522 #include <isl/map.h>
3523 __isl_give isl_printer *isl_printer_print_basic_map(
3524 __isl_take isl_printer *printer,
3525 __isl_keep isl_basic_map *bmap);
3526 __isl_give isl_printer *isl_printer_print_map(
3527 __isl_take isl_printer *printer,
3528 __isl_keep isl_map *map);
3530 #include <isl/union_set.h>
3531 __isl_give isl_printer *isl_printer_print_union_set(
3532 __isl_take isl_printer *p,
3533 __isl_keep isl_union_set *uset);
3535 #include <isl/union_map.h>
3536 __isl_give isl_printer *isl_printer_print_union_map(
3537 __isl_take isl_printer *p,
3538 __isl_keep isl_union_map *umap);
3540 #include <isl/val.h>
3541 __isl_give isl_printer *isl_printer_print_multi_val(
3542 __isl_take isl_printer *p,
3543 __isl_keep isl_multi_val *mv);
3545 #include <isl/aff.h>
3546 __isl_give isl_printer *isl_printer_print_aff(
3547 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3548 __isl_give isl_printer *isl_printer_print_multi_aff(
3549 __isl_take isl_printer *p,
3550 __isl_keep isl_multi_aff *maff);
3551 __isl_give isl_printer *isl_printer_print_pw_aff(
3552 __isl_take isl_printer *p,
3553 __isl_keep isl_pw_aff *pwaff);
3554 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3555 __isl_take isl_printer *p,
3556 __isl_keep isl_pw_multi_aff *pma);
3557 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3558 __isl_take isl_printer *p,
3559 __isl_keep isl_multi_pw_aff *mpa);
3560 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3561 __isl_take isl_printer *p,
3562 __isl_keep isl_union_pw_aff *upa);
3563 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3564 __isl_take isl_printer *p,
3565 __isl_keep isl_union_pw_multi_aff *upma);
3566 __isl_give isl_printer *
3567 isl_printer_print_multi_union_pw_aff(
3568 __isl_take isl_printer *p,
3569 __isl_keep isl_multi_union_pw_aff *mupa);
3571 #include <isl/polynomial.h>
3572 __isl_give isl_printer *isl_printer_print_qpolynomial(
3573 __isl_take isl_printer *p,
3574 __isl_keep isl_qpolynomial *qp);
3575 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3576 __isl_take isl_printer *p,
3577 __isl_keep isl_pw_qpolynomial *pwqp);
3578 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3579 __isl_take isl_printer *p,
3580 __isl_keep isl_union_pw_qpolynomial *upwqp);
3582 __isl_give isl_printer *
3583 isl_printer_print_pw_qpolynomial_fold(
3584 __isl_take isl_printer *p,
3585 __isl_keep isl_pw_qpolynomial_fold *pwf);
3586 __isl_give isl_printer *
3587 isl_printer_print_union_pw_qpolynomial_fold(
3588 __isl_take isl_printer *p,
3589 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3591 For C<isl_printer_print_qpolynomial>,
3592 C<isl_printer_print_pw_qpolynomial> and
3593 C<isl_printer_print_pw_qpolynomial_fold>,
3594 the output format of the printer
3595 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3596 For C<isl_printer_print_union_pw_qpolynomial> and
3597 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3599 In case of printing in C<ISL_FORMAT_C>, the user may want
3600 to set the names of all dimensions first.
3602 C<isl> also provides limited support for printing YAML documents,
3603 just enough for the internal use for printing such documents.
3605 #include <isl/printer.h>
3606 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3607 __isl_take isl_printer *p);
3608 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3609 __isl_take isl_printer *p);
3610 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3611 __isl_take isl_printer *p);
3612 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3613 __isl_take isl_printer *p);
3614 __isl_give isl_printer *isl_printer_yaml_next(
3615 __isl_take isl_printer *p);
3617 A document is started by a call to either
3618 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3619 Anything printed to the printer after such a call belong to the
3620 first key of the mapping or the first element in the sequence.
3621 The function C<isl_printer_yaml_next> moves to the value if
3622 we are currently printing a mapping key, the next key if we
3623 are printing a value or the next element if we are printing
3624 an element in a sequence.
3625 Nested mappings and sequences are initiated by the same
3626 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3627 Each call to these functions needs to have a corresponding call to
3628 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3630 When called on a file printer, the following function flushes
3631 the file. When called on a string printer, the buffer is cleared.
3633 __isl_give isl_printer *isl_printer_flush(
3634 __isl_take isl_printer *p);
3636 The following functions allow the user to attach
3637 notes to a printer in order to keep track of additional state.
3639 #include <isl/printer.h>
3640 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3641 __isl_keep isl_id *id);
3642 __isl_give isl_id *isl_printer_get_note(
3643 __isl_keep isl_printer *p, __isl_take isl_id *id);
3644 __isl_give isl_printer *isl_printer_set_note(
3645 __isl_take isl_printer *p,
3646 __isl_take isl_id *id, __isl_take isl_id *note);
3648 C<isl_printer_set_note> associates the given note to the given
3649 identifier in the printer.
3650 C<isl_printer_get_note> retrieves a note associated to an
3652 C<isl_printer_has_note> checks if there is such a note.
3653 C<isl_printer_get_note> fails if the requested note does not exist.
3655 Alternatively, a string representation can be obtained
3656 directly using the following functions, which always print
3659 #include <isl/space.h>
3660 __isl_give char *isl_space_to_str(
3661 __isl_keep isl_space *space);
3663 #include <isl/val.h>
3664 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3665 __isl_give char *isl_multi_val_to_str(
3666 __isl_keep isl_multi_val *mv);
3668 #include <isl/set.h>
3669 __isl_give char *isl_set_to_str(
3670 __isl_keep isl_set *set);
3672 #include <isl/union_set.h>
3673 __isl_give char *isl_union_set_to_str(
3674 __isl_keep isl_union_set *uset);
3676 #include <isl/map.h>
3677 __isl_give char *isl_map_to_str(
3678 __isl_keep isl_map *map);
3680 #include <isl/union_map.h>
3681 __isl_give char *isl_union_map_to_str(
3682 __isl_keep isl_union_map *umap);
3684 #include <isl/aff.h>
3685 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3686 __isl_give char *isl_pw_aff_to_str(
3687 __isl_keep isl_pw_aff *pa);
3688 __isl_give char *isl_multi_aff_to_str(
3689 __isl_keep isl_multi_aff *ma);
3690 __isl_give char *isl_pw_multi_aff_to_str(
3691 __isl_keep isl_pw_multi_aff *pma);
3692 __isl_give char *isl_multi_pw_aff_to_str(
3693 __isl_keep isl_multi_pw_aff *mpa);
3694 __isl_give char *isl_union_pw_aff_to_str(
3695 __isl_keep isl_union_pw_aff *upa);
3696 __isl_give char *isl_union_pw_multi_aff_to_str(
3697 __isl_keep isl_union_pw_multi_aff *upma);
3698 __isl_give char *isl_multi_union_pw_aff_to_str(
3699 __isl_keep isl_multi_union_pw_aff *mupa);
3703 =head3 Unary Properties
3709 The following functions test whether the given set or relation
3710 contains any integer points. The ``plain'' variants do not perform
3711 any computations, but simply check if the given set or relation
3712 is already known to be empty.
3714 isl_bool isl_basic_set_plain_is_empty(
3715 __isl_keep isl_basic_set *bset);
3716 isl_bool isl_basic_set_is_empty(
3717 __isl_keep isl_basic_set *bset);
3718 isl_bool isl_set_plain_is_empty(
3719 __isl_keep isl_set *set);
3720 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3721 isl_bool isl_union_set_is_empty(
3722 __isl_keep isl_union_set *uset);
3723 isl_bool isl_basic_map_plain_is_empty(
3724 __isl_keep isl_basic_map *bmap);
3725 isl_bool isl_basic_map_is_empty(
3726 __isl_keep isl_basic_map *bmap);
3727 isl_bool isl_map_plain_is_empty(
3728 __isl_keep isl_map *map);
3729 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3730 isl_bool isl_union_map_is_empty(
3731 __isl_keep isl_union_map *umap);
3733 =item * Universality
3735 isl_bool isl_basic_set_plain_is_universe(
3736 __isl_keep isl_basic_set *bset);
3737 isl_bool isl_basic_set_is_universe(
3738 __isl_keep isl_basic_set *bset);
3739 isl_bool isl_basic_map_plain_is_universe(
3740 __isl_keep isl_basic_map *bmap);
3741 isl_bool isl_basic_map_is_universe(
3742 __isl_keep isl_basic_map *bmap);
3743 isl_bool isl_set_plain_is_universe(
3744 __isl_keep isl_set *set);
3745 isl_bool isl_map_plain_is_universe(
3746 __isl_keep isl_map *map);
3748 =item * Single-valuedness
3750 #include <isl/set.h>
3751 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3753 #include <isl/map.h>
3754 isl_bool isl_basic_map_is_single_valued(
3755 __isl_keep isl_basic_map *bmap);
3756 isl_bool isl_map_plain_is_single_valued(
3757 __isl_keep isl_map *map);
3758 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3760 #include <isl/union_map.h>
3761 isl_bool isl_union_map_is_single_valued(
3762 __isl_keep isl_union_map *umap);
3766 isl_bool isl_map_plain_is_injective(
3767 __isl_keep isl_map *map);
3768 isl_bool isl_map_is_injective(
3769 __isl_keep isl_map *map);
3770 isl_bool isl_union_map_plain_is_injective(
3771 __isl_keep isl_union_map *umap);
3772 isl_bool isl_union_map_is_injective(
3773 __isl_keep isl_union_map *umap);
3777 isl_bool isl_map_is_bijective(
3778 __isl_keep isl_map *map);
3779 isl_bool isl_union_map_is_bijective(
3780 __isl_keep isl_union_map *umap);
3784 The following functions test whether the given relation
3785 only maps elements to themselves.
3787 #include <isl/map.h>
3788 isl_bool isl_map_is_identity(
3789 __isl_keep isl_map *map);
3791 #include <isl/union_map.h>
3792 isl_bool isl_union_map_is_identity(
3793 __isl_keep isl_union_map *umap);
3797 __isl_give isl_val *
3798 isl_basic_map_plain_get_val_if_fixed(
3799 __isl_keep isl_basic_map *bmap,
3800 enum isl_dim_type type, unsigned pos);
3801 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3802 __isl_keep isl_set *set,
3803 enum isl_dim_type type, unsigned pos);
3804 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3805 __isl_keep isl_map *map,
3806 enum isl_dim_type type, unsigned pos);
3808 If the set or relation obviously lies on a hyperplane where the given dimension
3809 has a fixed value, then return that value.
3810 Otherwise return NaN.
3814 isl_stat isl_set_dim_residue_class_val(
3815 __isl_keep isl_set *set,
3816 int pos, __isl_give isl_val **modulo,
3817 __isl_give isl_val **residue);
3819 Check if the values of the given set dimension are equal to a fixed
3820 value modulo some integer value. If so, assign the modulo to C<*modulo>
3821 and the fixed value to C<*residue>. If the given dimension attains only
3822 a single value, then assign C<0> to C<*modulo> and the fixed value to
3824 If the dimension does not attain only a single value and if no modulo
3825 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3829 To check whether the description of a set, relation or function depends
3830 on one or more given dimensions,
3831 the following functions can be used.
3833 #include <isl/constraint.h>
3834 isl_bool isl_constraint_involves_dims(
3835 __isl_keep isl_constraint *constraint,
3836 enum isl_dim_type type, unsigned first, unsigned n);
3838 #include <isl/set.h>
3839 isl_bool isl_basic_set_involves_dims(
3840 __isl_keep isl_basic_set *bset,
3841 enum isl_dim_type type, unsigned first, unsigned n);
3842 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3843 enum isl_dim_type type, unsigned first, unsigned n);
3845 #include <isl/map.h>
3846 isl_bool isl_basic_map_involves_dims(
3847 __isl_keep isl_basic_map *bmap,
3848 enum isl_dim_type type, unsigned first, unsigned n);
3849 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3850 enum isl_dim_type type, unsigned first, unsigned n);
3852 #include <isl/union_map.h>
3853 isl_bool isl_union_map_involves_dims(
3854 __isl_keep isl_union_map *umap,
3855 enum isl_dim_type type, unsigned first, unsigned n);
3857 #include <isl/aff.h>
3858 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3859 enum isl_dim_type type, unsigned first, unsigned n);
3860 isl_bool isl_pw_aff_involves_dims(
3861 __isl_keep isl_pw_aff *pwaff,
3862 enum isl_dim_type type, unsigned first, unsigned n);
3863 isl_bool isl_multi_aff_involves_dims(
3864 __isl_keep isl_multi_aff *ma,
3865 enum isl_dim_type type, unsigned first, unsigned n);
3866 isl_bool isl_multi_pw_aff_involves_dims(
3867 __isl_keep isl_multi_pw_aff *mpa,
3868 enum isl_dim_type type, unsigned first, unsigned n);
3870 #include <isl/polynomial.h>
3871 isl_bool isl_qpolynomial_involves_dims(
3872 __isl_keep isl_qpolynomial *qp,
3873 enum isl_dim_type type, unsigned first, unsigned n);
3875 Similarly, the following functions can be used to check whether
3876 a given dimension is involved in any lower or upper bound.
3878 #include <isl/set.h>
3879 isl_bool isl_set_dim_has_any_lower_bound(
3880 __isl_keep isl_set *set,
3881 enum isl_dim_type type, unsigned pos);
3882 isl_bool isl_set_dim_has_any_upper_bound(
3883 __isl_keep isl_set *set,
3884 enum isl_dim_type type, unsigned pos);
3886 Note that these functions return true even if there is a bound on
3887 the dimension on only some of the basic sets of C<set>.
3888 To check if they have a bound for all of the basic sets in C<set>,
3889 use the following functions instead.
3891 #include <isl/set.h>
3892 isl_bool isl_set_dim_has_lower_bound(
3893 __isl_keep isl_set *set,
3894 enum isl_dim_type type, unsigned pos);
3895 isl_bool isl_set_dim_has_upper_bound(
3896 __isl_keep isl_set *set,
3897 enum isl_dim_type type, unsigned pos);
3901 To check whether a set is a parameter domain, use this function:
3903 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3904 isl_bool isl_union_set_is_params(
3905 __isl_keep isl_union_set *uset);
3909 The following functions check whether the space of the given
3910 (basic) set or relation range is a wrapped relation.
3912 #include <isl/space.h>
3913 isl_bool isl_space_is_wrapping(
3914 __isl_keep isl_space *space);
3915 isl_bool isl_space_domain_is_wrapping(
3916 __isl_keep isl_space *space);
3917 isl_bool isl_space_range_is_wrapping(
3918 __isl_keep isl_space *space);
3920 #include <isl/set.h>
3921 isl_bool isl_basic_set_is_wrapping(
3922 __isl_keep isl_basic_set *bset);
3923 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3925 #include <isl/map.h>
3926 isl_bool isl_map_domain_is_wrapping(
3927 __isl_keep isl_map *map);
3928 isl_bool isl_map_range_is_wrapping(
3929 __isl_keep isl_map *map);
3931 #include <isl/val.h>
3932 isl_bool isl_multi_val_range_is_wrapping(
3933 __isl_keep isl_multi_val *mv);
3935 #include <isl/aff.h>
3936 isl_bool isl_multi_aff_range_is_wrapping(
3937 __isl_keep isl_multi_aff *ma);
3938 isl_bool isl_multi_pw_aff_range_is_wrapping(
3939 __isl_keep isl_multi_pw_aff *mpa);
3940 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3941 __isl_keep isl_multi_union_pw_aff *mupa);
3943 The input to C<isl_space_is_wrapping> should
3944 be the space of a set, while that of
3945 C<isl_space_domain_is_wrapping> and
3946 C<isl_space_range_is_wrapping> should be the space of a relation.
3948 =item * Internal Product
3950 isl_bool isl_basic_map_can_zip(
3951 __isl_keep isl_basic_map *bmap);
3952 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
3954 Check whether the product of domain and range of the given relation
3956 i.e., whether both domain and range are nested relations.
3960 #include <isl/space.h>
3961 isl_bool isl_space_can_curry(
3962 __isl_keep isl_space *space);
3964 #include <isl/map.h>
3965 isl_bool isl_basic_map_can_curry(
3966 __isl_keep isl_basic_map *bmap);
3967 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
3969 Check whether the domain of the (basic) relation is a wrapped relation.
3971 #include <isl/space.h>
3972 __isl_give isl_space *isl_space_uncurry(
3973 __isl_take isl_space *space);
3975 #include <isl/map.h>
3976 isl_bool isl_basic_map_can_uncurry(
3977 __isl_keep isl_basic_map *bmap);
3978 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
3980 Check whether the range of the (basic) relation is a wrapped relation.
3982 #include <isl/space.h>
3983 isl_bool isl_space_can_range_curry(
3984 __isl_keep isl_space *space);
3986 #include <isl/map.h>
3987 isl_bool isl_map_can_range_curry(
3988 __isl_keep isl_map *map);
3990 Check whether the domain of the relation wrapped in the range of
3991 the input is itself a wrapped relation.
3993 =item * Special Values
3995 #include <isl/aff.h>
3996 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
3997 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3998 isl_bool isl_multi_pw_aff_is_cst(
3999 __isl_keep isl_multi_pw_aff *mpa);
4001 Check whether the given expression is a constant.
4003 #include <isl/aff.h>
4004 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4005 isl_bool isl_pw_aff_involves_nan(
4006 __isl_keep isl_pw_aff *pa);
4008 #include <isl/polynomial.h>
4009 isl_bool isl_qpolynomial_fold_is_nan(
4010 __isl_keep isl_qpolynomial_fold *fold);
4012 Check whether the given expression is equal to or involves NaN.
4014 #include <isl/aff.h>
4015 isl_bool isl_aff_plain_is_zero(
4016 __isl_keep isl_aff *aff);
4018 Check whether the affine expression is obviously zero.
4022 =head3 Binary Properties
4028 The following functions check whether two objects
4029 represent the same set, relation or function.
4030 The C<plain> variants only return true if the objects
4031 are obviously the same. That is, they may return false
4032 even if the objects are the same, but they will never
4033 return true if the objects are not the same.
4035 #include <isl/set.h>
4036 isl_bool isl_basic_set_plain_is_equal(
4037 __isl_keep isl_basic_set *bset1,
4038 __isl_keep isl_basic_set *bset2);
4039 isl_bool isl_basic_set_is_equal(
4040 __isl_keep isl_basic_set *bset1,
4041 __isl_keep isl_basic_set *bset2);
4042 isl_bool isl_set_plain_is_equal(
4043 __isl_keep isl_set *set1,
4044 __isl_keep isl_set *set2);
4045 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4046 __isl_keep isl_set *set2);
4048 #include <isl/map.h>
4049 isl_bool isl_basic_map_is_equal(
4050 __isl_keep isl_basic_map *bmap1,
4051 __isl_keep isl_basic_map *bmap2);
4052 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4053 __isl_keep isl_map *map2);
4054 isl_bool isl_map_plain_is_equal(
4055 __isl_keep isl_map *map1,
4056 __isl_keep isl_map *map2);
4058 #include <isl/union_set.h>
4059 isl_bool isl_union_set_is_equal(
4060 __isl_keep isl_union_set *uset1,
4061 __isl_keep isl_union_set *uset2);
4063 #include <isl/union_map.h>
4064 isl_bool isl_union_map_is_equal(
4065 __isl_keep isl_union_map *umap1,
4066 __isl_keep isl_union_map *umap2);
4068 #include <isl/aff.h>
4069 isl_bool isl_aff_plain_is_equal(
4070 __isl_keep isl_aff *aff1,
4071 __isl_keep isl_aff *aff2);
4072 isl_bool isl_multi_aff_plain_is_equal(
4073 __isl_keep isl_multi_aff *maff1,
4074 __isl_keep isl_multi_aff *maff2);
4075 isl_bool isl_pw_aff_plain_is_equal(
4076 __isl_keep isl_pw_aff *pwaff1,
4077 __isl_keep isl_pw_aff *pwaff2);
4078 isl_bool isl_pw_multi_aff_plain_is_equal(
4079 __isl_keep isl_pw_multi_aff *pma1,
4080 __isl_keep isl_pw_multi_aff *pma2);
4081 isl_bool isl_multi_pw_aff_plain_is_equal(
4082 __isl_keep isl_multi_pw_aff *mpa1,
4083 __isl_keep isl_multi_pw_aff *mpa2);
4084 isl_bool isl_multi_pw_aff_is_equal(
4085 __isl_keep isl_multi_pw_aff *mpa1,
4086 __isl_keep isl_multi_pw_aff *mpa2);
4087 isl_bool isl_union_pw_aff_plain_is_equal(
4088 __isl_keep isl_union_pw_aff *upa1,
4089 __isl_keep isl_union_pw_aff *upa2);
4090 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4091 __isl_keep isl_union_pw_multi_aff *upma1,
4092 __isl_keep isl_union_pw_multi_aff *upma2);
4093 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4094 __isl_keep isl_multi_union_pw_aff *mupa1,
4095 __isl_keep isl_multi_union_pw_aff *mupa2);
4097 #include <isl/polynomial.h>
4098 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4099 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4100 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4101 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4102 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4103 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4105 =item * Disjointness
4107 #include <isl/set.h>
4108 isl_bool isl_basic_set_is_disjoint(
4109 __isl_keep isl_basic_set *bset1,
4110 __isl_keep isl_basic_set *bset2);
4111 isl_bool isl_set_plain_is_disjoint(
4112 __isl_keep isl_set *set1,
4113 __isl_keep isl_set *set2);
4114 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4115 __isl_keep isl_set *set2);
4117 #include <isl/map.h>
4118 isl_bool isl_basic_map_is_disjoint(
4119 __isl_keep isl_basic_map *bmap1,
4120 __isl_keep isl_basic_map *bmap2);
4121 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4122 __isl_keep isl_map *map2);
4124 #include <isl/union_set.h>
4125 isl_bool isl_union_set_is_disjoint(
4126 __isl_keep isl_union_set *uset1,
4127 __isl_keep isl_union_set *uset2);
4129 #include <isl/union_map.h>
4130 isl_bool isl_union_map_is_disjoint(
4131 __isl_keep isl_union_map *umap1,
4132 __isl_keep isl_union_map *umap2);
4136 isl_bool isl_basic_set_is_subset(
4137 __isl_keep isl_basic_set *bset1,
4138 __isl_keep isl_basic_set *bset2);
4139 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4140 __isl_keep isl_set *set2);
4141 isl_bool isl_set_is_strict_subset(
4142 __isl_keep isl_set *set1,
4143 __isl_keep isl_set *set2);
4144 isl_bool isl_union_set_is_subset(
4145 __isl_keep isl_union_set *uset1,
4146 __isl_keep isl_union_set *uset2);
4147 isl_bool isl_union_set_is_strict_subset(
4148 __isl_keep isl_union_set *uset1,
4149 __isl_keep isl_union_set *uset2);
4150 isl_bool isl_basic_map_is_subset(
4151 __isl_keep isl_basic_map *bmap1,
4152 __isl_keep isl_basic_map *bmap2);
4153 isl_bool isl_basic_map_is_strict_subset(
4154 __isl_keep isl_basic_map *bmap1,
4155 __isl_keep isl_basic_map *bmap2);
4156 isl_bool isl_map_is_subset(
4157 __isl_keep isl_map *map1,
4158 __isl_keep isl_map *map2);
4159 isl_bool isl_map_is_strict_subset(
4160 __isl_keep isl_map *map1,
4161 __isl_keep isl_map *map2);
4162 isl_bool isl_union_map_is_subset(
4163 __isl_keep isl_union_map *umap1,
4164 __isl_keep isl_union_map *umap2);
4165 isl_bool isl_union_map_is_strict_subset(
4166 __isl_keep isl_union_map *umap1,
4167 __isl_keep isl_union_map *umap2);
4169 Check whether the first argument is a (strict) subset of the
4174 Every comparison function returns a negative value if the first
4175 argument is considered smaller than the second, a positive value
4176 if the first argument is considered greater and zero if the two
4177 constraints are considered the same by the comparison criterion.
4179 #include <isl/constraint.h>
4180 int isl_constraint_plain_cmp(
4181 __isl_keep isl_constraint *c1,
4182 __isl_keep isl_constraint *c2);
4184 This function is useful for sorting C<isl_constraint>s.
4185 The order depends on the internal representation of the inputs.
4186 The order is fixed over different calls to the function (assuming
4187 the internal representation of the inputs has not changed), but may
4188 change over different versions of C<isl>.
4190 #include <isl/constraint.h>
4191 int isl_constraint_cmp_last_non_zero(
4192 __isl_keep isl_constraint *c1,
4193 __isl_keep isl_constraint *c2);
4195 This function can be used to sort constraints that live in the same
4196 local space. Constraints that involve ``earlier'' dimensions or
4197 that have a smaller coefficient for the shared latest dimension
4198 are considered smaller than other constraints.
4199 This function only defines a B<partial> order.
4201 #include <isl/set.h>
4202 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4203 __isl_keep isl_set *set2);
4205 This function is useful for sorting C<isl_set>s.
4206 The order depends on the internal representation of the inputs.
4207 The order is fixed over different calls to the function (assuming
4208 the internal representation of the inputs has not changed), but may
4209 change over different versions of C<isl>.
4211 #include <isl/aff.h>
4212 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4213 __isl_keep isl_pw_aff *pa2);
4215 The function C<isl_pw_aff_plain_cmp> can be used to sort
4216 C<isl_pw_aff>s. The order is not strictly defined.
4217 The current order sorts expressions that only involve
4218 earlier dimensions before those that involve later dimensions.
4222 =head2 Unary Operations
4228 __isl_give isl_set *isl_set_complement(
4229 __isl_take isl_set *set);
4230 __isl_give isl_map *isl_map_complement(
4231 __isl_take isl_map *map);
4235 #include <isl/space.h>
4236 __isl_give isl_space *isl_space_reverse(
4237 __isl_take isl_space *space);
4239 #include <isl/map.h>
4240 __isl_give isl_basic_map *isl_basic_map_reverse(
4241 __isl_take isl_basic_map *bmap);
4242 __isl_give isl_map *isl_map_reverse(
4243 __isl_take isl_map *map);
4245 #include <isl/union_map.h>
4246 __isl_give isl_union_map *isl_union_map_reverse(
4247 __isl_take isl_union_map *umap);
4251 #include <isl/space.h>
4252 __isl_give isl_space *isl_space_domain(
4253 __isl_take isl_space *space);
4254 __isl_give isl_space *isl_space_range(
4255 __isl_take isl_space *space);
4256 __isl_give isl_space *isl_space_params(
4257 __isl_take isl_space *space);
4259 #include <isl/local_space.h>
4260 __isl_give isl_local_space *isl_local_space_domain(
4261 __isl_take isl_local_space *ls);
4262 __isl_give isl_local_space *isl_local_space_range(
4263 __isl_take isl_local_space *ls);
4265 #include <isl/set.h>
4266 __isl_give isl_basic_set *isl_basic_set_project_out(
4267 __isl_take isl_basic_set *bset,
4268 enum isl_dim_type type, unsigned first, unsigned n);
4269 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4270 enum isl_dim_type type, unsigned first, unsigned n);
4271 __isl_give isl_map *isl_set_project_onto_map(
4272 __isl_take isl_set *set,
4273 enum isl_dim_type type, unsigned first,
4275 __isl_give isl_basic_set *isl_basic_set_params(
4276 __isl_take isl_basic_set *bset);
4277 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4279 The function C<isl_set_project_onto_map> returns a relation
4280 that projects the input set onto the given set dimensions.
4282 #include <isl/map.h>
4283 __isl_give isl_basic_map *isl_basic_map_project_out(
4284 __isl_take isl_basic_map *bmap,
4285 enum isl_dim_type type, unsigned first, unsigned n);
4286 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4287 enum isl_dim_type type, unsigned first, unsigned n);
4288 __isl_give isl_basic_set *isl_basic_map_domain(
4289 __isl_take isl_basic_map *bmap);
4290 __isl_give isl_basic_set *isl_basic_map_range(
4291 __isl_take isl_basic_map *bmap);
4292 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4293 __isl_give isl_set *isl_map_domain(
4294 __isl_take isl_map *bmap);
4295 __isl_give isl_set *isl_map_range(
4296 __isl_take isl_map *map);
4298 #include <isl/union_set.h>
4299 __isl_give isl_union_set *isl_union_set_project_out(
4300 __isl_take isl_union_set *uset,
4301 enum isl_dim_type type,
4302 unsigned first, unsigned n);
4303 __isl_give isl_set *isl_union_set_params(
4304 __isl_take isl_union_set *uset);
4306 The function C<isl_union_set_project_out> can only project out
4309 #include <isl/union_map.h>
4310 __isl_give isl_union_map *isl_union_map_project_out(
4311 __isl_take isl_union_map *umap,
4312 enum isl_dim_type type, unsigned first, unsigned n);
4313 __isl_give isl_set *isl_union_map_params(
4314 __isl_take isl_union_map *umap);
4315 __isl_give isl_union_set *isl_union_map_domain(
4316 __isl_take isl_union_map *umap);
4317 __isl_give isl_union_set *isl_union_map_range(
4318 __isl_take isl_union_map *umap);
4320 The function C<isl_union_map_project_out> can only project out
4323 #include <isl/aff.h>
4324 __isl_give isl_aff *isl_aff_project_domain_on_params(
4325 __isl_take isl_aff *aff);
4326 __isl_give isl_pw_multi_aff *
4327 isl_pw_multi_aff_project_domain_on_params(
4328 __isl_take isl_pw_multi_aff *pma);
4329 __isl_give isl_set *isl_pw_aff_domain(
4330 __isl_take isl_pw_aff *pwaff);
4331 __isl_give isl_set *isl_pw_multi_aff_domain(
4332 __isl_take isl_pw_multi_aff *pma);
4333 __isl_give isl_set *isl_multi_pw_aff_domain(
4334 __isl_take isl_multi_pw_aff *mpa);
4335 __isl_give isl_union_set *isl_union_pw_aff_domain(
4336 __isl_take isl_union_pw_aff *upa);
4337 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4338 __isl_take isl_union_pw_multi_aff *upma);
4339 __isl_give isl_union_set *
4340 isl_multi_union_pw_aff_domain(
4341 __isl_take isl_multi_union_pw_aff *mupa);
4342 __isl_give isl_set *isl_pw_aff_params(
4343 __isl_take isl_pw_aff *pwa);
4345 The function C<isl_multi_union_pw_aff_domain> requires its
4346 input to have at least one set dimension.
4348 #include <isl/polynomial.h>
4349 __isl_give isl_qpolynomial *
4350 isl_qpolynomial_project_domain_on_params(
4351 __isl_take isl_qpolynomial *qp);
4352 __isl_give isl_pw_qpolynomial *
4353 isl_pw_qpolynomial_project_domain_on_params(
4354 __isl_take isl_pw_qpolynomial *pwqp);
4355 __isl_give isl_pw_qpolynomial_fold *
4356 isl_pw_qpolynomial_fold_project_domain_on_params(
4357 __isl_take isl_pw_qpolynomial_fold *pwf);
4358 __isl_give isl_set *isl_pw_qpolynomial_domain(
4359 __isl_take isl_pw_qpolynomial *pwqp);
4360 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4361 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4362 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4363 __isl_take isl_union_pw_qpolynomial *upwqp);
4365 #include <isl/space.h>
4366 __isl_give isl_space *isl_space_domain_map(
4367 __isl_take isl_space *space);
4368 __isl_give isl_space *isl_space_range_map(
4369 __isl_take isl_space *space);
4371 #include <isl/map.h>
4372 __isl_give isl_map *isl_set_wrapped_domain_map(
4373 __isl_take isl_set *set);
4374 __isl_give isl_basic_map *isl_basic_map_domain_map(
4375 __isl_take isl_basic_map *bmap);
4376 __isl_give isl_basic_map *isl_basic_map_range_map(
4377 __isl_take isl_basic_map *bmap);
4378 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4379 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4381 #include <isl/union_map.h>
4382 __isl_give isl_union_map *isl_union_map_domain_map(
4383 __isl_take isl_union_map *umap);
4384 __isl_give isl_union_pw_multi_aff *
4385 isl_union_map_domain_map_union_pw_multi_aff(
4386 __isl_take isl_union_map *umap);
4387 __isl_give isl_union_map *isl_union_map_range_map(
4388 __isl_take isl_union_map *umap);
4389 __isl_give isl_union_map *
4390 isl_union_set_wrapped_domain_map(
4391 __isl_take isl_union_set *uset);
4393 The functions above construct a (basic, regular or union) relation
4394 that maps (a wrapped version of) the input relation to its domain or range.
4395 C<isl_set_wrapped_domain_map> maps the input set to the domain
4396 of its wrapped relation.
4400 __isl_give isl_basic_set *isl_basic_set_eliminate(
4401 __isl_take isl_basic_set *bset,
4402 enum isl_dim_type type,
4403 unsigned first, unsigned n);
4404 __isl_give isl_set *isl_set_eliminate(
4405 __isl_take isl_set *set, enum isl_dim_type type,
4406 unsigned first, unsigned n);
4407 __isl_give isl_basic_map *isl_basic_map_eliminate(
4408 __isl_take isl_basic_map *bmap,
4409 enum isl_dim_type type,
4410 unsigned first, unsigned n);
4411 __isl_give isl_map *isl_map_eliminate(
4412 __isl_take isl_map *map, enum isl_dim_type type,
4413 unsigned first, unsigned n);
4415 Eliminate the coefficients for the given dimensions from the constraints,
4416 without removing the dimensions.
4418 =item * Constructing a set from a parameter domain
4420 A zero-dimensional space or (basic) set can be constructed
4421 on a given parameter domain using the following functions.
4423 #include <isl/space.h>
4424 __isl_give isl_space *isl_space_set_from_params(
4425 __isl_take isl_space *space);
4427 #include <isl/set.h>
4428 __isl_give isl_basic_set *isl_basic_set_from_params(
4429 __isl_take isl_basic_set *bset);
4430 __isl_give isl_set *isl_set_from_params(
4431 __isl_take isl_set *set);
4433 =item * Constructing a relation from one or two sets
4435 Create a relation with the given set(s) as domain and/or range.
4436 If only the domain or the range is specified, then
4437 the range or domain of the created relation is a zero-dimensional
4438 flat anonymous space.
4440 #include <isl/space.h>
4441 __isl_give isl_space *isl_space_from_domain(
4442 __isl_take isl_space *space);
4443 __isl_give isl_space *isl_space_from_range(
4444 __isl_take isl_space *space);
4445 __isl_give isl_space *isl_space_map_from_set(
4446 __isl_take isl_space *space);
4447 __isl_give isl_space *isl_space_map_from_domain_and_range(
4448 __isl_take isl_space *domain,
4449 __isl_take isl_space *range);
4451 #include <isl/local_space.h>
4452 __isl_give isl_local_space *isl_local_space_from_domain(
4453 __isl_take isl_local_space *ls);
4455 #include <isl/map.h>
4456 __isl_give isl_map *isl_map_from_domain(
4457 __isl_take isl_set *set);
4458 __isl_give isl_map *isl_map_from_range(
4459 __isl_take isl_set *set);
4461 #include <isl/union_map.h>
4462 __isl_give isl_union_map *
4463 isl_union_map_from_domain_and_range(
4464 __isl_take isl_union_set *domain,
4465 __isl_take isl_union_set *range);
4467 #include <isl/val.h>
4468 __isl_give isl_multi_val *isl_multi_val_from_range(
4469 __isl_take isl_multi_val *mv);
4471 #include <isl/aff.h>
4472 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4473 __isl_take isl_multi_aff *ma);
4474 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4475 __isl_take isl_pw_aff *pwa);
4476 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4477 __isl_take isl_multi_pw_aff *mpa);
4478 __isl_give isl_multi_union_pw_aff *
4479 isl_multi_union_pw_aff_from_range(
4480 __isl_take isl_multi_union_pw_aff *mupa);
4481 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4482 __isl_take isl_set *set);
4483 __isl_give isl_union_pw_multi_aff *
4484 isl_union_pw_multi_aff_from_domain(
4485 __isl_take isl_union_set *uset);
4489 #include <isl/set.h>
4490 __isl_give isl_basic_set *isl_basic_set_fix_si(
4491 __isl_take isl_basic_set *bset,
4492 enum isl_dim_type type, unsigned pos, int value);
4493 __isl_give isl_basic_set *isl_basic_set_fix_val(
4494 __isl_take isl_basic_set *bset,
4495 enum isl_dim_type type, unsigned pos,
4496 __isl_take isl_val *v);
4497 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4498 enum isl_dim_type type, unsigned pos, int value);
4499 __isl_give isl_set *isl_set_fix_val(
4500 __isl_take isl_set *set,
4501 enum isl_dim_type type, unsigned pos,
4502 __isl_take isl_val *v);
4504 #include <isl/map.h>
4505 __isl_give isl_basic_map *isl_basic_map_fix_si(
4506 __isl_take isl_basic_map *bmap,
4507 enum isl_dim_type type, unsigned pos, int value);
4508 __isl_give isl_basic_map *isl_basic_map_fix_val(
4509 __isl_take isl_basic_map *bmap,
4510 enum isl_dim_type type, unsigned pos,
4511 __isl_take isl_val *v);
4512 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4513 enum isl_dim_type type, unsigned pos, int value);
4514 __isl_give isl_map *isl_map_fix_val(
4515 __isl_take isl_map *map,
4516 enum isl_dim_type type, unsigned pos,
4517 __isl_take isl_val *v);
4519 #include <isl/aff.h>
4520 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4521 __isl_take isl_pw_multi_aff *pma,
4522 enum isl_dim_type type, unsigned pos, int value);
4524 #include <isl/polynomial.h>
4525 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4526 __isl_take isl_pw_qpolynomial *pwqp,
4527 enum isl_dim_type type, unsigned n,
4528 __isl_take isl_val *v);
4530 Intersect the set, relation or function domain
4531 with the hyperplane where the given
4532 dimension has the fixed given value.
4534 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4535 __isl_take isl_basic_map *bmap,
4536 enum isl_dim_type type, unsigned pos, int value);
4537 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4538 __isl_take isl_basic_map *bmap,
4539 enum isl_dim_type type, unsigned pos, int value);
4540 __isl_give isl_set *isl_set_lower_bound_si(
4541 __isl_take isl_set *set,
4542 enum isl_dim_type type, unsigned pos, int value);
4543 __isl_give isl_set *isl_set_lower_bound_val(
4544 __isl_take isl_set *set,
4545 enum isl_dim_type type, unsigned pos,
4546 __isl_take isl_val *value);
4547 __isl_give isl_map *isl_map_lower_bound_si(
4548 __isl_take isl_map *map,
4549 enum isl_dim_type type, unsigned pos, int value);
4550 __isl_give isl_set *isl_set_upper_bound_si(
4551 __isl_take isl_set *set,
4552 enum isl_dim_type type, unsigned pos, int value);
4553 __isl_give isl_set *isl_set_upper_bound_val(
4554 __isl_take isl_set *set,
4555 enum isl_dim_type type, unsigned pos,
4556 __isl_take isl_val *value);
4557 __isl_give isl_map *isl_map_upper_bound_si(
4558 __isl_take isl_map *map,
4559 enum isl_dim_type type, unsigned pos, int value);
4561 Intersect the set or relation with the half-space where the given
4562 dimension has a value bounded by the fixed given integer value.
4564 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4565 enum isl_dim_type type1, int pos1,
4566 enum isl_dim_type type2, int pos2);
4567 __isl_give isl_basic_map *isl_basic_map_equate(
4568 __isl_take isl_basic_map *bmap,
4569 enum isl_dim_type type1, int pos1,
4570 enum isl_dim_type type2, int pos2);
4571 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4572 enum isl_dim_type type1, int pos1,
4573 enum isl_dim_type type2, int pos2);
4575 Intersect the set or relation with the hyperplane where the given
4576 dimensions are equal to each other.
4578 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4579 enum isl_dim_type type1, int pos1,
4580 enum isl_dim_type type2, int pos2);
4582 Intersect the relation with the hyperplane where the given
4583 dimensions have opposite values.
4585 __isl_give isl_map *isl_map_order_le(
4586 __isl_take isl_map *map,
4587 enum isl_dim_type type1, int pos1,
4588 enum isl_dim_type type2, int pos2);
4589 __isl_give isl_basic_map *isl_basic_map_order_ge(
4590 __isl_take isl_basic_map *bmap,
4591 enum isl_dim_type type1, int pos1,
4592 enum isl_dim_type type2, int pos2);
4593 __isl_give isl_map *isl_map_order_ge(
4594 __isl_take isl_map *map,
4595 enum isl_dim_type type1, int pos1,
4596 enum isl_dim_type type2, int pos2);
4597 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4598 enum isl_dim_type type1, int pos1,
4599 enum isl_dim_type type2, int pos2);
4600 __isl_give isl_basic_map *isl_basic_map_order_gt(
4601 __isl_take isl_basic_map *bmap,
4602 enum isl_dim_type type1, int pos1,
4603 enum isl_dim_type type2, int pos2);
4604 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4605 enum isl_dim_type type1, int pos1,
4606 enum isl_dim_type type2, int pos2);
4608 Intersect the relation with the half-space where the given
4609 dimensions satisfy the given ordering.
4613 #include <isl/aff.h>
4614 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4615 __isl_take isl_aff *aff);
4616 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4617 __isl_take isl_aff *aff);
4618 __isl_give isl_set *isl_pw_aff_pos_set(
4619 __isl_take isl_pw_aff *pa);
4620 __isl_give isl_set *isl_pw_aff_nonneg_set(
4621 __isl_take isl_pw_aff *pwaff);
4622 __isl_give isl_set *isl_pw_aff_zero_set(
4623 __isl_take isl_pw_aff *pwaff);
4624 __isl_give isl_set *isl_pw_aff_non_zero_set(
4625 __isl_take isl_pw_aff *pwaff);
4626 __isl_give isl_union_set *
4627 isl_union_pw_aff_zero_union_set(
4628 __isl_take isl_union_pw_aff *upa);
4629 __isl_give isl_union_set *
4630 isl_multi_union_pw_aff_zero_union_set(
4631 __isl_take isl_multi_union_pw_aff *mupa);
4633 The function C<isl_aff_neg_basic_set> returns a basic set
4634 containing those elements in the domain space
4635 of C<aff> where C<aff> is negative.
4636 The function C<isl_pw_aff_nonneg_set> returns a set
4637 containing those elements in the domain
4638 of C<pwaff> where C<pwaff> is non-negative.
4639 The function C<isl_multi_union_pw_aff_zero_union_set>
4640 returns a union set containing those elements
4641 in the domains of its elements where they are all zero.
4645 __isl_give isl_map *isl_set_identity(
4646 __isl_take isl_set *set);
4647 __isl_give isl_union_map *isl_union_set_identity(
4648 __isl_take isl_union_set *uset);
4649 __isl_give isl_union_pw_multi_aff *
4650 isl_union_set_identity_union_pw_multi_aff(
4651 __isl_take isl_union_set *uset);
4653 Construct an identity relation on the given (union) set.
4655 =item * Function Extraction
4657 A piecewise quasi affine expression that is equal to 1 on a set
4658 and 0 outside the set can be created using the following function.
4660 #include <isl/aff.h>
4661 __isl_give isl_pw_aff *isl_set_indicator_function(
4662 __isl_take isl_set *set);
4664 A piecewise multiple quasi affine expression can be extracted
4665 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4666 and the C<isl_map> is single-valued.
4667 In case of a conversion from an C<isl_union_map>
4668 to an C<isl_union_pw_multi_aff>, these properties need to hold
4669 in each domain space.
4670 A conversion to a C<isl_multi_union_pw_aff> additionally
4671 requires that the input is non-empty and involves only a single
4674 #include <isl/aff.h>
4675 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4676 __isl_take isl_set *set);
4677 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4678 __isl_take isl_map *map);
4680 __isl_give isl_union_pw_multi_aff *
4681 isl_union_pw_multi_aff_from_union_set(
4682 __isl_take isl_union_set *uset);
4683 __isl_give isl_union_pw_multi_aff *
4684 isl_union_pw_multi_aff_from_union_map(
4685 __isl_take isl_union_map *umap);
4687 __isl_give isl_multi_union_pw_aff *
4688 isl_multi_union_pw_aff_from_union_map(
4689 __isl_take isl_union_map *umap);
4693 __isl_give isl_basic_set *isl_basic_map_deltas(
4694 __isl_take isl_basic_map *bmap);
4695 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4696 __isl_give isl_union_set *isl_union_map_deltas(
4697 __isl_take isl_union_map *umap);
4699 These functions return a (basic) set containing the differences
4700 between image elements and corresponding domain elements in the input.
4702 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4703 __isl_take isl_basic_map *bmap);
4704 __isl_give isl_map *isl_map_deltas_map(
4705 __isl_take isl_map *map);
4706 __isl_give isl_union_map *isl_union_map_deltas_map(
4707 __isl_take isl_union_map *umap);
4709 The functions above construct a (basic, regular or union) relation
4710 that maps (a wrapped version of) the input relation to its delta set.
4714 Simplify the representation of a set, relation or functions by trying
4715 to combine pairs of basic sets or relations into a single
4716 basic set or relation.
4718 #include <isl/set.h>
4719 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4721 #include <isl/map.h>
4722 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4724 #include <isl/union_set.h>
4725 __isl_give isl_union_set *isl_union_set_coalesce(
4726 __isl_take isl_union_set *uset);
4728 #include <isl/union_map.h>
4729 __isl_give isl_union_map *isl_union_map_coalesce(
4730 __isl_take isl_union_map *umap);
4732 #include <isl/aff.h>
4733 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4734 __isl_take isl_pw_aff *pwqp);
4735 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4736 __isl_take isl_pw_multi_aff *pma);
4737 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4738 __isl_take isl_multi_pw_aff *mpa);
4739 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4740 __isl_take isl_union_pw_aff *upa);
4741 __isl_give isl_union_pw_multi_aff *
4742 isl_union_pw_multi_aff_coalesce(
4743 __isl_take isl_union_pw_multi_aff *upma);
4744 __isl_give isl_multi_union_pw_aff *
4745 isl_multi_union_pw_aff_coalesce(
4746 __isl_take isl_multi_union_pw_aff *aff);
4748 #include <isl/polynomial.h>
4749 __isl_give isl_pw_qpolynomial_fold *
4750 isl_pw_qpolynomial_fold_coalesce(
4751 __isl_take isl_pw_qpolynomial_fold *pwf);
4752 __isl_give isl_union_pw_qpolynomial *
4753 isl_union_pw_qpolynomial_coalesce(
4754 __isl_take isl_union_pw_qpolynomial *upwqp);
4755 __isl_give isl_union_pw_qpolynomial_fold *
4756 isl_union_pw_qpolynomial_fold_coalesce(
4757 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4759 One of the methods for combining pairs of basic sets or relations
4760 can result in coefficients that are much larger than those that appear
4761 in the constraints of the input. By default, the coefficients are
4762 not allowed to grow larger, but this can be changed by unsetting
4763 the following option.
4765 isl_stat isl_options_set_coalesce_bounded_wrapping(
4766 isl_ctx *ctx, int val);
4767 int isl_options_get_coalesce_bounded_wrapping(
4770 =item * Detecting equalities
4772 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4773 __isl_take isl_basic_set *bset);
4774 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4775 __isl_take isl_basic_map *bmap);
4776 __isl_give isl_set *isl_set_detect_equalities(
4777 __isl_take isl_set *set);
4778 __isl_give isl_map *isl_map_detect_equalities(
4779 __isl_take isl_map *map);
4780 __isl_give isl_union_set *isl_union_set_detect_equalities(
4781 __isl_take isl_union_set *uset);
4782 __isl_give isl_union_map *isl_union_map_detect_equalities(
4783 __isl_take isl_union_map *umap);
4785 Simplify the representation of a set or relation by detecting implicit
4788 =item * Removing redundant constraints
4790 #include <isl/set.h>
4791 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4792 __isl_take isl_basic_set *bset);
4793 __isl_give isl_set *isl_set_remove_redundancies(
4794 __isl_take isl_set *set);
4796 #include <isl/union_set.h>
4797 __isl_give isl_union_set *
4798 isl_union_set_remove_redundancies(
4799 __isl_take isl_union_set *uset);
4801 #include <isl/map.h>
4802 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4803 __isl_take isl_basic_map *bmap);
4804 __isl_give isl_map *isl_map_remove_redundancies(
4805 __isl_take isl_map *map);
4807 #include <isl/union_map.h>
4808 __isl_give isl_union_map *
4809 isl_union_map_remove_redundancies(
4810 __isl_take isl_union_map *umap);
4814 __isl_give isl_basic_set *isl_set_convex_hull(
4815 __isl_take isl_set *set);
4816 __isl_give isl_basic_map *isl_map_convex_hull(
4817 __isl_take isl_map *map);
4819 If the input set or relation has any existentially quantified
4820 variables, then the result of these operations is currently undefined.
4824 #include <isl/set.h>
4825 __isl_give isl_basic_set *
4826 isl_set_unshifted_simple_hull(
4827 __isl_take isl_set *set);
4828 __isl_give isl_basic_set *isl_set_simple_hull(
4829 __isl_take isl_set *set);
4830 __isl_give isl_basic_set *
4831 isl_set_plain_unshifted_simple_hull(
4832 __isl_take isl_set *set);
4833 __isl_give isl_basic_set *
4834 isl_set_unshifted_simple_hull_from_set_list(
4835 __isl_take isl_set *set,
4836 __isl_take isl_set_list *list);
4838 #include <isl/map.h>
4839 __isl_give isl_basic_map *
4840 isl_map_unshifted_simple_hull(
4841 __isl_take isl_map *map);
4842 __isl_give isl_basic_map *isl_map_simple_hull(
4843 __isl_take isl_map *map);
4844 __isl_give isl_basic_map *
4845 isl_map_plain_unshifted_simple_hull(
4846 __isl_take isl_map *map);
4847 __isl_give isl_basic_map *
4848 isl_map_unshifted_simple_hull_from_map_list(
4849 __isl_take isl_map *map,
4850 __isl_take isl_map_list *list);
4852 #include <isl/union_map.h>
4853 __isl_give isl_union_map *isl_union_map_simple_hull(
4854 __isl_take isl_union_map *umap);
4856 These functions compute a single basic set or relation
4857 that contains the whole input set or relation.
4858 In particular, the output is described by translates
4859 of the constraints describing the basic sets or relations in the input.
4860 In case of C<isl_set_unshifted_simple_hull>, only the original
4861 constraints are used, without any translation.
4862 In case of C<isl_set_plain_unshifted_simple_hull> and
4863 C<isl_map_plain_unshifted_simple_hull>, the result is described
4864 by original constraints that are obviously satisfied
4865 by the entire input set or relation.
4866 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4867 C<isl_map_unshifted_simple_hull_from_map_list>, the
4868 constraints are taken from the elements of the second argument.
4872 (See \autoref{s:simple hull}.)
4878 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4879 __isl_take isl_basic_set *bset);
4880 __isl_give isl_basic_set *isl_set_affine_hull(
4881 __isl_take isl_set *set);
4882 __isl_give isl_union_set *isl_union_set_affine_hull(
4883 __isl_take isl_union_set *uset);
4884 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4885 __isl_take isl_basic_map *bmap);
4886 __isl_give isl_basic_map *isl_map_affine_hull(
4887 __isl_take isl_map *map);
4888 __isl_give isl_union_map *isl_union_map_affine_hull(
4889 __isl_take isl_union_map *umap);
4891 In case of union sets and relations, the affine hull is computed
4894 =item * Polyhedral hull
4896 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4897 __isl_take isl_set *set);
4898 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4899 __isl_take isl_map *map);
4900 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4901 __isl_take isl_union_set *uset);
4902 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4903 __isl_take isl_union_map *umap);
4905 These functions compute a single basic set or relation
4906 not involving any existentially quantified variables
4907 that contains the whole input set or relation.
4908 In case of union sets and relations, the polyhedral hull is computed
4911 =item * Other approximations
4913 #include <isl/set.h>
4914 __isl_give isl_basic_set *
4915 isl_basic_set_drop_constraints_involving_dims(
4916 __isl_take isl_basic_set *bset,
4917 enum isl_dim_type type,
4918 unsigned first, unsigned n);
4919 __isl_give isl_basic_set *
4920 isl_basic_set_drop_constraints_not_involving_dims(
4921 __isl_take isl_basic_set *bset,
4922 enum isl_dim_type type,
4923 unsigned first, unsigned n);
4924 __isl_give isl_set *
4925 isl_set_drop_constraints_involving_dims(
4926 __isl_take isl_set *set,
4927 enum isl_dim_type type,
4928 unsigned first, unsigned n);
4929 __isl_give isl_set *
4930 isl_set_drop_constraints_not_involving_dims(
4931 __isl_take isl_set *set,
4932 enum isl_dim_type type,
4933 unsigned first, unsigned n);
4935 #include <isl/map.h>
4936 __isl_give isl_basic_map *
4937 isl_basic_map_drop_constraints_involving_dims(
4938 __isl_take isl_basic_map *bmap,
4939 enum isl_dim_type type,
4940 unsigned first, unsigned n);
4941 __isl_give isl_basic_map *
4942 isl_basic_map_drop_constraints_not_involving_dims(
4943 __isl_take isl_basic_map *bmap,
4944 enum isl_dim_type type,
4945 unsigned first, unsigned n);
4946 __isl_give isl_map *
4947 isl_map_drop_constraints_involving_dims(
4948 __isl_take isl_map *map,
4949 enum isl_dim_type type,
4950 unsigned first, unsigned n);
4951 __isl_give isl_map *
4952 isl_map_drop_constraints_not_involving_dims(
4953 __isl_take isl_map *map,
4954 enum isl_dim_type type,
4955 unsigned first, unsigned n);
4957 These functions drop any constraints (not) involving the specified dimensions.
4958 Note that the result depends on the representation of the input.
4960 #include <isl/polynomial.h>
4961 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4962 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4963 __isl_give isl_union_pw_qpolynomial *
4964 isl_union_pw_qpolynomial_to_polynomial(
4965 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4967 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4968 the polynomial will be an overapproximation. If C<sign> is negative,
4969 it will be an underapproximation. If C<sign> is zero, the approximation
4970 will lie somewhere in between.
4974 __isl_give isl_basic_set *isl_basic_set_sample(
4975 __isl_take isl_basic_set *bset);
4976 __isl_give isl_basic_set *isl_set_sample(
4977 __isl_take isl_set *set);
4978 __isl_give isl_basic_map *isl_basic_map_sample(
4979 __isl_take isl_basic_map *bmap);
4980 __isl_give isl_basic_map *isl_map_sample(
4981 __isl_take isl_map *map);
4983 If the input (basic) set or relation is non-empty, then return
4984 a singleton subset of the input. Otherwise, return an empty set.
4986 =item * Optimization
4988 #include <isl/ilp.h>
4989 __isl_give isl_val *isl_basic_set_max_val(
4990 __isl_keep isl_basic_set *bset,
4991 __isl_keep isl_aff *obj);
4992 __isl_give isl_val *isl_set_min_val(
4993 __isl_keep isl_set *set,
4994 __isl_keep isl_aff *obj);
4995 __isl_give isl_val *isl_set_max_val(
4996 __isl_keep isl_set *set,
4997 __isl_keep isl_aff *obj);
4998 __isl_give isl_multi_val *
4999 isl_union_set_min_multi_union_pw_aff(
5000 __isl_keep isl_union_set *set,
5001 __isl_keep isl_multi_union_pw_aff *obj);
5003 Compute the minimum or maximum of the integer affine expression C<obj>
5004 over the points in C<set>, returning the result in C<opt>.
5005 The result is C<NULL> in case of an error, the optimal value in case
5006 there is one, negative infinity or infinity if the problem is unbounded and
5007 NaN if the problem is empty.
5009 =item * Parametric optimization
5011 __isl_give isl_pw_aff *isl_set_dim_min(
5012 __isl_take isl_set *set, int pos);
5013 __isl_give isl_pw_aff *isl_set_dim_max(
5014 __isl_take isl_set *set, int pos);
5015 __isl_give isl_pw_aff *isl_map_dim_max(
5016 __isl_take isl_map *map, int pos);
5018 Compute the minimum or maximum of the given set or output dimension
5019 as a function of the parameters (and input dimensions), but independently
5020 of the other set or output dimensions.
5021 For lexicographic optimization, see L<"Lexicographic Optimization">.
5025 The following functions compute either the set of (rational) coefficient
5026 values of valid constraints for the given set or the set of (rational)
5027 values satisfying the constraints with coefficients from the given set.
5028 Internally, these two sets of functions perform essentially the
5029 same operations, except that the set of coefficients is assumed to
5030 be a cone, while the set of values may be any polyhedron.
5031 The current implementation is based on the Farkas lemma and
5032 Fourier-Motzkin elimination, but this may change or be made optional
5033 in future. In particular, future implementations may use different
5034 dualization algorithms or skip the elimination step.
5036 __isl_give isl_basic_set *isl_basic_set_coefficients(
5037 __isl_take isl_basic_set *bset);
5038 __isl_give isl_basic_set *isl_set_coefficients(
5039 __isl_take isl_set *set);
5040 __isl_give isl_union_set *isl_union_set_coefficients(
5041 __isl_take isl_union_set *bset);
5042 __isl_give isl_basic_set *isl_basic_set_solutions(
5043 __isl_take isl_basic_set *bset);
5044 __isl_give isl_basic_set *isl_set_solutions(
5045 __isl_take isl_set *set);
5046 __isl_give isl_union_set *isl_union_set_solutions(
5047 __isl_take isl_union_set *bset);
5051 __isl_give isl_map *isl_map_fixed_power_val(
5052 __isl_take isl_map *map,
5053 __isl_take isl_val *exp);
5054 __isl_give isl_union_map *
5055 isl_union_map_fixed_power_val(
5056 __isl_take isl_union_map *umap,
5057 __isl_take isl_val *exp);
5059 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5060 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5061 of C<map> is computed.
5063 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5065 __isl_give isl_union_map *isl_union_map_power(
5066 __isl_take isl_union_map *umap, int *exact);
5068 Compute a parametric representation for all positive powers I<k> of C<map>.
5069 The result maps I<k> to a nested relation corresponding to the
5070 I<k>th power of C<map>.
5071 The result may be an overapproximation. If the result is known to be exact,
5072 then C<*exact> is set to C<1>.
5074 =item * Transitive closure
5076 __isl_give isl_map *isl_map_transitive_closure(
5077 __isl_take isl_map *map, int *exact);
5078 __isl_give isl_union_map *isl_union_map_transitive_closure(
5079 __isl_take isl_union_map *umap, int *exact);
5081 Compute the transitive closure of C<map>.
5082 The result may be an overapproximation. If the result is known to be exact,
5083 then C<*exact> is set to C<1>.
5085 =item * Reaching path lengths
5087 __isl_give isl_map *isl_map_reaching_path_lengths(
5088 __isl_take isl_map *map, int *exact);
5090 Compute a relation that maps each element in the range of C<map>
5091 to the lengths of all paths composed of edges in C<map> that
5092 end up in the given element.
5093 The result may be an overapproximation. If the result is known to be exact,
5094 then C<*exact> is set to C<1>.
5095 To compute the I<maximal> path length, the resulting relation
5096 should be postprocessed by C<isl_map_lexmax>.
5097 In particular, if the input relation is a dependence relation
5098 (mapping sources to sinks), then the maximal path length corresponds
5099 to the free schedule.
5100 Note, however, that C<isl_map_lexmax> expects the maximum to be
5101 finite, so if the path lengths are unbounded (possibly due to
5102 the overapproximation), then you will get an error message.
5106 #include <isl/space.h>
5107 __isl_give isl_space *isl_space_wrap(
5108 __isl_take isl_space *space);
5109 __isl_give isl_space *isl_space_unwrap(
5110 __isl_take isl_space *space);
5112 #include <isl/local_space.h>
5113 __isl_give isl_local_space *isl_local_space_wrap(
5114 __isl_take isl_local_space *ls);
5116 #include <isl/set.h>
5117 __isl_give isl_basic_map *isl_basic_set_unwrap(
5118 __isl_take isl_basic_set *bset);
5119 __isl_give isl_map *isl_set_unwrap(
5120 __isl_take isl_set *set);
5122 #include <isl/map.h>
5123 __isl_give isl_basic_set *isl_basic_map_wrap(
5124 __isl_take isl_basic_map *bmap);
5125 __isl_give isl_set *isl_map_wrap(
5126 __isl_take isl_map *map);
5128 #include <isl/union_set.h>
5129 __isl_give isl_union_map *isl_union_set_unwrap(
5130 __isl_take isl_union_set *uset);
5132 #include <isl/union_map.h>
5133 __isl_give isl_union_set *isl_union_map_wrap(
5134 __isl_take isl_union_map *umap);
5136 The input to C<isl_space_unwrap> should
5137 be the space of a set, while that of
5138 C<isl_space_wrap> should be the space of a relation.
5139 Conversely, the output of C<isl_space_unwrap> is the space
5140 of a relation, while that of C<isl_space_wrap> is the space of a set.
5144 Remove any internal structure of domain (and range) of the given
5145 set or relation. If there is any such internal structure in the input,
5146 then the name of the space is also removed.
5148 #include <isl/local_space.h>
5149 __isl_give isl_local_space *
5150 isl_local_space_flatten_domain(
5151 __isl_take isl_local_space *ls);
5152 __isl_give isl_local_space *
5153 isl_local_space_flatten_range(
5154 __isl_take isl_local_space *ls);
5156 #include <isl/set.h>
5157 __isl_give isl_basic_set *isl_basic_set_flatten(
5158 __isl_take isl_basic_set *bset);
5159 __isl_give isl_set *isl_set_flatten(
5160 __isl_take isl_set *set);
5162 #include <isl/map.h>
5163 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5164 __isl_take isl_basic_map *bmap);
5165 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5166 __isl_take isl_basic_map *bmap);
5167 __isl_give isl_map *isl_map_flatten_range(
5168 __isl_take isl_map *map);
5169 __isl_give isl_map *isl_map_flatten_domain(
5170 __isl_take isl_map *map);
5171 __isl_give isl_basic_map *isl_basic_map_flatten(
5172 __isl_take isl_basic_map *bmap);
5173 __isl_give isl_map *isl_map_flatten(
5174 __isl_take isl_map *map);
5176 #include <isl/val.h>
5177 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5178 __isl_take isl_multi_val *mv);
5180 #include <isl/aff.h>
5181 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5182 __isl_take isl_multi_aff *ma);
5183 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5184 __isl_take isl_multi_aff *ma);
5185 __isl_give isl_multi_pw_aff *
5186 isl_multi_pw_aff_flatten_range(
5187 __isl_take isl_multi_pw_aff *mpa);
5188 __isl_give isl_multi_union_pw_aff *
5189 isl_multi_union_pw_aff_flatten_range(
5190 __isl_take isl_multi_union_pw_aff *mupa);
5192 #include <isl/map.h>
5193 __isl_give isl_map *isl_set_flatten_map(
5194 __isl_take isl_set *set);
5196 The function above constructs a relation
5197 that maps the input set to a flattened version of the set.
5201 Lift the input set to a space with extra dimensions corresponding
5202 to the existentially quantified variables in the input.
5203 In particular, the result lives in a wrapped map where the domain
5204 is the original space and the range corresponds to the original
5205 existentially quantified variables.
5207 #include <isl/set.h>
5208 __isl_give isl_basic_set *isl_basic_set_lift(
5209 __isl_take isl_basic_set *bset);
5210 __isl_give isl_set *isl_set_lift(
5211 __isl_take isl_set *set);
5212 __isl_give isl_union_set *isl_union_set_lift(
5213 __isl_take isl_union_set *uset);
5215 Given a local space that contains the existentially quantified
5216 variables of a set, a basic relation that, when applied to
5217 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5218 can be constructed using the following function.
5220 #include <isl/local_space.h>
5221 __isl_give isl_basic_map *isl_local_space_lifting(
5222 __isl_take isl_local_space *ls);
5224 #include <isl/aff.h>
5225 __isl_give isl_multi_aff *isl_multi_aff_lift(
5226 __isl_take isl_multi_aff *maff,
5227 __isl_give isl_local_space **ls);
5229 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5230 then it is assigned the local space that lies at the basis of
5231 the lifting applied.
5233 =item * Internal Product
5235 #include <isl/space.h>
5236 __isl_give isl_space *isl_space_zip(
5237 __isl_take isl_space *space);
5239 #include <isl/map.h>
5240 __isl_give isl_basic_map *isl_basic_map_zip(
5241 __isl_take isl_basic_map *bmap);
5242 __isl_give isl_map *isl_map_zip(
5243 __isl_take isl_map *map);
5245 #include <isl/union_map.h>
5246 __isl_give isl_union_map *isl_union_map_zip(
5247 __isl_take isl_union_map *umap);
5249 Given a relation with nested relations for domain and range,
5250 interchange the range of the domain with the domain of the range.
5254 #include <isl/space.h>
5255 __isl_give isl_space *isl_space_curry(
5256 __isl_take isl_space *space);
5257 __isl_give isl_space *isl_space_uncurry(
5258 __isl_take isl_space *space);
5260 #include <isl/map.h>
5261 __isl_give isl_basic_map *isl_basic_map_curry(
5262 __isl_take isl_basic_map *bmap);
5263 __isl_give isl_basic_map *isl_basic_map_uncurry(
5264 __isl_take isl_basic_map *bmap);
5265 __isl_give isl_map *isl_map_curry(
5266 __isl_take isl_map *map);
5267 __isl_give isl_map *isl_map_uncurry(
5268 __isl_take isl_map *map);
5270 #include <isl/union_map.h>
5271 __isl_give isl_union_map *isl_union_map_curry(
5272 __isl_take isl_union_map *umap);
5273 __isl_give isl_union_map *isl_union_map_uncurry(
5274 __isl_take isl_union_map *umap);
5276 Given a relation with a nested relation for domain,
5277 the C<curry> functions
5278 move the range of the nested relation out of the domain
5279 and use it as the domain of a nested relation in the range,
5280 with the original range as range of this nested relation.
5281 The C<uncurry> functions perform the inverse operation.
5283 #include <isl/space.h>
5284 __isl_give isl_space *isl_space_range_curry(
5285 __isl_take isl_space *space);
5287 #include <isl/map.h>
5288 __isl_give isl_map *isl_map_range_curry(
5289 __isl_take isl_map *map);
5291 #include <isl/union_map.h>
5292 __isl_give isl_union_map *isl_union_map_range_curry(
5293 __isl_take isl_union_map *umap);
5295 These functions apply the currying to the relation that
5296 is nested inside the range of the input.
5298 =item * Aligning parameters
5300 Change the order of the parameters of the given set, relation
5302 such that the first parameters match those of C<model>.
5303 This may involve the introduction of extra parameters.
5304 All parameters need to be named.
5306 #include <isl/space.h>
5307 __isl_give isl_space *isl_space_align_params(
5308 __isl_take isl_space *space1,
5309 __isl_take isl_space *space2)
5311 #include <isl/set.h>
5312 __isl_give isl_basic_set *isl_basic_set_align_params(
5313 __isl_take isl_basic_set *bset,
5314 __isl_take isl_space *model);
5315 __isl_give isl_set *isl_set_align_params(
5316 __isl_take isl_set *set,
5317 __isl_take isl_space *model);
5319 #include <isl/map.h>
5320 __isl_give isl_basic_map *isl_basic_map_align_params(
5321 __isl_take isl_basic_map *bmap,
5322 __isl_take isl_space *model);
5323 __isl_give isl_map *isl_map_align_params(
5324 __isl_take isl_map *map,
5325 __isl_take isl_space *model);
5327 #include <isl/val.h>
5328 __isl_give isl_multi_val *isl_multi_val_align_params(
5329 __isl_take isl_multi_val *mv,
5330 __isl_take isl_space *model);
5332 #include <isl/aff.h>
5333 __isl_give isl_aff *isl_aff_align_params(
5334 __isl_take isl_aff *aff,
5335 __isl_take isl_space *model);
5336 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5337 __isl_take isl_multi_aff *multi,
5338 __isl_take isl_space *model);
5339 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5340 __isl_take isl_pw_aff *pwaff,
5341 __isl_take isl_space *model);
5342 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5343 __isl_take isl_pw_multi_aff *pma,
5344 __isl_take isl_space *model);
5345 __isl_give isl_union_pw_aff *
5346 isl_union_pw_aff_align_params(
5347 __isl_take isl_union_pw_aff *upa,
5348 __isl_take isl_space *model);
5349 __isl_give isl_union_pw_multi_aff *
5350 isl_union_pw_multi_aff_align_params(
5351 __isl_take isl_union_pw_multi_aff *upma,
5352 __isl_take isl_space *model);
5353 __isl_give isl_multi_union_pw_aff *
5354 isl_multi_union_pw_aff_align_params(
5355 __isl_take isl_multi_union_pw_aff *mupa,
5356 __isl_take isl_space *model);
5358 #include <isl/polynomial.h>
5359 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5360 __isl_take isl_qpolynomial *qp,
5361 __isl_take isl_space *model);
5363 =item * Unary Arithmetic Operations
5365 #include <isl/set.h>
5366 __isl_give isl_set *isl_set_neg(
5367 __isl_take isl_set *set);
5368 #include <isl/map.h>
5369 __isl_give isl_map *isl_map_neg(
5370 __isl_take isl_map *map);
5372 C<isl_set_neg> constructs a set containing the opposites of
5373 the elements in its argument.
5374 The domain of the result of C<isl_map_neg> is the same
5375 as the domain of its argument. The corresponding range
5376 elements are the opposites of the corresponding range
5377 elements in the argument.
5379 #include <isl/val.h>
5380 __isl_give isl_multi_val *isl_multi_val_neg(
5381 __isl_take isl_multi_val *mv);
5383 #include <isl/aff.h>
5384 __isl_give isl_aff *isl_aff_neg(
5385 __isl_take isl_aff *aff);
5386 __isl_give isl_multi_aff *isl_multi_aff_neg(
5387 __isl_take isl_multi_aff *ma);
5388 __isl_give isl_pw_aff *isl_pw_aff_neg(
5389 __isl_take isl_pw_aff *pwaff);
5390 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5391 __isl_take isl_pw_multi_aff *pma);
5392 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5393 __isl_take isl_multi_pw_aff *mpa);
5394 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5395 __isl_take isl_union_pw_aff *upa);
5396 __isl_give isl_union_pw_multi_aff *
5397 isl_union_pw_multi_aff_neg(
5398 __isl_take isl_union_pw_multi_aff *upma);
5399 __isl_give isl_multi_union_pw_aff *
5400 isl_multi_union_pw_aff_neg(
5401 __isl_take isl_multi_union_pw_aff *mupa);
5402 __isl_give isl_aff *isl_aff_ceil(
5403 __isl_take isl_aff *aff);
5404 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5405 __isl_take isl_pw_aff *pwaff);
5406 __isl_give isl_aff *isl_aff_floor(
5407 __isl_take isl_aff *aff);
5408 __isl_give isl_multi_aff *isl_multi_aff_floor(
5409 __isl_take isl_multi_aff *ma);
5410 __isl_give isl_pw_aff *isl_pw_aff_floor(
5411 __isl_take isl_pw_aff *pwaff);
5412 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5413 __isl_take isl_union_pw_aff *upa);
5414 __isl_give isl_multi_union_pw_aff *
5415 isl_multi_union_pw_aff_floor(
5416 __isl_take isl_multi_union_pw_aff *mupa);
5418 #include <isl/aff.h>
5419 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5420 __isl_take isl_pw_aff_list *list);
5421 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5422 __isl_take isl_pw_aff_list *list);
5424 #include <isl/polynomial.h>
5425 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5426 __isl_take isl_qpolynomial *qp);
5427 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5428 __isl_take isl_pw_qpolynomial *pwqp);
5429 __isl_give isl_union_pw_qpolynomial *
5430 isl_union_pw_qpolynomial_neg(
5431 __isl_take isl_union_pw_qpolynomial *upwqp);
5432 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5433 __isl_take isl_qpolynomial *qp,
5435 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5436 __isl_take isl_pw_qpolynomial *pwqp,
5441 The following functions evaluate a function in a point.
5443 #include <isl/polynomial.h>
5444 __isl_give isl_val *isl_pw_qpolynomial_eval(
5445 __isl_take isl_pw_qpolynomial *pwqp,
5446 __isl_take isl_point *pnt);
5447 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5448 __isl_take isl_pw_qpolynomial_fold *pwf,
5449 __isl_take isl_point *pnt);
5450 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5451 __isl_take isl_union_pw_qpolynomial *upwqp,
5452 __isl_take isl_point *pnt);
5453 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5454 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5455 __isl_take isl_point *pnt);
5457 =item * Dimension manipulation
5459 It is usually not advisable to directly change the (input or output)
5460 space of a set or a relation as this removes the name and the internal
5461 structure of the space. However, the functions below can be useful
5462 to add new parameters, assuming
5463 C<isl_set_align_params> and C<isl_map_align_params>
5466 #include <isl/space.h>
5467 __isl_give isl_space *isl_space_add_dims(
5468 __isl_take isl_space *space,
5469 enum isl_dim_type type, unsigned n);
5470 __isl_give isl_space *isl_space_insert_dims(
5471 __isl_take isl_space *space,
5472 enum isl_dim_type type, unsigned pos, unsigned n);
5473 __isl_give isl_space *isl_space_drop_dims(
5474 __isl_take isl_space *space,
5475 enum isl_dim_type type, unsigned first, unsigned n);
5476 __isl_give isl_space *isl_space_move_dims(
5477 __isl_take isl_space *space,
5478 enum isl_dim_type dst_type, unsigned dst_pos,
5479 enum isl_dim_type src_type, unsigned src_pos,
5482 #include <isl/local_space.h>
5483 __isl_give isl_local_space *isl_local_space_add_dims(
5484 __isl_take isl_local_space *ls,
5485 enum isl_dim_type type, unsigned n);
5486 __isl_give isl_local_space *isl_local_space_insert_dims(
5487 __isl_take isl_local_space *ls,
5488 enum isl_dim_type type, unsigned first, unsigned n);
5489 __isl_give isl_local_space *isl_local_space_drop_dims(
5490 __isl_take isl_local_space *ls,
5491 enum isl_dim_type type, unsigned first, unsigned n);
5493 #include <isl/set.h>
5494 __isl_give isl_basic_set *isl_basic_set_add_dims(
5495 __isl_take isl_basic_set *bset,
5496 enum isl_dim_type type, unsigned n);
5497 __isl_give isl_set *isl_set_add_dims(
5498 __isl_take isl_set *set,
5499 enum isl_dim_type type, unsigned n);
5500 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5501 __isl_take isl_basic_set *bset,
5502 enum isl_dim_type type, unsigned pos,
5504 __isl_give isl_set *isl_set_insert_dims(
5505 __isl_take isl_set *set,
5506 enum isl_dim_type type, unsigned pos, unsigned n);
5507 __isl_give isl_basic_set *isl_basic_set_move_dims(
5508 __isl_take isl_basic_set *bset,
5509 enum isl_dim_type dst_type, unsigned dst_pos,
5510 enum isl_dim_type src_type, unsigned src_pos,
5512 __isl_give isl_set *isl_set_move_dims(
5513 __isl_take isl_set *set,
5514 enum isl_dim_type dst_type, unsigned dst_pos,
5515 enum isl_dim_type src_type, unsigned src_pos,
5518 #include <isl/map.h>
5519 __isl_give isl_basic_map *isl_basic_map_add_dims(
5520 __isl_take isl_basic_map *bmap,
5521 enum isl_dim_type type, unsigned n);
5522 __isl_give isl_map *isl_map_add_dims(
5523 __isl_take isl_map *map,
5524 enum isl_dim_type type, unsigned n);
5525 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5526 __isl_take isl_basic_map *bmap,
5527 enum isl_dim_type type, unsigned pos,
5529 __isl_give isl_map *isl_map_insert_dims(
5530 __isl_take isl_map *map,
5531 enum isl_dim_type type, unsigned pos, unsigned n);
5532 __isl_give isl_basic_map *isl_basic_map_move_dims(
5533 __isl_take isl_basic_map *bmap,
5534 enum isl_dim_type dst_type, unsigned dst_pos,
5535 enum isl_dim_type src_type, unsigned src_pos,
5537 __isl_give isl_map *isl_map_move_dims(
5538 __isl_take isl_map *map,
5539 enum isl_dim_type dst_type, unsigned dst_pos,
5540 enum isl_dim_type src_type, unsigned src_pos,
5543 #include <isl/val.h>
5544 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5545 __isl_take isl_multi_val *mv,
5546 enum isl_dim_type type, unsigned first, unsigned n);
5547 __isl_give isl_multi_val *isl_multi_val_add_dims(
5548 __isl_take isl_multi_val *mv,
5549 enum isl_dim_type type, unsigned n);
5550 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5551 __isl_take isl_multi_val *mv,
5552 enum isl_dim_type type, unsigned first, unsigned n);
5554 #include <isl/aff.h>
5555 __isl_give isl_aff *isl_aff_insert_dims(
5556 __isl_take isl_aff *aff,
5557 enum isl_dim_type type, unsigned first, unsigned n);
5558 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5559 __isl_take isl_multi_aff *ma,
5560 enum isl_dim_type type, unsigned first, unsigned n);
5561 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5562 __isl_take isl_pw_aff *pwaff,
5563 enum isl_dim_type type, unsigned first, unsigned n);
5564 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5565 __isl_take isl_multi_pw_aff *mpa,
5566 enum isl_dim_type type, unsigned first, unsigned n);
5567 __isl_give isl_aff *isl_aff_add_dims(
5568 __isl_take isl_aff *aff,
5569 enum isl_dim_type type, unsigned n);
5570 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5571 __isl_take isl_multi_aff *ma,
5572 enum isl_dim_type type, unsigned n);
5573 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5574 __isl_take isl_pw_aff *pwaff,
5575 enum isl_dim_type type, unsigned n);
5576 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5577 __isl_take isl_multi_pw_aff *mpa,
5578 enum isl_dim_type type, unsigned n);
5579 __isl_give isl_aff *isl_aff_drop_dims(
5580 __isl_take isl_aff *aff,
5581 enum isl_dim_type type, unsigned first, unsigned n);
5582 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5583 __isl_take isl_multi_aff *maff,
5584 enum isl_dim_type type, unsigned first, unsigned n);
5585 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5586 __isl_take isl_pw_aff *pwaff,
5587 enum isl_dim_type type, unsigned first, unsigned n);
5588 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5589 __isl_take isl_pw_multi_aff *pma,
5590 enum isl_dim_type type, unsigned first, unsigned n);
5591 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5592 __isl_take isl_union_pw_aff *upa,
5593 enum isl_dim_type type, unsigned first, unsigned n);
5594 __isl_give isl_union_pw_multi_aff *
5595 isl_union_pw_multi_aff_drop_dims(
5596 __isl_take isl_union_pw_multi_aff *upma,
5597 enum isl_dim_type type,
5598 unsigned first, unsigned n);
5599 __isl_give isl_multi_union_pw_aff *
5600 isl_multi_union_pw_aff_drop_dims(
5601 __isl_take isl_multi_union_pw_aff *mupa,
5602 enum isl_dim_type type, unsigned first,
5604 __isl_give isl_aff *isl_aff_move_dims(
5605 __isl_take isl_aff *aff,
5606 enum isl_dim_type dst_type, unsigned dst_pos,
5607 enum isl_dim_type src_type, unsigned src_pos,
5609 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5610 __isl_take isl_multi_aff *ma,
5611 enum isl_dim_type dst_type, unsigned dst_pos,
5612 enum isl_dim_type src_type, unsigned src_pos,
5614 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5615 __isl_take isl_pw_aff *pa,
5616 enum isl_dim_type dst_type, unsigned dst_pos,
5617 enum isl_dim_type src_type, unsigned src_pos,
5619 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5620 __isl_take isl_multi_pw_aff *pma,
5621 enum isl_dim_type dst_type, unsigned dst_pos,
5622 enum isl_dim_type src_type, unsigned src_pos,
5625 #include <isl/polynomial.h>
5626 __isl_give isl_union_pw_qpolynomial *
5627 isl_union_pw_qpolynomial_drop_dims(
5628 __isl_take isl_union_pw_qpolynomial *upwqp,
5629 enum isl_dim_type type,
5630 unsigned first, unsigned n);
5631 __isl_give isl_union_pw_qpolynomial_fold *
5632 isl_union_pw_qpolynomial_fold_drop_dims(
5633 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5634 enum isl_dim_type type,
5635 unsigned first, unsigned n);
5637 The operations on union expressions can only manipulate parameters.
5641 =head2 Binary Operations
5643 The two arguments of a binary operation not only need to live
5644 in the same C<isl_ctx>, they currently also need to have
5645 the same (number of) parameters.
5647 =head3 Basic Operations
5651 =item * Intersection
5653 #include <isl/local_space.h>
5654 __isl_give isl_local_space *isl_local_space_intersect(
5655 __isl_take isl_local_space *ls1,
5656 __isl_take isl_local_space *ls2);
5658 #include <isl/set.h>
5659 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5660 __isl_take isl_basic_set *bset1,
5661 __isl_take isl_basic_set *bset2);
5662 __isl_give isl_basic_set *isl_basic_set_intersect(
5663 __isl_take isl_basic_set *bset1,
5664 __isl_take isl_basic_set *bset2);
5665 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5666 __isl_take struct isl_basic_set_list *list);
5667 __isl_give isl_set *isl_set_intersect_params(
5668 __isl_take isl_set *set,
5669 __isl_take isl_set *params);
5670 __isl_give isl_set *isl_set_intersect(
5671 __isl_take isl_set *set1,
5672 __isl_take isl_set *set2);
5674 #include <isl/map.h>
5675 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5676 __isl_take isl_basic_map *bmap,
5677 __isl_take isl_basic_set *bset);
5678 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5679 __isl_take isl_basic_map *bmap,
5680 __isl_take isl_basic_set *bset);
5681 __isl_give isl_basic_map *isl_basic_map_intersect(
5682 __isl_take isl_basic_map *bmap1,
5683 __isl_take isl_basic_map *bmap2);
5684 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5685 __isl_take isl_basic_map_list *list);
5686 __isl_give isl_map *isl_map_intersect_params(
5687 __isl_take isl_map *map,
5688 __isl_take isl_set *params);
5689 __isl_give isl_map *isl_map_intersect_domain(
5690 __isl_take isl_map *map,
5691 __isl_take isl_set *set);
5692 __isl_give isl_map *isl_map_intersect_range(
5693 __isl_take isl_map *map,
5694 __isl_take isl_set *set);
5695 __isl_give isl_map *isl_map_intersect(
5696 __isl_take isl_map *map1,
5697 __isl_take isl_map *map2);
5699 #include <isl/union_set.h>
5700 __isl_give isl_union_set *isl_union_set_intersect_params(
5701 __isl_take isl_union_set *uset,
5702 __isl_take isl_set *set);
5703 __isl_give isl_union_set *isl_union_set_intersect(
5704 __isl_take isl_union_set *uset1,
5705 __isl_take isl_union_set *uset2);
5707 #include <isl/union_map.h>
5708 __isl_give isl_union_map *isl_union_map_intersect_params(
5709 __isl_take isl_union_map *umap,
5710 __isl_take isl_set *set);
5711 __isl_give isl_union_map *isl_union_map_intersect_domain(
5712 __isl_take isl_union_map *umap,
5713 __isl_take isl_union_set *uset);
5714 __isl_give isl_union_map *isl_union_map_intersect_range(
5715 __isl_take isl_union_map *umap,
5716 __isl_take isl_union_set *uset);
5717 __isl_give isl_union_map *isl_union_map_intersect(
5718 __isl_take isl_union_map *umap1,
5719 __isl_take isl_union_map *umap2);
5721 #include <isl/aff.h>
5722 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5723 __isl_take isl_pw_aff *pa,
5724 __isl_take isl_set *set);
5725 __isl_give isl_multi_pw_aff *
5726 isl_multi_pw_aff_intersect_domain(
5727 __isl_take isl_multi_pw_aff *mpa,
5728 __isl_take isl_set *domain);
5729 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5730 __isl_take isl_pw_multi_aff *pma,
5731 __isl_take isl_set *set);
5732 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5733 __isl_take isl_union_pw_aff *upa,
5734 __isl_take isl_union_set *uset);
5735 __isl_give isl_union_pw_multi_aff *
5736 isl_union_pw_multi_aff_intersect_domain(
5737 __isl_take isl_union_pw_multi_aff *upma,
5738 __isl_take isl_union_set *uset);
5739 __isl_give isl_multi_union_pw_aff *
5740 isl_multi_union_pw_aff_intersect_domain(
5741 __isl_take isl_multi_union_pw_aff *mupa,
5742 __isl_take isl_union_set *uset);
5743 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5744 __isl_take isl_pw_aff *pa,
5745 __isl_take isl_set *set);
5746 __isl_give isl_multi_pw_aff *
5747 isl_multi_pw_aff_intersect_params(
5748 __isl_take isl_multi_pw_aff *mpa,
5749 __isl_take isl_set *set);
5750 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5751 __isl_take isl_pw_multi_aff *pma,
5752 __isl_take isl_set *set);
5753 __isl_give isl_union_pw_aff *
5754 isl_union_pw_aff_intersect_params(
5755 __isl_take isl_union_pw_aff *upa,
5756 __isl_give isl_union_pw_multi_aff *
5757 isl_union_pw_multi_aff_intersect_params(
5758 __isl_take isl_union_pw_multi_aff *upma,
5759 __isl_take isl_set *set);
5760 __isl_give isl_multi_union_pw_aff *
5761 isl_multi_union_pw_aff_intersect_params(
5762 __isl_take isl_multi_union_pw_aff *mupa,
5763 __isl_take isl_set *params);
5764 isl_multi_union_pw_aff_intersect_range(
5765 __isl_take isl_multi_union_pw_aff *mupa,
5766 __isl_take isl_set *set);
5768 #include <isl/polynomial.h>
5769 __isl_give isl_pw_qpolynomial *
5770 isl_pw_qpolynomial_intersect_domain(
5771 __isl_take isl_pw_qpolynomial *pwpq,
5772 __isl_take isl_set *set);
5773 __isl_give isl_union_pw_qpolynomial *
5774 isl_union_pw_qpolynomial_intersect_domain(
5775 __isl_take isl_union_pw_qpolynomial *upwpq,
5776 __isl_take isl_union_set *uset);
5777 __isl_give isl_union_pw_qpolynomial_fold *
5778 isl_union_pw_qpolynomial_fold_intersect_domain(
5779 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5780 __isl_take isl_union_set *uset);
5781 __isl_give isl_pw_qpolynomial *
5782 isl_pw_qpolynomial_intersect_params(
5783 __isl_take isl_pw_qpolynomial *pwpq,
5784 __isl_take isl_set *set);
5785 __isl_give isl_pw_qpolynomial_fold *
5786 isl_pw_qpolynomial_fold_intersect_params(
5787 __isl_take isl_pw_qpolynomial_fold *pwf,
5788 __isl_take isl_set *set);
5789 __isl_give isl_union_pw_qpolynomial *
5790 isl_union_pw_qpolynomial_intersect_params(
5791 __isl_take isl_union_pw_qpolynomial *upwpq,
5792 __isl_take isl_set *set);
5793 __isl_give isl_union_pw_qpolynomial_fold *
5794 isl_union_pw_qpolynomial_fold_intersect_params(
5795 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5796 __isl_take isl_set *set);
5798 The second argument to the C<_params> functions needs to be
5799 a parametric (basic) set. For the other functions, a parametric set
5800 for either argument is only allowed if the other argument is
5801 a parametric set as well.
5802 The list passed to C<isl_basic_set_list_intersect> needs to have
5803 at least one element and all elements need to live in the same space.
5804 The function C<isl_multi_union_pw_aff_intersect_range>
5805 restricts the input function to those shared domain elements
5806 that map to the specified range.
5810 #include <isl/set.h>
5811 __isl_give isl_set *isl_basic_set_union(
5812 __isl_take isl_basic_set *bset1,
5813 __isl_take isl_basic_set *bset2);
5814 __isl_give isl_set *isl_set_union(
5815 __isl_take isl_set *set1,
5816 __isl_take isl_set *set2);
5817 __isl_give isl_set *isl_set_list_union(
5818 __isl_take isl_set_list *list);
5820 #include <isl/map.h>
5821 __isl_give isl_map *isl_basic_map_union(
5822 __isl_take isl_basic_map *bmap1,
5823 __isl_take isl_basic_map *bmap2);
5824 __isl_give isl_map *isl_map_union(
5825 __isl_take isl_map *map1,
5826 __isl_take isl_map *map2);
5828 #include <isl/union_set.h>
5829 __isl_give isl_union_set *isl_union_set_union(
5830 __isl_take isl_union_set *uset1,
5831 __isl_take isl_union_set *uset2);
5832 __isl_give isl_union_set *isl_union_set_list_union(
5833 __isl_take isl_union_set_list *list);
5835 #include <isl/union_map.h>
5836 __isl_give isl_union_map *isl_union_map_union(
5837 __isl_take isl_union_map *umap1,
5838 __isl_take isl_union_map *umap2);
5840 The list passed to C<isl_set_list_union> needs to have
5841 at least one element and all elements need to live in the same space.
5843 =item * Set difference
5845 #include <isl/set.h>
5846 __isl_give isl_set *isl_set_subtract(
5847 __isl_take isl_set *set1,
5848 __isl_take isl_set *set2);
5850 #include <isl/map.h>
5851 __isl_give isl_map *isl_map_subtract(
5852 __isl_take isl_map *map1,
5853 __isl_take isl_map *map2);
5854 __isl_give isl_map *isl_map_subtract_domain(
5855 __isl_take isl_map *map,
5856 __isl_take isl_set *dom);
5857 __isl_give isl_map *isl_map_subtract_range(
5858 __isl_take isl_map *map,
5859 __isl_take isl_set *dom);
5861 #include <isl/union_set.h>
5862 __isl_give isl_union_set *isl_union_set_subtract(
5863 __isl_take isl_union_set *uset1,
5864 __isl_take isl_union_set *uset2);
5866 #include <isl/union_map.h>
5867 __isl_give isl_union_map *isl_union_map_subtract(
5868 __isl_take isl_union_map *umap1,
5869 __isl_take isl_union_map *umap2);
5870 __isl_give isl_union_map *isl_union_map_subtract_domain(
5871 __isl_take isl_union_map *umap,
5872 __isl_take isl_union_set *dom);
5873 __isl_give isl_union_map *isl_union_map_subtract_range(
5874 __isl_take isl_union_map *umap,
5875 __isl_take isl_union_set *dom);
5877 #include <isl/aff.h>
5878 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5879 __isl_take isl_pw_aff *pa,
5880 __isl_take isl_set *set);
5881 __isl_give isl_pw_multi_aff *
5882 isl_pw_multi_aff_subtract_domain(
5883 __isl_take isl_pw_multi_aff *pma,
5884 __isl_take isl_set *set);
5885 __isl_give isl_union_pw_aff *
5886 isl_union_pw_aff_subtract_domain(
5887 __isl_take isl_union_pw_aff *upa,
5888 __isl_take isl_union_set *uset);
5889 __isl_give isl_union_pw_multi_aff *
5890 isl_union_pw_multi_aff_subtract_domain(
5891 __isl_take isl_union_pw_multi_aff *upma,
5892 __isl_take isl_set *set);
5894 #include <isl/polynomial.h>
5895 __isl_give isl_pw_qpolynomial *
5896 isl_pw_qpolynomial_subtract_domain(
5897 __isl_take isl_pw_qpolynomial *pwpq,
5898 __isl_take isl_set *set);
5899 __isl_give isl_pw_qpolynomial_fold *
5900 isl_pw_qpolynomial_fold_subtract_domain(
5901 __isl_take isl_pw_qpolynomial_fold *pwf,
5902 __isl_take isl_set *set);
5903 __isl_give isl_union_pw_qpolynomial *
5904 isl_union_pw_qpolynomial_subtract_domain(
5905 __isl_take isl_union_pw_qpolynomial *upwpq,
5906 __isl_take isl_union_set *uset);
5907 __isl_give isl_union_pw_qpolynomial_fold *
5908 isl_union_pw_qpolynomial_fold_subtract_domain(
5909 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5910 __isl_take isl_union_set *uset);
5914 #include <isl/space.h>
5915 __isl_give isl_space *isl_space_join(
5916 __isl_take isl_space *left,
5917 __isl_take isl_space *right);
5919 #include <isl/map.h>
5920 __isl_give isl_basic_set *isl_basic_set_apply(
5921 __isl_take isl_basic_set *bset,
5922 __isl_take isl_basic_map *bmap);
5923 __isl_give isl_set *isl_set_apply(
5924 __isl_take isl_set *set,
5925 __isl_take isl_map *map);
5926 __isl_give isl_union_set *isl_union_set_apply(
5927 __isl_take isl_union_set *uset,
5928 __isl_take isl_union_map *umap);
5929 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5930 __isl_take isl_basic_map *bmap1,
5931 __isl_take isl_basic_map *bmap2);
5932 __isl_give isl_basic_map *isl_basic_map_apply_range(
5933 __isl_take isl_basic_map *bmap1,
5934 __isl_take isl_basic_map *bmap2);
5935 __isl_give isl_map *isl_map_apply_domain(
5936 __isl_take isl_map *map1,
5937 __isl_take isl_map *map2);
5938 __isl_give isl_map *isl_map_apply_range(
5939 __isl_take isl_map *map1,
5940 __isl_take isl_map *map2);
5942 #include <isl/union_map.h>
5943 __isl_give isl_union_map *isl_union_map_apply_domain(
5944 __isl_take isl_union_map *umap1,
5945 __isl_take isl_union_map *umap2);
5946 __isl_give isl_union_map *isl_union_map_apply_range(
5947 __isl_take isl_union_map *umap1,
5948 __isl_take isl_union_map *umap2);
5950 #include <isl/aff.h>
5951 __isl_give isl_union_pw_aff *
5952 isl_multi_union_pw_aff_apply_aff(
5953 __isl_take isl_multi_union_pw_aff *mupa,
5954 __isl_take isl_aff *aff);
5955 __isl_give isl_union_pw_aff *
5956 isl_multi_union_pw_aff_apply_pw_aff(
5957 __isl_take isl_multi_union_pw_aff *mupa,
5958 __isl_take isl_pw_aff *pa);
5959 __isl_give isl_multi_union_pw_aff *
5960 isl_multi_union_pw_aff_apply_multi_aff(
5961 __isl_take isl_multi_union_pw_aff *mupa,
5962 __isl_take isl_multi_aff *ma);
5963 __isl_give isl_multi_union_pw_aff *
5964 isl_multi_union_pw_aff_apply_pw_multi_aff(
5965 __isl_take isl_multi_union_pw_aff *mupa,
5966 __isl_take isl_pw_multi_aff *pma);
5968 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5969 over the shared domain of the elements of the input. The dimension is
5970 required to be greater than zero.
5971 The C<isl_multi_union_pw_aff> argument of
5972 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5973 but only if the range of the C<isl_multi_aff> argument
5974 is also zero-dimensional.
5975 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5977 #include <isl/polynomial.h>
5978 __isl_give isl_pw_qpolynomial_fold *
5979 isl_set_apply_pw_qpolynomial_fold(
5980 __isl_take isl_set *set,
5981 __isl_take isl_pw_qpolynomial_fold *pwf,
5983 __isl_give isl_pw_qpolynomial_fold *
5984 isl_map_apply_pw_qpolynomial_fold(
5985 __isl_take isl_map *map,
5986 __isl_take isl_pw_qpolynomial_fold *pwf,
5988 __isl_give isl_union_pw_qpolynomial_fold *
5989 isl_union_set_apply_union_pw_qpolynomial_fold(
5990 __isl_take isl_union_set *uset,
5991 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5993 __isl_give isl_union_pw_qpolynomial_fold *
5994 isl_union_map_apply_union_pw_qpolynomial_fold(
5995 __isl_take isl_union_map *umap,
5996 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5999 The functions taking a map
6000 compose the given map with the given piecewise quasipolynomial reduction.
6001 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6002 over all elements in the intersection of the range of the map
6003 and the domain of the piecewise quasipolynomial reduction
6004 as a function of an element in the domain of the map.
6005 The functions taking a set compute a bound over all elements in the
6006 intersection of the set and the domain of the
6007 piecewise quasipolynomial reduction.
6011 #include <isl/set.h>
6012 __isl_give isl_basic_set *
6013 isl_basic_set_preimage_multi_aff(
6014 __isl_take isl_basic_set *bset,
6015 __isl_take isl_multi_aff *ma);
6016 __isl_give isl_set *isl_set_preimage_multi_aff(
6017 __isl_take isl_set *set,
6018 __isl_take isl_multi_aff *ma);
6019 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6020 __isl_take isl_set *set,
6021 __isl_take isl_pw_multi_aff *pma);
6022 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6023 __isl_take isl_set *set,
6024 __isl_take isl_multi_pw_aff *mpa);
6026 #include <isl/union_set.h>
6027 __isl_give isl_union_set *
6028 isl_union_set_preimage_multi_aff(
6029 __isl_take isl_union_set *uset,
6030 __isl_take isl_multi_aff *ma);
6031 __isl_give isl_union_set *
6032 isl_union_set_preimage_pw_multi_aff(
6033 __isl_take isl_union_set *uset,
6034 __isl_take isl_pw_multi_aff *pma);
6035 __isl_give isl_union_set *
6036 isl_union_set_preimage_union_pw_multi_aff(
6037 __isl_take isl_union_set *uset,
6038 __isl_take isl_union_pw_multi_aff *upma);
6040 #include <isl/map.h>
6041 __isl_give isl_basic_map *
6042 isl_basic_map_preimage_domain_multi_aff(
6043 __isl_take isl_basic_map *bmap,
6044 __isl_take isl_multi_aff *ma);
6045 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6046 __isl_take isl_map *map,
6047 __isl_take isl_multi_aff *ma);
6048 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6049 __isl_take isl_map *map,
6050 __isl_take isl_multi_aff *ma);
6051 __isl_give isl_map *
6052 isl_map_preimage_domain_pw_multi_aff(
6053 __isl_take isl_map *map,
6054 __isl_take isl_pw_multi_aff *pma);
6055 __isl_give isl_map *
6056 isl_map_preimage_range_pw_multi_aff(
6057 __isl_take isl_map *map,
6058 __isl_take isl_pw_multi_aff *pma);
6059 __isl_give isl_map *
6060 isl_map_preimage_domain_multi_pw_aff(
6061 __isl_take isl_map *map,
6062 __isl_take isl_multi_pw_aff *mpa);
6063 __isl_give isl_basic_map *
6064 isl_basic_map_preimage_range_multi_aff(
6065 __isl_take isl_basic_map *bmap,
6066 __isl_take isl_multi_aff *ma);
6068 #include <isl/union_map.h>
6069 __isl_give isl_union_map *
6070 isl_union_map_preimage_domain_multi_aff(
6071 __isl_take isl_union_map *umap,
6072 __isl_take isl_multi_aff *ma);
6073 __isl_give isl_union_map *
6074 isl_union_map_preimage_range_multi_aff(
6075 __isl_take isl_union_map *umap,
6076 __isl_take isl_multi_aff *ma);
6077 __isl_give isl_union_map *
6078 isl_union_map_preimage_domain_pw_multi_aff(
6079 __isl_take isl_union_map *umap,
6080 __isl_take isl_pw_multi_aff *pma);
6081 __isl_give isl_union_map *
6082 isl_union_map_preimage_range_pw_multi_aff(
6083 __isl_take isl_union_map *umap,
6084 __isl_take isl_pw_multi_aff *pma);
6085 __isl_give isl_union_map *
6086 isl_union_map_preimage_domain_union_pw_multi_aff(
6087 __isl_take isl_union_map *umap,
6088 __isl_take isl_union_pw_multi_aff *upma);
6089 __isl_give isl_union_map *
6090 isl_union_map_preimage_range_union_pw_multi_aff(
6091 __isl_take isl_union_map *umap,
6092 __isl_take isl_union_pw_multi_aff *upma);
6094 These functions compute the preimage of the given set or map domain/range under
6095 the given function. In other words, the expression is plugged
6096 into the set description or into the domain/range of the map.
6100 #include <isl/aff.h>
6101 __isl_give isl_aff *isl_aff_pullback_aff(
6102 __isl_take isl_aff *aff1,
6103 __isl_take isl_aff *aff2);
6104 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6105 __isl_take isl_aff *aff,
6106 __isl_take isl_multi_aff *ma);
6107 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6108 __isl_take isl_pw_aff *pa,
6109 __isl_take isl_multi_aff *ma);
6110 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6111 __isl_take isl_pw_aff *pa,
6112 __isl_take isl_pw_multi_aff *pma);
6113 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6114 __isl_take isl_pw_aff *pa,
6115 __isl_take isl_multi_pw_aff *mpa);
6116 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6117 __isl_take isl_multi_aff *ma1,
6118 __isl_take isl_multi_aff *ma2);
6119 __isl_give isl_pw_multi_aff *
6120 isl_pw_multi_aff_pullback_multi_aff(
6121 __isl_take isl_pw_multi_aff *pma,
6122 __isl_take isl_multi_aff *ma);
6123 __isl_give isl_multi_pw_aff *
6124 isl_multi_pw_aff_pullback_multi_aff(
6125 __isl_take isl_multi_pw_aff *mpa,
6126 __isl_take isl_multi_aff *ma);
6127 __isl_give isl_pw_multi_aff *
6128 isl_pw_multi_aff_pullback_pw_multi_aff(
6129 __isl_take isl_pw_multi_aff *pma1,
6130 __isl_take isl_pw_multi_aff *pma2);
6131 __isl_give isl_multi_pw_aff *
6132 isl_multi_pw_aff_pullback_pw_multi_aff(
6133 __isl_take isl_multi_pw_aff *mpa,
6134 __isl_take isl_pw_multi_aff *pma);
6135 __isl_give isl_multi_pw_aff *
6136 isl_multi_pw_aff_pullback_multi_pw_aff(
6137 __isl_take isl_multi_pw_aff *mpa1,
6138 __isl_take isl_multi_pw_aff *mpa2);
6139 __isl_give isl_union_pw_aff *
6140 isl_union_pw_aff_pullback_union_pw_multi_aff(
6141 __isl_take isl_union_pw_aff *upa,
6142 __isl_take isl_union_pw_multi_aff *upma);
6143 __isl_give isl_union_pw_multi_aff *
6144 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6145 __isl_take isl_union_pw_multi_aff *upma1,
6146 __isl_take isl_union_pw_multi_aff *upma2);
6147 __isl_give isl_multi_union_pw_aff *
6148 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6149 __isl_take isl_multi_union_pw_aff *mupa,
6150 __isl_take isl_union_pw_multi_aff *upma);
6152 These functions precompose the first expression by the second function.
6153 In other words, the second function is plugged
6154 into the first expression.
6158 #include <isl/aff.h>
6159 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6160 __isl_take isl_aff *aff1,
6161 __isl_take isl_aff *aff2);
6162 __isl_give isl_set *isl_aff_eq_set(
6163 __isl_take isl_aff *aff1,
6164 __isl_take isl_aff *aff2);
6165 __isl_give isl_basic_set *isl_aff_le_basic_set(
6166 __isl_take isl_aff *aff1,
6167 __isl_take isl_aff *aff2);
6168 __isl_give isl_set *isl_aff_le_set(
6169 __isl_take isl_aff *aff1,
6170 __isl_take isl_aff *aff2);
6171 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6172 __isl_take isl_aff *aff1,
6173 __isl_take isl_aff *aff2);
6174 __isl_give isl_set *isl_aff_ge_set(
6175 __isl_take isl_aff *aff1,
6176 __isl_take isl_aff *aff2);
6177 __isl_give isl_set *isl_pw_aff_eq_set(
6178 __isl_take isl_pw_aff *pwaff1,
6179 __isl_take isl_pw_aff *pwaff2);
6180 __isl_give isl_set *isl_pw_aff_ne_set(
6181 __isl_take isl_pw_aff *pwaff1,
6182 __isl_take isl_pw_aff *pwaff2);
6183 __isl_give isl_set *isl_pw_aff_le_set(
6184 __isl_take isl_pw_aff *pwaff1,
6185 __isl_take isl_pw_aff *pwaff2);
6186 __isl_give isl_set *isl_pw_aff_lt_set(
6187 __isl_take isl_pw_aff *pwaff1,
6188 __isl_take isl_pw_aff *pwaff2);
6189 __isl_give isl_set *isl_pw_aff_ge_set(
6190 __isl_take isl_pw_aff *pwaff1,
6191 __isl_take isl_pw_aff *pwaff2);
6192 __isl_give isl_set *isl_pw_aff_gt_set(
6193 __isl_take isl_pw_aff *pwaff1,
6194 __isl_take isl_pw_aff *pwaff2);
6196 __isl_give isl_set *isl_multi_aff_lex_le_set(
6197 __isl_take isl_multi_aff *ma1,
6198 __isl_take isl_multi_aff *ma2);
6199 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6200 __isl_take isl_multi_aff *ma1,
6201 __isl_take isl_multi_aff *ma2);
6202 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6203 __isl_take isl_multi_aff *ma1,
6204 __isl_take isl_multi_aff *ma2);
6205 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6206 __isl_take isl_multi_aff *ma1,
6207 __isl_take isl_multi_aff *ma2);
6209 __isl_give isl_set *isl_pw_aff_list_eq_set(
6210 __isl_take isl_pw_aff_list *list1,
6211 __isl_take isl_pw_aff_list *list2);
6212 __isl_give isl_set *isl_pw_aff_list_ne_set(
6213 __isl_take isl_pw_aff_list *list1,
6214 __isl_take isl_pw_aff_list *list2);
6215 __isl_give isl_set *isl_pw_aff_list_le_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_lt_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_ge_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_gt_set(
6225 __isl_take isl_pw_aff_list *list1,
6226 __isl_take isl_pw_aff_list *list2);
6228 The function C<isl_aff_ge_basic_set> returns a basic set
6229 containing those elements in the shared space
6230 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6231 The function C<isl_pw_aff_ge_set> returns a set
6232 containing those elements in the shared domain
6233 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6234 greater than or equal to C<pwaff2>.
6235 The function C<isl_multi_aff_lex_le_set> returns a set
6236 containing those elements in the shared domain space
6237 where C<ma1> is lexicographically smaller than or
6239 The functions operating on C<isl_pw_aff_list> apply the corresponding
6240 C<isl_pw_aff> function to each pair of elements in the two lists.
6242 #include <isl/aff.h>
6243 __isl_give isl_map *isl_pw_aff_eq_map(
6244 __isl_take isl_pw_aff *pa1,
6245 __isl_take isl_pw_aff *pa2);
6246 __isl_give isl_map *isl_pw_aff_lt_map(
6247 __isl_take isl_pw_aff *pa1,
6248 __isl_take isl_pw_aff *pa2);
6249 __isl_give isl_map *isl_pw_aff_gt_map(
6250 __isl_take isl_pw_aff *pa1,
6251 __isl_take isl_pw_aff *pa2);
6253 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6254 __isl_take isl_multi_pw_aff *mpa1,
6255 __isl_take isl_multi_pw_aff *mpa2);
6256 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6257 __isl_take isl_multi_pw_aff *mpa1,
6258 __isl_take isl_multi_pw_aff *mpa2);
6259 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6260 __isl_take isl_multi_pw_aff *mpa1,
6261 __isl_take isl_multi_pw_aff *mpa2);
6263 These functions return a map between domain elements of the arguments
6264 where the function values satisfy the given relation.
6266 #include <isl/union_map.h>
6267 __isl_give isl_union_map *
6268 isl_union_map_eq_at_multi_union_pw_aff(
6269 __isl_take isl_union_map *umap,
6270 __isl_take isl_multi_union_pw_aff *mupa);
6271 __isl_give isl_union_map *
6272 isl_union_map_lex_lt_at_multi_union_pw_aff(
6273 __isl_take isl_union_map *umap,
6274 __isl_take isl_multi_union_pw_aff *mupa);
6275 __isl_give isl_union_map *
6276 isl_union_map_lex_gt_at_multi_union_pw_aff(
6277 __isl_take isl_union_map *umap,
6278 __isl_take isl_multi_union_pw_aff *mupa);
6280 These functions select the subset of elements in the union map
6281 that have an equal or lexicographically smaller function value.
6283 =item * Cartesian Product
6285 #include <isl/space.h>
6286 __isl_give isl_space *isl_space_product(
6287 __isl_take isl_space *space1,
6288 __isl_take isl_space *space2);
6289 __isl_give isl_space *isl_space_domain_product(
6290 __isl_take isl_space *space1,
6291 __isl_take isl_space *space2);
6292 __isl_give isl_space *isl_space_range_product(
6293 __isl_take isl_space *space1,
6294 __isl_take isl_space *space2);
6297 C<isl_space_product>, C<isl_space_domain_product>
6298 and C<isl_space_range_product> take pairs or relation spaces and
6299 produce a single relations space, where either the domain, the range
6300 or both domain and range are wrapped spaces of relations between
6301 the domains and/or ranges of the input spaces.
6302 If the product is only constructed over the domain or the range
6303 then the ranges or the domains of the inputs should be the same.
6304 The function C<isl_space_product> also accepts a pair of set spaces,
6305 in which case it returns a wrapped space of a relation between the
6308 #include <isl/set.h>
6309 __isl_give isl_set *isl_set_product(
6310 __isl_take isl_set *set1,
6311 __isl_take isl_set *set2);
6313 #include <isl/map.h>
6314 __isl_give isl_basic_map *isl_basic_map_domain_product(
6315 __isl_take isl_basic_map *bmap1,
6316 __isl_take isl_basic_map *bmap2);
6317 __isl_give isl_basic_map *isl_basic_map_range_product(
6318 __isl_take isl_basic_map *bmap1,
6319 __isl_take isl_basic_map *bmap2);
6320 __isl_give isl_basic_map *isl_basic_map_product(
6321 __isl_take isl_basic_map *bmap1,
6322 __isl_take isl_basic_map *bmap2);
6323 __isl_give isl_map *isl_map_domain_product(
6324 __isl_take isl_map *map1,
6325 __isl_take isl_map *map2);
6326 __isl_give isl_map *isl_map_range_product(
6327 __isl_take isl_map *map1,
6328 __isl_take isl_map *map2);
6329 __isl_give isl_map *isl_map_product(
6330 __isl_take isl_map *map1,
6331 __isl_take isl_map *map2);
6333 #include <isl/union_set.h>
6334 __isl_give isl_union_set *isl_union_set_product(
6335 __isl_take isl_union_set *uset1,
6336 __isl_take isl_union_set *uset2);
6338 #include <isl/union_map.h>
6339 __isl_give isl_union_map *isl_union_map_domain_product(
6340 __isl_take isl_union_map *umap1,
6341 __isl_take isl_union_map *umap2);
6342 __isl_give isl_union_map *isl_union_map_range_product(
6343 __isl_take isl_union_map *umap1,
6344 __isl_take isl_union_map *umap2);
6345 __isl_give isl_union_map *isl_union_map_product(
6346 __isl_take isl_union_map *umap1,
6347 __isl_take isl_union_map *umap2);
6349 #include <isl/val.h>
6350 __isl_give isl_multi_val *isl_multi_val_range_product(
6351 __isl_take isl_multi_val *mv1,
6352 __isl_take isl_multi_val *mv2);
6353 __isl_give isl_multi_val *isl_multi_val_product(
6354 __isl_take isl_multi_val *mv1,
6355 __isl_take isl_multi_val *mv2);
6357 #include <isl/aff.h>
6358 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6359 __isl_take isl_multi_aff *ma1,
6360 __isl_take isl_multi_aff *ma2);
6361 __isl_give isl_multi_aff *isl_multi_aff_product(
6362 __isl_take isl_multi_aff *ma1,
6363 __isl_take isl_multi_aff *ma2);
6364 __isl_give isl_multi_pw_aff *
6365 isl_multi_pw_aff_range_product(
6366 __isl_take isl_multi_pw_aff *mpa1,
6367 __isl_take isl_multi_pw_aff *mpa2);
6368 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6369 __isl_take isl_multi_pw_aff *mpa1,
6370 __isl_take isl_multi_pw_aff *mpa2);
6371 __isl_give isl_pw_multi_aff *
6372 isl_pw_multi_aff_range_product(
6373 __isl_take isl_pw_multi_aff *pma1,
6374 __isl_take isl_pw_multi_aff *pma2);
6375 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6376 __isl_take isl_pw_multi_aff *pma1,
6377 __isl_take isl_pw_multi_aff *pma2);
6378 __isl_give isl_multi_union_pw_aff *
6379 isl_multi_union_pw_aff_range_product(
6380 __isl_take isl_multi_union_pw_aff *mupa1,
6381 __isl_take isl_multi_union_pw_aff *mupa2);
6383 The above functions compute the cross product of the given
6384 sets, relations or functions. The domains and ranges of the results
6385 are wrapped maps between domains and ranges of the inputs.
6386 To obtain a ``flat'' product, use the following functions
6389 #include <isl/set.h>
6390 __isl_give isl_basic_set *isl_basic_set_flat_product(
6391 __isl_take isl_basic_set *bset1,
6392 __isl_take isl_basic_set *bset2);
6393 __isl_give isl_set *isl_set_flat_product(
6394 __isl_take isl_set *set1,
6395 __isl_take isl_set *set2);
6397 #include <isl/map.h>
6398 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6399 __isl_take isl_basic_map *bmap1,
6400 __isl_take isl_basic_map *bmap2);
6401 __isl_give isl_map *isl_map_flat_domain_product(
6402 __isl_take isl_map *map1,
6403 __isl_take isl_map *map2);
6404 __isl_give isl_map *isl_map_flat_range_product(
6405 __isl_take isl_map *map1,
6406 __isl_take isl_map *map2);
6407 __isl_give isl_basic_map *isl_basic_map_flat_product(
6408 __isl_take isl_basic_map *bmap1,
6409 __isl_take isl_basic_map *bmap2);
6410 __isl_give isl_map *isl_map_flat_product(
6411 __isl_take isl_map *map1,
6412 __isl_take isl_map *map2);
6414 #include <isl/union_map.h>
6415 __isl_give isl_union_map *
6416 isl_union_map_flat_domain_product(
6417 __isl_take isl_union_map *umap1,
6418 __isl_take isl_union_map *umap2);
6419 __isl_give isl_union_map *
6420 isl_union_map_flat_range_product(
6421 __isl_take isl_union_map *umap1,
6422 __isl_take isl_union_map *umap2);
6424 #include <isl/val.h>
6425 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6426 __isl_take isl_multi_val *mv1,
6427 __isl_take isl_multi_aff *mv2);
6429 #include <isl/aff.h>
6430 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6431 __isl_take isl_multi_aff *ma1,
6432 __isl_take isl_multi_aff *ma2);
6433 __isl_give isl_pw_multi_aff *
6434 isl_pw_multi_aff_flat_range_product(
6435 __isl_take isl_pw_multi_aff *pma1,
6436 __isl_take isl_pw_multi_aff *pma2);
6437 __isl_give isl_multi_pw_aff *
6438 isl_multi_pw_aff_flat_range_product(
6439 __isl_take isl_multi_pw_aff *mpa1,
6440 __isl_take isl_multi_pw_aff *mpa2);
6441 __isl_give isl_union_pw_multi_aff *
6442 isl_union_pw_multi_aff_flat_range_product(
6443 __isl_take isl_union_pw_multi_aff *upma1,
6444 __isl_take isl_union_pw_multi_aff *upma2);
6445 __isl_give isl_multi_union_pw_aff *
6446 isl_multi_union_pw_aff_flat_range_product(
6447 __isl_take isl_multi_union_pw_aff *mupa1,
6448 __isl_take isl_multi_union_pw_aff *mupa2);
6450 #include <isl/space.h>
6451 __isl_give isl_space *isl_space_factor_domain(
6452 __isl_take isl_space *space);
6453 __isl_give isl_space *isl_space_factor_range(
6454 __isl_take isl_space *space);
6455 __isl_give isl_space *isl_space_domain_factor_domain(
6456 __isl_take isl_space *space);
6457 __isl_give isl_space *isl_space_domain_factor_range(
6458 __isl_take isl_space *space);
6459 __isl_give isl_space *isl_space_range_factor_domain(
6460 __isl_take isl_space *space);
6461 __isl_give isl_space *isl_space_range_factor_range(
6462 __isl_take isl_space *space);
6464 The functions C<isl_space_range_factor_domain> and
6465 C<isl_space_range_factor_range> extract the two arguments from
6466 the result of a call to C<isl_space_range_product>.
6468 The arguments of a call to a product can be extracted
6469 from the result using the following functions.
6471 #include <isl/map.h>
6472 __isl_give isl_map *isl_map_factor_domain(
6473 __isl_take isl_map *map);
6474 __isl_give isl_map *isl_map_factor_range(
6475 __isl_take isl_map *map);
6476 __isl_give isl_map *isl_map_domain_factor_domain(
6477 __isl_take isl_map *map);
6478 __isl_give isl_map *isl_map_domain_factor_range(
6479 __isl_take isl_map *map);
6480 __isl_give isl_map *isl_map_range_factor_domain(
6481 __isl_take isl_map *map);
6482 __isl_give isl_map *isl_map_range_factor_range(
6483 __isl_take isl_map *map);
6485 #include <isl/union_map.h>
6486 __isl_give isl_union_map *isl_union_map_factor_domain(
6487 __isl_take isl_union_map *umap);
6488 __isl_give isl_union_map *isl_union_map_factor_range(
6489 __isl_take isl_union_map *umap);
6490 __isl_give isl_union_map *
6491 isl_union_map_domain_factor_domain(
6492 __isl_take isl_union_map *umap);
6493 __isl_give isl_union_map *
6494 isl_union_map_domain_factor_range(
6495 __isl_take isl_union_map *umap);
6496 __isl_give isl_union_map *
6497 isl_union_map_range_factor_domain(
6498 __isl_take isl_union_map *umap);
6499 __isl_give isl_union_map *
6500 isl_union_map_range_factor_range(
6501 __isl_take isl_union_map *umap);
6503 #include <isl/val.h>
6504 __isl_give isl_multi_val *isl_multi_val_factor_range(
6505 __isl_take isl_multi_val *mv);
6506 __isl_give isl_multi_val *
6507 isl_multi_val_range_factor_domain(
6508 __isl_take isl_multi_val *mv);
6509 __isl_give isl_multi_val *
6510 isl_multi_val_range_factor_range(
6511 __isl_take isl_multi_val *mv);
6513 #include <isl/aff.h>
6514 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6515 __isl_take isl_multi_aff *ma);
6516 __isl_give isl_multi_aff *
6517 isl_multi_aff_range_factor_domain(
6518 __isl_take isl_multi_aff *ma);
6519 __isl_give isl_multi_aff *
6520 isl_multi_aff_range_factor_range(
6521 __isl_take isl_multi_aff *ma);
6522 __isl_give isl_multi_pw_aff *
6523 isl_multi_pw_aff_factor_range(
6524 __isl_take isl_multi_pw_aff *mpa);
6525 __isl_give isl_multi_pw_aff *
6526 isl_multi_pw_aff_range_factor_domain(
6527 __isl_take isl_multi_pw_aff *mpa);
6528 __isl_give isl_multi_pw_aff *
6529 isl_multi_pw_aff_range_factor_range(
6530 __isl_take isl_multi_pw_aff *mpa);
6531 __isl_give isl_multi_union_pw_aff *
6532 isl_multi_union_pw_aff_factor_range(
6533 __isl_take isl_multi_union_pw_aff *mupa);
6534 __isl_give isl_multi_union_pw_aff *
6535 isl_multi_union_pw_aff_range_factor_domain(
6536 __isl_take isl_multi_union_pw_aff *mupa);
6537 __isl_give isl_multi_union_pw_aff *
6538 isl_multi_union_pw_aff_range_factor_range(
6539 __isl_take isl_multi_union_pw_aff *mupa);
6541 The splice functions are a generalization of the flat product functions,
6542 where the second argument may be inserted at any position inside
6543 the first argument rather than being placed at the end.
6544 The functions C<isl_multi_val_factor_range>,
6545 C<isl_multi_aff_factor_range>,
6546 C<isl_multi_pw_aff_factor_range> and
6547 C<isl_multi_union_pw_aff_factor_range>
6548 take functions that live in a set space.
6550 #include <isl/val.h>
6551 __isl_give isl_multi_val *isl_multi_val_range_splice(
6552 __isl_take isl_multi_val *mv1, unsigned pos,
6553 __isl_take isl_multi_val *mv2);
6555 #include <isl/aff.h>
6556 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6557 __isl_take isl_multi_aff *ma1, unsigned pos,
6558 __isl_take isl_multi_aff *ma2);
6559 __isl_give isl_multi_aff *isl_multi_aff_splice(
6560 __isl_take isl_multi_aff *ma1,
6561 unsigned in_pos, unsigned out_pos,
6562 __isl_take isl_multi_aff *ma2);
6563 __isl_give isl_multi_pw_aff *
6564 isl_multi_pw_aff_range_splice(
6565 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6566 __isl_take isl_multi_pw_aff *mpa2);
6567 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6568 __isl_take isl_multi_pw_aff *mpa1,
6569 unsigned in_pos, unsigned out_pos,
6570 __isl_take isl_multi_pw_aff *mpa2);
6571 __isl_give isl_multi_union_pw_aff *
6572 isl_multi_union_pw_aff_range_splice(
6573 __isl_take isl_multi_union_pw_aff *mupa1,
6575 __isl_take isl_multi_union_pw_aff *mupa2);
6577 =item * Simplification
6579 When applied to a set or relation,
6580 the gist operation returns a set or relation that has the
6581 same intersection with the context as the input set or relation.
6582 Any implicit equality in the intersection is made explicit in the result,
6583 while all inequalities that are redundant with respect to the intersection
6585 In case of union sets and relations, the gist operation is performed
6588 When applied to a function,
6589 the gist operation applies the set gist operation to each of
6590 the cells in the domain of the input piecewise expression.
6591 The context is also exploited
6592 to simplify the expression associated to each cell.
6594 #include <isl/set.h>
6595 __isl_give isl_basic_set *isl_basic_set_gist(
6596 __isl_take isl_basic_set *bset,
6597 __isl_take isl_basic_set *context);
6598 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6599 __isl_take isl_set *context);
6600 __isl_give isl_set *isl_set_gist_params(
6601 __isl_take isl_set *set,
6602 __isl_take isl_set *context);
6604 #include <isl/map.h>
6605 __isl_give isl_basic_map *isl_basic_map_gist(
6606 __isl_take isl_basic_map *bmap,
6607 __isl_take isl_basic_map *context);
6608 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6609 __isl_take isl_basic_map *bmap,
6610 __isl_take isl_basic_set *context);
6611 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6612 __isl_take isl_map *context);
6613 __isl_give isl_map *isl_map_gist_params(
6614 __isl_take isl_map *map,
6615 __isl_take isl_set *context);
6616 __isl_give isl_map *isl_map_gist_domain(
6617 __isl_take isl_map *map,
6618 __isl_take isl_set *context);
6619 __isl_give isl_map *isl_map_gist_range(
6620 __isl_take isl_map *map,
6621 __isl_take isl_set *context);
6623 #include <isl/union_set.h>
6624 __isl_give isl_union_set *isl_union_set_gist(
6625 __isl_take isl_union_set *uset,
6626 __isl_take isl_union_set *context);
6627 __isl_give isl_union_set *isl_union_set_gist_params(
6628 __isl_take isl_union_set *uset,
6629 __isl_take isl_set *set);
6631 #include <isl/union_map.h>
6632 __isl_give isl_union_map *isl_union_map_gist(
6633 __isl_take isl_union_map *umap,
6634 __isl_take isl_union_map *context);
6635 __isl_give isl_union_map *isl_union_map_gist_params(
6636 __isl_take isl_union_map *umap,
6637 __isl_take isl_set *set);
6638 __isl_give isl_union_map *isl_union_map_gist_domain(
6639 __isl_take isl_union_map *umap,
6640 __isl_take isl_union_set *uset);
6641 __isl_give isl_union_map *isl_union_map_gist_range(
6642 __isl_take isl_union_map *umap,
6643 __isl_take isl_union_set *uset);
6645 #include <isl/aff.h>
6646 __isl_give isl_aff *isl_aff_gist_params(
6647 __isl_take isl_aff *aff,
6648 __isl_take isl_set *context);
6649 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6650 __isl_take isl_set *context);
6651 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6652 __isl_take isl_multi_aff *maff,
6653 __isl_take isl_set *context);
6654 __isl_give isl_multi_aff *isl_multi_aff_gist(
6655 __isl_take isl_multi_aff *maff,
6656 __isl_take isl_set *context);
6657 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6658 __isl_take isl_pw_aff *pwaff,
6659 __isl_take isl_set *context);
6660 __isl_give isl_pw_aff *isl_pw_aff_gist(
6661 __isl_take isl_pw_aff *pwaff,
6662 __isl_take isl_set *context);
6663 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6664 __isl_take isl_pw_multi_aff *pma,
6665 __isl_take isl_set *set);
6666 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6667 __isl_take isl_pw_multi_aff *pma,
6668 __isl_take isl_set *set);
6669 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6670 __isl_take isl_multi_pw_aff *mpa,
6671 __isl_take isl_set *set);
6672 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6673 __isl_take isl_multi_pw_aff *mpa,
6674 __isl_take isl_set *set);
6675 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6676 __isl_take isl_union_pw_aff *upa,
6677 __isl_take isl_union_set *context);
6678 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6679 __isl_take isl_union_pw_aff *upa,
6680 __isl_take isl_set *context);
6681 __isl_give isl_union_pw_multi_aff *
6682 isl_union_pw_multi_aff_gist_params(
6683 __isl_take isl_union_pw_multi_aff *upma,
6684 __isl_take isl_set *context);
6685 __isl_give isl_union_pw_multi_aff *
6686 isl_union_pw_multi_aff_gist(
6687 __isl_take isl_union_pw_multi_aff *upma,
6688 __isl_take isl_union_set *context);
6689 __isl_give isl_multi_union_pw_aff *
6690 isl_multi_union_pw_aff_gist_params(
6691 __isl_take isl_multi_union_pw_aff *aff,
6692 __isl_take isl_set *context);
6693 __isl_give isl_multi_union_pw_aff *
6694 isl_multi_union_pw_aff_gist(
6695 __isl_take isl_multi_union_pw_aff *aff,
6696 __isl_take isl_union_set *context);
6698 #include <isl/polynomial.h>
6699 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6700 __isl_take isl_qpolynomial *qp,
6701 __isl_take isl_set *context);
6702 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6703 __isl_take isl_qpolynomial *qp,
6704 __isl_take isl_set *context);
6705 __isl_give isl_qpolynomial_fold *
6706 isl_qpolynomial_fold_gist_params(
6707 __isl_take isl_qpolynomial_fold *fold,
6708 __isl_take isl_set *context);
6709 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6710 __isl_take isl_qpolynomial_fold *fold,
6711 __isl_take isl_set *context);
6712 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6713 __isl_take isl_pw_qpolynomial *pwqp,
6714 __isl_take isl_set *context);
6715 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6716 __isl_take isl_pw_qpolynomial *pwqp,
6717 __isl_take isl_set *context);
6718 __isl_give isl_pw_qpolynomial_fold *
6719 isl_pw_qpolynomial_fold_gist(
6720 __isl_take isl_pw_qpolynomial_fold *pwf,
6721 __isl_take isl_set *context);
6722 __isl_give isl_pw_qpolynomial_fold *
6723 isl_pw_qpolynomial_fold_gist_params(
6724 __isl_take isl_pw_qpolynomial_fold *pwf,
6725 __isl_take isl_set *context);
6726 __isl_give isl_union_pw_qpolynomial *
6727 isl_union_pw_qpolynomial_gist_params(
6728 __isl_take isl_union_pw_qpolynomial *upwqp,
6729 __isl_take isl_set *context);
6730 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6731 __isl_take isl_union_pw_qpolynomial *upwqp,
6732 __isl_take isl_union_set *context);
6733 __isl_give isl_union_pw_qpolynomial_fold *
6734 isl_union_pw_qpolynomial_fold_gist(
6735 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6736 __isl_take isl_union_set *context);
6737 __isl_give isl_union_pw_qpolynomial_fold *
6738 isl_union_pw_qpolynomial_fold_gist_params(
6739 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6740 __isl_take isl_set *context);
6742 =item * Binary Arithmetic Operations
6744 #include <isl/set.h>
6745 __isl_give isl_set *isl_set_sum(
6746 __isl_take isl_set *set1,
6747 __isl_take isl_set *set2);
6748 #include <isl/map.h>
6749 __isl_give isl_map *isl_map_sum(
6750 __isl_take isl_map *map1,
6751 __isl_take isl_map *map2);
6753 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6754 i.e., the set containing the sums of pairs of elements from
6755 C<set1> and C<set2>.
6756 The domain of the result of C<isl_map_sum> is the intersection
6757 of the domains of its two arguments. The corresponding range
6758 elements are the sums of the corresponding range elements
6759 in the two arguments.
6761 #include <isl/val.h>
6762 __isl_give isl_multi_val *isl_multi_val_add(
6763 __isl_take isl_multi_val *mv1,
6764 __isl_take isl_multi_val *mv2);
6765 __isl_give isl_multi_val *isl_multi_val_sub(
6766 __isl_take isl_multi_val *mv1,
6767 __isl_take isl_multi_val *mv2);
6769 #include <isl/aff.h>
6770 __isl_give isl_aff *isl_aff_add(
6771 __isl_take isl_aff *aff1,
6772 __isl_take isl_aff *aff2);
6773 __isl_give isl_multi_aff *isl_multi_aff_add(
6774 __isl_take isl_multi_aff *maff1,
6775 __isl_take isl_multi_aff *maff2);
6776 __isl_give isl_pw_aff *isl_pw_aff_add(
6777 __isl_take isl_pw_aff *pwaff1,
6778 __isl_take isl_pw_aff *pwaff2);
6779 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6780 __isl_take isl_multi_pw_aff *mpa1,
6781 __isl_take isl_multi_pw_aff *mpa2);
6782 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6783 __isl_take isl_pw_multi_aff *pma1,
6784 __isl_take isl_pw_multi_aff *pma2);
6785 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6786 __isl_take isl_union_pw_aff *upa1,
6787 __isl_take isl_union_pw_aff *upa2);
6788 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6789 __isl_take isl_union_pw_multi_aff *upma1,
6790 __isl_take isl_union_pw_multi_aff *upma2);
6791 __isl_give isl_multi_union_pw_aff *
6792 isl_multi_union_pw_aff_add(
6793 __isl_take isl_multi_union_pw_aff *mupa1,
6794 __isl_take isl_multi_union_pw_aff *mupa2);
6795 __isl_give isl_pw_aff *isl_pw_aff_min(
6796 __isl_take isl_pw_aff *pwaff1,
6797 __isl_take isl_pw_aff *pwaff2);
6798 __isl_give isl_pw_aff *isl_pw_aff_max(
6799 __isl_take isl_pw_aff *pwaff1,
6800 __isl_take isl_pw_aff *pwaff2);
6801 __isl_give isl_aff *isl_aff_sub(
6802 __isl_take isl_aff *aff1,
6803 __isl_take isl_aff *aff2);
6804 __isl_give isl_multi_aff *isl_multi_aff_sub(
6805 __isl_take isl_multi_aff *ma1,
6806 __isl_take isl_multi_aff *ma2);
6807 __isl_give isl_pw_aff *isl_pw_aff_sub(
6808 __isl_take isl_pw_aff *pwaff1,
6809 __isl_take isl_pw_aff *pwaff2);
6810 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6811 __isl_take isl_multi_pw_aff *mpa1,
6812 __isl_take isl_multi_pw_aff *mpa2);
6813 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6814 __isl_take isl_pw_multi_aff *pma1,
6815 __isl_take isl_pw_multi_aff *pma2);
6816 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6817 __isl_take isl_union_pw_aff *upa1,
6818 __isl_take isl_union_pw_aff *upa2);
6819 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6820 __isl_take isl_union_pw_multi_aff *upma1,
6821 __isl_take isl_union_pw_multi_aff *upma2);
6822 __isl_give isl_multi_union_pw_aff *
6823 isl_multi_union_pw_aff_sub(
6824 __isl_take isl_multi_union_pw_aff *mupa1,
6825 __isl_take isl_multi_union_pw_aff *mupa2);
6827 C<isl_aff_sub> subtracts the second argument from the first.
6829 #include <isl/polynomial.h>
6830 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6831 __isl_take isl_qpolynomial *qp1,
6832 __isl_take isl_qpolynomial *qp2);
6833 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6834 __isl_take isl_pw_qpolynomial *pwqp1,
6835 __isl_take isl_pw_qpolynomial *pwqp2);
6836 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6837 __isl_take isl_pw_qpolynomial *pwqp1,
6838 __isl_take isl_pw_qpolynomial *pwqp2);
6839 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6840 __isl_take isl_pw_qpolynomial_fold *pwf1,
6841 __isl_take isl_pw_qpolynomial_fold *pwf2);
6842 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6843 __isl_take isl_union_pw_qpolynomial *upwqp1,
6844 __isl_take isl_union_pw_qpolynomial *upwqp2);
6845 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6846 __isl_take isl_qpolynomial *qp1,
6847 __isl_take isl_qpolynomial *qp2);
6848 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6849 __isl_take isl_pw_qpolynomial *pwqp1,
6850 __isl_take isl_pw_qpolynomial *pwqp2);
6851 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6852 __isl_take isl_union_pw_qpolynomial *upwqp1,
6853 __isl_take isl_union_pw_qpolynomial *upwqp2);
6854 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6855 __isl_take isl_pw_qpolynomial_fold *pwf1,
6856 __isl_take isl_pw_qpolynomial_fold *pwf2);
6857 __isl_give isl_union_pw_qpolynomial_fold *
6858 isl_union_pw_qpolynomial_fold_fold(
6859 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6860 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6862 #include <isl/aff.h>
6863 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6864 __isl_take isl_pw_aff *pwaff1,
6865 __isl_take isl_pw_aff *pwaff2);
6866 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6867 __isl_take isl_pw_multi_aff *pma1,
6868 __isl_take isl_pw_multi_aff *pma2);
6869 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6870 __isl_take isl_union_pw_aff *upa1,
6871 __isl_take isl_union_pw_aff *upa2);
6872 __isl_give isl_union_pw_multi_aff *
6873 isl_union_pw_multi_aff_union_add(
6874 __isl_take isl_union_pw_multi_aff *upma1,
6875 __isl_take isl_union_pw_multi_aff *upma2);
6876 __isl_give isl_multi_union_pw_aff *
6877 isl_multi_union_pw_aff_union_add(
6878 __isl_take isl_multi_union_pw_aff *mupa1,
6879 __isl_take isl_multi_union_pw_aff *mupa2);
6880 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6881 __isl_take isl_pw_aff *pwaff1,
6882 __isl_take isl_pw_aff *pwaff2);
6883 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6884 __isl_take isl_pw_aff *pwaff1,
6885 __isl_take isl_pw_aff *pwaff2);
6887 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6888 expression with a domain that is the union of those of C<pwaff1> and
6889 C<pwaff2> and such that on each cell, the quasi-affine expression is
6890 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6891 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6892 associated expression is the defined one.
6893 This in contrast to the C<isl_pw_aff_max> function, which is
6894 only defined on the shared definition domain of the arguments.
6896 #include <isl/val.h>
6897 __isl_give isl_multi_val *isl_multi_val_add_val(
6898 __isl_take isl_multi_val *mv,
6899 __isl_take isl_val *v);
6900 __isl_give isl_multi_val *isl_multi_val_mod_val(
6901 __isl_take isl_multi_val *mv,
6902 __isl_take isl_val *v);
6903 __isl_give isl_multi_val *isl_multi_val_scale_val(
6904 __isl_take isl_multi_val *mv,
6905 __isl_take isl_val *v);
6906 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6907 __isl_take isl_multi_val *mv,
6908 __isl_take isl_val *v);
6910 #include <isl/aff.h>
6911 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6912 __isl_take isl_val *mod);
6913 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6914 __isl_take isl_pw_aff *pa,
6915 __isl_take isl_val *mod);
6916 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6917 __isl_take isl_union_pw_aff *upa,
6918 __isl_take isl_val *f);
6919 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6920 __isl_take isl_val *v);
6921 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6922 __isl_take isl_multi_aff *ma,
6923 __isl_take isl_val *v);
6924 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6925 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6926 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6927 __isl_take isl_multi_pw_aff *mpa,
6928 __isl_take isl_val *v);
6929 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6930 __isl_take isl_pw_multi_aff *pma,
6931 __isl_take isl_val *v);
6932 __isl_give isl_union_pw_multi_aff *
6933 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6934 __isl_take isl_union_pw_aff *upa,
6935 __isl_take isl_val *f);
6936 isl_union_pw_multi_aff_scale_val(
6937 __isl_take isl_union_pw_multi_aff *upma,
6938 __isl_take isl_val *val);
6939 __isl_give isl_multi_union_pw_aff *
6940 isl_multi_union_pw_aff_scale_val(
6941 __isl_take isl_multi_union_pw_aff *mupa,
6942 __isl_take isl_val *v);
6943 __isl_give isl_aff *isl_aff_scale_down_ui(
6944 __isl_take isl_aff *aff, unsigned f);
6945 __isl_give isl_aff *isl_aff_scale_down_val(
6946 __isl_take isl_aff *aff, __isl_take isl_val *v);
6947 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6948 __isl_take isl_multi_aff *ma,
6949 __isl_take isl_val *v);
6950 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6951 __isl_take isl_pw_aff *pa,
6952 __isl_take isl_val *f);
6953 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6954 __isl_take isl_multi_pw_aff *mpa,
6955 __isl_take isl_val *v);
6956 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6957 __isl_take isl_pw_multi_aff *pma,
6958 __isl_take isl_val *v);
6959 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6960 __isl_take isl_union_pw_aff *upa,
6961 __isl_take isl_val *v);
6962 __isl_give isl_union_pw_multi_aff *
6963 isl_union_pw_multi_aff_scale_down_val(
6964 __isl_take isl_union_pw_multi_aff *upma,
6965 __isl_take isl_val *val);
6966 __isl_give isl_multi_union_pw_aff *
6967 isl_multi_union_pw_aff_scale_down_val(
6968 __isl_take isl_multi_union_pw_aff *mupa,
6969 __isl_take isl_val *v);
6971 #include <isl/polynomial.h>
6972 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6973 __isl_take isl_qpolynomial *qp,
6974 __isl_take isl_val *v);
6975 __isl_give isl_qpolynomial_fold *
6976 isl_qpolynomial_fold_scale_val(
6977 __isl_take isl_qpolynomial_fold *fold,
6978 __isl_take isl_val *v);
6979 __isl_give isl_pw_qpolynomial *
6980 isl_pw_qpolynomial_scale_val(
6981 __isl_take isl_pw_qpolynomial *pwqp,
6982 __isl_take isl_val *v);
6983 __isl_give isl_pw_qpolynomial_fold *
6984 isl_pw_qpolynomial_fold_scale_val(
6985 __isl_take isl_pw_qpolynomial_fold *pwf,
6986 __isl_take isl_val *v);
6987 __isl_give isl_union_pw_qpolynomial *
6988 isl_union_pw_qpolynomial_scale_val(
6989 __isl_take isl_union_pw_qpolynomial *upwqp,
6990 __isl_take isl_val *v);
6991 __isl_give isl_union_pw_qpolynomial_fold *
6992 isl_union_pw_qpolynomial_fold_scale_val(
6993 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6994 __isl_take isl_val *v);
6995 __isl_give isl_qpolynomial *
6996 isl_qpolynomial_scale_down_val(
6997 __isl_take isl_qpolynomial *qp,
6998 __isl_take isl_val *v);
6999 __isl_give isl_qpolynomial_fold *
7000 isl_qpolynomial_fold_scale_down_val(
7001 __isl_take isl_qpolynomial_fold *fold,
7002 __isl_take isl_val *v);
7003 __isl_give isl_pw_qpolynomial *
7004 isl_pw_qpolynomial_scale_down_val(
7005 __isl_take isl_pw_qpolynomial *pwqp,
7006 __isl_take isl_val *v);
7007 __isl_give isl_pw_qpolynomial_fold *
7008 isl_pw_qpolynomial_fold_scale_down_val(
7009 __isl_take isl_pw_qpolynomial_fold *pwf,
7010 __isl_take isl_val *v);
7011 __isl_give isl_union_pw_qpolynomial *
7012 isl_union_pw_qpolynomial_scale_down_val(
7013 __isl_take isl_union_pw_qpolynomial *upwqp,
7014 __isl_take isl_val *v);
7015 __isl_give isl_union_pw_qpolynomial_fold *
7016 isl_union_pw_qpolynomial_fold_scale_down_val(
7017 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7018 __isl_take isl_val *v);
7020 #include <isl/val.h>
7021 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7022 __isl_take isl_multi_val *mv1,
7023 __isl_take isl_multi_val *mv2);
7024 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7025 __isl_take isl_multi_val *mv1,
7026 __isl_take isl_multi_val *mv2);
7027 __isl_give isl_multi_val *
7028 isl_multi_val_scale_down_multi_val(
7029 __isl_take isl_multi_val *mv1,
7030 __isl_take isl_multi_val *mv2);
7032 #include <isl/aff.h>
7033 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7034 __isl_take isl_multi_aff *ma,
7035 __isl_take isl_multi_val *mv);
7036 __isl_give isl_multi_union_pw_aff *
7037 isl_multi_union_pw_aff_mod_multi_val(
7038 __isl_take isl_multi_union_pw_aff *upma,
7039 __isl_take isl_multi_val *mv);
7040 __isl_give isl_multi_pw_aff *
7041 isl_multi_pw_aff_mod_multi_val(
7042 __isl_take isl_multi_pw_aff *mpa,
7043 __isl_take isl_multi_val *mv);
7044 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7045 __isl_take isl_multi_aff *ma,
7046 __isl_take isl_multi_val *mv);
7047 __isl_give isl_pw_multi_aff *
7048 isl_pw_multi_aff_scale_multi_val(
7049 __isl_take isl_pw_multi_aff *pma,
7050 __isl_take isl_multi_val *mv);
7051 __isl_give isl_multi_pw_aff *
7052 isl_multi_pw_aff_scale_multi_val(
7053 __isl_take isl_multi_pw_aff *mpa,
7054 __isl_take isl_multi_val *mv);
7055 __isl_give isl_multi_union_pw_aff *
7056 isl_multi_union_pw_aff_scale_multi_val(
7057 __isl_take isl_multi_union_pw_aff *mupa,
7058 __isl_take isl_multi_val *mv);
7059 __isl_give isl_union_pw_multi_aff *
7060 isl_union_pw_multi_aff_scale_multi_val(
7061 __isl_take isl_union_pw_multi_aff *upma,
7062 __isl_take isl_multi_val *mv);
7063 __isl_give isl_multi_aff *
7064 isl_multi_aff_scale_down_multi_val(
7065 __isl_take isl_multi_aff *ma,
7066 __isl_take isl_multi_val *mv);
7067 __isl_give isl_multi_pw_aff *
7068 isl_multi_pw_aff_scale_down_multi_val(
7069 __isl_take isl_multi_pw_aff *mpa,
7070 __isl_take isl_multi_val *mv);
7071 __isl_give isl_multi_union_pw_aff *
7072 isl_multi_union_pw_aff_scale_down_multi_val(
7073 __isl_take isl_multi_union_pw_aff *mupa,
7074 __isl_take isl_multi_val *mv);
7076 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7077 by the corresponding elements of C<mv>.
7079 #include <isl/aff.h>
7080 __isl_give isl_aff *isl_aff_mul(
7081 __isl_take isl_aff *aff1,
7082 __isl_take isl_aff *aff2);
7083 __isl_give isl_aff *isl_aff_div(
7084 __isl_take isl_aff *aff1,
7085 __isl_take isl_aff *aff2);
7086 __isl_give isl_pw_aff *isl_pw_aff_mul(
7087 __isl_take isl_pw_aff *pwaff1,
7088 __isl_take isl_pw_aff *pwaff2);
7089 __isl_give isl_pw_aff *isl_pw_aff_div(
7090 __isl_take isl_pw_aff *pa1,
7091 __isl_take isl_pw_aff *pa2);
7092 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7093 __isl_take isl_pw_aff *pa1,
7094 __isl_take isl_pw_aff *pa2);
7095 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7096 __isl_take isl_pw_aff *pa1,
7097 __isl_take isl_pw_aff *pa2);
7099 When multiplying two affine expressions, at least one of the two needs
7100 to be a constant. Similarly, when dividing an affine expression by another,
7101 the second expression needs to be a constant.
7102 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7103 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7106 #include <isl/polynomial.h>
7107 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7108 __isl_take isl_qpolynomial *qp1,
7109 __isl_take isl_qpolynomial *qp2);
7110 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7111 __isl_take isl_pw_qpolynomial *pwqp1,
7112 __isl_take isl_pw_qpolynomial *pwqp2);
7113 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7114 __isl_take isl_union_pw_qpolynomial *upwqp1,
7115 __isl_take isl_union_pw_qpolynomial *upwqp2);
7119 =head3 Lexicographic Optimization
7121 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7122 the following functions
7123 compute a set that contains the lexicographic minimum or maximum
7124 of the elements in C<set> (or C<bset>) for those values of the parameters
7125 that satisfy C<dom>.
7126 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7127 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7129 In other words, the union of the parameter values
7130 for which the result is non-empty and of C<*empty>
7133 #include <isl/set.h>
7134 __isl_give isl_set *isl_basic_set_partial_lexmin(
7135 __isl_take isl_basic_set *bset,
7136 __isl_take isl_basic_set *dom,
7137 __isl_give isl_set **empty);
7138 __isl_give isl_set *isl_basic_set_partial_lexmax(
7139 __isl_take isl_basic_set *bset,
7140 __isl_take isl_basic_set *dom,
7141 __isl_give isl_set **empty);
7142 __isl_give isl_set *isl_set_partial_lexmin(
7143 __isl_take isl_set *set, __isl_take isl_set *dom,
7144 __isl_give isl_set **empty);
7145 __isl_give isl_set *isl_set_partial_lexmax(
7146 __isl_take isl_set *set, __isl_take isl_set *dom,
7147 __isl_give isl_set **empty);
7149 Given a (basic) set C<set> (or C<bset>), the following functions simply
7150 return a set containing the lexicographic minimum or maximum
7151 of the elements in C<set> (or C<bset>).
7152 In case of union sets, the optimum is computed per space.
7154 #include <isl/set.h>
7155 __isl_give isl_set *isl_basic_set_lexmin(
7156 __isl_take isl_basic_set *bset);
7157 __isl_give isl_set *isl_basic_set_lexmax(
7158 __isl_take isl_basic_set *bset);
7159 __isl_give isl_set *isl_set_lexmin(
7160 __isl_take isl_set *set);
7161 __isl_give isl_set *isl_set_lexmax(
7162 __isl_take isl_set *set);
7163 __isl_give isl_union_set *isl_union_set_lexmin(
7164 __isl_take isl_union_set *uset);
7165 __isl_give isl_union_set *isl_union_set_lexmax(
7166 __isl_take isl_union_set *uset);
7168 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7169 the following functions
7170 compute a relation that maps each element of C<dom>
7171 to the single lexicographic minimum or maximum
7172 of the elements that are associated to that same
7173 element in C<map> (or C<bmap>).
7174 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7175 that contains the elements in C<dom> that do not map
7176 to any elements in C<map> (or C<bmap>).
7177 In other words, the union of the domain of the result and of C<*empty>
7180 #include <isl/map.h>
7181 __isl_give isl_map *isl_basic_map_partial_lexmax(
7182 __isl_take isl_basic_map *bmap,
7183 __isl_take isl_basic_set *dom,
7184 __isl_give isl_set **empty);
7185 __isl_give isl_map *isl_basic_map_partial_lexmin(
7186 __isl_take isl_basic_map *bmap,
7187 __isl_take isl_basic_set *dom,
7188 __isl_give isl_set **empty);
7189 __isl_give isl_map *isl_map_partial_lexmax(
7190 __isl_take isl_map *map, __isl_take isl_set *dom,
7191 __isl_give isl_set **empty);
7192 __isl_give isl_map *isl_map_partial_lexmin(
7193 __isl_take isl_map *map, __isl_take isl_set *dom,
7194 __isl_give isl_set **empty);
7196 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7197 return a map mapping each element in the domain of
7198 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7199 of all elements associated to that element.
7200 In case of union relations, the optimum is computed per space.
7202 #include <isl/map.h>
7203 __isl_give isl_map *isl_basic_map_lexmin(
7204 __isl_take isl_basic_map *bmap);
7205 __isl_give isl_map *isl_basic_map_lexmax(
7206 __isl_take isl_basic_map *bmap);
7207 __isl_give isl_map *isl_map_lexmin(
7208 __isl_take isl_map *map);
7209 __isl_give isl_map *isl_map_lexmax(
7210 __isl_take isl_map *map);
7211 __isl_give isl_union_map *isl_union_map_lexmin(
7212 __isl_take isl_union_map *umap);
7213 __isl_give isl_union_map *isl_union_map_lexmax(
7214 __isl_take isl_union_map *umap);
7216 The following functions return their result in the form of
7217 a piecewise multi-affine expression,
7218 but are otherwise equivalent to the corresponding functions
7219 returning a basic set or relation.
7221 #include <isl/set.h>
7222 __isl_give isl_pw_multi_aff *
7223 isl_basic_set_partial_lexmin_pw_multi_aff(
7224 __isl_take isl_basic_set *bset,
7225 __isl_take isl_basic_set *dom,
7226 __isl_give isl_set **empty);
7227 __isl_give isl_pw_multi_aff *
7228 isl_basic_set_partial_lexmax_pw_multi_aff(
7229 __isl_take isl_basic_set *bset,
7230 __isl_take isl_basic_set *dom,
7231 __isl_give isl_set **empty);
7232 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7233 __isl_take isl_set *set);
7234 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7235 __isl_take isl_set *set);
7237 #include <isl/map.h>
7238 __isl_give isl_pw_multi_aff *
7239 isl_basic_map_lexmin_pw_multi_aff(
7240 __isl_take isl_basic_map *bmap);
7241 __isl_give isl_pw_multi_aff *
7242 isl_basic_map_partial_lexmin_pw_multi_aff(
7243 __isl_take isl_basic_map *bmap,
7244 __isl_take isl_basic_set *dom,
7245 __isl_give isl_set **empty);
7246 __isl_give isl_pw_multi_aff *
7247 isl_basic_map_partial_lexmax_pw_multi_aff(
7248 __isl_take isl_basic_map *bmap,
7249 __isl_take isl_basic_set *dom,
7250 __isl_give isl_set **empty);
7251 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7252 __isl_take isl_map *map);
7253 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7254 __isl_take isl_map *map);
7256 The following functions return the lexicographic minimum or maximum
7257 on the shared domain of the inputs and the single defined function
7258 on those parts of the domain where only a single function is defined.
7260 #include <isl/aff.h>
7261 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7262 __isl_take isl_pw_multi_aff *pma1,
7263 __isl_take isl_pw_multi_aff *pma2);
7264 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7265 __isl_take isl_pw_multi_aff *pma1,
7266 __isl_take isl_pw_multi_aff *pma2);
7268 If the input to a lexicographic optimization problem has
7269 multiple constraints with the same coefficients for the optimized
7270 variables, then, by default, this symmetry is exploited by
7271 replacing those constraints by a single constraint with
7272 an abstract bound, which is in turn bounded by the corresponding terms
7273 in the original constraints.
7274 Without this optimization, the solver would typically consider
7275 all possible orderings of those original bounds, resulting in a needless
7276 decomposition of the domain.
7277 However, the optimization can also result in slowdowns since
7278 an extra parameter is introduced that may get used in additional
7280 The following option determines whether symmetry detection is applied
7281 during lexicographic optimization.
7283 #include <isl/options.h>
7284 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7286 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7290 See also \autoref{s:offline}.
7294 =head2 Ternary Operations
7296 #include <isl/aff.h>
7297 __isl_give isl_pw_aff *isl_pw_aff_cond(
7298 __isl_take isl_pw_aff *cond,
7299 __isl_take isl_pw_aff *pwaff_true,
7300 __isl_take isl_pw_aff *pwaff_false);
7302 The function C<isl_pw_aff_cond> performs a conditional operator
7303 and returns an expression that is equal to C<pwaff_true>
7304 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7305 where C<cond> is zero.
7309 Lists are defined over several element types, including
7310 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7311 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7312 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7313 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7314 Here we take lists of C<isl_set>s as an example.
7315 Lists can be created, copied, modified and freed using the following functions.
7317 #include <isl/set.h>
7318 __isl_give isl_set_list *isl_set_list_from_set(
7319 __isl_take isl_set *el);
7320 __isl_give isl_set_list *isl_set_list_alloc(
7321 isl_ctx *ctx, int n);
7322 __isl_give isl_set_list *isl_set_list_copy(
7323 __isl_keep isl_set_list *list);
7324 __isl_give isl_set_list *isl_set_list_insert(
7325 __isl_take isl_set_list *list, unsigned pos,
7326 __isl_take isl_set *el);
7327 __isl_give isl_set_list *isl_set_list_add(
7328 __isl_take isl_set_list *list,
7329 __isl_take isl_set *el);
7330 __isl_give isl_set_list *isl_set_list_drop(
7331 __isl_take isl_set_list *list,
7332 unsigned first, unsigned n);
7333 __isl_give isl_set_list *isl_set_list_set_set(
7334 __isl_take isl_set_list *list, int index,
7335 __isl_take isl_set *set);
7336 __isl_give isl_set_list *isl_set_list_concat(
7337 __isl_take isl_set_list *list1,
7338 __isl_take isl_set_list *list2);
7339 __isl_give isl_set_list *isl_set_list_sort(
7340 __isl_take isl_set_list *list,
7341 int (*cmp)(__isl_keep isl_set *a,
7342 __isl_keep isl_set *b, void *user),
7344 __isl_null isl_set_list *isl_set_list_free(
7345 __isl_take isl_set_list *list);
7347 C<isl_set_list_alloc> creates an empty list with an initial capacity
7348 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7349 add elements to a list, increasing its capacity as needed.
7350 C<isl_set_list_from_set> creates a list with a single element.
7352 Lists can be inspected using the following functions.
7354 #include <isl/set.h>
7355 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7356 __isl_give isl_set *isl_set_list_get_set(
7357 __isl_keep isl_set_list *list, int index);
7358 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7359 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7361 isl_stat isl_set_list_foreach_scc(
7362 __isl_keep isl_set_list *list,
7363 isl_bool (*follows)(__isl_keep isl_set *a,
7364 __isl_keep isl_set *b, void *user),
7366 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7369 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7370 strongly connected components of the graph with as vertices the elements
7371 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7372 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7373 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7375 Lists can be printed using
7377 #include <isl/set.h>
7378 __isl_give isl_printer *isl_printer_print_set_list(
7379 __isl_take isl_printer *p,
7380 __isl_keep isl_set_list *list);
7382 =head2 Associative arrays
7384 Associative arrays map isl objects of a specific type to isl objects
7385 of some (other) specific type. They are defined for several pairs
7386 of types, including (C<isl_map>, C<isl_basic_set>),
7387 (C<isl_id>, C<isl_ast_expr>),
7388 (C<isl_id>, C<isl_id>) and
7389 (C<isl_id>, C<isl_pw_aff>).
7390 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7393 Associative arrays can be created, copied and freed using
7394 the following functions.
7396 #include <isl/id_to_ast_expr.h>
7397 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7398 isl_ctx *ctx, int min_size);
7399 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7400 __isl_keep isl_id_to_ast_expr *id2expr);
7401 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7402 __isl_take isl_id_to_ast_expr *id2expr);
7404 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7405 to specify the expected size of the associative array.
7406 The associative array will be grown automatically as needed.
7408 Associative arrays can be inspected using the following functions.
7410 #include <isl/id_to_ast_expr.h>
7411 __isl_give isl_maybe_isl_ast_expr
7412 isl_id_to_ast_expr_try_get(
7413 __isl_keep isl_id_to_ast_expr *id2expr,
7414 __isl_keep isl_id *key);
7415 isl_bool isl_id_to_ast_expr_has(
7416 __isl_keep isl_id_to_ast_expr *id2expr,
7417 __isl_keep isl_id *key);
7418 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7419 __isl_keep isl_id_to_ast_expr *id2expr,
7420 __isl_take isl_id *key);
7421 isl_stat isl_id_to_ast_expr_foreach(
7422 __isl_keep isl_id_to_ast_expr *id2expr,
7423 isl_stat (*fn)(__isl_take isl_id *key,
7424 __isl_take isl_ast_expr *val, void *user),
7427 The function C<isl_id_to_ast_expr_try_get> returns a structure
7428 containing two elements, C<valid> and C<value>.
7429 If there is a value associated to the key, then C<valid>
7430 is set to C<isl_bool_true> and C<value> contains a copy of
7431 the associated value. Otherwise C<value> is C<NULL> and
7432 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7433 on whether some error has occurred or there simply is no associated value.
7434 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7435 in the structure and
7436 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7438 Associative arrays can be modified using the following functions.
7440 #include <isl/id_to_ast_expr.h>
7441 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7442 __isl_take isl_id_to_ast_expr *id2expr,
7443 __isl_take isl_id *key,
7444 __isl_take isl_ast_expr *val);
7445 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7446 __isl_take isl_id_to_ast_expr *id2expr,
7447 __isl_take isl_id *key);
7449 Associative arrays can be printed using the following function.
7451 #include <isl/id_to_ast_expr.h>
7452 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7453 __isl_take isl_printer *p,
7454 __isl_keep isl_id_to_ast_expr *id2expr);
7458 Vectors can be created, copied and freed using the following functions.
7460 #include <isl/vec.h>
7461 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7463 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7464 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7466 Note that the elements of a newly created vector may have arbitrary values.
7467 The elements can be changed and inspected using the following functions.
7469 int isl_vec_size(__isl_keep isl_vec *vec);
7470 __isl_give isl_val *isl_vec_get_element_val(
7471 __isl_keep isl_vec *vec, int pos);
7472 __isl_give isl_vec *isl_vec_set_element_si(
7473 __isl_take isl_vec *vec, int pos, int v);
7474 __isl_give isl_vec *isl_vec_set_element_val(
7475 __isl_take isl_vec *vec, int pos,
7476 __isl_take isl_val *v);
7477 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7479 __isl_give isl_vec *isl_vec_set_val(
7480 __isl_take isl_vec *vec, __isl_take isl_val *v);
7481 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7482 __isl_keep isl_vec *vec2, int pos);
7484 C<isl_vec_get_element> will return a negative value if anything went wrong.
7485 In that case, the value of C<*v> is undefined.
7487 The following function can be used to concatenate two vectors.
7489 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7490 __isl_take isl_vec *vec2);
7494 Matrices can be created, copied and freed using the following functions.
7496 #include <isl/mat.h>
7497 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7498 unsigned n_row, unsigned n_col);
7499 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7500 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7502 Note that the elements of a newly created matrix may have arbitrary values.
7503 The elements can be changed and inspected using the following functions.
7505 int isl_mat_rows(__isl_keep isl_mat *mat);
7506 int isl_mat_cols(__isl_keep isl_mat *mat);
7507 __isl_give isl_val *isl_mat_get_element_val(
7508 __isl_keep isl_mat *mat, int row, int col);
7509 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7510 int row, int col, int v);
7511 __isl_give isl_mat *isl_mat_set_element_val(
7512 __isl_take isl_mat *mat, int row, int col,
7513 __isl_take isl_val *v);
7515 C<isl_mat_get_element> will return a negative value if anything went wrong.
7516 In that case, the value of C<*v> is undefined.
7518 The following function can be used to compute the (right) inverse
7519 of a matrix, i.e., a matrix such that the product of the original
7520 and the inverse (in that order) is a multiple of the identity matrix.
7521 The input matrix is assumed to be of full row-rank.
7523 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7525 The following function can be used to compute the (right) kernel
7526 (or null space) of a matrix, i.e., a matrix such that the product of
7527 the original and the kernel (in that order) is the zero matrix.
7529 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7531 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7533 The following functions determine
7534 an upper or lower bound on a quasipolynomial over its domain.
7536 __isl_give isl_pw_qpolynomial_fold *
7537 isl_pw_qpolynomial_bound(
7538 __isl_take isl_pw_qpolynomial *pwqp,
7539 enum isl_fold type, int *tight);
7541 __isl_give isl_union_pw_qpolynomial_fold *
7542 isl_union_pw_qpolynomial_bound(
7543 __isl_take isl_union_pw_qpolynomial *upwqp,
7544 enum isl_fold type, int *tight);
7546 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7547 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7548 is the returned bound is known be tight, i.e., for each value
7549 of the parameters there is at least
7550 one element in the domain that reaches the bound.
7551 If the domain of C<pwqp> is not wrapping, then the bound is computed
7552 over all elements in that domain and the result has a purely parametric
7553 domain. If the domain of C<pwqp> is wrapping, then the bound is
7554 computed over the range of the wrapped relation. The domain of the
7555 wrapped relation becomes the domain of the result.
7557 =head2 Parametric Vertex Enumeration
7559 The parametric vertex enumeration described in this section
7560 is mainly intended to be used internally and by the C<barvinok>
7563 #include <isl/vertices.h>
7564 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7565 __isl_keep isl_basic_set *bset);
7567 The function C<isl_basic_set_compute_vertices> performs the
7568 actual computation of the parametric vertices and the chamber
7569 decomposition and store the result in an C<isl_vertices> object.
7570 This information can be queried by either iterating over all
7571 the vertices or iterating over all the chambers or cells
7572 and then iterating over all vertices that are active on the chamber.
7574 isl_stat isl_vertices_foreach_vertex(
7575 __isl_keep isl_vertices *vertices,
7576 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7577 void *user), void *user);
7579 isl_stat isl_vertices_foreach_cell(
7580 __isl_keep isl_vertices *vertices,
7581 isl_stat (*fn)(__isl_take isl_cell *cell,
7582 void *user), void *user);
7583 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7584 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7585 void *user), void *user);
7587 Other operations that can be performed on an C<isl_vertices> object are
7590 int isl_vertices_get_n_vertices(
7591 __isl_keep isl_vertices *vertices);
7592 void isl_vertices_free(__isl_take isl_vertices *vertices);
7594 Vertices can be inspected and destroyed using the following functions.
7596 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7597 __isl_give isl_basic_set *isl_vertex_get_domain(
7598 __isl_keep isl_vertex *vertex);
7599 __isl_give isl_multi_aff *isl_vertex_get_expr(
7600 __isl_keep isl_vertex *vertex);
7601 void isl_vertex_free(__isl_take isl_vertex *vertex);
7603 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7604 describing the vertex in terms of the parameters,
7605 while C<isl_vertex_get_domain> returns the activity domain
7608 Chambers can be inspected and destroyed using the following functions.
7610 __isl_give isl_basic_set *isl_cell_get_domain(
7611 __isl_keep isl_cell *cell);
7612 void isl_cell_free(__isl_take isl_cell *cell);
7614 =head1 Polyhedral Compilation Library
7616 This section collects functionality in C<isl> that has been specifically
7617 designed for use during polyhedral compilation.
7619 =head2 Schedule Trees
7621 A schedule tree is a structured representation of a schedule,
7622 assigning a relative order to a set of domain elements.
7623 The relative order expressed by the schedule tree is
7624 defined recursively. In particular, the order between
7625 two domain elements is determined by the node that is closest
7626 to the root that refers to both elements and that orders them apart.
7627 Each node in the tree is of one of several types.
7628 The root node is always of type C<isl_schedule_node_domain>
7629 (or C<isl_schedule_node_extension>)
7630 and it describes the (extra) domain elements to which the schedule applies.
7631 The other types of nodes are as follows.
7635 =item C<isl_schedule_node_band>
7637 A band of schedule dimensions. Each schedule dimension is represented
7638 by a union piecewise quasi-affine expression. If this expression
7639 assigns a different value to two domain elements, while all previous
7640 schedule dimensions in the same band assign them the same value,
7641 then the two domain elements are ordered according to these two
7643 Each expression is required to be total in the domain elements
7644 that reach the band node.
7646 =item C<isl_schedule_node_expansion>
7648 An expansion node maps each of the domain elements that reach the node
7649 to one or more domain elements. The image of this mapping forms
7650 the set of domain elements that reach the child of the expansion node.
7651 The function that maps each of the expanded domain elements
7652 to the original domain element from which it was expanded
7653 is called the contraction.
7655 =item C<isl_schedule_node_filter>
7657 A filter node does not impose any ordering, but rather intersects
7658 the set of domain elements that the current subtree refers to
7659 with a given union set. The subtree of the filter node only
7660 refers to domain elements in the intersection.
7661 A filter node is typically only used a child of a sequence or
7664 =item C<isl_schedule_node_leaf>
7666 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7668 =item C<isl_schedule_node_mark>
7670 A mark node can be used to attach any kind of information to a subtree
7671 of the schedule tree.
7673 =item C<isl_schedule_node_sequence>
7675 A sequence node has one or more children, each of which is a filter node.
7676 The filters on these filter nodes form a partition of
7677 the domain elements that the current subtree refers to.
7678 If two domain elements appear in distinct filters then the sequence
7679 node orders them according to the child positions of the corresponding
7682 =item C<isl_schedule_node_set>
7684 A set node is similar to a sequence node, except that
7685 it expresses that domain elements appearing in distinct filters
7686 may have any order. The order of the children of a set node
7687 is therefore also immaterial.
7691 The following node types are only supported by the AST generator.
7695 =item C<isl_schedule_node_context>
7697 The context describes constraints on the parameters and
7698 the schedule dimensions of outer
7699 bands that the AST generator may assume to hold. It is also the only
7700 kind of node that may introduce additional parameters.
7701 The space of the context is that of the flat product of the outer
7702 band nodes. In particular, if there are no outer band nodes, then
7703 this space is the unnamed zero-dimensional space.
7704 Since a context node references the outer band nodes, any tree
7705 containing a context node is considered to be anchored.
7707 =item C<isl_schedule_node_extension>
7709 An extension node instructs the AST generator to add additional
7710 domain elements that need to be scheduled.
7711 The additional domain elements are described by the range of
7712 the extension map in terms of the outer schedule dimensions,
7713 i.e., the flat product of the outer band nodes.
7714 Note that domain elements are added whenever the AST generator
7715 reaches the extension node, meaning that there are still some
7716 active domain elements for which an AST needs to be generated.
7717 The conditions under which some domain elements are still active
7718 may however not be completely described by the outer AST nodes
7719 generated at that point.
7721 An extension node may also appear as the root of a schedule tree,
7722 when it is intended to be inserted into another tree
7723 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7724 In this case, the domain of the extension node should
7725 correspond to the flat product of the outer band nodes
7726 in this other schedule tree at the point where the extension tree
7729 =item C<isl_schedule_node_guard>
7731 The guard describes constraints on the parameters and
7732 the schedule dimensions of outer
7733 bands that need to be enforced by the outer nodes
7734 in the generated AST.
7735 The space of the guard is that of the flat product of the outer
7736 band nodes. In particular, if there are no outer band nodes, then
7737 this space is the unnamed zero-dimensional space.
7738 Since a guard node references the outer band nodes, any tree
7739 containing a guard node is considered to be anchored.
7743 Except for the C<isl_schedule_node_context> nodes,
7744 none of the nodes may introduce any parameters that were not
7745 already present in the root domain node.
7747 A schedule tree is encapsulated in an C<isl_schedule> object.
7748 The simplest such objects, those with a tree consisting of single domain node,
7749 can be created using the following functions with either an empty
7750 domain or a given domain.
7752 #include <isl/schedule.h>
7753 __isl_give isl_schedule *isl_schedule_empty(
7754 __isl_take isl_space *space);
7755 __isl_give isl_schedule *isl_schedule_from_domain(
7756 __isl_take isl_union_set *domain);
7758 The function C<isl_schedule_constraints_compute_schedule> described
7759 in L</"Scheduling"> can also be used to construct schedules.
7761 C<isl_schedule> objects may be copied and freed using the following functions.
7763 #include <isl/schedule.h>
7764 __isl_give isl_schedule *isl_schedule_copy(
7765 __isl_keep isl_schedule *sched);
7766 __isl_null isl_schedule *isl_schedule_free(
7767 __isl_take isl_schedule *sched);
7769 The following functions checks whether two C<isl_schedule> objects
7770 are obviously the same.
7772 #include <isl/schedule.h>
7773 isl_bool isl_schedule_plain_is_equal(
7774 __isl_keep isl_schedule *schedule1,
7775 __isl_keep isl_schedule *schedule2);
7777 The domain of the schedule, i.e., the domain described by the root node,
7778 can be obtained using the following function.
7780 #include <isl/schedule.h>
7781 __isl_give isl_union_set *isl_schedule_get_domain(
7782 __isl_keep isl_schedule *schedule);
7784 An extra top-level band node (right underneath the domain node) can
7785 be introduced into the schedule using the following function.
7786 The schedule tree is assumed not to have any anchored nodes.
7788 #include <isl/schedule.h>
7789 __isl_give isl_schedule *
7790 isl_schedule_insert_partial_schedule(
7791 __isl_take isl_schedule *schedule,
7792 __isl_take isl_multi_union_pw_aff *partial);
7794 A top-level context node (right underneath the domain node) can
7795 be introduced into the schedule using the following function.
7797 #include <isl/schedule.h>
7798 __isl_give isl_schedule *isl_schedule_insert_context(
7799 __isl_take isl_schedule *schedule,
7800 __isl_take isl_set *context)
7802 A top-level guard node (right underneath the domain node) can
7803 be introduced into the schedule using the following function.
7805 #include <isl/schedule.h>
7806 __isl_give isl_schedule *isl_schedule_insert_guard(
7807 __isl_take isl_schedule *schedule,
7808 __isl_take isl_set *guard)
7810 A schedule that combines two schedules either in the given
7811 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7812 or an C<isl_schedule_node_set> node,
7813 can be created using the following functions.
7815 #include <isl/schedule.h>
7816 __isl_give isl_schedule *isl_schedule_sequence(
7817 __isl_take isl_schedule *schedule1,
7818 __isl_take isl_schedule *schedule2);
7819 __isl_give isl_schedule *isl_schedule_set(
7820 __isl_take isl_schedule *schedule1,
7821 __isl_take isl_schedule *schedule2);
7823 The domains of the two input schedules need to be disjoint.
7825 The following function can be used to restrict the domain
7826 of a schedule with a domain node as root to be a subset of the given union set.
7827 This operation may remove nodes in the tree that have become
7830 #include <isl/schedule.h>
7831 __isl_give isl_schedule *isl_schedule_intersect_domain(
7832 __isl_take isl_schedule *schedule,
7833 __isl_take isl_union_set *domain);
7835 The following function can be used to simplify the domain
7836 of a schedule with a domain node as root with respect to the given
7839 #include <isl/schedule.h>
7840 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7841 __isl_take isl_schedule *schedule,
7842 __isl_take isl_set *context);
7844 The following function resets the user pointers on all parameter
7845 and tuple identifiers referenced by the nodes of the given schedule.
7847 #include <isl/schedule.h>
7848 __isl_give isl_schedule *isl_schedule_reset_user(
7849 __isl_take isl_schedule *schedule);
7851 The following function aligns the parameters of all nodes
7852 in the given schedule to the given space.
7854 #include <isl/schedule.h>
7855 __isl_give isl_schedule *isl_schedule_align_params(
7856 __isl_take isl_schedule *schedule,
7857 __isl_take isl_space *space);
7859 The following function allows the user to plug in a given function
7860 in the iteration domains. The input schedule is not allowed to contain
7861 any expansion nodes.
7863 #include <isl/schedule.h>
7864 __isl_give isl_schedule *
7865 isl_schedule_pullback_union_pw_multi_aff(
7866 __isl_take isl_schedule *schedule,
7867 __isl_take isl_union_pw_multi_aff *upma);
7869 The following function can be used to plug in the schedule C<expansion>
7870 in the leaves of C<schedule>, where C<contraction> describes how
7871 the domain elements of C<expansion> map to the domain elements
7872 at the original leaves of C<schedule>.
7873 The resulting schedule will contain expansion nodes, unless
7874 C<contraction> is an identity function.
7876 #include <isl/schedule.h>
7877 __isl_give isl_schedule *isl_schedule_expand(
7878 __isl_take isl_schedule *schedule,
7879 __isl_take isl_union_pw_multi_aff *contraction,
7880 __isl_take isl_schedule *expansion);
7882 An C<isl_union_map> representation of the schedule can be obtained
7883 from an C<isl_schedule> using the following function.
7885 #include <isl/schedule.h>
7886 __isl_give isl_union_map *isl_schedule_get_map(
7887 __isl_keep isl_schedule *sched);
7889 The resulting relation encodes the same relative ordering as
7890 the schedule by mapping the domain elements to a common schedule space.
7891 If the schedule_separate_components option is set, then the order
7892 of the children of a set node is explicitly encoded in the result.
7893 If the tree contains any expansion nodes, then the relation
7894 is formulated in terms of the expanded domain elements.
7896 Schedules can be read from input using the following functions.
7898 #include <isl/schedule.h>
7899 __isl_give isl_schedule *isl_schedule_read_from_file(
7900 isl_ctx *ctx, FILE *input);
7901 __isl_give isl_schedule *isl_schedule_read_from_str(
7902 isl_ctx *ctx, const char *str);
7904 A representation of the schedule can be printed using
7906 #include <isl/schedule.h>
7907 __isl_give isl_printer *isl_printer_print_schedule(
7908 __isl_take isl_printer *p,
7909 __isl_keep isl_schedule *schedule);
7910 __isl_give char *isl_schedule_to_str(
7911 __isl_keep isl_schedule *schedule);
7913 C<isl_schedule_to_str> prints the schedule in flow format.
7915 The schedule tree can be traversed through the use of
7916 C<isl_schedule_node> objects that point to a particular
7917 position in the schedule tree. Whenever a C<isl_schedule_node>
7918 is use to modify a node in the schedule tree, the original schedule
7919 tree is left untouched and the modifications are performed to a copy
7920 of the tree. The returned C<isl_schedule_node> then points to
7921 this modified copy of the tree.
7923 The root of the schedule tree can be obtained using the following function.
7925 #include <isl/schedule.h>
7926 __isl_give isl_schedule_node *isl_schedule_get_root(
7927 __isl_keep isl_schedule *schedule);
7929 A pointer to a newly created schedule tree with a single domain
7930 node can be created using the following functions.
7932 #include <isl/schedule_node.h>
7933 __isl_give isl_schedule_node *
7934 isl_schedule_node_from_domain(
7935 __isl_take isl_union_set *domain);
7936 __isl_give isl_schedule_node *
7937 isl_schedule_node_from_extension(
7938 __isl_take isl_union_map *extension);
7940 C<isl_schedule_node_from_extension> creates a tree with an extension
7943 Schedule nodes can be copied and freed using the following functions.
7945 #include <isl/schedule_node.h>
7946 __isl_give isl_schedule_node *isl_schedule_node_copy(
7947 __isl_keep isl_schedule_node *node);
7948 __isl_null isl_schedule_node *isl_schedule_node_free(
7949 __isl_take isl_schedule_node *node);
7951 The following functions can be used to check if two schedule
7952 nodes point to the same position in the same schedule.
7954 #include <isl/schedule_node.h>
7955 isl_bool isl_schedule_node_is_equal(
7956 __isl_keep isl_schedule_node *node1,
7957 __isl_keep isl_schedule_node *node2);
7959 The following properties can be obtained from a schedule node.
7961 #include <isl/schedule_node.h>
7962 enum isl_schedule_node_type isl_schedule_node_get_type(
7963 __isl_keep isl_schedule_node *node);
7964 enum isl_schedule_node_type
7965 isl_schedule_node_get_parent_type(
7966 __isl_keep isl_schedule_node *node);
7967 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7968 __isl_keep isl_schedule_node *node);
7970 The function C<isl_schedule_node_get_type> returns the type of
7971 the node, while C<isl_schedule_node_get_parent_type> returns
7972 type of the parent of the node, which is required to exist.
7973 The function C<isl_schedule_node_get_schedule> returns a copy
7974 to the schedule to which the node belongs.
7976 The following functions can be used to move the schedule node
7977 to a different position in the tree or to check if such a position
7980 #include <isl/schedule_node.h>
7981 isl_bool isl_schedule_node_has_parent(
7982 __isl_keep isl_schedule_node *node);
7983 __isl_give isl_schedule_node *isl_schedule_node_parent(
7984 __isl_take isl_schedule_node *node);
7985 __isl_give isl_schedule_node *isl_schedule_node_root(
7986 __isl_take isl_schedule_node *node);
7987 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
7988 __isl_take isl_schedule_node *node,
7990 int isl_schedule_node_n_children(
7991 __isl_keep isl_schedule_node *node);
7992 __isl_give isl_schedule_node *isl_schedule_node_child(
7993 __isl_take isl_schedule_node *node, int pos);
7994 isl_bool isl_schedule_node_has_children(
7995 __isl_keep isl_schedule_node *node);
7996 __isl_give isl_schedule_node *isl_schedule_node_first_child(
7997 __isl_take isl_schedule_node *node);
7998 isl_bool isl_schedule_node_has_previous_sibling(
7999 __isl_keep isl_schedule_node *node);
8000 __isl_give isl_schedule_node *
8001 isl_schedule_node_previous_sibling(
8002 __isl_take isl_schedule_node *node);
8003 isl_bool isl_schedule_node_has_next_sibling(
8004 __isl_keep isl_schedule_node *node);
8005 __isl_give isl_schedule_node *
8006 isl_schedule_node_next_sibling(
8007 __isl_take isl_schedule_node *node);
8009 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8010 is the node itself, the ancestor of generation 1 is its parent and so on.
8012 It is also possible to query the number of ancestors of a node,
8013 the position of the current node
8014 within the children of its parent, the position of the subtree
8015 containing a node within the children of an ancestor
8016 or to obtain a copy of a given
8017 child without destroying the current node.
8018 Given two nodes that point to the same schedule, their closest
8019 shared ancestor can be obtained using
8020 C<isl_schedule_node_get_shared_ancestor>.
8022 #include <isl/schedule_node.h>
8023 int isl_schedule_node_get_tree_depth(
8024 __isl_keep isl_schedule_node *node);
8025 int isl_schedule_node_get_child_position(
8026 __isl_keep isl_schedule_node *node);
8027 int isl_schedule_node_get_ancestor_child_position(
8028 __isl_keep isl_schedule_node *node,
8029 __isl_keep isl_schedule_node *ancestor);
8030 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8031 __isl_keep isl_schedule_node *node, int pos);
8032 __isl_give isl_schedule_node *
8033 isl_schedule_node_get_shared_ancestor(
8034 __isl_keep isl_schedule_node *node1,
8035 __isl_keep isl_schedule_node *node2);
8037 All nodes in a schedule tree or
8038 all descendants of a specific node (including the node) can be visited
8039 in depth-first pre-order using the following functions.
8041 #include <isl/schedule.h>
8042 isl_stat isl_schedule_foreach_schedule_node_top_down(
8043 __isl_keep isl_schedule *sched,
8044 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8045 void *user), void *user);
8047 #include <isl/schedule_node.h>
8048 isl_stat isl_schedule_node_foreach_descendant_top_down(
8049 __isl_keep isl_schedule_node *node,
8050 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8051 void *user), void *user);
8053 The callback function is slightly different from the usual
8054 callbacks in that it not only indicates success (non-negative result)
8055 or failure (negative result), but also indicates whether the children
8056 of the given node should be visited. In particular, if the callback
8057 returns a positive value, then the children are visited, but if
8058 the callback returns zero, then the children are not visited.
8060 The ancestors of a node in a schedule tree can be visited from
8061 the root down to and including the parent of the node using
8062 the following function.
8064 #include <isl/schedule_node.h>
8065 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8066 __isl_keep isl_schedule_node *node,
8067 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8068 void *user), void *user);
8070 The following functions allows for a depth-first post-order
8071 traversal of the nodes in a schedule tree or
8072 of the descendants of a specific node (including the node
8073 itself), where the user callback is allowed to modify the
8076 #include <isl/schedule.h>
8077 __isl_give isl_schedule *
8078 isl_schedule_map_schedule_node_bottom_up(
8079 __isl_take isl_schedule *schedule,
8080 __isl_give isl_schedule_node *(*fn)(
8081 __isl_take isl_schedule_node *node,
8082 void *user), void *user);
8084 #include <isl/schedule_node.h>
8085 __isl_give isl_schedule_node *
8086 isl_schedule_node_map_descendant_bottom_up(
8087 __isl_take isl_schedule_node *node,
8088 __isl_give isl_schedule_node *(*fn)(
8089 __isl_take isl_schedule_node *node,
8090 void *user), void *user);
8092 The traversal continues from the node returned by the callback function.
8093 It is the responsibility of the user to ensure that this does not
8094 lead to an infinite loop. It is safest to always return a pointer
8095 to the same position (same ancestors and child positions) as the input node.
8097 The following function removes a node (along with its descendants)
8098 from a schedule tree and returns a pointer to the leaf at the
8099 same position in the updated tree.
8100 It is not allowed to remove the root of a schedule tree or
8101 a child of a set or sequence node.
8103 #include <isl/schedule_node.h>
8104 __isl_give isl_schedule_node *isl_schedule_node_cut(
8105 __isl_take isl_schedule_node *node);
8107 The following function removes a single node
8108 from a schedule tree and returns a pointer to the child
8109 of the node, now located at the position of the original node
8110 or to a leaf node at that position if there was no child.
8111 It is not allowed to remove the root of a schedule tree,
8112 a set or sequence node, a child of a set or sequence node or
8113 a band node with an anchored subtree.
8115 #include <isl/schedule_node.h>
8116 __isl_give isl_schedule_node *isl_schedule_node_delete(
8117 __isl_take isl_schedule_node *node);
8119 Most nodes in a schedule tree only contain local information.
8120 In some cases, however, a node may also refer to outer band nodes.
8121 This means that the position of the node within the tree should
8122 not be changed, or at least that no changes are performed to the
8123 outer band nodes. The following function can be used to test
8124 whether the subtree rooted at a given node contains any such nodes.
8126 #include <isl/schedule_node.h>
8127 isl_bool isl_schedule_node_is_subtree_anchored(
8128 __isl_keep isl_schedule_node *node);
8130 The following function resets the user pointers on all parameter
8131 and tuple identifiers referenced by the given schedule node.
8133 #include <isl/schedule_node.h>
8134 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8135 __isl_take isl_schedule_node *node);
8137 The following function aligns the parameters of the given schedule
8138 node to the given space.
8140 #include <isl/schedule_node.h>
8141 __isl_give isl_schedule_node *
8142 isl_schedule_node_align_params(
8143 __isl_take isl_schedule_node *node,
8144 __isl_take isl_space *space);
8146 Several node types have their own functions for querying
8147 (and in some cases setting) some node type specific properties.
8149 #include <isl/schedule_node.h>
8150 __isl_give isl_space *isl_schedule_node_band_get_space(
8151 __isl_keep isl_schedule_node *node);
8152 __isl_give isl_multi_union_pw_aff *
8153 isl_schedule_node_band_get_partial_schedule(
8154 __isl_keep isl_schedule_node *node);
8155 __isl_give isl_union_map *
8156 isl_schedule_node_band_get_partial_schedule_union_map(
8157 __isl_keep isl_schedule_node *node);
8158 unsigned isl_schedule_node_band_n_member(
8159 __isl_keep isl_schedule_node *node);
8160 isl_bool isl_schedule_node_band_member_get_coincident(
8161 __isl_keep isl_schedule_node *node, int pos);
8162 __isl_give isl_schedule_node *
8163 isl_schedule_node_band_member_set_coincident(
8164 __isl_take isl_schedule_node *node, int pos,
8166 isl_bool isl_schedule_node_band_get_permutable(
8167 __isl_keep isl_schedule_node *node);
8168 __isl_give isl_schedule_node *
8169 isl_schedule_node_band_set_permutable(
8170 __isl_take isl_schedule_node *node, int permutable);
8171 enum isl_ast_loop_type
8172 isl_schedule_node_band_member_get_ast_loop_type(
8173 __isl_keep isl_schedule_node *node, int pos);
8174 __isl_give isl_schedule_node *
8175 isl_schedule_node_band_member_set_ast_loop_type(
8176 __isl_take isl_schedule_node *node, int pos,
8177 enum isl_ast_loop_type type);
8178 __isl_give isl_union_set *
8179 enum isl_ast_loop_type
8180 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8181 __isl_keep isl_schedule_node *node, int pos);
8182 __isl_give isl_schedule_node *
8183 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8184 __isl_take isl_schedule_node *node, int pos,
8185 enum isl_ast_loop_type type);
8186 isl_schedule_node_band_get_ast_build_options(
8187 __isl_keep isl_schedule_node *node);
8188 __isl_give isl_schedule_node *
8189 isl_schedule_node_band_set_ast_build_options(
8190 __isl_take isl_schedule_node *node,
8191 __isl_take isl_union_set *options);
8193 The function C<isl_schedule_node_band_get_space> returns the space
8194 of the partial schedule of the band.
8195 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8196 returns a representation of the partial schedule of the band node
8197 in the form of an C<isl_union_map>.
8198 The coincident and permutable properties are set by
8199 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8201 A scheduling dimension is considered to be ``coincident''
8202 if it satisfies the coincidence constraints within its band.
8203 That is, if the dependence distances of the coincidence
8204 constraints are all zero in that direction (for fixed
8205 iterations of outer bands).
8206 A band is marked permutable if it was produced using the Pluto-like scheduler.
8207 Note that the scheduler may have to resort to a Feautrier style scheduling
8208 step even if the default scheduler is used.
8209 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8210 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8211 For the meaning of these loop AST generation types and the difference
8212 between the regular loop AST generation type and the isolate
8213 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8214 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8215 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8216 may return C<isl_ast_loop_error> if an error occurs.
8217 The AST build options govern how an AST is generated for
8218 the individual schedule dimensions during AST generation.
8219 See L</"AST Generation Options (Schedule Tree)">.
8221 #include <isl/schedule_node.h>
8222 __isl_give isl_set *
8223 isl_schedule_node_context_get_context(
8224 __isl_keep isl_schedule_node *node);
8226 #include <isl/schedule_node.h>
8227 __isl_give isl_union_set *
8228 isl_schedule_node_domain_get_domain(
8229 __isl_keep isl_schedule_node *node);
8231 #include <isl/schedule_node.h>
8232 __isl_give isl_union_map *
8233 isl_schedule_node_expansion_get_expansion(
8234 __isl_keep isl_schedule_node *node);
8235 __isl_give isl_union_pw_multi_aff *
8236 isl_schedule_node_expansion_get_contraction(
8237 __isl_keep isl_schedule_node *node);
8239 #include <isl/schedule_node.h>
8240 __isl_give isl_union_map *
8241 isl_schedule_node_extension_get_extension(
8242 __isl_keep isl_schedule_node *node);
8244 #include <isl/schedule_node.h>
8245 __isl_give isl_union_set *
8246 isl_schedule_node_filter_get_filter(
8247 __isl_keep isl_schedule_node *node);
8249 #include <isl/schedule_node.h>
8250 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8251 __isl_keep isl_schedule_node *node);
8253 #include <isl/schedule_node.h>
8254 __isl_give isl_id *isl_schedule_node_mark_get_id(
8255 __isl_keep isl_schedule_node *node);
8257 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8258 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8259 partial schedules related to the node.
8261 #include <isl/schedule_node.h>
8262 __isl_give isl_multi_union_pw_aff *
8263 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8264 __isl_keep isl_schedule_node *node);
8265 __isl_give isl_union_pw_multi_aff *
8266 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8267 __isl_keep isl_schedule_node *node);
8268 __isl_give isl_union_map *
8269 isl_schedule_node_get_prefix_schedule_union_map(
8270 __isl_keep isl_schedule_node *node);
8271 __isl_give isl_union_map *
8272 isl_schedule_node_get_prefix_schedule_relation(
8273 __isl_keep isl_schedule_node *node);
8274 __isl_give isl_union_map *
8275 isl_schedule_node_get_subtree_schedule_union_map(
8276 __isl_keep isl_schedule_node *node);
8278 In particular, the functions
8279 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8280 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8281 and C<isl_schedule_node_get_prefix_schedule_union_map>
8282 return a relative ordering on the domain elements that reach the given
8283 node determined by its ancestors.
8284 The function C<isl_schedule_node_get_prefix_schedule_relation>
8285 additionally includes the domain constraints in the result.
8286 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8287 returns a representation of the partial schedule defined by the
8288 subtree rooted at the given node.
8289 If the tree contains any expansion nodes, then the subtree schedule
8290 is formulated in terms of the expanded domain elements.
8291 The tree passed to functions returning a prefix schedule
8292 may only contain extension nodes if these would not affect
8293 the result of these functions. That is, if one of the ancestors
8294 is an extension node, then all of the domain elements that were
8295 added by the extension node need to have been filtered out
8296 by filter nodes between the extension node and the input node.
8297 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8298 may not contain in extension nodes in the selected subtree.
8300 The expansion/contraction defined by an entire subtree, combining
8301 the expansions/contractions
8302 on the expansion nodes in the subtree, can be obtained using
8303 the following functions.
8305 #include <isl/schedule_node.h>
8306 __isl_give isl_union_map *
8307 isl_schedule_node_get_subtree_expansion(
8308 __isl_keep isl_schedule_node *node);
8309 __isl_give isl_union_pw_multi_aff *
8310 isl_schedule_node_get_subtree_contraction(
8311 __isl_keep isl_schedule_node *node);
8313 The total number of outer band members of given node, i.e.,
8314 the shared output dimension of the maps in the result
8315 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8316 using the following function.
8318 #include <isl/schedule_node.h>
8319 int isl_schedule_node_get_schedule_depth(
8320 __isl_keep isl_schedule_node *node);
8322 The following functions return the elements that reach the given node
8323 or the union of universes in the spaces that contain these elements.
8325 #include <isl/schedule_node.h>
8326 __isl_give isl_union_set *
8327 isl_schedule_node_get_domain(
8328 __isl_keep isl_schedule_node *node);
8329 __isl_give isl_union_set *
8330 isl_schedule_node_get_universe_domain(
8331 __isl_keep isl_schedule_node *node);
8333 The input tree of C<isl_schedule_node_get_domain>
8334 may only contain extension nodes if these would not affect
8335 the result of this function. That is, if one of the ancestors
8336 is an extension node, then all of the domain elements that were
8337 added by the extension node need to have been filtered out
8338 by filter nodes between the extension node and the input node.
8340 The following functions can be used to introduce additional nodes
8341 in the schedule tree. The new node is introduced at the point
8342 in the tree where the C<isl_schedule_node> points to and
8343 the results points to the new node.
8345 #include <isl/schedule_node.h>
8346 __isl_give isl_schedule_node *
8347 isl_schedule_node_insert_partial_schedule(
8348 __isl_take isl_schedule_node *node,
8349 __isl_take isl_multi_union_pw_aff *schedule);
8351 This function inserts a new band node with (the greatest integer
8352 part of) the given partial schedule.
8353 The subtree rooted at the given node is assumed not to have
8356 #include <isl/schedule_node.h>
8357 __isl_give isl_schedule_node *
8358 isl_schedule_node_insert_context(
8359 __isl_take isl_schedule_node *node,
8360 __isl_take isl_set *context);
8362 This function inserts a new context node with the given context constraints.
8364 #include <isl/schedule_node.h>
8365 __isl_give isl_schedule_node *
8366 isl_schedule_node_insert_filter(
8367 __isl_take isl_schedule_node *node,
8368 __isl_take isl_union_set *filter);
8370 This function inserts a new filter node with the given filter.
8371 If the original node already pointed to a filter node, then the
8372 two filter nodes are merged into one.
8374 #include <isl/schedule_node.h>
8375 __isl_give isl_schedule_node *
8376 isl_schedule_node_insert_guard(
8377 __isl_take isl_schedule_node *node,
8378 __isl_take isl_set *guard);
8380 This function inserts a new guard node with the given guard constraints.
8382 #include <isl/schedule_node.h>
8383 __isl_give isl_schedule_node *
8384 isl_schedule_node_insert_mark(
8385 __isl_take isl_schedule_node *node,
8386 __isl_take isl_id *mark);
8388 This function inserts a new mark node with the give mark identifier.
8390 #include <isl/schedule_node.h>
8391 __isl_give isl_schedule_node *
8392 isl_schedule_node_insert_sequence(
8393 __isl_take isl_schedule_node *node,
8394 __isl_take isl_union_set_list *filters);
8395 __isl_give isl_schedule_node *
8396 isl_schedule_node_insert_set(
8397 __isl_take isl_schedule_node *node,
8398 __isl_take isl_union_set_list *filters);
8400 These functions insert a new sequence or set node with the given
8401 filters as children.
8403 #include <isl/schedule_node.h>
8404 __isl_give isl_schedule_node *isl_schedule_node_group(
8405 __isl_take isl_schedule_node *node,
8406 __isl_take isl_id *group_id);
8408 This function introduces an expansion node in between the current
8409 node and its parent that expands instances of a space with tuple
8410 identifier C<group_id> to the original domain elements that reach
8411 the node. The group instances are identified by the prefix schedule
8412 of those domain elements. The ancestors of the node are adjusted
8413 to refer to the group instances instead of the original domain
8414 elements. The return value points to the same node in the updated
8415 schedule tree as the input node, i.e., to the child of the newly
8416 introduced expansion node. Grouping instances of different statements
8417 ensures that they will be treated as a single statement by the
8418 AST generator up to the point of the expansion node.
8420 The following function can be used to flatten a nested
8423 #include <isl/schedule_node.h>
8424 __isl_give isl_schedule_node *
8425 isl_schedule_node_sequence_splice_child(
8426 __isl_take isl_schedule_node *node, int pos);
8428 That is, given a sequence node C<node> that has another sequence node
8429 in its child at position C<pos> (in particular, the child of that filter
8430 node is a sequence node), attach the children of that other sequence
8431 node as children of C<node>, replacing the original child at position
8434 The partial schedule of a band node can be scaled (down) or reduced using
8435 the following functions.
8437 #include <isl/schedule_node.h>
8438 __isl_give isl_schedule_node *
8439 isl_schedule_node_band_scale(
8440 __isl_take isl_schedule_node *node,
8441 __isl_take isl_multi_val *mv);
8442 __isl_give isl_schedule_node *
8443 isl_schedule_node_band_scale_down(
8444 __isl_take isl_schedule_node *node,
8445 __isl_take isl_multi_val *mv);
8446 __isl_give isl_schedule_node *
8447 isl_schedule_node_band_mod(
8448 __isl_take isl_schedule_node *node,
8449 __isl_take isl_multi_val *mv);
8451 The spaces of the two arguments need to match.
8452 After scaling, the partial schedule is replaced by its greatest
8453 integer part to ensure that the schedule remains integral.
8455 The partial schedule of a band node can be shifted by an
8456 C<isl_multi_union_pw_aff> with a domain that is a superset
8457 of the domain of the partial schedule using
8458 the following function.
8460 #include <isl/schedule_node.h>
8461 __isl_give isl_schedule_node *
8462 isl_schedule_node_band_shift(
8463 __isl_take isl_schedule_node *node,
8464 __isl_take isl_multi_union_pw_aff *shift);
8466 A band node can be tiled using the following function.
8468 #include <isl/schedule_node.h>
8469 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8470 __isl_take isl_schedule_node *node,
8471 __isl_take isl_multi_val *sizes);
8473 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8475 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8476 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8478 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8480 The C<isl_schedule_node_band_tile> function tiles
8481 the band using the given tile sizes inside its schedule.
8482 A new child band node is created to represent the point loops and it is
8483 inserted between the modified band and its children.
8484 The subtree rooted at the given node is assumed not to have
8486 The C<tile_scale_tile_loops> option specifies whether the tile
8487 loops iterators should be scaled by the tile sizes.
8488 If the C<tile_shift_point_loops> option is set, then the point loops
8489 are shifted to start at zero.
8491 A band node can be split into two nested band nodes
8492 using the following function.
8494 #include <isl/schedule_node.h>
8495 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8496 __isl_take isl_schedule_node *node, int pos);
8498 The resulting outer band node contains the first C<pos> dimensions of
8499 the schedule of C<node> while the inner band contains the remaining dimensions.
8500 The schedules of the two band nodes live in anonymous spaces.
8502 A band node can be moved down to the leaves of the subtree rooted
8503 at the band node using the following function.
8505 #include <isl/schedule_node.h>
8506 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8507 __isl_take isl_schedule_node *node);
8509 The subtree rooted at the given node is assumed not to have
8511 The result points to the node in the resulting tree that is in the same
8512 position as the node pointed to by C<node> in the original tree.
8514 #include <isl/schedule_node.h>
8515 __isl_give isl_schedule_node *
8516 isl_schedule_node_order_before(
8517 __isl_take isl_schedule_node *node,
8518 __isl_take isl_union_set *filter);
8519 __isl_give isl_schedule_node *
8520 isl_schedule_node_order_after(
8521 __isl_take isl_schedule_node *node,
8522 __isl_take isl_union_set *filter);
8524 These functions split the domain elements that reach C<node>
8525 into those that satisfy C<filter> and those that do not and
8526 arranges for the elements that do satisfy the filter to be
8527 executed before (in case of C<isl_schedule_node_order_before>)
8528 or after (in case of C<isl_schedule_node_order_after>)
8529 those that do not. The order is imposed by
8530 a sequence node, possibly reusing the grandparent of C<node>
8531 on two copies of the subtree attached to the original C<node>.
8532 Both copies are simplified with respect to their filter.
8534 Return a pointer to the copy of the subtree that does not
8535 satisfy C<filter>. If there is no such copy (because all
8536 reaching domain elements satisfy the filter), then return
8537 the original pointer.
8539 #include <isl/schedule_node.h>
8540 __isl_give isl_schedule_node *
8541 isl_schedule_node_graft_before(
8542 __isl_take isl_schedule_node *node,
8543 __isl_take isl_schedule_node *graft);
8544 __isl_give isl_schedule_node *
8545 isl_schedule_node_graft_after(
8546 __isl_take isl_schedule_node *node,
8547 __isl_take isl_schedule_node *graft);
8549 This function inserts the C<graft> tree into the tree containing C<node>
8550 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8551 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8552 The root node of C<graft>
8553 should be an extension node where the domain of the extension
8554 is the flat product of all outer band nodes of C<node>.
8555 The root node may also be a domain node.
8556 The elements of the domain or the range of the extension may not
8557 intersect with the domain elements that reach "node".
8558 The schedule tree of C<graft> may not be anchored.
8560 The schedule tree of C<node> is modified to include an extension node
8561 corresponding to the root node of C<graft> as a child of the original
8562 parent of C<node>. The original node that C<node> points to and the
8563 child of the root node of C<graft> are attached to this extension node
8564 through a sequence, with appropriate filters and with the child
8565 of C<graft> appearing before or after the original C<node>.
8567 If C<node> already appears inside a sequence that is the child of
8568 an extension node and if the spaces of the new domain elements
8569 do not overlap with those of the original domain elements,
8570 then that extension node is extended with the new extension
8571 rather than introducing a new segment of extension and sequence nodes.
8573 Return a pointer to the same node in the modified tree that
8574 C<node> pointed to in the original tree.
8576 A representation of the schedule node can be printed using
8578 #include <isl/schedule_node.h>
8579 __isl_give isl_printer *isl_printer_print_schedule_node(
8580 __isl_take isl_printer *p,
8581 __isl_keep isl_schedule_node *node);
8582 __isl_give char *isl_schedule_node_to_str(
8583 __isl_keep isl_schedule_node *node);
8585 C<isl_schedule_node_to_str> prints the schedule node in block format.
8587 =head2 Dependence Analysis
8589 C<isl> contains specialized functionality for performing
8590 array dataflow analysis. That is, given a I<sink> access relation
8591 and a collection of possible I<source> access relations,
8592 C<isl> can compute relations that describe
8593 for each iteration of the sink access, which iteration
8594 of which of the source access relations was the last
8595 to access the same data element before the given iteration
8597 The resulting dependence relations map source iterations
8598 to either the corresponding sink iterations or
8599 pairs of corresponding sink iterations and accessed data elements.
8600 To compute standard flow dependences, the sink should be
8601 a read, while the sources should be writes.
8602 If any of the source accesses are marked as being I<may>
8603 accesses, then there will be a dependence from the last
8604 I<must> access B<and> from any I<may> access that follows
8605 this last I<must> access.
8606 In particular, if I<all> sources are I<may> accesses,
8607 then memory based dependence analysis is performed.
8608 If, on the other hand, all sources are I<must> accesses,
8609 then value based dependence analysis is performed.
8611 =head3 High-level Interface
8613 A high-level interface to dependence analysis is provided
8614 by the following function.
8616 #include <isl/flow.h>
8617 __isl_give isl_union_flow *
8618 isl_union_access_info_compute_flow(
8619 __isl_take isl_union_access_info *access);
8621 The input C<isl_union_access_info> object describes the sink
8622 access relations, the source access relations and a schedule,
8623 while the output C<isl_union_flow> object describes
8624 the resulting dependence relations and the subsets of the
8625 sink relations for which no source was found.
8627 An C<isl_union_access_info> is created, modified, copied and freed using
8628 the following functions.
8630 #include <isl/flow.h>
8631 __isl_give isl_union_access_info *
8632 isl_union_access_info_from_sink(
8633 __isl_take isl_union_map *sink);
8634 __isl_give isl_union_access_info *
8635 isl_union_access_info_set_must_source(
8636 __isl_take isl_union_access_info *access,
8637 __isl_take isl_union_map *must_source);
8638 __isl_give isl_union_access_info *
8639 isl_union_access_info_set_may_source(
8640 __isl_take isl_union_access_info *access,
8641 __isl_take isl_union_map *may_source);
8642 __isl_give isl_union_access_info *
8643 isl_union_access_info_set_schedule(
8644 __isl_take isl_union_access_info *access,
8645 __isl_take isl_schedule *schedule);
8646 __isl_give isl_union_access_info *
8647 isl_union_access_info_set_schedule_map(
8648 __isl_take isl_union_access_info *access,
8649 __isl_take isl_union_map *schedule_map);
8650 __isl_give isl_union_access_info *
8651 isl_union_access_info_copy(
8652 __isl_keep isl_union_access_info *access);
8653 __isl_null isl_union_access_info *
8654 isl_union_access_info_free(
8655 __isl_take isl_union_access_info *access);
8657 The may sources set by C<isl_union_access_info_set_may_source>
8658 do not need to include the must sources set by
8659 C<isl_union_access_info_set_must_source> as a subset.
8660 The user is free not to call one (or both) of these functions,
8661 in which case the corresponding set is kept to its empty default.
8662 Similarly, the default schedule initialized by
8663 C<isl_union_access_info_from_sink> is empty.
8664 The current schedule is determined by the last call to either
8665 C<isl_union_access_info_set_schedule> or
8666 C<isl_union_access_info_set_schedule_map>.
8667 The domain of the schedule corresponds to the domains of
8668 the access relations. In particular, the domains of the access
8669 relations are effectively intersected with the domain of the schedule
8670 and only the resulting accesses are considered by the dependence analysis.
8672 A representation of the information contained in an object
8673 of type C<isl_union_access_info> can be obtained using
8675 #include <isl/flow.h>
8676 __isl_give isl_printer *
8677 isl_printer_print_union_access_info(
8678 __isl_take isl_printer *p,
8679 __isl_keep isl_union_access_info *access);
8680 __isl_give char *isl_union_access_info_to_str(
8681 __isl_keep isl_union_access_info *access);
8683 C<isl_union_access_info_to_str> prints the information in flow format.
8685 The output of C<isl_union_access_info_compute_flow> can be examined
8686 and freed using the following functions.
8688 #include <isl/flow.h>
8689 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8690 __isl_keep isl_union_flow *flow);
8691 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8692 __isl_keep isl_union_flow *flow);
8693 __isl_give isl_union_map *
8694 isl_union_flow_get_full_must_dependence(
8695 __isl_keep isl_union_flow *flow);
8696 __isl_give isl_union_map *
8697 isl_union_flow_get_full_may_dependence(
8698 __isl_keep isl_union_flow *flow);
8699 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8700 __isl_keep isl_union_flow *flow);
8701 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8702 __isl_keep isl_union_flow *flow);
8703 __isl_null isl_union_flow *isl_union_flow_free(
8704 __isl_take isl_union_flow *flow);
8706 The relation returned by C<isl_union_flow_get_must_dependence>
8707 relates domain elements of must sources to domain elements of the sink.
8708 The relation returned by C<isl_union_flow_get_may_dependence>
8709 relates domain elements of must or may sources to domain elements of the sink
8710 and includes the previous relation as a subset.
8711 The relation returned by C<isl_union_flow_get_full_must_dependence>
8712 relates domain elements of must sources to pairs of domain elements of the sink
8713 and accessed data elements.
8714 The relation returned by C<isl_union_flow_get_full_may_dependence>
8715 relates domain elements of must or may sources to pairs of
8716 domain elements of the sink and accessed data elements.
8717 This relation includes the previous relation as a subset.
8718 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8719 of the sink relation for which no dependences have been found.
8720 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8721 of the sink relation for which no definite dependences have been found.
8722 That is, it contains those sink access that do not contribute to any
8723 of the elements in the relation returned
8724 by C<isl_union_flow_get_must_dependence>.
8726 A representation of the information contained in an object
8727 of type C<isl_union_flow> can be obtained using
8729 #include <isl/flow.h>
8730 __isl_give isl_printer *isl_printer_print_union_flow(
8731 __isl_take isl_printer *p,
8732 __isl_keep isl_union_flow *flow);
8733 __isl_give char *isl_union_flow_to_str(
8734 __isl_keep isl_union_flow *flow);
8736 C<isl_union_flow_to_str> prints the information in flow format.
8738 =head3 Low-level Interface
8740 A lower-level interface is provided by the following functions.
8742 #include <isl/flow.h>
8744 typedef int (*isl_access_level_before)(void *first, void *second);
8746 __isl_give isl_access_info *isl_access_info_alloc(
8747 __isl_take isl_map *sink,
8748 void *sink_user, isl_access_level_before fn,
8750 __isl_give isl_access_info *isl_access_info_add_source(
8751 __isl_take isl_access_info *acc,
8752 __isl_take isl_map *source, int must,
8754 __isl_null isl_access_info *isl_access_info_free(
8755 __isl_take isl_access_info *acc);
8757 __isl_give isl_flow *isl_access_info_compute_flow(
8758 __isl_take isl_access_info *acc);
8760 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8761 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8762 void *dep_user, void *user),
8764 __isl_give isl_map *isl_flow_get_no_source(
8765 __isl_keep isl_flow *deps, int must);
8766 void isl_flow_free(__isl_take isl_flow *deps);
8768 The function C<isl_access_info_compute_flow> performs the actual
8769 dependence analysis. The other functions are used to construct
8770 the input for this function or to read off the output.
8772 The input is collected in an C<isl_access_info>, which can
8773 be created through a call to C<isl_access_info_alloc>.
8774 The arguments to this functions are the sink access relation
8775 C<sink>, a token C<sink_user> used to identify the sink
8776 access to the user, a callback function for specifying the
8777 relative order of source and sink accesses, and the number
8778 of source access relations that will be added.
8779 The callback function has type C<int (*)(void *first, void *second)>.
8780 The function is called with two user supplied tokens identifying
8781 either a source or the sink and it should return the shared nesting
8782 level and the relative order of the two accesses.
8783 In particular, let I<n> be the number of loops shared by
8784 the two accesses. If C<first> precedes C<second> textually,
8785 then the function should return I<2 * n + 1>; otherwise,
8786 it should return I<2 * n>.
8787 The sources can be added to the C<isl_access_info> by performing
8788 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8789 C<must> indicates whether the source is a I<must> access
8790 or a I<may> access. Note that a multi-valued access relation
8791 should only be marked I<must> if every iteration in the domain
8792 of the relation accesses I<all> elements in its image.
8793 The C<source_user> token is again used to identify
8794 the source access. The range of the source access relation
8795 C<source> should have the same dimension as the range
8796 of the sink access relation.
8797 The C<isl_access_info_free> function should usually not be
8798 called explicitly, because it is called implicitly by
8799 C<isl_access_info_compute_flow>.
8801 The result of the dependence analysis is collected in an
8802 C<isl_flow>. There may be elements of
8803 the sink access for which no preceding source access could be
8804 found or for which all preceding sources are I<may> accesses.
8805 The relations containing these elements can be obtained through
8806 calls to C<isl_flow_get_no_source>, the first with C<must> set
8807 and the second with C<must> unset.
8808 In the case of standard flow dependence analysis,
8809 with the sink a read and the sources I<must> writes,
8810 the first relation corresponds to the reads from uninitialized
8811 array elements and the second relation is empty.
8812 The actual flow dependences can be extracted using
8813 C<isl_flow_foreach>. This function will call the user-specified
8814 callback function C<fn> for each B<non-empty> dependence between
8815 a source and the sink. The callback function is called
8816 with four arguments, the actual flow dependence relation
8817 mapping source iterations to sink iterations, a boolean that
8818 indicates whether it is a I<must> or I<may> dependence, a token
8819 identifying the source and an additional C<void *> with value
8820 equal to the third argument of the C<isl_flow_foreach> call.
8821 A dependence is marked I<must> if it originates from a I<must>
8822 source and if it is not followed by any I<may> sources.
8824 After finishing with an C<isl_flow>, the user should call
8825 C<isl_flow_free> to free all associated memory.
8827 =head3 Interaction with the Low-level Interface
8829 During the dependence analysis, we frequently need to perform
8830 the following operation. Given a relation between sink iterations
8831 and potential source iterations from a particular source domain,
8832 what is the last potential source iteration corresponding to each
8833 sink iteration. It can sometimes be convenient to adjust
8834 the set of potential source iterations before or after each such operation.
8835 The prototypical example is fuzzy array dataflow analysis,
8836 where we need to analyze if, based on data-dependent constraints,
8837 the sink iteration can ever be executed without one or more of
8838 the corresponding potential source iterations being executed.
8839 If so, we can introduce extra parameters and select an unknown
8840 but fixed source iteration from the potential source iterations.
8841 To be able to perform such manipulations, C<isl> provides the following
8844 #include <isl/flow.h>
8846 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8847 __isl_keep isl_map *source_map,
8848 __isl_keep isl_set *sink, void *source_user,
8850 __isl_give isl_access_info *isl_access_info_set_restrict(
8851 __isl_take isl_access_info *acc,
8852 isl_access_restrict fn, void *user);
8854 The function C<isl_access_info_set_restrict> should be called
8855 before calling C<isl_access_info_compute_flow> and registers a callback function
8856 that will be called any time C<isl> is about to compute the last
8857 potential source. The first argument is the (reverse) proto-dependence,
8858 mapping sink iterations to potential source iterations.
8859 The second argument represents the sink iterations for which
8860 we want to compute the last source iteration.
8861 The third argument is the token corresponding to the source
8862 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8863 The callback is expected to return a restriction on either the input or
8864 the output of the operation computing the last potential source.
8865 If the input needs to be restricted then restrictions are needed
8866 for both the source and the sink iterations. The sink iterations
8867 and the potential source iterations will be intersected with these sets.
8868 If the output needs to be restricted then only a restriction on the source
8869 iterations is required.
8870 If any error occurs, the callback should return C<NULL>.
8871 An C<isl_restriction> object can be created, freed and inspected
8872 using the following functions.
8874 #include <isl/flow.h>
8876 __isl_give isl_restriction *isl_restriction_input(
8877 __isl_take isl_set *source_restr,
8878 __isl_take isl_set *sink_restr);
8879 __isl_give isl_restriction *isl_restriction_output(
8880 __isl_take isl_set *source_restr);
8881 __isl_give isl_restriction *isl_restriction_none(
8882 __isl_take isl_map *source_map);
8883 __isl_give isl_restriction *isl_restriction_empty(
8884 __isl_take isl_map *source_map);
8885 __isl_null isl_restriction *isl_restriction_free(
8886 __isl_take isl_restriction *restr);
8888 C<isl_restriction_none> and C<isl_restriction_empty> are special
8889 cases of C<isl_restriction_input>. C<isl_restriction_none>
8890 is essentially equivalent to
8892 isl_restriction_input(isl_set_universe(
8893 isl_space_range(isl_map_get_space(source_map))),
8895 isl_space_domain(isl_map_get_space(source_map))));
8897 whereas C<isl_restriction_empty> is essentially equivalent to
8899 isl_restriction_input(isl_set_empty(
8900 isl_space_range(isl_map_get_space(source_map))),
8902 isl_space_domain(isl_map_get_space(source_map))));
8906 #include <isl/schedule.h>
8907 __isl_give isl_schedule *
8908 isl_schedule_constraints_compute_schedule(
8909 __isl_take isl_schedule_constraints *sc);
8911 The function C<isl_schedule_constraints_compute_schedule> can be
8912 used to compute a schedule that satisfies the given schedule constraints.
8913 These schedule constraints include the iteration domain for which
8914 a schedule should be computed and dependences between pairs of
8915 iterations. In particular, these dependences include
8916 I<validity> dependences and I<proximity> dependences.
8917 By default, the algorithm used to construct the schedule is similar
8918 to that of C<Pluto>.
8919 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8921 The generated schedule respects all validity dependences.
8922 That is, all dependence distances over these dependences in the
8923 scheduled space are lexicographically positive.
8925 The default algorithm tries to ensure that the dependence distances
8926 over coincidence constraints are zero and to minimize the
8927 dependence distances over proximity dependences.
8928 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8929 for groups of domains where the dependence distances over validity
8930 dependences have only non-negative values.
8931 Note that when minimizing the maximal dependence distance
8932 over proximity dependences, a single affine expression in the parameters
8933 is constructed that bounds all dependence distances. If no such expression
8934 exists, then the algorithm will fail and resort to an alternative
8935 scheduling algorithm. In particular, this means that adding proximity
8936 dependences may eliminate valid solutions. A typical example where this
8937 phenomenon may occur is when some subset of the proximity dependences
8938 has no restriction on some parameter, forcing the coefficient of that
8939 parameter to be zero, while some other subset forces the dependence
8940 distance to depend on that parameter, requiring the same coefficient
8942 When using Feautrier's algorithm, the coincidence and proximity constraints
8943 are only taken into account during the extension to a
8944 full-dimensional schedule.
8946 An C<isl_schedule_constraints> object can be constructed
8947 and manipulated using the following functions.
8949 #include <isl/schedule.h>
8950 __isl_give isl_schedule_constraints *
8951 isl_schedule_constraints_copy(
8952 __isl_keep isl_schedule_constraints *sc);
8953 __isl_give isl_schedule_constraints *
8954 isl_schedule_constraints_on_domain(
8955 __isl_take isl_union_set *domain);
8956 __isl_give isl_schedule_constraints *
8957 isl_schedule_constraints_set_context(
8958 __isl_take isl_schedule_constraints *sc,
8959 __isl_take isl_set *context);
8960 __isl_give isl_schedule_constraints *
8961 isl_schedule_constraints_set_validity(
8962 __isl_take isl_schedule_constraints *sc,
8963 __isl_take isl_union_map *validity);
8964 __isl_give isl_schedule_constraints *
8965 isl_schedule_constraints_set_coincidence(
8966 __isl_take isl_schedule_constraints *sc,
8967 __isl_take isl_union_map *coincidence);
8968 __isl_give isl_schedule_constraints *
8969 isl_schedule_constraints_set_proximity(
8970 __isl_take isl_schedule_constraints *sc,
8971 __isl_take isl_union_map *proximity);
8972 __isl_give isl_schedule_constraints *
8973 isl_schedule_constraints_set_conditional_validity(
8974 __isl_take isl_schedule_constraints *sc,
8975 __isl_take isl_union_map *condition,
8976 __isl_take isl_union_map *validity);
8977 __isl_give isl_schedule_constraints *
8978 isl_schedule_constraints_apply(
8979 __isl_take isl_schedule_constraints *sc,
8980 __isl_take isl_union_map *umap);
8981 __isl_null isl_schedule_constraints *
8982 isl_schedule_constraints_free(
8983 __isl_take isl_schedule_constraints *sc);
8985 The initial C<isl_schedule_constraints> object created by
8986 C<isl_schedule_constraints_on_domain> does not impose any constraints.
8987 That is, it has an empty set of dependences.
8988 The function C<isl_schedule_constraints_set_context> allows the user
8989 to specify additional constraints on the parameters that may
8990 be assumed to hold during the construction of the schedule.
8991 The function C<isl_schedule_constraints_set_validity> replaces the
8992 validity dependences, mapping domain elements I<i> to domain
8993 elements that should be scheduled after I<i>.
8994 The function C<isl_schedule_constraints_set_coincidence> replaces the
8995 coincidence dependences, mapping domain elements I<i> to domain
8996 elements that should be scheduled together with I<I>, if possible.
8997 The function C<isl_schedule_constraints_set_proximity> replaces the
8998 proximity dependences, mapping domain elements I<i> to domain
8999 elements that should be scheduled either before I<I>
9000 or as early as possible after I<i>.
9002 The function C<isl_schedule_constraints_set_conditional_validity>
9003 replaces the conditional validity constraints.
9004 A conditional validity constraint is only imposed when any of the corresponding
9005 conditions is satisfied, i.e., when any of them is non-zero.
9006 That is, the scheduler ensures that within each band if the dependence
9007 distances over the condition constraints are not all zero
9008 then all corresponding conditional validity constraints are respected.
9009 A conditional validity constraint corresponds to a condition
9010 if the two are adjacent, i.e., if the domain of one relation intersect
9011 the range of the other relation.
9012 The typical use case of conditional validity constraints is
9013 to allow order constraints between live ranges to be violated
9014 as long as the live ranges themselves are local to the band.
9015 To allow more fine-grained control over which conditions correspond
9016 to which conditional validity constraints, the domains and ranges
9017 of these relations may include I<tags>. That is, the domains and
9018 ranges of those relation may themselves be wrapped relations
9019 where the iteration domain appears in the domain of those wrapped relations
9020 and the range of the wrapped relations can be arbitrarily chosen
9021 by the user. Conditions and conditional validity constraints are only
9022 considered adjacent to each other if the entire wrapped relation matches.
9023 In particular, a relation with a tag will never be considered adjacent
9024 to a relation without a tag.
9026 The function C<isl_schedule_constraints_compute_schedule> takes
9027 schedule constraints that are defined on some set of domain elements
9028 and transforms them to schedule constraints on the elements
9029 to which these domain elements are mapped by the given transformation.
9031 An C<isl_schedule_constraints> object can be inspected
9032 using the following functions.
9034 #include <isl/schedule.h>
9035 __isl_give isl_union_set *
9036 isl_schedule_constraints_get_domain(
9037 __isl_keep isl_schedule_constraints *sc);
9038 __isl_give isl_union_map *
9039 isl_schedule_constraints_get_validity(
9040 __isl_keep isl_schedule_constraints *sc);
9041 __isl_give isl_union_map *
9042 isl_schedule_constraints_get_coincidence(
9043 __isl_keep isl_schedule_constraints *sc);
9044 __isl_give isl_union_map *
9045 isl_schedule_constraints_get_proximity(
9046 __isl_keep isl_schedule_constraints *sc);
9047 __isl_give isl_union_map *
9048 isl_schedule_constraints_get_conditional_validity(
9049 __isl_keep isl_schedule_constraints *sc);
9050 __isl_give isl_union_map *
9051 isl_schedule_constraints_get_conditional_validity_condition(
9052 __isl_keep isl_schedule_constraints *sc);
9054 The following function computes a schedule directly from
9055 an iteration domain and validity and proximity dependences
9056 and is implemented in terms of the functions described above.
9057 The use of C<isl_union_set_compute_schedule> is discouraged.
9059 #include <isl/schedule.h>
9060 __isl_give isl_schedule *isl_union_set_compute_schedule(
9061 __isl_take isl_union_set *domain,
9062 __isl_take isl_union_map *validity,
9063 __isl_take isl_union_map *proximity);
9065 The generated schedule represents a schedule tree.
9066 For more information on schedule trees, see
9067 L</"Schedule Trees">.
9071 #include <isl/schedule.h>
9072 isl_stat isl_options_set_schedule_max_coefficient(
9073 isl_ctx *ctx, int val);
9074 int isl_options_get_schedule_max_coefficient(
9076 isl_stat isl_options_set_schedule_max_constant_term(
9077 isl_ctx *ctx, int val);
9078 int isl_options_get_schedule_max_constant_term(
9080 isl_stat isl_options_set_schedule_serialize_sccs(
9081 isl_ctx *ctx, int val);
9082 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9083 isl_stat isl_options_set_schedule_whole_component(
9084 isl_ctx *ctx, int val);
9085 int isl_options_get_schedule_whole_component(
9087 isl_stat isl_options_set_schedule_maximize_band_depth(
9088 isl_ctx *ctx, int val);
9089 int isl_options_get_schedule_maximize_band_depth(
9091 isl_stat isl_options_set_schedule_maximize_coincidence(
9092 isl_ctx *ctx, int val);
9093 int isl_options_get_schedule_maximize_coincidence(
9095 isl_stat isl_options_set_schedule_outer_coincidence(
9096 isl_ctx *ctx, int val);
9097 int isl_options_get_schedule_outer_coincidence(
9099 isl_stat isl_options_set_schedule_split_scaled(
9100 isl_ctx *ctx, int val);
9101 int isl_options_get_schedule_split_scaled(
9103 isl_stat isl_options_set_schedule_treat_coalescing(
9104 isl_ctx *ctx, int val);
9105 int isl_options_get_schedule_treat_coalescing(
9107 isl_stat isl_options_set_schedule_algorithm(
9108 isl_ctx *ctx, int val);
9109 int isl_options_get_schedule_algorithm(
9111 isl_stat isl_options_set_schedule_separate_components(
9112 isl_ctx *ctx, int val);
9113 int isl_options_get_schedule_separate_components(
9118 =item * schedule_max_coefficient
9120 This option enforces that the coefficients for variable and parameter
9121 dimensions in the calculated schedule are not larger than the specified value.
9122 This option can significantly increase the speed of the scheduling calculation
9123 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9124 this option does not introduce bounds on the variable or parameter
9127 =item * schedule_max_constant_term
9129 This option enforces that the constant coefficients in the calculated schedule
9130 are not larger than the maximal constant term. This option can significantly
9131 increase the speed of the scheduling calculation and may also prevent fusing of
9132 unrelated dimensions. A value of -1 means that this option does not introduce
9133 bounds on the constant coefficients.
9135 =item * schedule_serialize_sccs
9137 If this option is set, then all strongly connected components
9138 in the dependence graph are serialized as soon as they are detected.
9139 This means in particular that instances of statements will only
9140 appear in the same band node if these statements belong
9141 to the same strongly connected component at the point where
9142 the band node is constructed.
9144 =item * schedule_whole_component
9146 If this option is set, then entire (weakly) connected
9147 components in the dependence graph are scheduled together
9149 Otherwise, each strongly connected component within
9150 such a weakly connected component is first scheduled separately
9151 and then combined with other strongly connected components.
9152 This option has no effect if C<schedule_serialize_sccs> is set.
9154 =item * schedule_maximize_band_depth
9156 If this option is set, then the scheduler tries to maximize
9157 the width of the bands. Wider bands give more possibilities for tiling.
9158 In particular, if the C<schedule_whole_component> option is set,
9159 then bands are split if this might result in wider bands.
9160 Otherwise, the effect of this option is to only allow
9161 strongly connected components to be combined if this does
9162 not reduce the width of the bands.
9163 Note that if the C<schedule_serialize_sccs> options is set, then
9164 the C<schedule_maximize_band_depth> option therefore has no effect.
9166 =item * schedule_maximize_coincidence
9168 This option is only effective if the C<schedule_whole_component>
9169 option is turned off.
9170 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9171 strongly connected components are only combined with each other
9172 if this does not reduce the number of coincident band members.
9174 =item * schedule_outer_coincidence
9176 If this option is set, then we try to construct schedules
9177 where the outermost scheduling dimension in each band
9178 satisfies the coincidence constraints.
9180 =item * schedule_algorithm
9182 Selects the scheduling algorithm to be used.
9183 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9184 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9186 =item * schedule_split_scaled
9188 If this option is set, then we try to construct schedules in which the
9189 constant term is split off from the linear part if the linear parts of
9190 the scheduling rows for all nodes in the graphs have a common non-trivial
9192 The constant term is then placed in a separate band and the linear
9194 This option is only effective when the Feautrier style scheduler is
9195 being used, either as the main scheduler or as a fallback for the
9196 Pluto-like scheduler.
9198 =item * schedule_treat_coalescing
9200 If this option is set, then the scheduler will try and avoid
9201 producing schedules that perform loop coalescing.
9202 In particular, for the Pluto-like scheduler, this option places
9203 bounds on the schedule coefficients based on the sizes of the instance sets.
9204 For the Feautrier style scheduler, this option detects potentially
9205 coalescing schedules and then tries to adjust the schedule to avoid
9208 =item * schedule_separate_components
9210 If this option is set then the function C<isl_schedule_get_map>
9211 will treat set nodes in the same way as sequence nodes.
9215 =head2 AST Generation
9217 This section describes the C<isl> functionality for generating
9218 ASTs that visit all the elements
9219 in a domain in an order specified by a schedule tree or
9221 In case the schedule given as a C<isl_union_map>, an AST is generated
9222 that visits all the elements in the domain of the C<isl_union_map>
9223 according to the lexicographic order of the corresponding image
9224 element(s). If the range of the C<isl_union_map> consists of
9225 elements in more than one space, then each of these spaces is handled
9226 separately in an arbitrary order.
9227 It should be noted that the schedule tree or the image elements
9228 in a schedule map only specify the I<order>
9229 in which the corresponding domain elements should be visited.
9230 No direct relation between the partial schedule values
9231 or the image elements on the one hand and the loop iterators
9232 in the generated AST on the other hand should be assumed.
9234 Each AST is generated within a build. The initial build
9235 simply specifies the constraints on the parameters (if any)
9236 and can be created, inspected, copied and freed using the following functions.
9238 #include <isl/ast_build.h>
9239 __isl_give isl_ast_build *isl_ast_build_alloc(
9241 __isl_give isl_ast_build *isl_ast_build_from_context(
9242 __isl_take isl_set *set);
9243 __isl_give isl_ast_build *isl_ast_build_copy(
9244 __isl_keep isl_ast_build *build);
9245 __isl_null isl_ast_build *isl_ast_build_free(
9246 __isl_take isl_ast_build *build);
9248 The C<set> argument is usually a parameter set with zero or more parameters.
9249 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9250 this set is required to be a parameter set.
9251 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9252 specify any parameter constraints.
9253 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9254 and L</"Fine-grained Control over AST Generation">.
9255 Finally, the AST itself can be constructed using one of the following
9258 #include <isl/ast_build.h>
9259 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9260 __isl_keep isl_ast_build *build,
9261 __isl_take isl_schedule *schedule);
9262 __isl_give isl_ast_node *
9263 isl_ast_build_node_from_schedule_map(
9264 __isl_keep isl_ast_build *build,
9265 __isl_take isl_union_map *schedule);
9267 =head3 Inspecting the AST
9269 The basic properties of an AST node can be obtained as follows.
9271 #include <isl/ast.h>
9272 enum isl_ast_node_type isl_ast_node_get_type(
9273 __isl_keep isl_ast_node *node);
9275 The type of an AST node is one of
9276 C<isl_ast_node_for>,
9278 C<isl_ast_node_block>,
9279 C<isl_ast_node_mark> or
9280 C<isl_ast_node_user>.
9281 An C<isl_ast_node_for> represents a for node.
9282 An C<isl_ast_node_if> represents an if node.
9283 An C<isl_ast_node_block> represents a compound node.
9284 An C<isl_ast_node_mark> introduces a mark in the AST.
9285 An C<isl_ast_node_user> represents an expression statement.
9286 An expression statement typically corresponds to a domain element, i.e.,
9287 one of the elements that is visited by the AST.
9289 Each type of node has its own additional properties.
9291 #include <isl/ast.h>
9292 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9293 __isl_keep isl_ast_node *node);
9294 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9295 __isl_keep isl_ast_node *node);
9296 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9297 __isl_keep isl_ast_node *node);
9298 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9299 __isl_keep isl_ast_node *node);
9300 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9301 __isl_keep isl_ast_node *node);
9302 isl_bool isl_ast_node_for_is_degenerate(
9303 __isl_keep isl_ast_node *node);
9305 An C<isl_ast_for> is considered degenerate if it is known to execute
9308 #include <isl/ast.h>
9309 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9310 __isl_keep isl_ast_node *node);
9311 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9312 __isl_keep isl_ast_node *node);
9313 isl_bool isl_ast_node_if_has_else(
9314 __isl_keep isl_ast_node *node);
9315 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9316 __isl_keep isl_ast_node *node);
9318 __isl_give isl_ast_node_list *
9319 isl_ast_node_block_get_children(
9320 __isl_keep isl_ast_node *node);
9322 __isl_give isl_id *isl_ast_node_mark_get_id(
9323 __isl_keep isl_ast_node *node);
9324 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9325 __isl_keep isl_ast_node *node);
9327 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9328 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9330 #include <isl/ast.h>
9331 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9332 __isl_keep isl_ast_node *node);
9334 All descendants of a specific node in the AST (including the node itself)
9336 in depth-first pre-order using the following function.
9338 #include <isl/ast.h>
9339 isl_stat isl_ast_node_foreach_descendant_top_down(
9340 __isl_keep isl_ast_node *node,
9341 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9342 void *user), void *user);
9344 The callback function should return C<isl_bool_true> if the children
9345 of the given node should be visited and C<isl_bool_false> if they should not.
9346 It should return C<isl_bool_error> in case of failure, in which case
9347 the entire traversal is aborted.
9349 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9350 the following functions.
9352 #include <isl/ast.h>
9353 enum isl_ast_expr_type isl_ast_expr_get_type(
9354 __isl_keep isl_ast_expr *expr);
9356 The type of an AST expression is one of
9358 C<isl_ast_expr_id> or
9359 C<isl_ast_expr_int>.
9360 An C<isl_ast_expr_op> represents the result of an operation.
9361 An C<isl_ast_expr_id> represents an identifier.
9362 An C<isl_ast_expr_int> represents an integer value.
9364 Each type of expression has its own additional properties.
9366 #include <isl/ast.h>
9367 enum isl_ast_op_type isl_ast_expr_get_op_type(
9368 __isl_keep isl_ast_expr *expr);
9369 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9370 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9371 __isl_keep isl_ast_expr *expr, int pos);
9372 isl_stat isl_ast_expr_foreach_ast_op_type(
9373 __isl_keep isl_ast_expr *expr,
9374 isl_stat (*fn)(enum isl_ast_op_type type,
9375 void *user), void *user);
9376 isl_stat isl_ast_node_foreach_ast_op_type(
9377 __isl_keep isl_ast_node *node,
9378 isl_stat (*fn)(enum isl_ast_op_type type,
9379 void *user), void *user);
9381 C<isl_ast_expr_get_op_type> returns the type of the operation
9382 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9383 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9385 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9386 C<isl_ast_op_type> that appears in C<expr>.
9387 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9388 C<isl_ast_op_type> that appears in C<node>.
9389 The operation type is one of the following.
9393 =item C<isl_ast_op_and>
9395 Logical I<and> of two arguments.
9396 Both arguments can be evaluated.
9398 =item C<isl_ast_op_and_then>
9400 Logical I<and> of two arguments.
9401 The second argument can only be evaluated if the first evaluates to true.
9403 =item C<isl_ast_op_or>
9405 Logical I<or> of two arguments.
9406 Both arguments can be evaluated.
9408 =item C<isl_ast_op_or_else>
9410 Logical I<or> of two arguments.
9411 The second argument can only be evaluated if the first evaluates to false.
9413 =item C<isl_ast_op_max>
9415 Maximum of two or more arguments.
9417 =item C<isl_ast_op_min>
9419 Minimum of two or more arguments.
9421 =item C<isl_ast_op_minus>
9425 =item C<isl_ast_op_add>
9427 Sum of two arguments.
9429 =item C<isl_ast_op_sub>
9431 Difference of two arguments.
9433 =item C<isl_ast_op_mul>
9435 Product of two arguments.
9437 =item C<isl_ast_op_div>
9439 Exact division. That is, the result is known to be an integer.
9441 =item C<isl_ast_op_fdiv_q>
9443 Result of integer division, rounded towards negative
9446 =item C<isl_ast_op_pdiv_q>
9448 Result of integer division, where dividend is known to be non-negative.
9450 =item C<isl_ast_op_pdiv_r>
9452 Remainder of integer division, where dividend is known to be non-negative.
9454 =item C<isl_ast_op_zdiv_r>
9456 Equal to zero iff the remainder on integer division is zero.
9458 =item C<isl_ast_op_cond>
9460 Conditional operator defined on three arguments.
9461 If the first argument evaluates to true, then the result
9462 is equal to the second argument. Otherwise, the result
9463 is equal to the third argument.
9464 The second and third argument may only be evaluated if
9465 the first argument evaluates to true and false, respectively.
9466 Corresponds to C<a ? b : c> in C.
9468 =item C<isl_ast_op_select>
9470 Conditional operator defined on three arguments.
9471 If the first argument evaluates to true, then the result
9472 is equal to the second argument. Otherwise, the result
9473 is equal to the third argument.
9474 The second and third argument may be evaluated independently
9475 of the value of the first argument.
9476 Corresponds to C<a * b + (1 - a) * c> in C.
9478 =item C<isl_ast_op_eq>
9482 =item C<isl_ast_op_le>
9484 Less than or equal relation.
9486 =item C<isl_ast_op_lt>
9490 =item C<isl_ast_op_ge>
9492 Greater than or equal relation.
9494 =item C<isl_ast_op_gt>
9496 Greater than relation.
9498 =item C<isl_ast_op_call>
9501 The number of arguments of the C<isl_ast_expr> is one more than
9502 the number of arguments in the function call, the first argument
9503 representing the function being called.
9505 =item C<isl_ast_op_access>
9508 The number of arguments of the C<isl_ast_expr> is one more than
9509 the number of index expressions in the array access, the first argument
9510 representing the array being accessed.
9512 =item C<isl_ast_op_member>
9515 This operation has two arguments, a structure and the name of
9516 the member of the structure being accessed.
9520 #include <isl/ast.h>
9521 __isl_give isl_id *isl_ast_expr_get_id(
9522 __isl_keep isl_ast_expr *expr);
9524 Return the identifier represented by the AST expression.
9526 #include <isl/ast.h>
9527 __isl_give isl_val *isl_ast_expr_get_val(
9528 __isl_keep isl_ast_expr *expr);
9530 Return the integer represented by the AST expression.
9532 =head3 Properties of ASTs
9534 #include <isl/ast.h>
9535 isl_bool isl_ast_expr_is_equal(
9536 __isl_keep isl_ast_expr *expr1,
9537 __isl_keep isl_ast_expr *expr2);
9539 Check if two C<isl_ast_expr>s are equal to each other.
9541 =head3 Manipulating and printing the AST
9543 AST nodes can be copied and freed using the following functions.
9545 #include <isl/ast.h>
9546 __isl_give isl_ast_node *isl_ast_node_copy(
9547 __isl_keep isl_ast_node *node);
9548 __isl_null isl_ast_node *isl_ast_node_free(
9549 __isl_take isl_ast_node *node);
9551 AST expressions can be copied and freed using the following functions.
9553 #include <isl/ast.h>
9554 __isl_give isl_ast_expr *isl_ast_expr_copy(
9555 __isl_keep isl_ast_expr *expr);
9556 __isl_null isl_ast_expr *isl_ast_expr_free(
9557 __isl_take isl_ast_expr *expr);
9559 New AST expressions can be created either directly or within
9560 the context of an C<isl_ast_build>.
9562 #include <isl/ast.h>
9563 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9564 __isl_take isl_val *v);
9565 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9566 __isl_take isl_id *id);
9567 __isl_give isl_ast_expr *isl_ast_expr_neg(
9568 __isl_take isl_ast_expr *expr);
9569 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9570 __isl_take isl_ast_expr *expr);
9571 __isl_give isl_ast_expr *isl_ast_expr_add(
9572 __isl_take isl_ast_expr *expr1,
9573 __isl_take isl_ast_expr *expr2);
9574 __isl_give isl_ast_expr *isl_ast_expr_sub(
9575 __isl_take isl_ast_expr *expr1,
9576 __isl_take isl_ast_expr *expr2);
9577 __isl_give isl_ast_expr *isl_ast_expr_mul(
9578 __isl_take isl_ast_expr *expr1,
9579 __isl_take isl_ast_expr *expr2);
9580 __isl_give isl_ast_expr *isl_ast_expr_div(
9581 __isl_take isl_ast_expr *expr1,
9582 __isl_take isl_ast_expr *expr2);
9583 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9584 __isl_take isl_ast_expr *expr1,
9585 __isl_take isl_ast_expr *expr2);
9586 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9587 __isl_take isl_ast_expr *expr1,
9588 __isl_take isl_ast_expr *expr2);
9589 __isl_give isl_ast_expr *isl_ast_expr_and(
9590 __isl_take isl_ast_expr *expr1,
9591 __isl_take isl_ast_expr *expr2)
9592 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9593 __isl_take isl_ast_expr *expr1,
9594 __isl_take isl_ast_expr *expr2)
9595 __isl_give isl_ast_expr *isl_ast_expr_or(
9596 __isl_take isl_ast_expr *expr1,
9597 __isl_take isl_ast_expr *expr2)
9598 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9599 __isl_take isl_ast_expr *expr1,
9600 __isl_take isl_ast_expr *expr2)
9601 __isl_give isl_ast_expr *isl_ast_expr_eq(
9602 __isl_take isl_ast_expr *expr1,
9603 __isl_take isl_ast_expr *expr2);
9604 __isl_give isl_ast_expr *isl_ast_expr_le(
9605 __isl_take isl_ast_expr *expr1,
9606 __isl_take isl_ast_expr *expr2);
9607 __isl_give isl_ast_expr *isl_ast_expr_lt(
9608 __isl_take isl_ast_expr *expr1,
9609 __isl_take isl_ast_expr *expr2);
9610 __isl_give isl_ast_expr *isl_ast_expr_ge(
9611 __isl_take isl_ast_expr *expr1,
9612 __isl_take isl_ast_expr *expr2);
9613 __isl_give isl_ast_expr *isl_ast_expr_gt(
9614 __isl_take isl_ast_expr *expr1,
9615 __isl_take isl_ast_expr *expr2);
9616 __isl_give isl_ast_expr *isl_ast_expr_access(
9617 __isl_take isl_ast_expr *array,
9618 __isl_take isl_ast_expr_list *indices);
9619 __isl_give isl_ast_expr *isl_ast_expr_call(
9620 __isl_take isl_ast_expr *function,
9621 __isl_take isl_ast_expr_list *arguments);
9623 The function C<isl_ast_expr_address_of> can be applied to an
9624 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9625 to represent the address of the C<isl_ast_expr_access>. The function
9626 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9627 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9629 #include <isl/ast_build.h>
9630 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9631 __isl_keep isl_ast_build *build,
9632 __isl_take isl_set *set);
9633 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9634 __isl_keep isl_ast_build *build,
9635 __isl_take isl_pw_aff *pa);
9636 __isl_give isl_ast_expr *
9637 isl_ast_build_access_from_pw_multi_aff(
9638 __isl_keep isl_ast_build *build,
9639 __isl_take isl_pw_multi_aff *pma);
9640 __isl_give isl_ast_expr *
9641 isl_ast_build_access_from_multi_pw_aff(
9642 __isl_keep isl_ast_build *build,
9643 __isl_take isl_multi_pw_aff *mpa);
9644 __isl_give isl_ast_expr *
9645 isl_ast_build_call_from_pw_multi_aff(
9646 __isl_keep isl_ast_build *build,
9647 __isl_take isl_pw_multi_aff *pma);
9648 __isl_give isl_ast_expr *
9649 isl_ast_build_call_from_multi_pw_aff(
9650 __isl_keep isl_ast_build *build,
9651 __isl_take isl_multi_pw_aff *mpa);
9654 the domains of C<pa>, C<mpa> and C<pma> should correspond
9655 to the schedule space of C<build>.
9656 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9657 the function being called.
9658 If the accessed space is a nested relation, then it is taken
9659 to represent an access of the member specified by the range
9660 of this nested relation of the structure specified by the domain
9661 of the nested relation.
9663 The following functions can be used to modify an C<isl_ast_expr>.
9665 #include <isl/ast.h>
9666 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9667 __isl_take isl_ast_expr *expr, int pos,
9668 __isl_take isl_ast_expr *arg);
9670 Replace the argument of C<expr> at position C<pos> by C<arg>.
9672 #include <isl/ast.h>
9673 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9674 __isl_take isl_ast_expr *expr,
9675 __isl_take isl_id_to_ast_expr *id2expr);
9677 The function C<isl_ast_expr_substitute_ids> replaces the
9678 subexpressions of C<expr> of type C<isl_ast_expr_id>
9679 by the corresponding expression in C<id2expr>, if there is any.
9682 User specified data can be attached to an C<isl_ast_node> and obtained
9683 from the same C<isl_ast_node> using the following functions.
9685 #include <isl/ast.h>
9686 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9687 __isl_take isl_ast_node *node,
9688 __isl_take isl_id *annotation);
9689 __isl_give isl_id *isl_ast_node_get_annotation(
9690 __isl_keep isl_ast_node *node);
9692 Basic printing can be performed using the following functions.
9694 #include <isl/ast.h>
9695 __isl_give isl_printer *isl_printer_print_ast_expr(
9696 __isl_take isl_printer *p,
9697 __isl_keep isl_ast_expr *expr);
9698 __isl_give isl_printer *isl_printer_print_ast_node(
9699 __isl_take isl_printer *p,
9700 __isl_keep isl_ast_node *node);
9701 __isl_give char *isl_ast_expr_to_str(
9702 __isl_keep isl_ast_expr *expr);
9704 More advanced printing can be performed using the following functions.
9706 #include <isl/ast.h>
9707 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9708 __isl_take isl_printer *p,
9709 enum isl_ast_op_type type,
9710 __isl_keep const char *name);
9711 isl_stat isl_options_set_ast_print_macro_once(
9712 isl_ctx *ctx, int val);
9713 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9714 __isl_give isl_printer *isl_ast_op_type_print_macro(
9715 enum isl_ast_op_type type,
9716 __isl_take isl_printer *p);
9717 __isl_give isl_printer *isl_ast_expr_print_macros(
9718 __isl_keep isl_ast_expr *expr,
9719 __isl_take isl_printer *p);
9720 __isl_give isl_printer *isl_ast_node_print_macros(
9721 __isl_keep isl_ast_node *node,
9722 __isl_take isl_printer *p);
9723 __isl_give isl_printer *isl_ast_node_print(
9724 __isl_keep isl_ast_node *node,
9725 __isl_take isl_printer *p,
9726 __isl_take isl_ast_print_options *options);
9727 __isl_give isl_printer *isl_ast_node_for_print(
9728 __isl_keep isl_ast_node *node,
9729 __isl_take isl_printer *p,
9730 __isl_take isl_ast_print_options *options);
9731 __isl_give isl_printer *isl_ast_node_if_print(
9732 __isl_keep isl_ast_node *node,
9733 __isl_take isl_printer *p,
9734 __isl_take isl_ast_print_options *options);
9736 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9737 C<isl> may print out an AST that makes use of macros such
9738 as C<floord>, C<min> and C<max>.
9739 The names of these macros may be modified by a call
9740 to C<isl_ast_op_type_set_print_name>. The user-specified
9741 names are associated to the printer object.
9742 C<isl_ast_op_type_print_macro> prints out the macro
9743 corresponding to a specific C<isl_ast_op_type>.
9744 If the print-macro-once option is set, then a given macro definition
9745 is only printed once to any given printer object.
9746 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9747 for subexpressions where these macros would be used and prints
9748 out the required macro definitions.
9749 Essentially, C<isl_ast_expr_print_macros> calls
9750 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9751 as function argument.
9752 C<isl_ast_node_print_macros> does the same
9753 for expressions in its C<isl_ast_node> argument.
9754 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9755 C<isl_ast_node_if_print> print an C<isl_ast_node>
9756 in C<ISL_FORMAT_C>, but allow for some extra control
9757 through an C<isl_ast_print_options> object.
9758 This object can be created using the following functions.
9760 #include <isl/ast.h>
9761 __isl_give isl_ast_print_options *
9762 isl_ast_print_options_alloc(isl_ctx *ctx);
9763 __isl_give isl_ast_print_options *
9764 isl_ast_print_options_copy(
9765 __isl_keep isl_ast_print_options *options);
9766 __isl_null isl_ast_print_options *
9767 isl_ast_print_options_free(
9768 __isl_take isl_ast_print_options *options);
9770 __isl_give isl_ast_print_options *
9771 isl_ast_print_options_set_print_user(
9772 __isl_take isl_ast_print_options *options,
9773 __isl_give isl_printer *(*print_user)(
9774 __isl_take isl_printer *p,
9775 __isl_take isl_ast_print_options *options,
9776 __isl_keep isl_ast_node *node, void *user),
9778 __isl_give isl_ast_print_options *
9779 isl_ast_print_options_set_print_for(
9780 __isl_take isl_ast_print_options *options,
9781 __isl_give isl_printer *(*print_for)(
9782 __isl_take isl_printer *p,
9783 __isl_take isl_ast_print_options *options,
9784 __isl_keep isl_ast_node *node, void *user),
9787 The callback set by C<isl_ast_print_options_set_print_user>
9788 is called whenever a node of type C<isl_ast_node_user> needs to
9790 The callback set by C<isl_ast_print_options_set_print_for>
9791 is called whenever a node of type C<isl_ast_node_for> needs to
9793 Note that C<isl_ast_node_for_print> will I<not> call the
9794 callback set by C<isl_ast_print_options_set_print_for> on the node
9795 on which C<isl_ast_node_for_print> is called, but only on nested
9796 nodes of type C<isl_ast_node_for>. It is therefore safe to
9797 call C<isl_ast_node_for_print> from within the callback set by
9798 C<isl_ast_print_options_set_print_for>.
9800 The following option determines the type to be used for iterators
9801 while printing the AST.
9803 isl_stat isl_options_set_ast_iterator_type(
9804 isl_ctx *ctx, const char *val);
9805 const char *isl_options_get_ast_iterator_type(
9808 The AST printer only prints body nodes as blocks if these
9809 blocks cannot be safely omitted.
9810 For example, a C<for> node with one body node will not be
9811 surrounded with braces in C<ISL_FORMAT_C>.
9812 A block will always be printed by setting the following option.
9814 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9816 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9820 #include <isl/ast_build.h>
9821 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9822 isl_ctx *ctx, int val);
9823 int isl_options_get_ast_build_atomic_upper_bound(
9825 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9827 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9828 isl_stat isl_options_set_ast_build_detect_min_max(
9829 isl_ctx *ctx, int val);
9830 int isl_options_get_ast_build_detect_min_max(
9832 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9833 isl_ctx *ctx, int val);
9834 int isl_options_get_ast_build_exploit_nested_bounds(
9836 isl_stat isl_options_set_ast_build_group_coscheduled(
9837 isl_ctx *ctx, int val);
9838 int isl_options_get_ast_build_group_coscheduled(
9840 isl_stat isl_options_set_ast_build_scale_strides(
9841 isl_ctx *ctx, int val);
9842 int isl_options_get_ast_build_scale_strides(
9844 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9846 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9847 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9849 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9853 =item * ast_build_atomic_upper_bound
9855 Generate loop upper bounds that consist of the current loop iterator,
9856 an operator and an expression not involving the iterator.
9857 If this option is not set, then the current loop iterator may appear
9858 several times in the upper bound.
9859 For example, when this option is turned off, AST generation
9862 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9866 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9869 When the option is turned on, the following AST is generated
9871 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9874 =item * ast_build_prefer_pdiv
9876 If this option is turned off, then the AST generation will
9877 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9878 operators, but no C<isl_ast_op_pdiv_q> or
9879 C<isl_ast_op_pdiv_r> operators.
9880 If this option is turned on, then C<isl> will try to convert
9881 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9882 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9884 =item * ast_build_detect_min_max
9886 If this option is turned on, then C<isl> will try and detect
9887 min or max-expressions when building AST expressions from
9888 piecewise affine expressions.
9890 =item * ast_build_exploit_nested_bounds
9892 Simplify conditions based on bounds of nested for loops.
9893 In particular, remove conditions that are implied by the fact
9894 that one or more nested loops have at least one iteration,
9895 meaning that the upper bound is at least as large as the lower bound.
9896 For example, when this option is turned off, AST generation
9899 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
9905 for (int c0 = 0; c0 <= N; c0 += 1)
9906 for (int c1 = 0; c1 <= M; c1 += 1)
9909 When the option is turned on, the following AST is generated
9911 for (int c0 = 0; c0 <= N; c0 += 1)
9912 for (int c1 = 0; c1 <= M; c1 += 1)
9915 =item * ast_build_group_coscheduled
9917 If two domain elements are assigned the same schedule point, then
9918 they may be executed in any order and they may even appear in different
9919 loops. If this options is set, then the AST generator will make
9920 sure that coscheduled domain elements do not appear in separate parts
9921 of the AST. This is useful in case of nested AST generation
9922 if the outer AST generation is given only part of a schedule
9923 and the inner AST generation should handle the domains that are
9924 coscheduled by this initial part of the schedule together.
9925 For example if an AST is generated for a schedule
9927 { A[i] -> [0]; B[i] -> [0] }
9929 then the C<isl_ast_build_set_create_leaf> callback described
9930 below may get called twice, once for each domain.
9931 Setting this option ensures that the callback is only called once
9932 on both domains together.
9934 =item * ast_build_separation_bounds
9936 This option specifies which bounds to use during separation.
9937 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
9938 then all (possibly implicit) bounds on the current dimension will
9939 be used during separation.
9940 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
9941 then only those bounds that are explicitly available will
9942 be used during separation.
9944 =item * ast_build_scale_strides
9946 This option specifies whether the AST generator is allowed
9947 to scale down iterators of strided loops.
9949 =item * ast_build_allow_else
9951 This option specifies whether the AST generator is allowed
9952 to construct if statements with else branches.
9954 =item * ast_build_allow_or
9956 This option specifies whether the AST generator is allowed
9957 to construct if conditions with disjunctions.
9961 =head3 AST Generation Options (Schedule Tree)
9963 In case of AST construction from a schedule tree, the options
9964 that control how an AST is created from the individual schedule
9965 dimensions are stored in the band nodes of the tree
9966 (see L</"Schedule Trees">).
9968 In particular, a schedule dimension can be handled in four
9969 different ways, atomic, separate, unroll or the default.
9970 This loop AST generation type can be set using
9971 C<isl_schedule_node_band_member_set_ast_loop_type>.
9973 the first three can be selected by including a one-dimensional
9974 element with as value the position of the schedule dimension
9975 within the band and as name one of C<atomic>, C<separate>
9976 or C<unroll> in the options
9977 set by C<isl_schedule_node_band_set_ast_build_options>.
9978 Only one of these three may be specified for
9979 any given schedule dimension within a band node.
9980 If none of these is specified, then the default
9981 is used. The meaning of the options is as follows.
9987 When this option is specified, the AST generator will make
9988 sure that a given domains space only appears in a single
9989 loop at the specified level.
9991 For example, for the schedule tree
9993 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9995 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9996 options: "{ atomic[x] }"
9998 the following AST will be generated
10000 for (int c0 = 0; c0 <= 10; c0 += 1) {
10007 On the other hand, for the schedule tree
10009 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10011 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10012 options: "{ separate[x] }"
10014 the following AST will be generated
10018 for (int c0 = 1; c0 <= 9; c0 += 1) {
10025 If neither C<atomic> nor C<separate> is specified, then the AST generator
10026 may produce either of these two results or some intermediate form.
10030 When this option is specified, the AST generator will
10031 split the domain of the specified schedule dimension
10032 into pieces with a fixed set of statements for which
10033 instances need to be executed by the iterations in
10034 the schedule domain part. This option tends to avoid
10035 the generation of guards inside the corresponding loops.
10036 See also the C<atomic> option.
10040 When this option is specified, the AST generator will
10041 I<completely> unroll the corresponding schedule dimension.
10042 It is the responsibility of the user to ensure that such
10043 unrolling is possible.
10044 To obtain a partial unrolling, the user should apply an additional
10045 strip-mining to the schedule and fully unroll the inner schedule
10050 The C<isolate> option is a bit more involved. It allows the user
10051 to isolate a range of schedule dimension values from smaller and
10052 greater values. Additionally, the user may specify a different
10053 atomic/separate/unroll choice for the isolated part and the remaining
10054 parts. The typical use case of the C<isolate> option is to isolate
10055 full tiles from partial tiles.
10056 The part that needs to be isolated may depend on outer schedule dimensions.
10057 The option therefore needs to be able to reference those outer schedule
10058 dimensions. In particular, the space of the C<isolate> option is that
10059 of a wrapped map with as domain the flat product of all outer band nodes
10060 and as range the space of the current band node.
10061 The atomic/separate/unroll choice for the isolated part is determined
10062 by an option that lives in an unnamed wrapped space with as domain
10063 a zero-dimensional C<isolate> space and as range the regular
10064 C<atomic>, C<separate> or C<unroll> space.
10065 This option may also be set directly using
10066 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10067 The atomic/separate/unroll choice for the remaining part is determined
10068 by the regular C<atomic>, C<separate> or C<unroll> option.
10069 The use of the C<isolate> option causes any tree containing the node
10070 to be considered anchored.
10072 As an example, consider the isolation of full tiles from partial tiles
10073 in a tiling of a triangular domain. The original schedule is as follows.
10075 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10077 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10078 { A[i,j] -> [floor(j/10)] }, \
10079 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10083 for (int c0 = 0; c0 <= 10; c0 += 1)
10084 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10085 for (int c2 = 10 * c0;
10086 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10087 for (int c3 = 10 * c1;
10088 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10091 Isolating the full tiles, we have the following input
10093 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10095 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10096 { A[i,j] -> [floor(j/10)] }, \
10097 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10098 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10099 10a+9+10b+9 <= 100 }"
10104 for (int c0 = 0; c0 <= 8; c0 += 1) {
10105 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10106 for (int c2 = 10 * c0;
10107 c2 <= 10 * c0 + 9; c2 += 1)
10108 for (int c3 = 10 * c1;
10109 c3 <= 10 * c1 + 9; c3 += 1)
10111 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10112 for (int c2 = 10 * c0;
10113 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10114 for (int c3 = 10 * c1;
10115 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10118 for (int c0 = 9; c0 <= 10; c0 += 1)
10119 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10120 for (int c2 = 10 * c0;
10121 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10122 for (int c3 = 10 * c1;
10123 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10127 We may then additionally unroll the innermost loop of the isolated part
10129 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10131 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10132 { A[i,j] -> [floor(j/10)] }, \
10133 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10134 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10135 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10140 for (int c0 = 0; c0 <= 8; c0 += 1) {
10141 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10142 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10144 A(c2, 10 * c1 + 1);
10145 A(c2, 10 * c1 + 2);
10146 A(c2, 10 * c1 + 3);
10147 A(c2, 10 * c1 + 4);
10148 A(c2, 10 * c1 + 5);
10149 A(c2, 10 * c1 + 6);
10150 A(c2, 10 * c1 + 7);
10151 A(c2, 10 * c1 + 8);
10152 A(c2, 10 * c1 + 9);
10154 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10155 for (int c2 = 10 * c0;
10156 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10157 for (int c3 = 10 * c1;
10158 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10161 for (int c0 = 9; c0 <= 10; c0 += 1)
10162 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10163 for (int c2 = 10 * c0;
10164 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10165 for (int c3 = 10 * c1;
10166 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10171 =head3 AST Generation Options (Schedule Map)
10173 In case of AST construction using
10174 C<isl_ast_build_node_from_schedule_map>, the options
10175 that control how an AST is created from the individual schedule
10176 dimensions are stored in the C<isl_ast_build>.
10177 They can be set using the following function.
10179 #include <isl/ast_build.h>
10180 __isl_give isl_ast_build *
10181 isl_ast_build_set_options(
10182 __isl_take isl_ast_build *control,
10183 __isl_take isl_union_map *options);
10185 The options are encoded in an C<isl_union_map>.
10186 The domain of this union relation refers to the schedule domain,
10187 i.e., the range of the schedule passed
10188 to C<isl_ast_build_node_from_schedule_map>.
10189 In the case of nested AST generation (see L</"Nested AST Generation">),
10190 the domain of C<options> should refer to the extra piece of the schedule.
10191 That is, it should be equal to the range of the wrapped relation in the
10192 range of the schedule.
10193 The range of the options can consist of elements in one or more spaces,
10194 the names of which determine the effect of the option.
10195 The values of the range typically also refer to the schedule dimension
10196 to which the option applies. In case of nested AST generation
10197 (see L</"Nested AST Generation">), these values refer to the position
10198 of the schedule dimension within the innermost AST generation.
10199 The constraints on the domain elements of
10200 the option should only refer to this dimension and earlier dimensions.
10201 We consider the following spaces.
10205 =item C<separation_class>
10207 B<This option has been deprecated. Use the isolate option on
10208 schedule trees instead.>
10210 This space is a wrapped relation between two one dimensional spaces.
10211 The input space represents the schedule dimension to which the option
10212 applies and the output space represents the separation class.
10213 While constructing a loop corresponding to the specified schedule
10214 dimension(s), the AST generator will try to generate separate loops
10215 for domain elements that are assigned different classes.
10216 If only some of the elements are assigned a class, then those elements
10217 that are not assigned any class will be treated as belonging to a class
10218 that is separate from the explicitly assigned classes.
10219 The typical use case for this option is to separate full tiles from
10221 The other options, described below, are applied after the separation
10224 As an example, consider the separation into full and partial tiles
10225 of a tiling of a triangular domain.
10226 Take, for example, the domain
10228 { A[i,j] : 0 <= i,j and i + j <= 100 }
10230 and a tiling into tiles of 10 by 10. The input to the AST generator
10231 is then the schedule
10233 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10236 Without any options, the following AST is generated
10238 for (int c0 = 0; c0 <= 10; c0 += 1)
10239 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10240 for (int c2 = 10 * c0;
10241 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10243 for (int c3 = 10 * c1;
10244 c3 <= min(10 * c1 + 9, -c2 + 100);
10248 Separation into full and partial tiles can be obtained by assigning
10249 a class, say C<0>, to the full tiles. The full tiles are represented by those
10250 values of the first and second schedule dimensions for which there are
10251 values of the third and fourth dimensions to cover an entire tile.
10252 That is, we need to specify the following option
10254 { [a,b,c,d] -> separation_class[[0]->[0]] :
10255 exists b': 0 <= 10a,10b' and
10256 10a+9+10b'+9 <= 100;
10257 [a,b,c,d] -> separation_class[[1]->[0]] :
10258 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10260 which simplifies to
10262 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10263 a >= 0 and b >= 0 and b <= 8 - a;
10264 [a, b, c, d] -> separation_class[[0] -> [0]] :
10265 a >= 0 and a <= 8 }
10267 With this option, the generated AST is as follows
10270 for (int c0 = 0; c0 <= 8; c0 += 1) {
10271 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10272 for (int c2 = 10 * c0;
10273 c2 <= 10 * c0 + 9; c2 += 1)
10274 for (int c3 = 10 * c1;
10275 c3 <= 10 * c1 + 9; c3 += 1)
10277 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10278 for (int c2 = 10 * c0;
10279 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10281 for (int c3 = 10 * c1;
10282 c3 <= min(-c2 + 100, 10 * c1 + 9);
10286 for (int c0 = 9; c0 <= 10; c0 += 1)
10287 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10288 for (int c2 = 10 * c0;
10289 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10291 for (int c3 = 10 * c1;
10292 c3 <= min(10 * c1 + 9, -c2 + 100);
10299 This is a single-dimensional space representing the schedule dimension(s)
10300 to which ``separation'' should be applied. Separation tries to split
10301 a loop into several pieces if this can avoid the generation of guards
10303 See also the C<atomic> option.
10307 This is a single-dimensional space representing the schedule dimension(s)
10308 for which the domains should be considered ``atomic''. That is, the
10309 AST generator will make sure that any given domain space will only appear
10310 in a single loop at the specified level.
10312 Consider the following schedule
10314 { a[i] -> [i] : 0 <= i < 10;
10315 b[i] -> [i+1] : 0 <= i < 10 }
10317 If the following option is specified
10319 { [i] -> separate[x] }
10321 then the following AST will be generated
10325 for (int c0 = 1; c0 <= 9; c0 += 1) {
10332 If, on the other hand, the following option is specified
10334 { [i] -> atomic[x] }
10336 then the following AST will be generated
10338 for (int c0 = 0; c0 <= 10; c0 += 1) {
10345 If neither C<atomic> nor C<separate> is specified, then the AST generator
10346 may produce either of these two results or some intermediate form.
10350 This is a single-dimensional space representing the schedule dimension(s)
10351 that should be I<completely> unrolled.
10352 To obtain a partial unrolling, the user should apply an additional
10353 strip-mining to the schedule and fully unroll the inner loop.
10357 =head3 Fine-grained Control over AST Generation
10359 Besides specifying the constraints on the parameters,
10360 an C<isl_ast_build> object can be used to control
10361 various aspects of the AST generation process.
10362 In case of AST construction using
10363 C<isl_ast_build_node_from_schedule_map>,
10364 the most prominent way of control is through ``options'',
10365 as explained above.
10367 Additional control is available through the following functions.
10369 #include <isl/ast_build.h>
10370 __isl_give isl_ast_build *
10371 isl_ast_build_set_iterators(
10372 __isl_take isl_ast_build *control,
10373 __isl_take isl_id_list *iterators);
10375 The function C<isl_ast_build_set_iterators> allows the user to
10376 specify a list of iterator C<isl_id>s to be used as iterators.
10377 If the input schedule is injective, then
10378 the number of elements in this list should be as large as the dimension
10379 of the schedule space, but no direct correspondence should be assumed
10380 between dimensions and elements.
10381 If the input schedule is not injective, then an additional number
10382 of C<isl_id>s equal to the largest dimension of the input domains
10384 If the number of provided C<isl_id>s is insufficient, then additional
10385 names are automatically generated.
10387 #include <isl/ast_build.h>
10388 __isl_give isl_ast_build *
10389 isl_ast_build_set_create_leaf(
10390 __isl_take isl_ast_build *control,
10391 __isl_give isl_ast_node *(*fn)(
10392 __isl_take isl_ast_build *build,
10393 void *user), void *user);
10396 C<isl_ast_build_set_create_leaf> function allows for the
10397 specification of a callback that should be called whenever the AST
10398 generator arrives at an element of the schedule domain.
10399 The callback should return an AST node that should be inserted
10400 at the corresponding position of the AST. The default action (when
10401 the callback is not set) is to continue generating parts of the AST to scan
10402 all the domain elements associated to the schedule domain element
10403 and to insert user nodes, ``calling'' the domain element, for each of them.
10404 The C<build> argument contains the current state of the C<isl_ast_build>.
10405 To ease nested AST generation (see L</"Nested AST Generation">),
10406 all control information that is
10407 specific to the current AST generation such as the options and
10408 the callbacks has been removed from this C<isl_ast_build>.
10409 The callback would typically return the result of a nested
10410 AST generation or a
10411 user defined node created using the following function.
10413 #include <isl/ast.h>
10414 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10415 __isl_take isl_ast_expr *expr);
10417 #include <isl/ast_build.h>
10418 __isl_give isl_ast_build *
10419 isl_ast_build_set_at_each_domain(
10420 __isl_take isl_ast_build *build,
10421 __isl_give isl_ast_node *(*fn)(
10422 __isl_take isl_ast_node *node,
10423 __isl_keep isl_ast_build *build,
10424 void *user), void *user);
10425 __isl_give isl_ast_build *
10426 isl_ast_build_set_before_each_for(
10427 __isl_take isl_ast_build *build,
10428 __isl_give isl_id *(*fn)(
10429 __isl_keep isl_ast_build *build,
10430 void *user), void *user);
10431 __isl_give isl_ast_build *
10432 isl_ast_build_set_after_each_for(
10433 __isl_take isl_ast_build *build,
10434 __isl_give isl_ast_node *(*fn)(
10435 __isl_take isl_ast_node *node,
10436 __isl_keep isl_ast_build *build,
10437 void *user), void *user);
10438 __isl_give isl_ast_build *
10439 isl_ast_build_set_before_each_mark(
10440 __isl_take isl_ast_build *build,
10441 isl_stat (*fn)(__isl_keep isl_id *mark,
10442 __isl_keep isl_ast_build *build,
10443 void *user), void *user);
10444 __isl_give isl_ast_build *
10445 isl_ast_build_set_after_each_mark(
10446 __isl_take isl_ast_build *build,
10447 __isl_give isl_ast_node *(*fn)(
10448 __isl_take isl_ast_node *node,
10449 __isl_keep isl_ast_build *build,
10450 void *user), void *user);
10452 The callback set by C<isl_ast_build_set_at_each_domain> will
10453 be called for each domain AST node.
10454 The callbacks set by C<isl_ast_build_set_before_each_for>
10455 and C<isl_ast_build_set_after_each_for> will be called
10456 for each for AST node. The first will be called in depth-first
10457 pre-order, while the second will be called in depth-first post-order.
10458 Since C<isl_ast_build_set_before_each_for> is called before the for
10459 node is actually constructed, it is only passed an C<isl_ast_build>.
10460 The returned C<isl_id> will be added as an annotation (using
10461 C<isl_ast_node_set_annotation>) to the constructed for node.
10462 In particular, if the user has also specified an C<after_each_for>
10463 callback, then the annotation can be retrieved from the node passed to
10464 that callback using C<isl_ast_node_get_annotation>.
10465 The callbacks set by C<isl_ast_build_set_before_each_mark>
10466 and C<isl_ast_build_set_after_each_mark> will be called for each
10467 mark AST node that is created, i.e., for each mark schedule node
10468 in the input schedule tree. The first will be called in depth-first
10469 pre-order, while the second will be called in depth-first post-order.
10470 Since the callback set by C<isl_ast_build_set_before_each_mark>
10471 is called before the mark AST node is actually constructed, it is passed
10472 the identifier of the mark node.
10473 All callbacks should C<NULL> (or -1) on failure.
10474 The given C<isl_ast_build> can be used to create new
10475 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10476 or C<isl_ast_build_call_from_pw_multi_aff>.
10478 =head3 Nested AST Generation
10480 C<isl> allows the user to create an AST within the context
10481 of another AST. These nested ASTs are created using the
10482 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10483 the outer AST. The C<build> argument should be an C<isl_ast_build>
10484 passed to a callback set by
10485 C<isl_ast_build_set_create_leaf>.
10486 The space of the range of the C<schedule> argument should refer
10487 to this build. In particular, the space should be a wrapped
10488 relation and the domain of this wrapped relation should be the
10489 same as that of the range of the schedule returned by
10490 C<isl_ast_build_get_schedule> below.
10491 In practice, the new schedule is typically
10492 created by calling C<isl_union_map_range_product> on the old schedule
10493 and some extra piece of the schedule.
10494 The space of the schedule domain is also available from
10495 the C<isl_ast_build>.
10497 #include <isl/ast_build.h>
10498 __isl_give isl_union_map *isl_ast_build_get_schedule(
10499 __isl_keep isl_ast_build *build);
10500 __isl_give isl_space *isl_ast_build_get_schedule_space(
10501 __isl_keep isl_ast_build *build);
10502 __isl_give isl_ast_build *isl_ast_build_restrict(
10503 __isl_take isl_ast_build *build,
10504 __isl_take isl_set *set);
10506 The C<isl_ast_build_get_schedule> function returns a (partial)
10507 schedule for the domains elements for which part of the AST still needs to
10508 be generated in the current build.
10509 In particular, the domain elements are mapped to those iterations of the loops
10510 enclosing the current point of the AST generation inside which
10511 the domain elements are executed.
10512 No direct correspondence between
10513 the input schedule and this schedule should be assumed.
10514 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10515 to create a set for C<isl_ast_build_restrict> to intersect
10516 with the current build. In particular, the set passed to
10517 C<isl_ast_build_restrict> can have additional parameters.
10518 The ids of the set dimensions in the space returned by
10519 C<isl_ast_build_get_schedule_space> correspond to the
10520 iterators of the already generated loops.
10521 The user should not rely on the ids of the output dimensions
10522 of the relations in the union relation returned by
10523 C<isl_ast_build_get_schedule> having any particular value.
10525 =head1 Applications
10527 Although C<isl> is mainly meant to be used as a library,
10528 it also contains some basic applications that use some
10529 of the functionality of C<isl>.
10530 The input may be specified in either the L<isl format>
10531 or the L<PolyLib format>.
10533 =head2 C<isl_polyhedron_sample>
10535 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10536 an integer element of the polyhedron, if there is any.
10537 The first column in the output is the denominator and is always
10538 equal to 1. If the polyhedron contains no integer points,
10539 then a vector of length zero is printed.
10543 C<isl_pip> takes the same input as the C<example> program
10544 from the C<piplib> distribution, i.e., a set of constraints
10545 on the parameters, a line containing only -1 and finally a set
10546 of constraints on a parametric polyhedron.
10547 The coefficients of the parameters appear in the last columns
10548 (but before the final constant column).
10549 The output is the lexicographic minimum of the parametric polyhedron.
10550 As C<isl> currently does not have its own output format, the output
10551 is just a dump of the internal state.
10553 =head2 C<isl_polyhedron_minimize>
10555 C<isl_polyhedron_minimize> computes the minimum of some linear
10556 or affine objective function over the integer points in a polyhedron.
10557 If an affine objective function
10558 is given, then the constant should appear in the last column.
10560 =head2 C<isl_polytope_scan>
10562 Given a polytope, C<isl_polytope_scan> prints
10563 all integer points in the polytope.
10565 =head2 C<isl_codegen>
10567 Given a schedule, a context set and an options relation,
10568 C<isl_codegen> prints out an AST that scans the domain elements
10569 of the schedule in the order of their image(s) taking into account
10570 the constraints in the context set.