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://freshmeat.net/projects/isl/>.
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 *ma,
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_basic_set *isl_basic_set_params(
4272 __isl_take isl_basic_set *bset);
4273 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4275 #include <isl/map.h>
4276 __isl_give isl_basic_map *isl_basic_map_project_out(
4277 __isl_take isl_basic_map *bmap,
4278 enum isl_dim_type type, unsigned first, unsigned n);
4279 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4280 enum isl_dim_type type, unsigned first, unsigned n);
4281 __isl_give isl_basic_set *isl_basic_map_domain(
4282 __isl_take isl_basic_map *bmap);
4283 __isl_give isl_basic_set *isl_basic_map_range(
4284 __isl_take isl_basic_map *bmap);
4285 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4286 __isl_give isl_set *isl_map_domain(
4287 __isl_take isl_map *bmap);
4288 __isl_give isl_set *isl_map_range(
4289 __isl_take isl_map *map);
4291 #include <isl/union_set.h>
4292 __isl_give isl_union_set *isl_union_set_project_out(
4293 __isl_take isl_union_set *uset,
4294 enum isl_dim_type type,
4295 unsigned first, unsigned n);
4296 __isl_give isl_set *isl_union_set_params(
4297 __isl_take isl_union_set *uset);
4299 The function C<isl_union_set_project_out> can only project out
4302 #include <isl/union_map.h>
4303 __isl_give isl_union_map *isl_union_map_project_out(
4304 __isl_take isl_union_map *umap,
4305 enum isl_dim_type type, unsigned first, unsigned n);
4306 __isl_give isl_set *isl_union_map_params(
4307 __isl_take isl_union_map *umap);
4308 __isl_give isl_union_set *isl_union_map_domain(
4309 __isl_take isl_union_map *umap);
4310 __isl_give isl_union_set *isl_union_map_range(
4311 __isl_take isl_union_map *umap);
4313 The function C<isl_union_map_project_out> can only project out
4316 #include <isl/aff.h>
4317 __isl_give isl_aff *isl_aff_project_domain_on_params(
4318 __isl_take isl_aff *aff);
4319 __isl_give isl_pw_multi_aff *
4320 isl_pw_multi_aff_project_domain_on_params(
4321 __isl_take isl_pw_multi_aff *pma);
4322 __isl_give isl_set *isl_pw_aff_domain(
4323 __isl_take isl_pw_aff *pwaff);
4324 __isl_give isl_set *isl_pw_multi_aff_domain(
4325 __isl_take isl_pw_multi_aff *pma);
4326 __isl_give isl_set *isl_multi_pw_aff_domain(
4327 __isl_take isl_multi_pw_aff *mpa);
4328 __isl_give isl_union_set *isl_union_pw_aff_domain(
4329 __isl_take isl_union_pw_aff *upa);
4330 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4331 __isl_take isl_union_pw_multi_aff *upma);
4332 __isl_give isl_union_set *
4333 isl_multi_union_pw_aff_domain(
4334 __isl_take isl_multi_union_pw_aff *mupa);
4335 __isl_give isl_set *isl_pw_aff_params(
4336 __isl_take isl_pw_aff *pwa);
4338 The function C<isl_multi_union_pw_aff_domain> requires its
4339 input to have at least one set dimension.
4341 #include <isl/polynomial.h>
4342 __isl_give isl_qpolynomial *
4343 isl_qpolynomial_project_domain_on_params(
4344 __isl_take isl_qpolynomial *qp);
4345 __isl_give isl_pw_qpolynomial *
4346 isl_pw_qpolynomial_project_domain_on_params(
4347 __isl_take isl_pw_qpolynomial *pwqp);
4348 __isl_give isl_pw_qpolynomial_fold *
4349 isl_pw_qpolynomial_fold_project_domain_on_params(
4350 __isl_take isl_pw_qpolynomial_fold *pwf);
4351 __isl_give isl_set *isl_pw_qpolynomial_domain(
4352 __isl_take isl_pw_qpolynomial *pwqp);
4353 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4354 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4355 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4356 __isl_take isl_union_pw_qpolynomial *upwqp);
4358 #include <isl/space.h>
4359 __isl_give isl_space *isl_space_domain_map(
4360 __isl_take isl_space *space);
4361 __isl_give isl_space *isl_space_range_map(
4362 __isl_take isl_space *space);
4364 #include <isl/map.h>
4365 __isl_give isl_map *isl_set_wrapped_domain_map(
4366 __isl_take isl_set *set);
4367 __isl_give isl_basic_map *isl_basic_map_domain_map(
4368 __isl_take isl_basic_map *bmap);
4369 __isl_give isl_basic_map *isl_basic_map_range_map(
4370 __isl_take isl_basic_map *bmap);
4371 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4372 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4374 #include <isl/union_map.h>
4375 __isl_give isl_union_map *isl_union_map_domain_map(
4376 __isl_take isl_union_map *umap);
4377 __isl_give isl_union_pw_multi_aff *
4378 isl_union_map_domain_map_union_pw_multi_aff(
4379 __isl_take isl_union_map *umap);
4380 __isl_give isl_union_map *isl_union_map_range_map(
4381 __isl_take isl_union_map *umap);
4382 __isl_give isl_union_map *
4383 isl_union_set_wrapped_domain_map(
4384 __isl_take isl_union_set *uset);
4386 The functions above construct a (basic, regular or union) relation
4387 that maps (a wrapped version of) the input relation to its domain or range.
4388 C<isl_set_wrapped_domain_map> maps the input set to the domain
4389 of its wrapped relation.
4393 __isl_give isl_basic_set *isl_basic_set_eliminate(
4394 __isl_take isl_basic_set *bset,
4395 enum isl_dim_type type,
4396 unsigned first, unsigned n);
4397 __isl_give isl_set *isl_set_eliminate(
4398 __isl_take isl_set *set, enum isl_dim_type type,
4399 unsigned first, unsigned n);
4400 __isl_give isl_basic_map *isl_basic_map_eliminate(
4401 __isl_take isl_basic_map *bmap,
4402 enum isl_dim_type type,
4403 unsigned first, unsigned n);
4404 __isl_give isl_map *isl_map_eliminate(
4405 __isl_take isl_map *map, enum isl_dim_type type,
4406 unsigned first, unsigned n);
4408 Eliminate the coefficients for the given dimensions from the constraints,
4409 without removing the dimensions.
4411 =item * Constructing a set from a parameter domain
4413 A zero-dimensional space or (basic) set can be constructed
4414 on a given parameter domain using the following functions.
4416 #include <isl/space.h>
4417 __isl_give isl_space *isl_space_set_from_params(
4418 __isl_take isl_space *space);
4420 #include <isl/set.h>
4421 __isl_give isl_basic_set *isl_basic_set_from_params(
4422 __isl_take isl_basic_set *bset);
4423 __isl_give isl_set *isl_set_from_params(
4424 __isl_take isl_set *set);
4426 =item * Constructing a relation from one or two sets
4428 Create a relation with the given set(s) as domain and/or range.
4429 If only the domain or the range is specified, then
4430 the range or domain of the created relation is a zero-dimensional
4431 flat anonymous space.
4433 #include <isl/space.h>
4434 __isl_give isl_space *isl_space_from_domain(
4435 __isl_take isl_space *space);
4436 __isl_give isl_space *isl_space_from_range(
4437 __isl_take isl_space *space);
4438 __isl_give isl_space *isl_space_map_from_set(
4439 __isl_take isl_space *space);
4440 __isl_give isl_space *isl_space_map_from_domain_and_range(
4441 __isl_take isl_space *domain,
4442 __isl_take isl_space *range);
4444 #include <isl/local_space.h>
4445 __isl_give isl_local_space *isl_local_space_from_domain(
4446 __isl_take isl_local_space *ls);
4448 #include <isl/map.h>
4449 __isl_give isl_map *isl_map_from_domain(
4450 __isl_take isl_set *set);
4451 __isl_give isl_map *isl_map_from_range(
4452 __isl_take isl_set *set);
4454 #include <isl/union_map.h>
4455 __isl_give isl_union_map *
4456 isl_union_map_from_domain_and_range(
4457 __isl_take isl_union_set *domain,
4458 __isl_take isl_union_set *range);
4460 #include <isl/val.h>
4461 __isl_give isl_multi_val *isl_multi_val_from_range(
4462 __isl_take isl_multi_val *mv);
4464 #include <isl/aff.h>
4465 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4466 __isl_take isl_multi_aff *ma);
4467 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4468 __isl_take isl_pw_aff *pwa);
4469 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4470 __isl_take isl_multi_pw_aff *mpa);
4471 __isl_give isl_multi_union_pw_aff *
4472 isl_multi_union_pw_aff_from_range(
4473 __isl_take isl_multi_union_pw_aff *mupa);
4474 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4475 __isl_take isl_set *set);
4476 __isl_give isl_union_pw_multi_aff *
4477 isl_union_pw_multi_aff_from_domain(
4478 __isl_take isl_union_set *uset);
4482 #include <isl/set.h>
4483 __isl_give isl_basic_set *isl_basic_set_fix_si(
4484 __isl_take isl_basic_set *bset,
4485 enum isl_dim_type type, unsigned pos, int value);
4486 __isl_give isl_basic_set *isl_basic_set_fix_val(
4487 __isl_take isl_basic_set *bset,
4488 enum isl_dim_type type, unsigned pos,
4489 __isl_take isl_val *v);
4490 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4491 enum isl_dim_type type, unsigned pos, int value);
4492 __isl_give isl_set *isl_set_fix_val(
4493 __isl_take isl_set *set,
4494 enum isl_dim_type type, unsigned pos,
4495 __isl_take isl_val *v);
4497 #include <isl/map.h>
4498 __isl_give isl_basic_map *isl_basic_map_fix_si(
4499 __isl_take isl_basic_map *bmap,
4500 enum isl_dim_type type, unsigned pos, int value);
4501 __isl_give isl_basic_map *isl_basic_map_fix_val(
4502 __isl_take isl_basic_map *bmap,
4503 enum isl_dim_type type, unsigned pos,
4504 __isl_take isl_val *v);
4505 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4506 enum isl_dim_type type, unsigned pos, int value);
4507 __isl_give isl_map *isl_map_fix_val(
4508 __isl_take isl_map *map,
4509 enum isl_dim_type type, unsigned pos,
4510 __isl_take isl_val *v);
4512 #include <isl/aff.h>
4513 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4514 __isl_take isl_pw_multi_aff *pma,
4515 enum isl_dim_type type, unsigned pos, int value);
4517 #include <isl/polynomial.h>
4518 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4519 __isl_take isl_pw_qpolynomial *pwqp,
4520 enum isl_dim_type type, unsigned n,
4521 __isl_take isl_val *v);
4523 Intersect the set, relation or function domain
4524 with the hyperplane where the given
4525 dimension has the fixed given value.
4527 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4528 __isl_take isl_basic_map *bmap,
4529 enum isl_dim_type type, unsigned pos, int value);
4530 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4531 __isl_take isl_basic_map *bmap,
4532 enum isl_dim_type type, unsigned pos, int value);
4533 __isl_give isl_set *isl_set_lower_bound_si(
4534 __isl_take isl_set *set,
4535 enum isl_dim_type type, unsigned pos, int value);
4536 __isl_give isl_set *isl_set_lower_bound_val(
4537 __isl_take isl_set *set,
4538 enum isl_dim_type type, unsigned pos,
4539 __isl_take isl_val *value);
4540 __isl_give isl_map *isl_map_lower_bound_si(
4541 __isl_take isl_map *map,
4542 enum isl_dim_type type, unsigned pos, int value);
4543 __isl_give isl_set *isl_set_upper_bound_si(
4544 __isl_take isl_set *set,
4545 enum isl_dim_type type, unsigned pos, int value);
4546 __isl_give isl_set *isl_set_upper_bound_val(
4547 __isl_take isl_set *set,
4548 enum isl_dim_type type, unsigned pos,
4549 __isl_take isl_val *value);
4550 __isl_give isl_map *isl_map_upper_bound_si(
4551 __isl_take isl_map *map,
4552 enum isl_dim_type type, unsigned pos, int value);
4554 Intersect the set or relation with the half-space where the given
4555 dimension has a value bounded by the fixed given integer value.
4557 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4558 enum isl_dim_type type1, int pos1,
4559 enum isl_dim_type type2, int pos2);
4560 __isl_give isl_basic_map *isl_basic_map_equate(
4561 __isl_take isl_basic_map *bmap,
4562 enum isl_dim_type type1, int pos1,
4563 enum isl_dim_type type2, int pos2);
4564 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4565 enum isl_dim_type type1, int pos1,
4566 enum isl_dim_type type2, int pos2);
4568 Intersect the set or relation with the hyperplane where the given
4569 dimensions are equal to each other.
4571 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4572 enum isl_dim_type type1, int pos1,
4573 enum isl_dim_type type2, int pos2);
4575 Intersect the relation with the hyperplane where the given
4576 dimensions have opposite values.
4578 __isl_give isl_map *isl_map_order_le(
4579 __isl_take isl_map *map,
4580 enum isl_dim_type type1, int pos1,
4581 enum isl_dim_type type2, int pos2);
4582 __isl_give isl_basic_map *isl_basic_map_order_ge(
4583 __isl_take isl_basic_map *bmap,
4584 enum isl_dim_type type1, int pos1,
4585 enum isl_dim_type type2, int pos2);
4586 __isl_give isl_map *isl_map_order_ge(
4587 __isl_take isl_map *map,
4588 enum isl_dim_type type1, int pos1,
4589 enum isl_dim_type type2, int pos2);
4590 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4591 enum isl_dim_type type1, int pos1,
4592 enum isl_dim_type type2, int pos2);
4593 __isl_give isl_basic_map *isl_basic_map_order_gt(
4594 __isl_take isl_basic_map *bmap,
4595 enum isl_dim_type type1, int pos1,
4596 enum isl_dim_type type2, int pos2);
4597 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4598 enum isl_dim_type type1, int pos1,
4599 enum isl_dim_type type2, int pos2);
4601 Intersect the relation with the half-space where the given
4602 dimensions satisfy the given ordering.
4606 #include <isl/aff.h>
4607 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4608 __isl_take isl_aff *aff);
4609 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4610 __isl_take isl_aff *aff);
4611 __isl_give isl_set *isl_pw_aff_pos_set(
4612 __isl_take isl_pw_aff *pa);
4613 __isl_give isl_set *isl_pw_aff_nonneg_set(
4614 __isl_take isl_pw_aff *pwaff);
4615 __isl_give isl_set *isl_pw_aff_zero_set(
4616 __isl_take isl_pw_aff *pwaff);
4617 __isl_give isl_set *isl_pw_aff_non_zero_set(
4618 __isl_take isl_pw_aff *pwaff);
4619 __isl_give isl_union_set *
4620 isl_union_pw_aff_zero_union_set(
4621 __isl_take isl_union_pw_aff *upa);
4622 __isl_give isl_union_set *
4623 isl_multi_union_pw_aff_zero_union_set(
4624 __isl_take isl_multi_union_pw_aff *mupa);
4626 The function C<isl_aff_neg_basic_set> returns a basic set
4627 containing those elements in the domain space
4628 of C<aff> where C<aff> is negative.
4629 The function C<isl_pw_aff_nonneg_set> returns a set
4630 containing those elements in the domain
4631 of C<pwaff> where C<pwaff> is non-negative.
4632 The function C<isl_multi_union_pw_aff_zero_union_set>
4633 returns a union set containing those elements
4634 in the domains of its elements where they are all zero.
4638 __isl_give isl_map *isl_set_identity(
4639 __isl_take isl_set *set);
4640 __isl_give isl_union_map *isl_union_set_identity(
4641 __isl_take isl_union_set *uset);
4642 __isl_give isl_union_pw_multi_aff *
4643 isl_union_set_identity_union_pw_multi_aff(
4644 __isl_take isl_union_set *uset);
4646 Construct an identity relation on the given (union) set.
4648 =item * Function Extraction
4650 A piecewise quasi affine expression that is equal to 1 on a set
4651 and 0 outside the set can be created using the following function.
4653 #include <isl/aff.h>
4654 __isl_give isl_pw_aff *isl_set_indicator_function(
4655 __isl_take isl_set *set);
4657 A piecewise multiple quasi affine expression can be extracted
4658 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4659 and the C<isl_map> is single-valued.
4660 In case of a conversion from an C<isl_union_map>
4661 to an C<isl_union_pw_multi_aff>, these properties need to hold
4662 in each domain space.
4663 A conversion to a C<isl_multi_union_pw_aff> additionally
4664 requires that the input is non-empty and involves only a single
4667 #include <isl/aff.h>
4668 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4669 __isl_take isl_set *set);
4670 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4671 __isl_take isl_map *map);
4673 __isl_give isl_union_pw_multi_aff *
4674 isl_union_pw_multi_aff_from_union_set(
4675 __isl_take isl_union_set *uset);
4676 __isl_give isl_union_pw_multi_aff *
4677 isl_union_pw_multi_aff_from_union_map(
4678 __isl_take isl_union_map *umap);
4680 __isl_give isl_multi_union_pw_aff *
4681 isl_multi_union_pw_aff_from_union_map(
4682 __isl_take isl_union_map *umap);
4686 __isl_give isl_basic_set *isl_basic_map_deltas(
4687 __isl_take isl_basic_map *bmap);
4688 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4689 __isl_give isl_union_set *isl_union_map_deltas(
4690 __isl_take isl_union_map *umap);
4692 These functions return a (basic) set containing the differences
4693 between image elements and corresponding domain elements in the input.
4695 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4696 __isl_take isl_basic_map *bmap);
4697 __isl_give isl_map *isl_map_deltas_map(
4698 __isl_take isl_map *map);
4699 __isl_give isl_union_map *isl_union_map_deltas_map(
4700 __isl_take isl_union_map *umap);
4702 The functions above construct a (basic, regular or union) relation
4703 that maps (a wrapped version of) the input relation to its delta set.
4707 Simplify the representation of a set, relation or functions by trying
4708 to combine pairs of basic sets or relations into a single
4709 basic set or relation.
4711 #include <isl/set.h>
4712 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4714 #include <isl/map.h>
4715 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4717 #include <isl/union_set.h>
4718 __isl_give isl_union_set *isl_union_set_coalesce(
4719 __isl_take isl_union_set *uset);
4721 #include <isl/union_map.h>
4722 __isl_give isl_union_map *isl_union_map_coalesce(
4723 __isl_take isl_union_map *umap);
4725 #include <isl/aff.h>
4726 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4727 __isl_take isl_pw_aff *pwqp);
4728 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4729 __isl_take isl_pw_multi_aff *pma);
4730 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4731 __isl_take isl_multi_pw_aff *mpa);
4732 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4733 __isl_take isl_union_pw_aff *upa);
4734 __isl_give isl_union_pw_multi_aff *
4735 isl_union_pw_multi_aff_coalesce(
4736 __isl_take isl_union_pw_multi_aff *upma);
4737 __isl_give isl_multi_union_pw_aff *
4738 isl_multi_union_pw_aff_coalesce(
4739 __isl_take isl_multi_union_pw_aff *aff);
4741 #include <isl/polynomial.h>
4742 __isl_give isl_pw_qpolynomial_fold *
4743 isl_pw_qpolynomial_fold_coalesce(
4744 __isl_take isl_pw_qpolynomial_fold *pwf);
4745 __isl_give isl_union_pw_qpolynomial *
4746 isl_union_pw_qpolynomial_coalesce(
4747 __isl_take isl_union_pw_qpolynomial *upwqp);
4748 __isl_give isl_union_pw_qpolynomial_fold *
4749 isl_union_pw_qpolynomial_fold_coalesce(
4750 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4752 One of the methods for combining pairs of basic sets or relations
4753 can result in coefficients that are much larger than those that appear
4754 in the constraints of the input. By default, the coefficients are
4755 not allowed to grow larger, but this can be changed by unsetting
4756 the following option.
4758 isl_stat isl_options_set_coalesce_bounded_wrapping(
4759 isl_ctx *ctx, int val);
4760 int isl_options_get_coalesce_bounded_wrapping(
4763 =item * Detecting equalities
4765 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4766 __isl_take isl_basic_set *bset);
4767 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4768 __isl_take isl_basic_map *bmap);
4769 __isl_give isl_set *isl_set_detect_equalities(
4770 __isl_take isl_set *set);
4771 __isl_give isl_map *isl_map_detect_equalities(
4772 __isl_take isl_map *map);
4773 __isl_give isl_union_set *isl_union_set_detect_equalities(
4774 __isl_take isl_union_set *uset);
4775 __isl_give isl_union_map *isl_union_map_detect_equalities(
4776 __isl_take isl_union_map *umap);
4778 Simplify the representation of a set or relation by detecting implicit
4781 =item * Removing redundant constraints
4783 #include <isl/set.h>
4784 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4785 __isl_take isl_basic_set *bset);
4786 __isl_give isl_set *isl_set_remove_redundancies(
4787 __isl_take isl_set *set);
4789 #include <isl/union_set.h>
4790 __isl_give isl_union_set *
4791 isl_union_set_remove_redundancies(
4792 __isl_take isl_union_set *uset);
4794 #include <isl/map.h>
4795 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4796 __isl_take isl_basic_map *bmap);
4797 __isl_give isl_map *isl_map_remove_redundancies(
4798 __isl_take isl_map *map);
4800 #include <isl/union_map.h>
4801 __isl_give isl_union_map *
4802 isl_union_map_remove_redundancies(
4803 __isl_take isl_union_map *umap);
4807 __isl_give isl_basic_set *isl_set_convex_hull(
4808 __isl_take isl_set *set);
4809 __isl_give isl_basic_map *isl_map_convex_hull(
4810 __isl_take isl_map *map);
4812 If the input set or relation has any existentially quantified
4813 variables, then the result of these operations is currently undefined.
4817 #include <isl/set.h>
4818 __isl_give isl_basic_set *
4819 isl_set_unshifted_simple_hull(
4820 __isl_take isl_set *set);
4821 __isl_give isl_basic_set *isl_set_simple_hull(
4822 __isl_take isl_set *set);
4823 __isl_give isl_basic_set *
4824 isl_set_unshifted_simple_hull_from_set_list(
4825 __isl_take isl_set *set,
4826 __isl_take isl_set_list *list);
4828 #include <isl/map.h>
4829 __isl_give isl_basic_map *
4830 isl_map_unshifted_simple_hull(
4831 __isl_take isl_map *map);
4832 __isl_give isl_basic_map *isl_map_simple_hull(
4833 __isl_take isl_map *map);
4834 __isl_give isl_basic_map *
4835 isl_map_unshifted_simple_hull_from_map_list(
4836 __isl_take isl_map *map,
4837 __isl_take isl_map_list *list);
4839 #include <isl/union_map.h>
4840 __isl_give isl_union_map *isl_union_map_simple_hull(
4841 __isl_take isl_union_map *umap);
4843 These functions compute a single basic set or relation
4844 that contains the whole input set or relation.
4845 In particular, the output is described by translates
4846 of the constraints describing the basic sets or relations in the input.
4847 In case of C<isl_set_unshifted_simple_hull>, only the original
4848 constraints are used, without any translation.
4849 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4850 C<isl_map_unshifted_simple_hull_from_map_list>, the
4851 constraints are taken from the elements of the second argument.
4855 (See \autoref{s:simple hull}.)
4861 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4862 __isl_take isl_basic_set *bset);
4863 __isl_give isl_basic_set *isl_set_affine_hull(
4864 __isl_take isl_set *set);
4865 __isl_give isl_union_set *isl_union_set_affine_hull(
4866 __isl_take isl_union_set *uset);
4867 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4868 __isl_take isl_basic_map *bmap);
4869 __isl_give isl_basic_map *isl_map_affine_hull(
4870 __isl_take isl_map *map);
4871 __isl_give isl_union_map *isl_union_map_affine_hull(
4872 __isl_take isl_union_map *umap);
4874 In case of union sets and relations, the affine hull is computed
4877 =item * Polyhedral hull
4879 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4880 __isl_take isl_set *set);
4881 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4882 __isl_take isl_map *map);
4883 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4884 __isl_take isl_union_set *uset);
4885 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4886 __isl_take isl_union_map *umap);
4888 These functions compute a single basic set or relation
4889 not involving any existentially quantified variables
4890 that contains the whole input set or relation.
4891 In case of union sets and relations, the polyhedral hull is computed
4894 =item * Other approximations
4896 #include <isl/set.h>
4897 __isl_give isl_basic_set *
4898 isl_basic_set_drop_constraints_involving_dims(
4899 __isl_take isl_basic_set *bset,
4900 enum isl_dim_type type,
4901 unsigned first, unsigned n);
4902 __isl_give isl_basic_set *
4903 isl_basic_set_drop_constraints_not_involving_dims(
4904 __isl_take isl_basic_set *bset,
4905 enum isl_dim_type type,
4906 unsigned first, unsigned n);
4907 __isl_give isl_set *
4908 isl_set_drop_constraints_involving_dims(
4909 __isl_take isl_set *set,
4910 enum isl_dim_type type,
4911 unsigned first, unsigned n);
4913 #include <isl/map.h>
4914 __isl_give isl_basic_map *
4915 isl_basic_map_drop_constraints_involving_dims(
4916 __isl_take isl_basic_map *bmap,
4917 enum isl_dim_type type,
4918 unsigned first, unsigned n);
4919 __isl_give isl_basic_map *
4920 isl_basic_map_drop_constraints_not_involving_dims(
4921 __isl_take isl_basic_map *bmap,
4922 enum isl_dim_type type,
4923 unsigned first, unsigned n);
4924 __isl_give isl_map *
4925 isl_map_drop_constraints_involving_dims(
4926 __isl_take isl_map *map,
4927 enum isl_dim_type type,
4928 unsigned first, unsigned n);
4930 These functions drop any constraints (not) involving the specified dimensions.
4931 Note that the result depends on the representation of the input.
4933 #include <isl/polynomial.h>
4934 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4935 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4936 __isl_give isl_union_pw_qpolynomial *
4937 isl_union_pw_qpolynomial_to_polynomial(
4938 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4940 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4941 the polynomial will be an overapproximation. If C<sign> is negative,
4942 it will be an underapproximation. If C<sign> is zero, the approximation
4943 will lie somewhere in between.
4947 __isl_give isl_basic_set *isl_basic_set_sample(
4948 __isl_take isl_basic_set *bset);
4949 __isl_give isl_basic_set *isl_set_sample(
4950 __isl_take isl_set *set);
4951 __isl_give isl_basic_map *isl_basic_map_sample(
4952 __isl_take isl_basic_map *bmap);
4953 __isl_give isl_basic_map *isl_map_sample(
4954 __isl_take isl_map *map);
4956 If the input (basic) set or relation is non-empty, then return
4957 a singleton subset of the input. Otherwise, return an empty set.
4959 =item * Optimization
4961 #include <isl/ilp.h>
4962 __isl_give isl_val *isl_basic_set_max_val(
4963 __isl_keep isl_basic_set *bset,
4964 __isl_keep isl_aff *obj);
4965 __isl_give isl_val *isl_set_min_val(
4966 __isl_keep isl_set *set,
4967 __isl_keep isl_aff *obj);
4968 __isl_give isl_val *isl_set_max_val(
4969 __isl_keep isl_set *set,
4970 __isl_keep isl_aff *obj);
4971 __isl_give isl_multi_val *
4972 isl_union_set_min_multi_union_pw_aff(
4973 __isl_keep isl_union_set *set,
4974 __isl_keep isl_multi_union_pw_aff *obj);
4976 Compute the minimum or maximum of the integer affine expression C<obj>
4977 over the points in C<set>, returning the result in C<opt>.
4978 The result is C<NULL> in case of an error, the optimal value in case
4979 there is one, negative infinity or infinity if the problem is unbounded and
4980 NaN if the problem is empty.
4982 =item * Parametric optimization
4984 __isl_give isl_pw_aff *isl_set_dim_min(
4985 __isl_take isl_set *set, int pos);
4986 __isl_give isl_pw_aff *isl_set_dim_max(
4987 __isl_take isl_set *set, int pos);
4988 __isl_give isl_pw_aff *isl_map_dim_max(
4989 __isl_take isl_map *map, int pos);
4991 Compute the minimum or maximum of the given set or output dimension
4992 as a function of the parameters (and input dimensions), but independently
4993 of the other set or output dimensions.
4994 For lexicographic optimization, see L<"Lexicographic Optimization">.
4998 The following functions compute either the set of (rational) coefficient
4999 values of valid constraints for the given set or the set of (rational)
5000 values satisfying the constraints with coefficients from the given set.
5001 Internally, these two sets of functions perform essentially the
5002 same operations, except that the set of coefficients is assumed to
5003 be a cone, while the set of values may be any polyhedron.
5004 The current implementation is based on the Farkas lemma and
5005 Fourier-Motzkin elimination, but this may change or be made optional
5006 in future. In particular, future implementations may use different
5007 dualization algorithms or skip the elimination step.
5009 __isl_give isl_basic_set *isl_basic_set_coefficients(
5010 __isl_take isl_basic_set *bset);
5011 __isl_give isl_basic_set *isl_set_coefficients(
5012 __isl_take isl_set *set);
5013 __isl_give isl_union_set *isl_union_set_coefficients(
5014 __isl_take isl_union_set *bset);
5015 __isl_give isl_basic_set *isl_basic_set_solutions(
5016 __isl_take isl_basic_set *bset);
5017 __isl_give isl_basic_set *isl_set_solutions(
5018 __isl_take isl_set *set);
5019 __isl_give isl_union_set *isl_union_set_solutions(
5020 __isl_take isl_union_set *bset);
5024 __isl_give isl_map *isl_map_fixed_power_val(
5025 __isl_take isl_map *map,
5026 __isl_take isl_val *exp);
5027 __isl_give isl_union_map *
5028 isl_union_map_fixed_power_val(
5029 __isl_take isl_union_map *umap,
5030 __isl_take isl_val *exp);
5032 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5033 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5034 of C<map> is computed.
5036 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5038 __isl_give isl_union_map *isl_union_map_power(
5039 __isl_take isl_union_map *umap, int *exact);
5041 Compute a parametric representation for all positive powers I<k> of C<map>.
5042 The result maps I<k> to a nested relation corresponding to the
5043 I<k>th power of C<map>.
5044 The result may be an overapproximation. If the result is known to be exact,
5045 then C<*exact> is set to C<1>.
5047 =item * Transitive closure
5049 __isl_give isl_map *isl_map_transitive_closure(
5050 __isl_take isl_map *map, int *exact);
5051 __isl_give isl_union_map *isl_union_map_transitive_closure(
5052 __isl_take isl_union_map *umap, int *exact);
5054 Compute the transitive closure of C<map>.
5055 The result may be an overapproximation. If the result is known to be exact,
5056 then C<*exact> is set to C<1>.
5058 =item * Reaching path lengths
5060 __isl_give isl_map *isl_map_reaching_path_lengths(
5061 __isl_take isl_map *map, int *exact);
5063 Compute a relation that maps each element in the range of C<map>
5064 to the lengths of all paths composed of edges in C<map> that
5065 end up in the given element.
5066 The result may be an overapproximation. If the result is known to be exact,
5067 then C<*exact> is set to C<1>.
5068 To compute the I<maximal> path length, the resulting relation
5069 should be postprocessed by C<isl_map_lexmax>.
5070 In particular, if the input relation is a dependence relation
5071 (mapping sources to sinks), then the maximal path length corresponds
5072 to the free schedule.
5073 Note, however, that C<isl_map_lexmax> expects the maximum to be
5074 finite, so if the path lengths are unbounded (possibly due to
5075 the overapproximation), then you will get an error message.
5079 #include <isl/space.h>
5080 __isl_give isl_space *isl_space_wrap(
5081 __isl_take isl_space *space);
5082 __isl_give isl_space *isl_space_unwrap(
5083 __isl_take isl_space *space);
5085 #include <isl/local_space.h>
5086 __isl_give isl_local_space *isl_local_space_wrap(
5087 __isl_take isl_local_space *ls);
5089 #include <isl/set.h>
5090 __isl_give isl_basic_map *isl_basic_set_unwrap(
5091 __isl_take isl_basic_set *bset);
5092 __isl_give isl_map *isl_set_unwrap(
5093 __isl_take isl_set *set);
5095 #include <isl/map.h>
5096 __isl_give isl_basic_set *isl_basic_map_wrap(
5097 __isl_take isl_basic_map *bmap);
5098 __isl_give isl_set *isl_map_wrap(
5099 __isl_take isl_map *map);
5101 #include <isl/union_set.h>
5102 __isl_give isl_union_map *isl_union_set_unwrap(
5103 __isl_take isl_union_set *uset);
5105 #include <isl/union_map.h>
5106 __isl_give isl_union_set *isl_union_map_wrap(
5107 __isl_take isl_union_map *umap);
5109 The input to C<isl_space_unwrap> should
5110 be the space of a set, while that of
5111 C<isl_space_wrap> should be the space of a relation.
5112 Conversely, the output of C<isl_space_unwrap> is the space
5113 of a relation, while that of C<isl_space_wrap> is the space of a set.
5117 Remove any internal structure of domain (and range) of the given
5118 set or relation. If there is any such internal structure in the input,
5119 then the name of the space is also removed.
5121 #include <isl/local_space.h>
5122 __isl_give isl_local_space *
5123 isl_local_space_flatten_domain(
5124 __isl_take isl_local_space *ls);
5125 __isl_give isl_local_space *
5126 isl_local_space_flatten_range(
5127 __isl_take isl_local_space *ls);
5129 #include <isl/set.h>
5130 __isl_give isl_basic_set *isl_basic_set_flatten(
5131 __isl_take isl_basic_set *bset);
5132 __isl_give isl_set *isl_set_flatten(
5133 __isl_take isl_set *set);
5135 #include <isl/map.h>
5136 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5137 __isl_take isl_basic_map *bmap);
5138 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5139 __isl_take isl_basic_map *bmap);
5140 __isl_give isl_map *isl_map_flatten_range(
5141 __isl_take isl_map *map);
5142 __isl_give isl_map *isl_map_flatten_domain(
5143 __isl_take isl_map *map);
5144 __isl_give isl_basic_map *isl_basic_map_flatten(
5145 __isl_take isl_basic_map *bmap);
5146 __isl_give isl_map *isl_map_flatten(
5147 __isl_take isl_map *map);
5149 #include <isl/val.h>
5150 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5151 __isl_take isl_multi_val *mv);
5153 #include <isl/aff.h>
5154 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5155 __isl_take isl_multi_aff *ma);
5156 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5157 __isl_take isl_multi_aff *ma);
5158 __isl_give isl_multi_pw_aff *
5159 isl_multi_pw_aff_flatten_range(
5160 __isl_take isl_multi_pw_aff *mpa);
5161 __isl_give isl_multi_union_pw_aff *
5162 isl_multi_union_pw_aff_flatten_range(
5163 __isl_take isl_multi_union_pw_aff *mupa);
5165 #include <isl/map.h>
5166 __isl_give isl_map *isl_set_flatten_map(
5167 __isl_take isl_set *set);
5169 The function above constructs a relation
5170 that maps the input set to a flattened version of the set.
5174 Lift the input set to a space with extra dimensions corresponding
5175 to the existentially quantified variables in the input.
5176 In particular, the result lives in a wrapped map where the domain
5177 is the original space and the range corresponds to the original
5178 existentially quantified variables.
5180 #include <isl/set.h>
5181 __isl_give isl_basic_set *isl_basic_set_lift(
5182 __isl_take isl_basic_set *bset);
5183 __isl_give isl_set *isl_set_lift(
5184 __isl_take isl_set *set);
5185 __isl_give isl_union_set *isl_union_set_lift(
5186 __isl_take isl_union_set *uset);
5188 Given a local space that contains the existentially quantified
5189 variables of a set, a basic relation that, when applied to
5190 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5191 can be constructed using the following function.
5193 #include <isl/local_space.h>
5194 __isl_give isl_basic_map *isl_local_space_lifting(
5195 __isl_take isl_local_space *ls);
5197 #include <isl/aff.h>
5198 __isl_give isl_multi_aff *isl_multi_aff_lift(
5199 __isl_take isl_multi_aff *maff,
5200 __isl_give isl_local_space **ls);
5202 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5203 then it is assigned the local space that lies at the basis of
5204 the lifting applied.
5206 =item * Internal Product
5208 #include <isl/space.h>
5209 __isl_give isl_space *isl_space_zip(
5210 __isl_take isl_space *space);
5212 #include <isl/map.h>
5213 __isl_give isl_basic_map *isl_basic_map_zip(
5214 __isl_take isl_basic_map *bmap);
5215 __isl_give isl_map *isl_map_zip(
5216 __isl_take isl_map *map);
5218 #include <isl/union_map.h>
5219 __isl_give isl_union_map *isl_union_map_zip(
5220 __isl_take isl_union_map *umap);
5222 Given a relation with nested relations for domain and range,
5223 interchange the range of the domain with the domain of the range.
5227 #include <isl/space.h>
5228 __isl_give isl_space *isl_space_curry(
5229 __isl_take isl_space *space);
5230 __isl_give isl_space *isl_space_uncurry(
5231 __isl_take isl_space *space);
5233 #include <isl/map.h>
5234 __isl_give isl_basic_map *isl_basic_map_curry(
5235 __isl_take isl_basic_map *bmap);
5236 __isl_give isl_basic_map *isl_basic_map_uncurry(
5237 __isl_take isl_basic_map *bmap);
5238 __isl_give isl_map *isl_map_curry(
5239 __isl_take isl_map *map);
5240 __isl_give isl_map *isl_map_uncurry(
5241 __isl_take isl_map *map);
5243 #include <isl/union_map.h>
5244 __isl_give isl_union_map *isl_union_map_curry(
5245 __isl_take isl_union_map *umap);
5246 __isl_give isl_union_map *isl_union_map_uncurry(
5247 __isl_take isl_union_map *umap);
5249 Given a relation with a nested relation for domain,
5250 the C<curry> functions
5251 move the range of the nested relation out of the domain
5252 and use it as the domain of a nested relation in the range,
5253 with the original range as range of this nested relation.
5254 The C<uncurry> functions perform the inverse operation.
5256 #include <isl/space.h>
5257 __isl_give isl_space *isl_space_range_curry(
5258 __isl_take isl_space *space);
5260 #include <isl/map.h>
5261 __isl_give isl_map *isl_map_range_curry(
5262 __isl_take isl_map *map);
5264 #include <isl/union_map.h>
5265 __isl_give isl_union_map *isl_union_map_range_curry(
5266 __isl_take isl_union_map *umap);
5268 These functions apply the currying to the relation that
5269 is nested inside the range of the input.
5271 =item * Aligning parameters
5273 Change the order of the parameters of the given set, relation
5275 such that the first parameters match those of C<model>.
5276 This may involve the introduction of extra parameters.
5277 All parameters need to be named.
5279 #include <isl/space.h>
5280 __isl_give isl_space *isl_space_align_params(
5281 __isl_take isl_space *space1,
5282 __isl_take isl_space *space2)
5284 #include <isl/set.h>
5285 __isl_give isl_basic_set *isl_basic_set_align_params(
5286 __isl_take isl_basic_set *bset,
5287 __isl_take isl_space *model);
5288 __isl_give isl_set *isl_set_align_params(
5289 __isl_take isl_set *set,
5290 __isl_take isl_space *model);
5292 #include <isl/map.h>
5293 __isl_give isl_basic_map *isl_basic_map_align_params(
5294 __isl_take isl_basic_map *bmap,
5295 __isl_take isl_space *model);
5296 __isl_give isl_map *isl_map_align_params(
5297 __isl_take isl_map *map,
5298 __isl_take isl_space *model);
5300 #include <isl/val.h>
5301 __isl_give isl_multi_val *isl_multi_val_align_params(
5302 __isl_take isl_multi_val *mv,
5303 __isl_take isl_space *model);
5305 #include <isl/aff.h>
5306 __isl_give isl_aff *isl_aff_align_params(
5307 __isl_take isl_aff *aff,
5308 __isl_take isl_space *model);
5309 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5310 __isl_take isl_multi_aff *multi,
5311 __isl_take isl_space *model);
5312 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5313 __isl_take isl_pw_aff *pwaff,
5314 __isl_take isl_space *model);
5315 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5316 __isl_take isl_pw_multi_aff *pma,
5317 __isl_take isl_space *model);
5318 __isl_give isl_union_pw_aff *
5319 isl_union_pw_aff_align_params(
5320 __isl_take isl_union_pw_aff *upa,
5321 __isl_take isl_space *model);
5322 __isl_give isl_union_pw_multi_aff *
5323 isl_union_pw_multi_aff_align_params(
5324 __isl_take isl_union_pw_multi_aff *upma,
5325 __isl_take isl_space *model);
5326 __isl_give isl_multi_union_pw_aff *
5327 isl_multi_union_pw_aff_align_params(
5328 __isl_take isl_multi_union_pw_aff *mupa,
5329 __isl_take isl_space *model);
5331 #include <isl/polynomial.h>
5332 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5333 __isl_take isl_qpolynomial *qp,
5334 __isl_take isl_space *model);
5336 =item * Unary Arithmetic Operations
5338 #include <isl/set.h>
5339 __isl_give isl_set *isl_set_neg(
5340 __isl_take isl_set *set);
5341 #include <isl/map.h>
5342 __isl_give isl_map *isl_map_neg(
5343 __isl_take isl_map *map);
5345 C<isl_set_neg> constructs a set containing the opposites of
5346 the elements in its argument.
5347 The domain of the result of C<isl_map_neg> is the same
5348 as the domain of its argument. The corresponding range
5349 elements are the opposites of the corresponding range
5350 elements in the argument.
5352 #include <isl/val.h>
5353 __isl_give isl_multi_val *isl_multi_val_neg(
5354 __isl_take isl_multi_val *mv);
5356 #include <isl/aff.h>
5357 __isl_give isl_aff *isl_aff_neg(
5358 __isl_take isl_aff *aff);
5359 __isl_give isl_multi_aff *isl_multi_aff_neg(
5360 __isl_take isl_multi_aff *ma);
5361 __isl_give isl_pw_aff *isl_pw_aff_neg(
5362 __isl_take isl_pw_aff *pwaff);
5363 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5364 __isl_take isl_pw_multi_aff *pma);
5365 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5366 __isl_take isl_multi_pw_aff *mpa);
5367 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5368 __isl_take isl_union_pw_aff *upa);
5369 __isl_give isl_union_pw_multi_aff *
5370 isl_union_pw_multi_aff_neg(
5371 __isl_take isl_union_pw_multi_aff *upma);
5372 __isl_give isl_multi_union_pw_aff *
5373 isl_multi_union_pw_aff_neg(
5374 __isl_take isl_multi_union_pw_aff *mupa);
5375 __isl_give isl_aff *isl_aff_ceil(
5376 __isl_take isl_aff *aff);
5377 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5378 __isl_take isl_pw_aff *pwaff);
5379 __isl_give isl_aff *isl_aff_floor(
5380 __isl_take isl_aff *aff);
5381 __isl_give isl_multi_aff *isl_multi_aff_floor(
5382 __isl_take isl_multi_aff *ma);
5383 __isl_give isl_pw_aff *isl_pw_aff_floor(
5384 __isl_take isl_pw_aff *pwaff);
5385 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5386 __isl_take isl_union_pw_aff *upa);
5387 __isl_give isl_multi_union_pw_aff *
5388 isl_multi_union_pw_aff_floor(
5389 __isl_take isl_multi_union_pw_aff *mupa);
5391 #include <isl/aff.h>
5392 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5393 __isl_take isl_pw_aff_list *list);
5394 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5395 __isl_take isl_pw_aff_list *list);
5397 #include <isl/polynomial.h>
5398 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5399 __isl_take isl_qpolynomial *qp);
5400 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5401 __isl_take isl_pw_qpolynomial *pwqp);
5402 __isl_give isl_union_pw_qpolynomial *
5403 isl_union_pw_qpolynomial_neg(
5404 __isl_take isl_union_pw_qpolynomial *upwqp);
5405 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5406 __isl_take isl_qpolynomial *qp,
5408 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5409 __isl_take isl_pw_qpolynomial *pwqp,
5414 The following functions evaluate a function in a point.
5416 #include <isl/polynomial.h>
5417 __isl_give isl_val *isl_pw_qpolynomial_eval(
5418 __isl_take isl_pw_qpolynomial *pwqp,
5419 __isl_take isl_point *pnt);
5420 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5421 __isl_take isl_pw_qpolynomial_fold *pwf,
5422 __isl_take isl_point *pnt);
5423 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5424 __isl_take isl_union_pw_qpolynomial *upwqp,
5425 __isl_take isl_point *pnt);
5426 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5427 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5428 __isl_take isl_point *pnt);
5430 =item * Dimension manipulation
5432 It is usually not advisable to directly change the (input or output)
5433 space of a set or a relation as this removes the name and the internal
5434 structure of the space. However, the functions below can be useful
5435 to add new parameters, assuming
5436 C<isl_set_align_params> and C<isl_map_align_params>
5439 #include <isl/space.h>
5440 __isl_give isl_space *isl_space_add_dims(
5441 __isl_take isl_space *space,
5442 enum isl_dim_type type, unsigned n);
5443 __isl_give isl_space *isl_space_insert_dims(
5444 __isl_take isl_space *space,
5445 enum isl_dim_type type, unsigned pos, unsigned n);
5446 __isl_give isl_space *isl_space_drop_dims(
5447 __isl_take isl_space *space,
5448 enum isl_dim_type type, unsigned first, unsigned n);
5449 __isl_give isl_space *isl_space_move_dims(
5450 __isl_take isl_space *space,
5451 enum isl_dim_type dst_type, unsigned dst_pos,
5452 enum isl_dim_type src_type, unsigned src_pos,
5455 #include <isl/local_space.h>
5456 __isl_give isl_local_space *isl_local_space_add_dims(
5457 __isl_take isl_local_space *ls,
5458 enum isl_dim_type type, unsigned n);
5459 __isl_give isl_local_space *isl_local_space_insert_dims(
5460 __isl_take isl_local_space *ls,
5461 enum isl_dim_type type, unsigned first, unsigned n);
5462 __isl_give isl_local_space *isl_local_space_drop_dims(
5463 __isl_take isl_local_space *ls,
5464 enum isl_dim_type type, unsigned first, unsigned n);
5466 #include <isl/set.h>
5467 __isl_give isl_basic_set *isl_basic_set_add_dims(
5468 __isl_take isl_basic_set *bset,
5469 enum isl_dim_type type, unsigned n);
5470 __isl_give isl_set *isl_set_add_dims(
5471 __isl_take isl_set *set,
5472 enum isl_dim_type type, unsigned n);
5473 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5474 __isl_take isl_basic_set *bset,
5475 enum isl_dim_type type, unsigned pos,
5477 __isl_give isl_set *isl_set_insert_dims(
5478 __isl_take isl_set *set,
5479 enum isl_dim_type type, unsigned pos, unsigned n);
5480 __isl_give isl_basic_set *isl_basic_set_move_dims(
5481 __isl_take isl_basic_set *bset,
5482 enum isl_dim_type dst_type, unsigned dst_pos,
5483 enum isl_dim_type src_type, unsigned src_pos,
5485 __isl_give isl_set *isl_set_move_dims(
5486 __isl_take isl_set *set,
5487 enum isl_dim_type dst_type, unsigned dst_pos,
5488 enum isl_dim_type src_type, unsigned src_pos,
5491 #include <isl/map.h>
5492 __isl_give isl_basic_map *isl_basic_map_add_dims(
5493 __isl_take isl_basic_map *bmap,
5494 enum isl_dim_type type, unsigned n);
5495 __isl_give isl_map *isl_map_add_dims(
5496 __isl_take isl_map *map,
5497 enum isl_dim_type type, unsigned n);
5498 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5499 __isl_take isl_basic_map *bmap,
5500 enum isl_dim_type type, unsigned pos,
5502 __isl_give isl_map *isl_map_insert_dims(
5503 __isl_take isl_map *map,
5504 enum isl_dim_type type, unsigned pos, unsigned n);
5505 __isl_give isl_basic_map *isl_basic_map_move_dims(
5506 __isl_take isl_basic_map *bmap,
5507 enum isl_dim_type dst_type, unsigned dst_pos,
5508 enum isl_dim_type src_type, unsigned src_pos,
5510 __isl_give isl_map *isl_map_move_dims(
5511 __isl_take isl_map *map,
5512 enum isl_dim_type dst_type, unsigned dst_pos,
5513 enum isl_dim_type src_type, unsigned src_pos,
5516 #include <isl/val.h>
5517 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5518 __isl_take isl_multi_val *mv,
5519 enum isl_dim_type type, unsigned first, unsigned n);
5520 __isl_give isl_multi_val *isl_multi_val_add_dims(
5521 __isl_take isl_multi_val *mv,
5522 enum isl_dim_type type, unsigned n);
5523 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5524 __isl_take isl_multi_val *mv,
5525 enum isl_dim_type type, unsigned first, unsigned n);
5527 #include <isl/aff.h>
5528 __isl_give isl_aff *isl_aff_insert_dims(
5529 __isl_take isl_aff *aff,
5530 enum isl_dim_type type, unsigned first, unsigned n);
5531 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5532 __isl_take isl_multi_aff *ma,
5533 enum isl_dim_type type, unsigned first, unsigned n);
5534 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5535 __isl_take isl_pw_aff *pwaff,
5536 enum isl_dim_type type, unsigned first, unsigned n);
5537 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5538 __isl_take isl_multi_pw_aff *mpa,
5539 enum isl_dim_type type, unsigned first, unsigned n);
5540 __isl_give isl_aff *isl_aff_add_dims(
5541 __isl_take isl_aff *aff,
5542 enum isl_dim_type type, unsigned n);
5543 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5544 __isl_take isl_multi_aff *ma,
5545 enum isl_dim_type type, unsigned n);
5546 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5547 __isl_take isl_pw_aff *pwaff,
5548 enum isl_dim_type type, unsigned n);
5549 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5550 __isl_take isl_multi_pw_aff *mpa,
5551 enum isl_dim_type type, unsigned n);
5552 __isl_give isl_aff *isl_aff_drop_dims(
5553 __isl_take isl_aff *aff,
5554 enum isl_dim_type type, unsigned first, unsigned n);
5555 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5556 __isl_take isl_multi_aff *maff,
5557 enum isl_dim_type type, unsigned first, unsigned n);
5558 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5559 __isl_take isl_pw_aff *pwaff,
5560 enum isl_dim_type type, unsigned first, unsigned n);
5561 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5562 __isl_take isl_pw_multi_aff *pma,
5563 enum isl_dim_type type, unsigned first, unsigned n);
5564 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5565 __isl_take isl_union_pw_aff *upa,
5566 enum isl_dim_type type, unsigned first, unsigned n);
5567 __isl_give isl_union_pw_multi_aff *
5568 isl_union_pw_multi_aff_drop_dims(
5569 __isl_take isl_union_pw_multi_aff *upma,
5570 enum isl_dim_type type,
5571 unsigned first, unsigned n);
5572 __isl_give isl_multi_union_pw_aff *
5573 isl_multi_union_pw_aff_drop_dims(
5574 __isl_take isl_multi_union_pw_aff *mupa,
5575 enum isl_dim_type type, unsigned first,
5577 __isl_give isl_aff *isl_aff_move_dims(
5578 __isl_take isl_aff *aff,
5579 enum isl_dim_type dst_type, unsigned dst_pos,
5580 enum isl_dim_type src_type, unsigned src_pos,
5582 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5583 __isl_take isl_multi_aff *ma,
5584 enum isl_dim_type dst_type, unsigned dst_pos,
5585 enum isl_dim_type src_type, unsigned src_pos,
5587 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5588 __isl_take isl_pw_aff *pa,
5589 enum isl_dim_type dst_type, unsigned dst_pos,
5590 enum isl_dim_type src_type, unsigned src_pos,
5592 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5593 __isl_take isl_multi_pw_aff *pma,
5594 enum isl_dim_type dst_type, unsigned dst_pos,
5595 enum isl_dim_type src_type, unsigned src_pos,
5598 #include <isl/polynomial.h>
5599 __isl_give isl_union_pw_qpolynomial *
5600 isl_union_pw_qpolynomial_drop_dims(
5601 __isl_take isl_union_pw_qpolynomial *upwqp,
5602 enum isl_dim_type type,
5603 unsigned first, unsigned n);
5604 __isl_give isl_union_pw_qpolynomial_fold *
5605 isl_union_pw_qpolynomial_fold_drop_dims(
5606 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5607 enum isl_dim_type type,
5608 unsigned first, unsigned n);
5610 The operations on union expressions can only manipulate parameters.
5614 =head2 Binary Operations
5616 The two arguments of a binary operation not only need to live
5617 in the same C<isl_ctx>, they currently also need to have
5618 the same (number of) parameters.
5620 =head3 Basic Operations
5624 =item * Intersection
5626 #include <isl/local_space.h>
5627 __isl_give isl_local_space *isl_local_space_intersect(
5628 __isl_take isl_local_space *ls1,
5629 __isl_take isl_local_space *ls2);
5631 #include <isl/set.h>
5632 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5633 __isl_take isl_basic_set *bset1,
5634 __isl_take isl_basic_set *bset2);
5635 __isl_give isl_basic_set *isl_basic_set_intersect(
5636 __isl_take isl_basic_set *bset1,
5637 __isl_take isl_basic_set *bset2);
5638 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5639 __isl_take struct isl_basic_set_list *list);
5640 __isl_give isl_set *isl_set_intersect_params(
5641 __isl_take isl_set *set,
5642 __isl_take isl_set *params);
5643 __isl_give isl_set *isl_set_intersect(
5644 __isl_take isl_set *set1,
5645 __isl_take isl_set *set2);
5647 #include <isl/map.h>
5648 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5649 __isl_take isl_basic_map *bmap,
5650 __isl_take isl_basic_set *bset);
5651 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5652 __isl_take isl_basic_map *bmap,
5653 __isl_take isl_basic_set *bset);
5654 __isl_give isl_basic_map *isl_basic_map_intersect(
5655 __isl_take isl_basic_map *bmap1,
5656 __isl_take isl_basic_map *bmap2);
5657 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5658 __isl_take isl_basic_map_list *list);
5659 __isl_give isl_map *isl_map_intersect_params(
5660 __isl_take isl_map *map,
5661 __isl_take isl_set *params);
5662 __isl_give isl_map *isl_map_intersect_domain(
5663 __isl_take isl_map *map,
5664 __isl_take isl_set *set);
5665 __isl_give isl_map *isl_map_intersect_range(
5666 __isl_take isl_map *map,
5667 __isl_take isl_set *set);
5668 __isl_give isl_map *isl_map_intersect(
5669 __isl_take isl_map *map1,
5670 __isl_take isl_map *map2);
5672 #include <isl/union_set.h>
5673 __isl_give isl_union_set *isl_union_set_intersect_params(
5674 __isl_take isl_union_set *uset,
5675 __isl_take isl_set *set);
5676 __isl_give isl_union_set *isl_union_set_intersect(
5677 __isl_take isl_union_set *uset1,
5678 __isl_take isl_union_set *uset2);
5680 #include <isl/union_map.h>
5681 __isl_give isl_union_map *isl_union_map_intersect_params(
5682 __isl_take isl_union_map *umap,
5683 __isl_take isl_set *set);
5684 __isl_give isl_union_map *isl_union_map_intersect_domain(
5685 __isl_take isl_union_map *umap,
5686 __isl_take isl_union_set *uset);
5687 __isl_give isl_union_map *isl_union_map_intersect_range(
5688 __isl_take isl_union_map *umap,
5689 __isl_take isl_union_set *uset);
5690 __isl_give isl_union_map *isl_union_map_intersect(
5691 __isl_take isl_union_map *umap1,
5692 __isl_take isl_union_map *umap2);
5694 #include <isl/aff.h>
5695 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5696 __isl_take isl_pw_aff *pa,
5697 __isl_take isl_set *set);
5698 __isl_give isl_multi_pw_aff *
5699 isl_multi_pw_aff_intersect_domain(
5700 __isl_take isl_multi_pw_aff *mpa,
5701 __isl_take isl_set *domain);
5702 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5703 __isl_take isl_pw_multi_aff *pma,
5704 __isl_take isl_set *set);
5705 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5706 __isl_take isl_union_pw_aff *upa,
5707 __isl_take isl_union_set *uset);
5708 __isl_give isl_union_pw_multi_aff *
5709 isl_union_pw_multi_aff_intersect_domain(
5710 __isl_take isl_union_pw_multi_aff *upma,
5711 __isl_take isl_union_set *uset);
5712 __isl_give isl_multi_union_pw_aff *
5713 isl_multi_union_pw_aff_intersect_domain(
5714 __isl_take isl_multi_union_pw_aff *mupa,
5715 __isl_take isl_union_set *uset);
5716 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5717 __isl_take isl_pw_aff *pa,
5718 __isl_take isl_set *set);
5719 __isl_give isl_multi_pw_aff *
5720 isl_multi_pw_aff_intersect_params(
5721 __isl_take isl_multi_pw_aff *mpa,
5722 __isl_take isl_set *set);
5723 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5724 __isl_take isl_pw_multi_aff *pma,
5725 __isl_take isl_set *set);
5726 __isl_give isl_union_pw_aff *
5727 isl_union_pw_aff_intersect_params(
5728 __isl_take isl_union_pw_aff *upa,
5729 __isl_give isl_union_pw_multi_aff *
5730 isl_union_pw_multi_aff_intersect_params(
5731 __isl_take isl_union_pw_multi_aff *upma,
5732 __isl_take isl_set *set);
5733 __isl_give isl_multi_union_pw_aff *
5734 isl_multi_union_pw_aff_intersect_params(
5735 __isl_take isl_multi_union_pw_aff *mupa,
5736 __isl_take isl_set *params);
5737 isl_multi_union_pw_aff_intersect_range(
5738 __isl_take isl_multi_union_pw_aff *mupa,
5739 __isl_take isl_set *set);
5741 #include <isl/polynomial.h>
5742 __isl_give isl_pw_qpolynomial *
5743 isl_pw_qpolynomial_intersect_domain(
5744 __isl_take isl_pw_qpolynomial *pwpq,
5745 __isl_take isl_set *set);
5746 __isl_give isl_union_pw_qpolynomial *
5747 isl_union_pw_qpolynomial_intersect_domain(
5748 __isl_take isl_union_pw_qpolynomial *upwpq,
5749 __isl_take isl_union_set *uset);
5750 __isl_give isl_union_pw_qpolynomial_fold *
5751 isl_union_pw_qpolynomial_fold_intersect_domain(
5752 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5753 __isl_take isl_union_set *uset);
5754 __isl_give isl_pw_qpolynomial *
5755 isl_pw_qpolynomial_intersect_params(
5756 __isl_take isl_pw_qpolynomial *pwpq,
5757 __isl_take isl_set *set);
5758 __isl_give isl_pw_qpolynomial_fold *
5759 isl_pw_qpolynomial_fold_intersect_params(
5760 __isl_take isl_pw_qpolynomial_fold *pwf,
5761 __isl_take isl_set *set);
5762 __isl_give isl_union_pw_qpolynomial *
5763 isl_union_pw_qpolynomial_intersect_params(
5764 __isl_take isl_union_pw_qpolynomial *upwpq,
5765 __isl_take isl_set *set);
5766 __isl_give isl_union_pw_qpolynomial_fold *
5767 isl_union_pw_qpolynomial_fold_intersect_params(
5768 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5769 __isl_take isl_set *set);
5771 The second argument to the C<_params> functions needs to be
5772 a parametric (basic) set. For the other functions, a parametric set
5773 for either argument is only allowed if the other argument is
5774 a parametric set as well.
5775 The list passed to C<isl_basic_set_list_intersect> needs to have
5776 at least one element and all elements need to live in the same space.
5777 The function C<isl_multi_union_pw_aff_intersect_range>
5778 restricts the input function to those shared domain elements
5779 that map to the specified range.
5783 #include <isl/set.h>
5784 __isl_give isl_set *isl_basic_set_union(
5785 __isl_take isl_basic_set *bset1,
5786 __isl_take isl_basic_set *bset2);
5787 __isl_give isl_set *isl_set_union(
5788 __isl_take isl_set *set1,
5789 __isl_take isl_set *set2);
5790 __isl_give isl_set *isl_set_list_union(
5791 __isl_take isl_set_list *list);
5793 #include <isl/map.h>
5794 __isl_give isl_map *isl_basic_map_union(
5795 __isl_take isl_basic_map *bmap1,
5796 __isl_take isl_basic_map *bmap2);
5797 __isl_give isl_map *isl_map_union(
5798 __isl_take isl_map *map1,
5799 __isl_take isl_map *map2);
5801 #include <isl/union_set.h>
5802 __isl_give isl_union_set *isl_union_set_union(
5803 __isl_take isl_union_set *uset1,
5804 __isl_take isl_union_set *uset2);
5805 __isl_give isl_union_set *isl_union_set_list_union(
5806 __isl_take isl_union_set_list *list);
5808 #include <isl/union_map.h>
5809 __isl_give isl_union_map *isl_union_map_union(
5810 __isl_take isl_union_map *umap1,
5811 __isl_take isl_union_map *umap2);
5813 The list passed to C<isl_set_list_union> needs to have
5814 at least one element and all elements need to live in the same space.
5816 =item * Set difference
5818 #include <isl/set.h>
5819 __isl_give isl_set *isl_set_subtract(
5820 __isl_take isl_set *set1,
5821 __isl_take isl_set *set2);
5823 #include <isl/map.h>
5824 __isl_give isl_map *isl_map_subtract(
5825 __isl_take isl_map *map1,
5826 __isl_take isl_map *map2);
5827 __isl_give isl_map *isl_map_subtract_domain(
5828 __isl_take isl_map *map,
5829 __isl_take isl_set *dom);
5830 __isl_give isl_map *isl_map_subtract_range(
5831 __isl_take isl_map *map,
5832 __isl_take isl_set *dom);
5834 #include <isl/union_set.h>
5835 __isl_give isl_union_set *isl_union_set_subtract(
5836 __isl_take isl_union_set *uset1,
5837 __isl_take isl_union_set *uset2);
5839 #include <isl/union_map.h>
5840 __isl_give isl_union_map *isl_union_map_subtract(
5841 __isl_take isl_union_map *umap1,
5842 __isl_take isl_union_map *umap2);
5843 __isl_give isl_union_map *isl_union_map_subtract_domain(
5844 __isl_take isl_union_map *umap,
5845 __isl_take isl_union_set *dom);
5846 __isl_give isl_union_map *isl_union_map_subtract_range(
5847 __isl_take isl_union_map *umap,
5848 __isl_take isl_union_set *dom);
5850 #include <isl/aff.h>
5851 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5852 __isl_take isl_pw_aff *pa,
5853 __isl_take isl_set *set);
5854 __isl_give isl_pw_multi_aff *
5855 isl_pw_multi_aff_subtract_domain(
5856 __isl_take isl_pw_multi_aff *pma,
5857 __isl_take isl_set *set);
5858 __isl_give isl_union_pw_aff *
5859 isl_union_pw_aff_subtract_domain(
5860 __isl_take isl_union_pw_aff *upa,
5861 __isl_take isl_union_set *uset);
5862 __isl_give isl_union_pw_multi_aff *
5863 isl_union_pw_multi_aff_subtract_domain(
5864 __isl_take isl_union_pw_multi_aff *upma,
5865 __isl_take isl_set *set);
5867 #include <isl/polynomial.h>
5868 __isl_give isl_pw_qpolynomial *
5869 isl_pw_qpolynomial_subtract_domain(
5870 __isl_take isl_pw_qpolynomial *pwpq,
5871 __isl_take isl_set *set);
5872 __isl_give isl_pw_qpolynomial_fold *
5873 isl_pw_qpolynomial_fold_subtract_domain(
5874 __isl_take isl_pw_qpolynomial_fold *pwf,
5875 __isl_take isl_set *set);
5876 __isl_give isl_union_pw_qpolynomial *
5877 isl_union_pw_qpolynomial_subtract_domain(
5878 __isl_take isl_union_pw_qpolynomial *upwpq,
5879 __isl_take isl_union_set *uset);
5880 __isl_give isl_union_pw_qpolynomial_fold *
5881 isl_union_pw_qpolynomial_fold_subtract_domain(
5882 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5883 __isl_take isl_union_set *uset);
5887 #include <isl/space.h>
5888 __isl_give isl_space *isl_space_join(
5889 __isl_take isl_space *left,
5890 __isl_take isl_space *right);
5892 #include <isl/map.h>
5893 __isl_give isl_basic_set *isl_basic_set_apply(
5894 __isl_take isl_basic_set *bset,
5895 __isl_take isl_basic_map *bmap);
5896 __isl_give isl_set *isl_set_apply(
5897 __isl_take isl_set *set,
5898 __isl_take isl_map *map);
5899 __isl_give isl_union_set *isl_union_set_apply(
5900 __isl_take isl_union_set *uset,
5901 __isl_take isl_union_map *umap);
5902 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5903 __isl_take isl_basic_map *bmap1,
5904 __isl_take isl_basic_map *bmap2);
5905 __isl_give isl_basic_map *isl_basic_map_apply_range(
5906 __isl_take isl_basic_map *bmap1,
5907 __isl_take isl_basic_map *bmap2);
5908 __isl_give isl_map *isl_map_apply_domain(
5909 __isl_take isl_map *map1,
5910 __isl_take isl_map *map2);
5911 __isl_give isl_map *isl_map_apply_range(
5912 __isl_take isl_map *map1,
5913 __isl_take isl_map *map2);
5915 #include <isl/union_map.h>
5916 __isl_give isl_union_map *isl_union_map_apply_domain(
5917 __isl_take isl_union_map *umap1,
5918 __isl_take isl_union_map *umap2);
5919 __isl_give isl_union_map *isl_union_map_apply_range(
5920 __isl_take isl_union_map *umap1,
5921 __isl_take isl_union_map *umap2);
5923 #include <isl/aff.h>
5924 __isl_give isl_union_pw_aff *
5925 isl_multi_union_pw_aff_apply_aff(
5926 __isl_take isl_multi_union_pw_aff *mupa,
5927 __isl_take isl_aff *aff);
5928 __isl_give isl_union_pw_aff *
5929 isl_multi_union_pw_aff_apply_pw_aff(
5930 __isl_take isl_multi_union_pw_aff *mupa,
5931 __isl_take isl_pw_aff *pa);
5932 __isl_give isl_multi_union_pw_aff *
5933 isl_multi_union_pw_aff_apply_multi_aff(
5934 __isl_take isl_multi_union_pw_aff *mupa,
5935 __isl_take isl_multi_aff *ma);
5936 __isl_give isl_multi_union_pw_aff *
5937 isl_multi_union_pw_aff_apply_pw_multi_aff(
5938 __isl_take isl_multi_union_pw_aff *mupa,
5939 __isl_take isl_pw_multi_aff *pma);
5941 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5942 over the shared domain of the elements of the input. The dimension is
5943 required to be greater than zero.
5944 The C<isl_multi_union_pw_aff> argument of
5945 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5946 but only if the range of the C<isl_multi_aff> argument
5947 is also zero-dimensional.
5948 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5950 #include <isl/polynomial.h>
5951 __isl_give isl_pw_qpolynomial_fold *
5952 isl_set_apply_pw_qpolynomial_fold(
5953 __isl_take isl_set *set,
5954 __isl_take isl_pw_qpolynomial_fold *pwf,
5956 __isl_give isl_pw_qpolynomial_fold *
5957 isl_map_apply_pw_qpolynomial_fold(
5958 __isl_take isl_map *map,
5959 __isl_take isl_pw_qpolynomial_fold *pwf,
5961 __isl_give isl_union_pw_qpolynomial_fold *
5962 isl_union_set_apply_union_pw_qpolynomial_fold(
5963 __isl_take isl_union_set *uset,
5964 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5966 __isl_give isl_union_pw_qpolynomial_fold *
5967 isl_union_map_apply_union_pw_qpolynomial_fold(
5968 __isl_take isl_union_map *umap,
5969 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5972 The functions taking a map
5973 compose the given map with the given piecewise quasipolynomial reduction.
5974 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5975 over all elements in the intersection of the range of the map
5976 and the domain of the piecewise quasipolynomial reduction
5977 as a function of an element in the domain of the map.
5978 The functions taking a set compute a bound over all elements in the
5979 intersection of the set and the domain of the
5980 piecewise quasipolynomial reduction.
5984 #include <isl/set.h>
5985 __isl_give isl_basic_set *
5986 isl_basic_set_preimage_multi_aff(
5987 __isl_take isl_basic_set *bset,
5988 __isl_take isl_multi_aff *ma);
5989 __isl_give isl_set *isl_set_preimage_multi_aff(
5990 __isl_take isl_set *set,
5991 __isl_take isl_multi_aff *ma);
5992 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5993 __isl_take isl_set *set,
5994 __isl_take isl_pw_multi_aff *pma);
5995 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5996 __isl_take isl_set *set,
5997 __isl_take isl_multi_pw_aff *mpa);
5999 #include <isl/union_set.h>
6000 __isl_give isl_union_set *
6001 isl_union_set_preimage_multi_aff(
6002 __isl_take isl_union_set *uset,
6003 __isl_take isl_multi_aff *ma);
6004 __isl_give isl_union_set *
6005 isl_union_set_preimage_pw_multi_aff(
6006 __isl_take isl_union_set *uset,
6007 __isl_take isl_pw_multi_aff *pma);
6008 __isl_give isl_union_set *
6009 isl_union_set_preimage_union_pw_multi_aff(
6010 __isl_take isl_union_set *uset,
6011 __isl_take isl_union_pw_multi_aff *upma);
6013 #include <isl/map.h>
6014 __isl_give isl_basic_map *
6015 isl_basic_map_preimage_domain_multi_aff(
6016 __isl_take isl_basic_map *bmap,
6017 __isl_take isl_multi_aff *ma);
6018 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6019 __isl_take isl_map *map,
6020 __isl_take isl_multi_aff *ma);
6021 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6022 __isl_take isl_map *map,
6023 __isl_take isl_multi_aff *ma);
6024 __isl_give isl_map *
6025 isl_map_preimage_domain_pw_multi_aff(
6026 __isl_take isl_map *map,
6027 __isl_take isl_pw_multi_aff *pma);
6028 __isl_give isl_map *
6029 isl_map_preimage_range_pw_multi_aff(
6030 __isl_take isl_map *map,
6031 __isl_take isl_pw_multi_aff *pma);
6032 __isl_give isl_map *
6033 isl_map_preimage_domain_multi_pw_aff(
6034 __isl_take isl_map *map,
6035 __isl_take isl_multi_pw_aff *mpa);
6036 __isl_give isl_basic_map *
6037 isl_basic_map_preimage_range_multi_aff(
6038 __isl_take isl_basic_map *bmap,
6039 __isl_take isl_multi_aff *ma);
6041 #include <isl/union_map.h>
6042 __isl_give isl_union_map *
6043 isl_union_map_preimage_domain_multi_aff(
6044 __isl_take isl_union_map *umap,
6045 __isl_take isl_multi_aff *ma);
6046 __isl_give isl_union_map *
6047 isl_union_map_preimage_range_multi_aff(
6048 __isl_take isl_union_map *umap,
6049 __isl_take isl_multi_aff *ma);
6050 __isl_give isl_union_map *
6051 isl_union_map_preimage_domain_pw_multi_aff(
6052 __isl_take isl_union_map *umap,
6053 __isl_take isl_pw_multi_aff *pma);
6054 __isl_give isl_union_map *
6055 isl_union_map_preimage_range_pw_multi_aff(
6056 __isl_take isl_union_map *umap,
6057 __isl_take isl_pw_multi_aff *pma);
6058 __isl_give isl_union_map *
6059 isl_union_map_preimage_domain_union_pw_multi_aff(
6060 __isl_take isl_union_map *umap,
6061 __isl_take isl_union_pw_multi_aff *upma);
6062 __isl_give isl_union_map *
6063 isl_union_map_preimage_range_union_pw_multi_aff(
6064 __isl_take isl_union_map *umap,
6065 __isl_take isl_union_pw_multi_aff *upma);
6067 These functions compute the preimage of the given set or map domain/range under
6068 the given function. In other words, the expression is plugged
6069 into the set description or into the domain/range of the map.
6073 #include <isl/aff.h>
6074 __isl_give isl_aff *isl_aff_pullback_aff(
6075 __isl_take isl_aff *aff1,
6076 __isl_take isl_aff *aff2);
6077 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6078 __isl_take isl_aff *aff,
6079 __isl_take isl_multi_aff *ma);
6080 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6081 __isl_take isl_pw_aff *pa,
6082 __isl_take isl_multi_aff *ma);
6083 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6084 __isl_take isl_pw_aff *pa,
6085 __isl_take isl_pw_multi_aff *pma);
6086 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6087 __isl_take isl_pw_aff *pa,
6088 __isl_take isl_multi_pw_aff *mpa);
6089 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6090 __isl_take isl_multi_aff *ma1,
6091 __isl_take isl_multi_aff *ma2);
6092 __isl_give isl_pw_multi_aff *
6093 isl_pw_multi_aff_pullback_multi_aff(
6094 __isl_take isl_pw_multi_aff *pma,
6095 __isl_take isl_multi_aff *ma);
6096 __isl_give isl_multi_pw_aff *
6097 isl_multi_pw_aff_pullback_multi_aff(
6098 __isl_take isl_multi_pw_aff *mpa,
6099 __isl_take isl_multi_aff *ma);
6100 __isl_give isl_pw_multi_aff *
6101 isl_pw_multi_aff_pullback_pw_multi_aff(
6102 __isl_take isl_pw_multi_aff *pma1,
6103 __isl_take isl_pw_multi_aff *pma2);
6104 __isl_give isl_multi_pw_aff *
6105 isl_multi_pw_aff_pullback_pw_multi_aff(
6106 __isl_take isl_multi_pw_aff *mpa,
6107 __isl_take isl_pw_multi_aff *pma);
6108 __isl_give isl_multi_pw_aff *
6109 isl_multi_pw_aff_pullback_multi_pw_aff(
6110 __isl_take isl_multi_pw_aff *mpa1,
6111 __isl_take isl_multi_pw_aff *mpa2);
6112 __isl_give isl_union_pw_aff *
6113 isl_union_pw_aff_pullback_union_pw_multi_aff(
6114 __isl_take isl_union_pw_aff *upa,
6115 __isl_take isl_union_pw_multi_aff *upma);
6116 __isl_give isl_union_pw_multi_aff *
6117 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6118 __isl_take isl_union_pw_multi_aff *upma1,
6119 __isl_take isl_union_pw_multi_aff *upma2);
6120 __isl_give isl_multi_union_pw_aff *
6121 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6122 __isl_take isl_multi_union_pw_aff *mupa,
6123 __isl_take isl_union_pw_multi_aff *upma);
6125 These functions precompose the first expression by the second function.
6126 In other words, the second function is plugged
6127 into the first expression.
6131 #include <isl/aff.h>
6132 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6133 __isl_take isl_aff *aff1,
6134 __isl_take isl_aff *aff2);
6135 __isl_give isl_set *isl_aff_eq_set(
6136 __isl_take isl_aff *aff1,
6137 __isl_take isl_aff *aff2);
6138 __isl_give isl_basic_set *isl_aff_le_basic_set(
6139 __isl_take isl_aff *aff1,
6140 __isl_take isl_aff *aff2);
6141 __isl_give isl_set *isl_aff_le_set(
6142 __isl_take isl_aff *aff1,
6143 __isl_take isl_aff *aff2);
6144 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6145 __isl_take isl_aff *aff1,
6146 __isl_take isl_aff *aff2);
6147 __isl_give isl_set *isl_aff_ge_set(
6148 __isl_take isl_aff *aff1,
6149 __isl_take isl_aff *aff2);
6150 __isl_give isl_set *isl_pw_aff_eq_set(
6151 __isl_take isl_pw_aff *pwaff1,
6152 __isl_take isl_pw_aff *pwaff2);
6153 __isl_give isl_set *isl_pw_aff_ne_set(
6154 __isl_take isl_pw_aff *pwaff1,
6155 __isl_take isl_pw_aff *pwaff2);
6156 __isl_give isl_set *isl_pw_aff_le_set(
6157 __isl_take isl_pw_aff *pwaff1,
6158 __isl_take isl_pw_aff *pwaff2);
6159 __isl_give isl_set *isl_pw_aff_lt_set(
6160 __isl_take isl_pw_aff *pwaff1,
6161 __isl_take isl_pw_aff *pwaff2);
6162 __isl_give isl_set *isl_pw_aff_ge_set(
6163 __isl_take isl_pw_aff *pwaff1,
6164 __isl_take isl_pw_aff *pwaff2);
6165 __isl_give isl_set *isl_pw_aff_gt_set(
6166 __isl_take isl_pw_aff *pwaff1,
6167 __isl_take isl_pw_aff *pwaff2);
6169 __isl_give isl_set *isl_multi_aff_lex_le_set(
6170 __isl_take isl_multi_aff *ma1,
6171 __isl_take isl_multi_aff *ma2);
6172 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6173 __isl_take isl_multi_aff *ma1,
6174 __isl_take isl_multi_aff *ma2);
6175 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6176 __isl_take isl_multi_aff *ma1,
6177 __isl_take isl_multi_aff *ma2);
6178 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6179 __isl_take isl_multi_aff *ma1,
6180 __isl_take isl_multi_aff *ma2);
6182 __isl_give isl_set *isl_pw_aff_list_eq_set(
6183 __isl_take isl_pw_aff_list *list1,
6184 __isl_take isl_pw_aff_list *list2);
6185 __isl_give isl_set *isl_pw_aff_list_ne_set(
6186 __isl_take isl_pw_aff_list *list1,
6187 __isl_take isl_pw_aff_list *list2);
6188 __isl_give isl_set *isl_pw_aff_list_le_set(
6189 __isl_take isl_pw_aff_list *list1,
6190 __isl_take isl_pw_aff_list *list2);
6191 __isl_give isl_set *isl_pw_aff_list_lt_set(
6192 __isl_take isl_pw_aff_list *list1,
6193 __isl_take isl_pw_aff_list *list2);
6194 __isl_give isl_set *isl_pw_aff_list_ge_set(
6195 __isl_take isl_pw_aff_list *list1,
6196 __isl_take isl_pw_aff_list *list2);
6197 __isl_give isl_set *isl_pw_aff_list_gt_set(
6198 __isl_take isl_pw_aff_list *list1,
6199 __isl_take isl_pw_aff_list *list2);
6201 The function C<isl_aff_ge_basic_set> returns a basic set
6202 containing those elements in the shared space
6203 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6204 The function C<isl_pw_aff_ge_set> returns a set
6205 containing those elements in the shared domain
6206 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6207 greater than or equal to C<pwaff2>.
6208 The function C<isl_multi_aff_lex_le_set> returns a set
6209 containing those elements in the shared domain space
6210 where C<ma1> is lexicographically smaller than or
6212 The functions operating on C<isl_pw_aff_list> apply the corresponding
6213 C<isl_pw_aff> function to each pair of elements in the two lists.
6215 #include <isl/aff.h>
6216 __isl_give isl_map *isl_pw_aff_eq_map(
6217 __isl_take isl_pw_aff *pa1,
6218 __isl_take isl_pw_aff *pa2);
6219 __isl_give isl_map *isl_pw_aff_lt_map(
6220 __isl_take isl_pw_aff *pa1,
6221 __isl_take isl_pw_aff *pa2);
6222 __isl_give isl_map *isl_pw_aff_gt_map(
6223 __isl_take isl_pw_aff *pa1,
6224 __isl_take isl_pw_aff *pa2);
6226 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6227 __isl_take isl_multi_pw_aff *mpa1,
6228 __isl_take isl_multi_pw_aff *mpa2);
6229 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6230 __isl_take isl_multi_pw_aff *mpa1,
6231 __isl_take isl_multi_pw_aff *mpa2);
6232 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6233 __isl_take isl_multi_pw_aff *mpa1,
6234 __isl_take isl_multi_pw_aff *mpa2);
6236 These functions return a map between domain elements of the arguments
6237 where the function values satisfy the given relation.
6239 #include <isl/union_map.h>
6240 __isl_give isl_union_map *
6241 isl_union_map_eq_at_multi_union_pw_aff(
6242 __isl_take isl_union_map *umap,
6243 __isl_take isl_multi_union_pw_aff *mupa);
6244 __isl_give isl_union_map *
6245 isl_union_map_lex_lt_at_multi_union_pw_aff(
6246 __isl_take isl_union_map *umap,
6247 __isl_take isl_multi_union_pw_aff *mupa);
6248 __isl_give isl_union_map *
6249 isl_union_map_lex_gt_at_multi_union_pw_aff(
6250 __isl_take isl_union_map *umap,
6251 __isl_take isl_multi_union_pw_aff *mupa);
6253 These functions select the subset of elements in the union map
6254 that have an equal or lexicographically smaller function value.
6256 =item * Cartesian Product
6258 #include <isl/space.h>
6259 __isl_give isl_space *isl_space_product(
6260 __isl_take isl_space *space1,
6261 __isl_take isl_space *space2);
6262 __isl_give isl_space *isl_space_domain_product(
6263 __isl_take isl_space *space1,
6264 __isl_take isl_space *space2);
6265 __isl_give isl_space *isl_space_range_product(
6266 __isl_take isl_space *space1,
6267 __isl_take isl_space *space2);
6270 C<isl_space_product>, C<isl_space_domain_product>
6271 and C<isl_space_range_product> take pairs or relation spaces and
6272 produce a single relations space, where either the domain, the range
6273 or both domain and range are wrapped spaces of relations between
6274 the domains and/or ranges of the input spaces.
6275 If the product is only constructed over the domain or the range
6276 then the ranges or the domains of the inputs should be the same.
6277 The function C<isl_space_product> also accepts a pair of set spaces,
6278 in which case it returns a wrapped space of a relation between the
6281 #include <isl/set.h>
6282 __isl_give isl_set *isl_set_product(
6283 __isl_take isl_set *set1,
6284 __isl_take isl_set *set2);
6286 #include <isl/map.h>
6287 __isl_give isl_basic_map *isl_basic_map_domain_product(
6288 __isl_take isl_basic_map *bmap1,
6289 __isl_take isl_basic_map *bmap2);
6290 __isl_give isl_basic_map *isl_basic_map_range_product(
6291 __isl_take isl_basic_map *bmap1,
6292 __isl_take isl_basic_map *bmap2);
6293 __isl_give isl_basic_map *isl_basic_map_product(
6294 __isl_take isl_basic_map *bmap1,
6295 __isl_take isl_basic_map *bmap2);
6296 __isl_give isl_map *isl_map_domain_product(
6297 __isl_take isl_map *map1,
6298 __isl_take isl_map *map2);
6299 __isl_give isl_map *isl_map_range_product(
6300 __isl_take isl_map *map1,
6301 __isl_take isl_map *map2);
6302 __isl_give isl_map *isl_map_product(
6303 __isl_take isl_map *map1,
6304 __isl_take isl_map *map2);
6306 #include <isl/union_set.h>
6307 __isl_give isl_union_set *isl_union_set_product(
6308 __isl_take isl_union_set *uset1,
6309 __isl_take isl_union_set *uset2);
6311 #include <isl/union_map.h>
6312 __isl_give isl_union_map *isl_union_map_domain_product(
6313 __isl_take isl_union_map *umap1,
6314 __isl_take isl_union_map *umap2);
6315 __isl_give isl_union_map *isl_union_map_range_product(
6316 __isl_take isl_union_map *umap1,
6317 __isl_take isl_union_map *umap2);
6318 __isl_give isl_union_map *isl_union_map_product(
6319 __isl_take isl_union_map *umap1,
6320 __isl_take isl_union_map *umap2);
6322 #include <isl/val.h>
6323 __isl_give isl_multi_val *isl_multi_val_range_product(
6324 __isl_take isl_multi_val *mv1,
6325 __isl_take isl_multi_val *mv2);
6326 __isl_give isl_multi_val *isl_multi_val_product(
6327 __isl_take isl_multi_val *mv1,
6328 __isl_take isl_multi_val *mv2);
6330 #include <isl/aff.h>
6331 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6332 __isl_take isl_multi_aff *ma1,
6333 __isl_take isl_multi_aff *ma2);
6334 __isl_give isl_multi_aff *isl_multi_aff_product(
6335 __isl_take isl_multi_aff *ma1,
6336 __isl_take isl_multi_aff *ma2);
6337 __isl_give isl_multi_pw_aff *
6338 isl_multi_pw_aff_range_product(
6339 __isl_take isl_multi_pw_aff *mpa1,
6340 __isl_take isl_multi_pw_aff *mpa2);
6341 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6342 __isl_take isl_multi_pw_aff *mpa1,
6343 __isl_take isl_multi_pw_aff *mpa2);
6344 __isl_give isl_pw_multi_aff *
6345 isl_pw_multi_aff_range_product(
6346 __isl_take isl_pw_multi_aff *pma1,
6347 __isl_take isl_pw_multi_aff *pma2);
6348 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6349 __isl_take isl_pw_multi_aff *pma1,
6350 __isl_take isl_pw_multi_aff *pma2);
6351 __isl_give isl_multi_union_pw_aff *
6352 isl_multi_union_pw_aff_range_product(
6353 __isl_take isl_multi_union_pw_aff *mupa1,
6354 __isl_take isl_multi_union_pw_aff *mupa2);
6356 The above functions compute the cross product of the given
6357 sets, relations or functions. The domains and ranges of the results
6358 are wrapped maps between domains and ranges of the inputs.
6359 To obtain a ``flat'' product, use the following functions
6362 #include <isl/set.h>
6363 __isl_give isl_basic_set *isl_basic_set_flat_product(
6364 __isl_take isl_basic_set *bset1,
6365 __isl_take isl_basic_set *bset2);
6366 __isl_give isl_set *isl_set_flat_product(
6367 __isl_take isl_set *set1,
6368 __isl_take isl_set *set2);
6370 #include <isl/map.h>
6371 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6372 __isl_take isl_basic_map *bmap1,
6373 __isl_take isl_basic_map *bmap2);
6374 __isl_give isl_map *isl_map_flat_domain_product(
6375 __isl_take isl_map *map1,
6376 __isl_take isl_map *map2);
6377 __isl_give isl_map *isl_map_flat_range_product(
6378 __isl_take isl_map *map1,
6379 __isl_take isl_map *map2);
6380 __isl_give isl_basic_map *isl_basic_map_flat_product(
6381 __isl_take isl_basic_map *bmap1,
6382 __isl_take isl_basic_map *bmap2);
6383 __isl_give isl_map *isl_map_flat_product(
6384 __isl_take isl_map *map1,
6385 __isl_take isl_map *map2);
6387 #include <isl/union_map.h>
6388 __isl_give isl_union_map *
6389 isl_union_map_flat_domain_product(
6390 __isl_take isl_union_map *umap1,
6391 __isl_take isl_union_map *umap2);
6392 __isl_give isl_union_map *
6393 isl_union_map_flat_range_product(
6394 __isl_take isl_union_map *umap1,
6395 __isl_take isl_union_map *umap2);
6397 #include <isl/val.h>
6398 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6399 __isl_take isl_multi_val *mv1,
6400 __isl_take isl_multi_aff *mv2);
6402 #include <isl/aff.h>
6403 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6404 __isl_take isl_multi_aff *ma1,
6405 __isl_take isl_multi_aff *ma2);
6406 __isl_give isl_pw_multi_aff *
6407 isl_pw_multi_aff_flat_range_product(
6408 __isl_take isl_pw_multi_aff *pma1,
6409 __isl_take isl_pw_multi_aff *pma2);
6410 __isl_give isl_multi_pw_aff *
6411 isl_multi_pw_aff_flat_range_product(
6412 __isl_take isl_multi_pw_aff *mpa1,
6413 __isl_take isl_multi_pw_aff *mpa2);
6414 __isl_give isl_union_pw_multi_aff *
6415 isl_union_pw_multi_aff_flat_range_product(
6416 __isl_take isl_union_pw_multi_aff *upma1,
6417 __isl_take isl_union_pw_multi_aff *upma2);
6418 __isl_give isl_multi_union_pw_aff *
6419 isl_multi_union_pw_aff_flat_range_product(
6420 __isl_take isl_multi_union_pw_aff *mupa1,
6421 __isl_take isl_multi_union_pw_aff *mupa2);
6423 #include <isl/space.h>
6424 __isl_give isl_space *isl_space_factor_domain(
6425 __isl_take isl_space *space);
6426 __isl_give isl_space *isl_space_factor_range(
6427 __isl_take isl_space *space);
6428 __isl_give isl_space *isl_space_domain_factor_domain(
6429 __isl_take isl_space *space);
6430 __isl_give isl_space *isl_space_domain_factor_range(
6431 __isl_take isl_space *space);
6432 __isl_give isl_space *isl_space_range_factor_domain(
6433 __isl_take isl_space *space);
6434 __isl_give isl_space *isl_space_range_factor_range(
6435 __isl_take isl_space *space);
6437 The functions C<isl_space_range_factor_domain> and
6438 C<isl_space_range_factor_range> extract the two arguments from
6439 the result of a call to C<isl_space_range_product>.
6441 The arguments of a call to a product can be extracted
6442 from the result using the following functions.
6444 #include <isl/map.h>
6445 __isl_give isl_map *isl_map_factor_domain(
6446 __isl_take isl_map *map);
6447 __isl_give isl_map *isl_map_factor_range(
6448 __isl_take isl_map *map);
6449 __isl_give isl_map *isl_map_domain_factor_domain(
6450 __isl_take isl_map *map);
6451 __isl_give isl_map *isl_map_domain_factor_range(
6452 __isl_take isl_map *map);
6453 __isl_give isl_map *isl_map_range_factor_domain(
6454 __isl_take isl_map *map);
6455 __isl_give isl_map *isl_map_range_factor_range(
6456 __isl_take isl_map *map);
6458 #include <isl/union_map.h>
6459 __isl_give isl_union_map *isl_union_map_factor_domain(
6460 __isl_take isl_union_map *umap);
6461 __isl_give isl_union_map *isl_union_map_factor_range(
6462 __isl_take isl_union_map *umap);
6463 __isl_give isl_union_map *
6464 isl_union_map_domain_factor_domain(
6465 __isl_take isl_union_map *umap);
6466 __isl_give isl_union_map *
6467 isl_union_map_domain_factor_range(
6468 __isl_take isl_union_map *umap);
6469 __isl_give isl_union_map *
6470 isl_union_map_range_factor_domain(
6471 __isl_take isl_union_map *umap);
6472 __isl_give isl_union_map *
6473 isl_union_map_range_factor_range(
6474 __isl_take isl_union_map *umap);
6476 #include <isl/val.h>
6477 __isl_give isl_multi_val *isl_multi_val_factor_range(
6478 __isl_take isl_multi_val *mv);
6479 __isl_give isl_multi_val *
6480 isl_multi_val_range_factor_domain(
6481 __isl_take isl_multi_val *mv);
6482 __isl_give isl_multi_val *
6483 isl_multi_val_range_factor_range(
6484 __isl_take isl_multi_val *mv);
6486 #include <isl/aff.h>
6487 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6488 __isl_take isl_multi_aff *ma);
6489 __isl_give isl_multi_aff *
6490 isl_multi_aff_range_factor_domain(
6491 __isl_take isl_multi_aff *ma);
6492 __isl_give isl_multi_aff *
6493 isl_multi_aff_range_factor_range(
6494 __isl_take isl_multi_aff *ma);
6495 __isl_give isl_multi_pw_aff *
6496 isl_multi_pw_aff_factor_range(
6497 __isl_take isl_multi_pw_aff *mpa);
6498 __isl_give isl_multi_pw_aff *
6499 isl_multi_pw_aff_range_factor_domain(
6500 __isl_take isl_multi_pw_aff *mpa);
6501 __isl_give isl_multi_pw_aff *
6502 isl_multi_pw_aff_range_factor_range(
6503 __isl_take isl_multi_pw_aff *mpa);
6504 __isl_give isl_multi_union_pw_aff *
6505 isl_multi_union_pw_aff_factor_range(
6506 __isl_take isl_multi_union_pw_aff *mupa);
6507 __isl_give isl_multi_union_pw_aff *
6508 isl_multi_union_pw_aff_range_factor_domain(
6509 __isl_take isl_multi_union_pw_aff *mupa);
6510 __isl_give isl_multi_union_pw_aff *
6511 isl_multi_union_pw_aff_range_factor_range(
6512 __isl_take isl_multi_union_pw_aff *mupa);
6514 The splice functions are a generalization of the flat product functions,
6515 where the second argument may be inserted at any position inside
6516 the first argument rather than being placed at the end.
6517 The functions C<isl_multi_val_factor_range>,
6518 C<isl_multi_aff_factor_range>,
6519 C<isl_multi_pw_aff_factor_range> and
6520 C<isl_multi_union_pw_aff_factor_range>
6521 take functions that live in a set space.
6523 #include <isl/val.h>
6524 __isl_give isl_multi_val *isl_multi_val_range_splice(
6525 __isl_take isl_multi_val *mv1, unsigned pos,
6526 __isl_take isl_multi_val *mv2);
6528 #include <isl/aff.h>
6529 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6530 __isl_take isl_multi_aff *ma1, unsigned pos,
6531 __isl_take isl_multi_aff *ma2);
6532 __isl_give isl_multi_aff *isl_multi_aff_splice(
6533 __isl_take isl_multi_aff *ma1,
6534 unsigned in_pos, unsigned out_pos,
6535 __isl_take isl_multi_aff *ma2);
6536 __isl_give isl_multi_pw_aff *
6537 isl_multi_pw_aff_range_splice(
6538 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6539 __isl_take isl_multi_pw_aff *mpa2);
6540 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6541 __isl_take isl_multi_pw_aff *mpa1,
6542 unsigned in_pos, unsigned out_pos,
6543 __isl_take isl_multi_pw_aff *mpa2);
6544 __isl_give isl_multi_union_pw_aff *
6545 isl_multi_union_pw_aff_range_splice(
6546 __isl_take isl_multi_union_pw_aff *mupa1,
6548 __isl_take isl_multi_union_pw_aff *mupa2);
6550 =item * Simplification
6552 When applied to a set or relation,
6553 the gist operation returns a set or relation that has the
6554 same intersection with the context as the input set or relation.
6555 Any implicit equality in the intersection is made explicit in the result,
6556 while all inequalities that are redundant with respect to the intersection
6558 In case of union sets and relations, the gist operation is performed
6561 When applied to a function,
6562 the gist operation applies the set gist operation to each of
6563 the cells in the domain of the input piecewise expression.
6564 The context is also exploited
6565 to simplify the expression associated to each cell.
6567 #include <isl/set.h>
6568 __isl_give isl_basic_set *isl_basic_set_gist(
6569 __isl_take isl_basic_set *bset,
6570 __isl_take isl_basic_set *context);
6571 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6572 __isl_take isl_set *context);
6573 __isl_give isl_set *isl_set_gist_params(
6574 __isl_take isl_set *set,
6575 __isl_take isl_set *context);
6577 #include <isl/map.h>
6578 __isl_give isl_basic_map *isl_basic_map_gist(
6579 __isl_take isl_basic_map *bmap,
6580 __isl_take isl_basic_map *context);
6581 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6582 __isl_take isl_basic_map *bmap,
6583 __isl_take isl_basic_set *context);
6584 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6585 __isl_take isl_map *context);
6586 __isl_give isl_map *isl_map_gist_params(
6587 __isl_take isl_map *map,
6588 __isl_take isl_set *context);
6589 __isl_give isl_map *isl_map_gist_domain(
6590 __isl_take isl_map *map,
6591 __isl_take isl_set *context);
6592 __isl_give isl_map *isl_map_gist_range(
6593 __isl_take isl_map *map,
6594 __isl_take isl_set *context);
6596 #include <isl/union_set.h>
6597 __isl_give isl_union_set *isl_union_set_gist(
6598 __isl_take isl_union_set *uset,
6599 __isl_take isl_union_set *context);
6600 __isl_give isl_union_set *isl_union_set_gist_params(
6601 __isl_take isl_union_set *uset,
6602 __isl_take isl_set *set);
6604 #include <isl/union_map.h>
6605 __isl_give isl_union_map *isl_union_map_gist(
6606 __isl_take isl_union_map *umap,
6607 __isl_take isl_union_map *context);
6608 __isl_give isl_union_map *isl_union_map_gist_params(
6609 __isl_take isl_union_map *umap,
6610 __isl_take isl_set *set);
6611 __isl_give isl_union_map *isl_union_map_gist_domain(
6612 __isl_take isl_union_map *umap,
6613 __isl_take isl_union_set *uset);
6614 __isl_give isl_union_map *isl_union_map_gist_range(
6615 __isl_take isl_union_map *umap,
6616 __isl_take isl_union_set *uset);
6618 #include <isl/aff.h>
6619 __isl_give isl_aff *isl_aff_gist_params(
6620 __isl_take isl_aff *aff,
6621 __isl_take isl_set *context);
6622 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6623 __isl_take isl_set *context);
6624 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6625 __isl_take isl_multi_aff *maff,
6626 __isl_take isl_set *context);
6627 __isl_give isl_multi_aff *isl_multi_aff_gist(
6628 __isl_take isl_multi_aff *maff,
6629 __isl_take isl_set *context);
6630 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6631 __isl_take isl_pw_aff *pwaff,
6632 __isl_take isl_set *context);
6633 __isl_give isl_pw_aff *isl_pw_aff_gist(
6634 __isl_take isl_pw_aff *pwaff,
6635 __isl_take isl_set *context);
6636 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6637 __isl_take isl_pw_multi_aff *pma,
6638 __isl_take isl_set *set);
6639 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6640 __isl_take isl_pw_multi_aff *pma,
6641 __isl_take isl_set *set);
6642 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6643 __isl_take isl_multi_pw_aff *mpa,
6644 __isl_take isl_set *set);
6645 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6646 __isl_take isl_multi_pw_aff *mpa,
6647 __isl_take isl_set *set);
6648 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6649 __isl_take isl_union_pw_aff *upa,
6650 __isl_take isl_union_set *context);
6651 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6652 __isl_take isl_union_pw_aff *upa,
6653 __isl_take isl_set *context);
6654 __isl_give isl_union_pw_multi_aff *
6655 isl_union_pw_multi_aff_gist_params(
6656 __isl_take isl_union_pw_multi_aff *upma,
6657 __isl_take isl_set *context);
6658 __isl_give isl_union_pw_multi_aff *
6659 isl_union_pw_multi_aff_gist(
6660 __isl_take isl_union_pw_multi_aff *upma,
6661 __isl_take isl_union_set *context);
6662 __isl_give isl_multi_union_pw_aff *
6663 isl_multi_union_pw_aff_gist_params(
6664 __isl_take isl_multi_union_pw_aff *aff,
6665 __isl_take isl_set *context);
6666 __isl_give isl_multi_union_pw_aff *
6667 isl_multi_union_pw_aff_gist(
6668 __isl_take isl_multi_union_pw_aff *aff,
6669 __isl_take isl_union_set *context);
6671 #include <isl/polynomial.h>
6672 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6673 __isl_take isl_qpolynomial *qp,
6674 __isl_take isl_set *context);
6675 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6676 __isl_take isl_qpolynomial *qp,
6677 __isl_take isl_set *context);
6678 __isl_give isl_qpolynomial_fold *
6679 isl_qpolynomial_fold_gist_params(
6680 __isl_take isl_qpolynomial_fold *fold,
6681 __isl_take isl_set *context);
6682 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6683 __isl_take isl_qpolynomial_fold *fold,
6684 __isl_take isl_set *context);
6685 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6686 __isl_take isl_pw_qpolynomial *pwqp,
6687 __isl_take isl_set *context);
6688 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6689 __isl_take isl_pw_qpolynomial *pwqp,
6690 __isl_take isl_set *context);
6691 __isl_give isl_pw_qpolynomial_fold *
6692 isl_pw_qpolynomial_fold_gist(
6693 __isl_take isl_pw_qpolynomial_fold *pwf,
6694 __isl_take isl_set *context);
6695 __isl_give isl_pw_qpolynomial_fold *
6696 isl_pw_qpolynomial_fold_gist_params(
6697 __isl_take isl_pw_qpolynomial_fold *pwf,
6698 __isl_take isl_set *context);
6699 __isl_give isl_union_pw_qpolynomial *
6700 isl_union_pw_qpolynomial_gist_params(
6701 __isl_take isl_union_pw_qpolynomial *upwqp,
6702 __isl_take isl_set *context);
6703 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6704 __isl_take isl_union_pw_qpolynomial *upwqp,
6705 __isl_take isl_union_set *context);
6706 __isl_give isl_union_pw_qpolynomial_fold *
6707 isl_union_pw_qpolynomial_fold_gist(
6708 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6709 __isl_take isl_union_set *context);
6710 __isl_give isl_union_pw_qpolynomial_fold *
6711 isl_union_pw_qpolynomial_fold_gist_params(
6712 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6713 __isl_take isl_set *context);
6715 =item * Binary Arithmetic Operations
6717 #include <isl/set.h>
6718 __isl_give isl_set *isl_set_sum(
6719 __isl_take isl_set *set1,
6720 __isl_take isl_set *set2);
6721 #include <isl/map.h>
6722 __isl_give isl_map *isl_map_sum(
6723 __isl_take isl_map *map1,
6724 __isl_take isl_map *map2);
6726 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6727 i.e., the set containing the sums of pairs of elements from
6728 C<set1> and C<set2>.
6729 The domain of the result of C<isl_map_sum> is the intersection
6730 of the domains of its two arguments. The corresponding range
6731 elements are the sums of the corresponding range elements
6732 in the two arguments.
6734 #include <isl/val.h>
6735 __isl_give isl_multi_val *isl_multi_val_add(
6736 __isl_take isl_multi_val *mv1,
6737 __isl_take isl_multi_val *mv2);
6738 __isl_give isl_multi_val *isl_multi_val_sub(
6739 __isl_take isl_multi_val *mv1,
6740 __isl_take isl_multi_val *mv2);
6742 #include <isl/aff.h>
6743 __isl_give isl_aff *isl_aff_add(
6744 __isl_take isl_aff *aff1,
6745 __isl_take isl_aff *aff2);
6746 __isl_give isl_multi_aff *isl_multi_aff_add(
6747 __isl_take isl_multi_aff *maff1,
6748 __isl_take isl_multi_aff *maff2);
6749 __isl_give isl_pw_aff *isl_pw_aff_add(
6750 __isl_take isl_pw_aff *pwaff1,
6751 __isl_take isl_pw_aff *pwaff2);
6752 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6753 __isl_take isl_multi_pw_aff *mpa1,
6754 __isl_take isl_multi_pw_aff *mpa2);
6755 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6756 __isl_take isl_pw_multi_aff *pma1,
6757 __isl_take isl_pw_multi_aff *pma2);
6758 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6759 __isl_take isl_union_pw_aff *upa1,
6760 __isl_take isl_union_pw_aff *upa2);
6761 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6762 __isl_take isl_union_pw_multi_aff *upma1,
6763 __isl_take isl_union_pw_multi_aff *upma2);
6764 __isl_give isl_multi_union_pw_aff *
6765 isl_multi_union_pw_aff_add(
6766 __isl_take isl_multi_union_pw_aff *mupa1,
6767 __isl_take isl_multi_union_pw_aff *mupa2);
6768 __isl_give isl_pw_aff *isl_pw_aff_min(
6769 __isl_take isl_pw_aff *pwaff1,
6770 __isl_take isl_pw_aff *pwaff2);
6771 __isl_give isl_pw_aff *isl_pw_aff_max(
6772 __isl_take isl_pw_aff *pwaff1,
6773 __isl_take isl_pw_aff *pwaff2);
6774 __isl_give isl_aff *isl_aff_sub(
6775 __isl_take isl_aff *aff1,
6776 __isl_take isl_aff *aff2);
6777 __isl_give isl_multi_aff *isl_multi_aff_sub(
6778 __isl_take isl_multi_aff *ma1,
6779 __isl_take isl_multi_aff *ma2);
6780 __isl_give isl_pw_aff *isl_pw_aff_sub(
6781 __isl_take isl_pw_aff *pwaff1,
6782 __isl_take isl_pw_aff *pwaff2);
6783 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6784 __isl_take isl_multi_pw_aff *mpa1,
6785 __isl_take isl_multi_pw_aff *mpa2);
6786 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6787 __isl_take isl_pw_multi_aff *pma1,
6788 __isl_take isl_pw_multi_aff *pma2);
6789 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6790 __isl_take isl_union_pw_aff *upa1,
6791 __isl_take isl_union_pw_aff *upa2);
6792 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6793 __isl_take isl_union_pw_multi_aff *upma1,
6794 __isl_take isl_union_pw_multi_aff *upma2);
6795 __isl_give isl_multi_union_pw_aff *
6796 isl_multi_union_pw_aff_sub(
6797 __isl_take isl_multi_union_pw_aff *mupa1,
6798 __isl_take isl_multi_union_pw_aff *mupa2);
6800 C<isl_aff_sub> subtracts the second argument from the first.
6802 #include <isl/polynomial.h>
6803 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6804 __isl_take isl_qpolynomial *qp1,
6805 __isl_take isl_qpolynomial *qp2);
6806 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6807 __isl_take isl_pw_qpolynomial *pwqp1,
6808 __isl_take isl_pw_qpolynomial *pwqp2);
6809 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6810 __isl_take isl_pw_qpolynomial *pwqp1,
6811 __isl_take isl_pw_qpolynomial *pwqp2);
6812 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6813 __isl_take isl_pw_qpolynomial_fold *pwf1,
6814 __isl_take isl_pw_qpolynomial_fold *pwf2);
6815 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6816 __isl_take isl_union_pw_qpolynomial *upwqp1,
6817 __isl_take isl_union_pw_qpolynomial *upwqp2);
6818 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6819 __isl_take isl_qpolynomial *qp1,
6820 __isl_take isl_qpolynomial *qp2);
6821 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6822 __isl_take isl_pw_qpolynomial *pwqp1,
6823 __isl_take isl_pw_qpolynomial *pwqp2);
6824 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6825 __isl_take isl_union_pw_qpolynomial *upwqp1,
6826 __isl_take isl_union_pw_qpolynomial *upwqp2);
6827 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6828 __isl_take isl_pw_qpolynomial_fold *pwf1,
6829 __isl_take isl_pw_qpolynomial_fold *pwf2);
6830 __isl_give isl_union_pw_qpolynomial_fold *
6831 isl_union_pw_qpolynomial_fold_fold(
6832 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6833 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6835 #include <isl/aff.h>
6836 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6837 __isl_take isl_pw_aff *pwaff1,
6838 __isl_take isl_pw_aff *pwaff2);
6839 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6840 __isl_take isl_pw_multi_aff *pma1,
6841 __isl_take isl_pw_multi_aff *pma2);
6842 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6843 __isl_take isl_union_pw_aff *upa1,
6844 __isl_take isl_union_pw_aff *upa2);
6845 __isl_give isl_union_pw_multi_aff *
6846 isl_union_pw_multi_aff_union_add(
6847 __isl_take isl_union_pw_multi_aff *upma1,
6848 __isl_take isl_union_pw_multi_aff *upma2);
6849 __isl_give isl_multi_union_pw_aff *
6850 isl_multi_union_pw_aff_union_add(
6851 __isl_take isl_multi_union_pw_aff *mupa1,
6852 __isl_take isl_multi_union_pw_aff *mupa2);
6853 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6854 __isl_take isl_pw_aff *pwaff1,
6855 __isl_take isl_pw_aff *pwaff2);
6856 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6857 __isl_take isl_pw_aff *pwaff1,
6858 __isl_take isl_pw_aff *pwaff2);
6860 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6861 expression with a domain that is the union of those of C<pwaff1> and
6862 C<pwaff2> and such that on each cell, the quasi-affine expression is
6863 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6864 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6865 associated expression is the defined one.
6866 This in contrast to the C<isl_pw_aff_max> function, which is
6867 only defined on the shared definition domain of the arguments.
6869 #include <isl/val.h>
6870 __isl_give isl_multi_val *isl_multi_val_add_val(
6871 __isl_take isl_multi_val *mv,
6872 __isl_take isl_val *v);
6873 __isl_give isl_multi_val *isl_multi_val_mod_val(
6874 __isl_take isl_multi_val *mv,
6875 __isl_take isl_val *v);
6876 __isl_give isl_multi_val *isl_multi_val_scale_val(
6877 __isl_take isl_multi_val *mv,
6878 __isl_take isl_val *v);
6879 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6880 __isl_take isl_multi_val *mv,
6881 __isl_take isl_val *v);
6883 #include <isl/aff.h>
6884 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6885 __isl_take isl_val *mod);
6886 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6887 __isl_take isl_pw_aff *pa,
6888 __isl_take isl_val *mod);
6889 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6890 __isl_take isl_union_pw_aff *upa,
6891 __isl_take isl_val *f);
6892 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6893 __isl_take isl_val *v);
6894 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6895 __isl_take isl_multi_aff *ma,
6896 __isl_take isl_val *v);
6897 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6898 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6899 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6900 __isl_take isl_multi_pw_aff *mpa,
6901 __isl_take isl_val *v);
6902 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6903 __isl_take isl_pw_multi_aff *pma,
6904 __isl_take isl_val *v);
6905 __isl_give isl_union_pw_multi_aff *
6906 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6907 __isl_take isl_union_pw_aff *upa,
6908 __isl_take isl_val *f);
6909 isl_union_pw_multi_aff_scale_val(
6910 __isl_take isl_union_pw_multi_aff *upma,
6911 __isl_take isl_val *val);
6912 __isl_give isl_multi_union_pw_aff *
6913 isl_multi_union_pw_aff_scale_val(
6914 __isl_take isl_multi_union_pw_aff *mupa,
6915 __isl_take isl_val *v);
6916 __isl_give isl_aff *isl_aff_scale_down_ui(
6917 __isl_take isl_aff *aff, unsigned f);
6918 __isl_give isl_aff *isl_aff_scale_down_val(
6919 __isl_take isl_aff *aff, __isl_take isl_val *v);
6920 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6921 __isl_take isl_multi_aff *ma,
6922 __isl_take isl_val *v);
6923 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6924 __isl_take isl_pw_aff *pa,
6925 __isl_take isl_val *f);
6926 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_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_down_val(
6930 __isl_take isl_pw_multi_aff *pma,
6931 __isl_take isl_val *v);
6932 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6933 __isl_take isl_union_pw_aff *upa,
6934 __isl_take isl_val *v);
6935 __isl_give isl_union_pw_multi_aff *
6936 isl_union_pw_multi_aff_scale_down_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_down_val(
6941 __isl_take isl_multi_union_pw_aff *mupa,
6942 __isl_take isl_val *v);
6944 #include <isl/polynomial.h>
6945 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6946 __isl_take isl_qpolynomial *qp,
6947 __isl_take isl_val *v);
6948 __isl_give isl_qpolynomial_fold *
6949 isl_qpolynomial_fold_scale_val(
6950 __isl_take isl_qpolynomial_fold *fold,
6951 __isl_take isl_val *v);
6952 __isl_give isl_pw_qpolynomial *
6953 isl_pw_qpolynomial_scale_val(
6954 __isl_take isl_pw_qpolynomial *pwqp,
6955 __isl_take isl_val *v);
6956 __isl_give isl_pw_qpolynomial_fold *
6957 isl_pw_qpolynomial_fold_scale_val(
6958 __isl_take isl_pw_qpolynomial_fold *pwf,
6959 __isl_take isl_val *v);
6960 __isl_give isl_union_pw_qpolynomial *
6961 isl_union_pw_qpolynomial_scale_val(
6962 __isl_take isl_union_pw_qpolynomial *upwqp,
6963 __isl_take isl_val *v);
6964 __isl_give isl_union_pw_qpolynomial_fold *
6965 isl_union_pw_qpolynomial_fold_scale_val(
6966 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6967 __isl_take isl_val *v);
6968 __isl_give isl_qpolynomial *
6969 isl_qpolynomial_scale_down_val(
6970 __isl_take isl_qpolynomial *qp,
6971 __isl_take isl_val *v);
6972 __isl_give isl_qpolynomial_fold *
6973 isl_qpolynomial_fold_scale_down_val(
6974 __isl_take isl_qpolynomial_fold *fold,
6975 __isl_take isl_val *v);
6976 __isl_give isl_pw_qpolynomial *
6977 isl_pw_qpolynomial_scale_down_val(
6978 __isl_take isl_pw_qpolynomial *pwqp,
6979 __isl_take isl_val *v);
6980 __isl_give isl_pw_qpolynomial_fold *
6981 isl_pw_qpolynomial_fold_scale_down_val(
6982 __isl_take isl_pw_qpolynomial_fold *pwf,
6983 __isl_take isl_val *v);
6984 __isl_give isl_union_pw_qpolynomial *
6985 isl_union_pw_qpolynomial_scale_down_val(
6986 __isl_take isl_union_pw_qpolynomial *upwqp,
6987 __isl_take isl_val *v);
6988 __isl_give isl_union_pw_qpolynomial_fold *
6989 isl_union_pw_qpolynomial_fold_scale_down_val(
6990 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6991 __isl_take isl_val *v);
6993 #include <isl/val.h>
6994 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6995 __isl_take isl_multi_val *mv1,
6996 __isl_take isl_multi_val *mv2);
6997 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6998 __isl_take isl_multi_val *mv1,
6999 __isl_take isl_multi_val *mv2);
7000 __isl_give isl_multi_val *
7001 isl_multi_val_scale_down_multi_val(
7002 __isl_take isl_multi_val *mv1,
7003 __isl_take isl_multi_val *mv2);
7005 #include <isl/aff.h>
7006 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7007 __isl_take isl_multi_aff *ma,
7008 __isl_take isl_multi_val *mv);
7009 __isl_give isl_multi_union_pw_aff *
7010 isl_multi_union_pw_aff_mod_multi_val(
7011 __isl_take isl_multi_union_pw_aff *upma,
7012 __isl_take isl_multi_val *mv);
7013 __isl_give isl_multi_pw_aff *
7014 isl_multi_pw_aff_mod_multi_val(
7015 __isl_take isl_multi_pw_aff *mpa,
7016 __isl_take isl_multi_val *mv);
7017 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7018 __isl_take isl_multi_aff *ma,
7019 __isl_take isl_multi_val *mv);
7020 __isl_give isl_pw_multi_aff *
7021 isl_pw_multi_aff_scale_multi_val(
7022 __isl_take isl_pw_multi_aff *pma,
7023 __isl_take isl_multi_val *mv);
7024 __isl_give isl_multi_pw_aff *
7025 isl_multi_pw_aff_scale_multi_val(
7026 __isl_take isl_multi_pw_aff *mpa,
7027 __isl_take isl_multi_val *mv);
7028 __isl_give isl_multi_union_pw_aff *
7029 isl_multi_union_pw_aff_scale_multi_val(
7030 __isl_take isl_multi_union_pw_aff *mupa,
7031 __isl_take isl_multi_val *mv);
7032 __isl_give isl_union_pw_multi_aff *
7033 isl_union_pw_multi_aff_scale_multi_val(
7034 __isl_take isl_union_pw_multi_aff *upma,
7035 __isl_take isl_multi_val *mv);
7036 __isl_give isl_multi_aff *
7037 isl_multi_aff_scale_down_multi_val(
7038 __isl_take isl_multi_aff *ma,
7039 __isl_take isl_multi_val *mv);
7040 __isl_give isl_multi_pw_aff *
7041 isl_multi_pw_aff_scale_down_multi_val(
7042 __isl_take isl_multi_pw_aff *mpa,
7043 __isl_take isl_multi_val *mv);
7044 __isl_give isl_multi_union_pw_aff *
7045 isl_multi_union_pw_aff_scale_down_multi_val(
7046 __isl_take isl_multi_union_pw_aff *mupa,
7047 __isl_take isl_multi_val *mv);
7049 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7050 by the corresponding elements of C<mv>.
7052 #include <isl/aff.h>
7053 __isl_give isl_aff *isl_aff_mul(
7054 __isl_take isl_aff *aff1,
7055 __isl_take isl_aff *aff2);
7056 __isl_give isl_aff *isl_aff_div(
7057 __isl_take isl_aff *aff1,
7058 __isl_take isl_aff *aff2);
7059 __isl_give isl_pw_aff *isl_pw_aff_mul(
7060 __isl_take isl_pw_aff *pwaff1,
7061 __isl_take isl_pw_aff *pwaff2);
7062 __isl_give isl_pw_aff *isl_pw_aff_div(
7063 __isl_take isl_pw_aff *pa1,
7064 __isl_take isl_pw_aff *pa2);
7065 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7066 __isl_take isl_pw_aff *pa1,
7067 __isl_take isl_pw_aff *pa2);
7068 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7069 __isl_take isl_pw_aff *pa1,
7070 __isl_take isl_pw_aff *pa2);
7072 When multiplying two affine expressions, at least one of the two needs
7073 to be a constant. Similarly, when dividing an affine expression by another,
7074 the second expression needs to be a constant.
7075 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7076 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7079 #include <isl/polynomial.h>
7080 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7081 __isl_take isl_qpolynomial *qp1,
7082 __isl_take isl_qpolynomial *qp2);
7083 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7084 __isl_take isl_pw_qpolynomial *pwqp1,
7085 __isl_take isl_pw_qpolynomial *pwqp2);
7086 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7087 __isl_take isl_union_pw_qpolynomial *upwqp1,
7088 __isl_take isl_union_pw_qpolynomial *upwqp2);
7092 =head3 Lexicographic Optimization
7094 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7095 the following functions
7096 compute a set that contains the lexicographic minimum or maximum
7097 of the elements in C<set> (or C<bset>) for those values of the parameters
7098 that satisfy C<dom>.
7099 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7100 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7102 In other words, the union of the parameter values
7103 for which the result is non-empty and of C<*empty>
7106 #include <isl/set.h>
7107 __isl_give isl_set *isl_basic_set_partial_lexmin(
7108 __isl_take isl_basic_set *bset,
7109 __isl_take isl_basic_set *dom,
7110 __isl_give isl_set **empty);
7111 __isl_give isl_set *isl_basic_set_partial_lexmax(
7112 __isl_take isl_basic_set *bset,
7113 __isl_take isl_basic_set *dom,
7114 __isl_give isl_set **empty);
7115 __isl_give isl_set *isl_set_partial_lexmin(
7116 __isl_take isl_set *set, __isl_take isl_set *dom,
7117 __isl_give isl_set **empty);
7118 __isl_give isl_set *isl_set_partial_lexmax(
7119 __isl_take isl_set *set, __isl_take isl_set *dom,
7120 __isl_give isl_set **empty);
7122 Given a (basic) set C<set> (or C<bset>), the following functions simply
7123 return a set containing the lexicographic minimum or maximum
7124 of the elements in C<set> (or C<bset>).
7125 In case of union sets, the optimum is computed per space.
7127 #include <isl/set.h>
7128 __isl_give isl_set *isl_basic_set_lexmin(
7129 __isl_take isl_basic_set *bset);
7130 __isl_give isl_set *isl_basic_set_lexmax(
7131 __isl_take isl_basic_set *bset);
7132 __isl_give isl_set *isl_set_lexmin(
7133 __isl_take isl_set *set);
7134 __isl_give isl_set *isl_set_lexmax(
7135 __isl_take isl_set *set);
7136 __isl_give isl_union_set *isl_union_set_lexmin(
7137 __isl_take isl_union_set *uset);
7138 __isl_give isl_union_set *isl_union_set_lexmax(
7139 __isl_take isl_union_set *uset);
7141 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7142 the following functions
7143 compute a relation that maps each element of C<dom>
7144 to the single lexicographic minimum or maximum
7145 of the elements that are associated to that same
7146 element in C<map> (or C<bmap>).
7147 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7148 that contains the elements in C<dom> that do not map
7149 to any elements in C<map> (or C<bmap>).
7150 In other words, the union of the domain of the result and of C<*empty>
7153 #include <isl/map.h>
7154 __isl_give isl_map *isl_basic_map_partial_lexmax(
7155 __isl_take isl_basic_map *bmap,
7156 __isl_take isl_basic_set *dom,
7157 __isl_give isl_set **empty);
7158 __isl_give isl_map *isl_basic_map_partial_lexmin(
7159 __isl_take isl_basic_map *bmap,
7160 __isl_take isl_basic_set *dom,
7161 __isl_give isl_set **empty);
7162 __isl_give isl_map *isl_map_partial_lexmax(
7163 __isl_take isl_map *map, __isl_take isl_set *dom,
7164 __isl_give isl_set **empty);
7165 __isl_give isl_map *isl_map_partial_lexmin(
7166 __isl_take isl_map *map, __isl_take isl_set *dom,
7167 __isl_give isl_set **empty);
7169 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7170 return a map mapping each element in the domain of
7171 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7172 of all elements associated to that element.
7173 In case of union relations, the optimum is computed per space.
7175 #include <isl/map.h>
7176 __isl_give isl_map *isl_basic_map_lexmin(
7177 __isl_take isl_basic_map *bmap);
7178 __isl_give isl_map *isl_basic_map_lexmax(
7179 __isl_take isl_basic_map *bmap);
7180 __isl_give isl_map *isl_map_lexmin(
7181 __isl_take isl_map *map);
7182 __isl_give isl_map *isl_map_lexmax(
7183 __isl_take isl_map *map);
7184 __isl_give isl_union_map *isl_union_map_lexmin(
7185 __isl_take isl_union_map *umap);
7186 __isl_give isl_union_map *isl_union_map_lexmax(
7187 __isl_take isl_union_map *umap);
7189 The following functions return their result in the form of
7190 a piecewise multi-affine expression,
7191 but are otherwise equivalent to the corresponding functions
7192 returning a basic set or relation.
7194 #include <isl/set.h>
7195 __isl_give isl_pw_multi_aff *
7196 isl_basic_set_partial_lexmin_pw_multi_aff(
7197 __isl_take isl_basic_set *bset,
7198 __isl_take isl_basic_set *dom,
7199 __isl_give isl_set **empty);
7200 __isl_give isl_pw_multi_aff *
7201 isl_basic_set_partial_lexmax_pw_multi_aff(
7202 __isl_take isl_basic_set *bset,
7203 __isl_take isl_basic_set *dom,
7204 __isl_give isl_set **empty);
7205 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7206 __isl_take isl_set *set);
7207 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7208 __isl_take isl_set *set);
7210 #include <isl/map.h>
7211 __isl_give isl_pw_multi_aff *
7212 isl_basic_map_lexmin_pw_multi_aff(
7213 __isl_take isl_basic_map *bmap);
7214 __isl_give isl_pw_multi_aff *
7215 isl_basic_map_partial_lexmin_pw_multi_aff(
7216 __isl_take isl_basic_map *bmap,
7217 __isl_take isl_basic_set *dom,
7218 __isl_give isl_set **empty);
7219 __isl_give isl_pw_multi_aff *
7220 isl_basic_map_partial_lexmax_pw_multi_aff(
7221 __isl_take isl_basic_map *bmap,
7222 __isl_take isl_basic_set *dom,
7223 __isl_give isl_set **empty);
7224 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7225 __isl_take isl_map *map);
7226 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7227 __isl_take isl_map *map);
7229 The following functions return the lexicographic minimum or maximum
7230 on the shared domain of the inputs and the single defined function
7231 on those parts of the domain where only a single function is defined.
7233 #include <isl/aff.h>
7234 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7235 __isl_take isl_pw_multi_aff *pma1,
7236 __isl_take isl_pw_multi_aff *pma2);
7237 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7238 __isl_take isl_pw_multi_aff *pma1,
7239 __isl_take isl_pw_multi_aff *pma2);
7241 =head2 Ternary Operations
7243 #include <isl/aff.h>
7244 __isl_give isl_pw_aff *isl_pw_aff_cond(
7245 __isl_take isl_pw_aff *cond,
7246 __isl_take isl_pw_aff *pwaff_true,
7247 __isl_take isl_pw_aff *pwaff_false);
7249 The function C<isl_pw_aff_cond> performs a conditional operator
7250 and returns an expression that is equal to C<pwaff_true>
7251 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7252 where C<cond> is zero.
7256 Lists are defined over several element types, including
7257 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7258 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7259 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7260 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7261 Here we take lists of C<isl_set>s as an example.
7262 Lists can be created, copied, modified and freed using the following functions.
7264 #include <isl/set.h>
7265 __isl_give isl_set_list *isl_set_list_from_set(
7266 __isl_take isl_set *el);
7267 __isl_give isl_set_list *isl_set_list_alloc(
7268 isl_ctx *ctx, int n);
7269 __isl_give isl_set_list *isl_set_list_copy(
7270 __isl_keep isl_set_list *list);
7271 __isl_give isl_set_list *isl_set_list_insert(
7272 __isl_take isl_set_list *list, unsigned pos,
7273 __isl_take isl_set *el);
7274 __isl_give isl_set_list *isl_set_list_add(
7275 __isl_take isl_set_list *list,
7276 __isl_take isl_set *el);
7277 __isl_give isl_set_list *isl_set_list_drop(
7278 __isl_take isl_set_list *list,
7279 unsigned first, unsigned n);
7280 __isl_give isl_set_list *isl_set_list_set_set(
7281 __isl_take isl_set_list *list, int index,
7282 __isl_take isl_set *set);
7283 __isl_give isl_set_list *isl_set_list_concat(
7284 __isl_take isl_set_list *list1,
7285 __isl_take isl_set_list *list2);
7286 __isl_give isl_set_list *isl_set_list_sort(
7287 __isl_take isl_set_list *list,
7288 int (*cmp)(__isl_keep isl_set *a,
7289 __isl_keep isl_set *b, void *user),
7291 __isl_null isl_set_list *isl_set_list_free(
7292 __isl_take isl_set_list *list);
7294 C<isl_set_list_alloc> creates an empty list with an initial capacity
7295 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7296 add elements to a list, increasing its capacity as needed.
7297 C<isl_set_list_from_set> creates a list with a single element.
7299 Lists can be inspected using the following functions.
7301 #include <isl/set.h>
7302 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7303 __isl_give isl_set *isl_set_list_get_set(
7304 __isl_keep isl_set_list *list, int index);
7305 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7306 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7308 isl_stat isl_set_list_foreach_scc(
7309 __isl_keep isl_set_list *list,
7310 isl_bool (*follows)(__isl_keep isl_set *a,
7311 __isl_keep isl_set *b, void *user),
7313 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7316 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7317 strongly connected components of the graph with as vertices the elements
7318 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7319 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
7320 should return C<-1> on error.
7322 Lists can be printed using
7324 #include <isl/set.h>
7325 __isl_give isl_printer *isl_printer_print_set_list(
7326 __isl_take isl_printer *p,
7327 __isl_keep isl_set_list *list);
7329 =head2 Associative arrays
7331 Associative arrays map isl objects of a specific type to isl objects
7332 of some (other) specific type. They are defined for several pairs
7333 of types, including (C<isl_map>, C<isl_basic_set>),
7334 (C<isl_id>, C<isl_ast_expr>),
7335 (C<isl_id>, C<isl_id>) and
7336 (C<isl_id>, C<isl_pw_aff>).
7337 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7340 Associative arrays can be created, copied and freed using
7341 the following functions.
7343 #include <isl/id_to_ast_expr.h>
7344 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7345 isl_ctx *ctx, int min_size);
7346 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7347 __isl_keep isl_id_to_ast_expr *id2expr);
7348 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7349 __isl_take isl_id_to_ast_expr *id2expr);
7351 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7352 to specify the expected size of the associative array.
7353 The associative array will be grown automatically as needed.
7355 Associative arrays can be inspected using the following functions.
7357 #include <isl/id_to_ast_expr.h>
7358 __isl_give isl_maybe_isl_ast_expr
7359 isl_id_to_ast_expr_try_get(
7360 __isl_keep isl_id_to_ast_expr *id2expr,
7361 __isl_keep isl_id *key);
7362 isl_bool isl_id_to_ast_expr_has(
7363 __isl_keep isl_id_to_ast_expr *id2expr,
7364 __isl_keep isl_id *key);
7365 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7366 __isl_keep isl_id_to_ast_expr *id2expr,
7367 __isl_take isl_id *key);
7368 isl_stat isl_id_to_ast_expr_foreach(
7369 __isl_keep isl_id_to_ast_expr *id2expr,
7370 isl_stat (*fn)(__isl_take isl_id *key,
7371 __isl_take isl_ast_expr *val, void *user),
7374 The function C<isl_id_to_ast_expr_try_get> returns a structure
7375 containing two elements, C<valid> and C<value>.
7376 If there is a value associated to the key, then C<valid>
7377 is set to C<isl_bool_true> and C<value> contains a copy of
7378 the associated value. Otherwise C<value> is C<NULL> and
7379 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7380 on whether some error has occurred or there simply is no associated value.
7381 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7382 in the structure and
7383 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7385 Associative arrays can be modified using the following functions.
7387 #include <isl/id_to_ast_expr.h>
7388 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7389 __isl_take isl_id_to_ast_expr *id2expr,
7390 __isl_take isl_id *key,
7391 __isl_take isl_ast_expr *val);
7392 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7393 __isl_take isl_id_to_ast_expr *id2expr,
7394 __isl_take isl_id *key);
7396 Associative arrays can be printed using the following function.
7398 #include <isl/id_to_ast_expr.h>
7399 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7400 __isl_take isl_printer *p,
7401 __isl_keep isl_id_to_ast_expr *id2expr);
7405 Vectors can be created, copied and freed using the following functions.
7407 #include <isl/vec.h>
7408 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7410 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7411 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7413 Note that the elements of a newly created vector may have arbitrary values.
7414 The elements can be changed and inspected using the following functions.
7416 int isl_vec_size(__isl_keep isl_vec *vec);
7417 __isl_give isl_val *isl_vec_get_element_val(
7418 __isl_keep isl_vec *vec, int pos);
7419 __isl_give isl_vec *isl_vec_set_element_si(
7420 __isl_take isl_vec *vec, int pos, int v);
7421 __isl_give isl_vec *isl_vec_set_element_val(
7422 __isl_take isl_vec *vec, int pos,
7423 __isl_take isl_val *v);
7424 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7426 __isl_give isl_vec *isl_vec_set_val(
7427 __isl_take isl_vec *vec, __isl_take isl_val *v);
7428 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7429 __isl_keep isl_vec *vec2, int pos);
7431 C<isl_vec_get_element> will return a negative value if anything went wrong.
7432 In that case, the value of C<*v> is undefined.
7434 The following function can be used to concatenate two vectors.
7436 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7437 __isl_take isl_vec *vec2);
7441 Matrices can be created, copied and freed using the following functions.
7443 #include <isl/mat.h>
7444 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7445 unsigned n_row, unsigned n_col);
7446 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7447 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7449 Note that the elements of a newly created matrix may have arbitrary values.
7450 The elements can be changed and inspected using the following functions.
7452 int isl_mat_rows(__isl_keep isl_mat *mat);
7453 int isl_mat_cols(__isl_keep isl_mat *mat);
7454 __isl_give isl_val *isl_mat_get_element_val(
7455 __isl_keep isl_mat *mat, int row, int col);
7456 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7457 int row, int col, int v);
7458 __isl_give isl_mat *isl_mat_set_element_val(
7459 __isl_take isl_mat *mat, int row, int col,
7460 __isl_take isl_val *v);
7462 C<isl_mat_get_element> will return a negative value if anything went wrong.
7463 In that case, the value of C<*v> is undefined.
7465 The following function can be used to compute the (right) inverse
7466 of a matrix, i.e., a matrix such that the product of the original
7467 and the inverse (in that order) is a multiple of the identity matrix.
7468 The input matrix is assumed to be of full row-rank.
7470 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7472 The following function can be used to compute the (right) kernel
7473 (or null space) of a matrix, i.e., a matrix such that the product of
7474 the original and the kernel (in that order) is the zero matrix.
7476 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7478 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7480 The following functions determine
7481 an upper or lower bound on a quasipolynomial over its domain.
7483 __isl_give isl_pw_qpolynomial_fold *
7484 isl_pw_qpolynomial_bound(
7485 __isl_take isl_pw_qpolynomial *pwqp,
7486 enum isl_fold type, int *tight);
7488 __isl_give isl_union_pw_qpolynomial_fold *
7489 isl_union_pw_qpolynomial_bound(
7490 __isl_take isl_union_pw_qpolynomial *upwqp,
7491 enum isl_fold type, int *tight);
7493 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7494 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7495 is the returned bound is known be tight, i.e., for each value
7496 of the parameters there is at least
7497 one element in the domain that reaches the bound.
7498 If the domain of C<pwqp> is not wrapping, then the bound is computed
7499 over all elements in that domain and the result has a purely parametric
7500 domain. If the domain of C<pwqp> is wrapping, then the bound is
7501 computed over the range of the wrapped relation. The domain of the
7502 wrapped relation becomes the domain of the result.
7504 =head2 Parametric Vertex Enumeration
7506 The parametric vertex enumeration described in this section
7507 is mainly intended to be used internally and by the C<barvinok>
7510 #include <isl/vertices.h>
7511 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7512 __isl_keep isl_basic_set *bset);
7514 The function C<isl_basic_set_compute_vertices> performs the
7515 actual computation of the parametric vertices and the chamber
7516 decomposition and store the result in an C<isl_vertices> object.
7517 This information can be queried by either iterating over all
7518 the vertices or iterating over all the chambers or cells
7519 and then iterating over all vertices that are active on the chamber.
7521 isl_stat isl_vertices_foreach_vertex(
7522 __isl_keep isl_vertices *vertices,
7523 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7524 void *user), void *user);
7526 isl_stat isl_vertices_foreach_cell(
7527 __isl_keep isl_vertices *vertices,
7528 isl_stat (*fn)(__isl_take isl_cell *cell,
7529 void *user), void *user);
7530 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7531 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7532 void *user), void *user);
7534 Other operations that can be performed on an C<isl_vertices> object are
7537 int isl_vertices_get_n_vertices(
7538 __isl_keep isl_vertices *vertices);
7539 void isl_vertices_free(__isl_take isl_vertices *vertices);
7541 Vertices can be inspected and destroyed using the following functions.
7543 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7544 __isl_give isl_basic_set *isl_vertex_get_domain(
7545 __isl_keep isl_vertex *vertex);
7546 __isl_give isl_multi_aff *isl_vertex_get_expr(
7547 __isl_keep isl_vertex *vertex);
7548 void isl_vertex_free(__isl_take isl_vertex *vertex);
7550 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7551 describing the vertex in terms of the parameters,
7552 while C<isl_vertex_get_domain> returns the activity domain
7555 Chambers can be inspected and destroyed using the following functions.
7557 __isl_give isl_basic_set *isl_cell_get_domain(
7558 __isl_keep isl_cell *cell);
7559 void isl_cell_free(__isl_take isl_cell *cell);
7561 =head1 Polyhedral Compilation Library
7563 This section collects functionality in C<isl> that has been specifically
7564 designed for use during polyhedral compilation.
7566 =head2 Schedule Trees
7568 A schedule tree is a structured representation of a schedule,
7569 assigning a relative order to a set of domain elements.
7570 The relative order expressed by the schedule tree is
7571 defined recursively. In particular, the order between
7572 two domain elements is determined by the node that is closest
7573 to the root that refers to both elements and that orders them apart.
7574 Each node in the tree is of one of several types.
7575 The root node is always of type C<isl_schedule_node_domain>
7576 (or C<isl_schedule_node_extension>)
7577 and it describes the (extra) domain elements to which the schedule applies.
7578 The other types of nodes are as follows.
7582 =item C<isl_schedule_node_band>
7584 A band of schedule dimensions. Each schedule dimension is represented
7585 by a union piecewise quasi-affine expression. If this expression
7586 assigns a different value to two domain elements, while all previous
7587 schedule dimensions in the same band assign them the same value,
7588 then the two domain elements are ordered according to these two
7590 Each expression is required to be total in the domain elements
7591 that reach the band node.
7593 =item C<isl_schedule_node_expansion>
7595 An expansion node maps each of the domain elements that reach the node
7596 to one or more domain elements. The image of this mapping forms
7597 the set of domain elements that reach the child of the expansion node.
7598 The function that maps each of the expanded domain elements
7599 to the original domain element from which it was expanded
7600 is called the contraction.
7602 =item C<isl_schedule_node_filter>
7604 A filter node does not impose any ordering, but rather intersects
7605 the set of domain elements that the current subtree refers to
7606 with a given union set. The subtree of the filter node only
7607 refers to domain elements in the intersection.
7608 A filter node is typically only used a child of a sequence or
7611 =item C<isl_schedule_node_leaf>
7613 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7615 =item C<isl_schedule_node_mark>
7617 A mark node can be used to attach any kind of information to a subtree
7618 of the schedule tree.
7620 =item C<isl_schedule_node_sequence>
7622 A sequence node has one or more children, each of which is a filter node.
7623 The filters on these filter nodes form a partition of
7624 the domain elements that the current subtree refers to.
7625 If two domain elements appear in distinct filters then the sequence
7626 node orders them according to the child positions of the corresponding
7629 =item C<isl_schedule_node_set>
7631 A set node is similar to a sequence node, except that
7632 it expresses that domain elements appearing in distinct filters
7633 may have any order. The order of the children of a set node
7634 is therefore also immaterial.
7638 The following node types are only supported by the AST generator.
7642 =item C<isl_schedule_node_context>
7644 The context describes constraints on the parameters and
7645 the schedule dimensions of outer
7646 bands that the AST generator may assume to hold. It is also the only
7647 kind of node that may introduce additional parameters.
7648 The space of the context is that of the flat product of the outer
7649 band nodes. In particular, if there are no outer band nodes, then
7650 this space is the unnamed zero-dimensional space.
7651 Since a context node references the outer band nodes, any tree
7652 containing a context node is considered to be anchored.
7654 =item C<isl_schedule_node_extension>
7656 An extension node instructs the AST generator to add additional
7657 domain elements that need to be scheduled.
7658 The additional domain elements are described by the range of
7659 the extension map in terms of the outer schedule dimensions,
7660 i.e., the flat product of the outer band nodes.
7661 Note that domain elements are added whenever the AST generator
7662 reaches the extension node, meaning that there are still some
7663 active domain elements for which an AST needs to be generated.
7664 The conditions under which some domain elements are still active
7665 may however not be completely described by the outer AST nodes
7666 generated at that point.
7668 An extension node may also appear as the root of a schedule tree,
7669 when it is intended to be inserted into another tree
7670 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7671 In this case, the domain of the extension node should
7672 correspond to the flat product of the outer band nodes
7673 in this other schedule tree at the point where the extension tree
7676 =item C<isl_schedule_node_guard>
7678 The guard describes constraints on the parameters and
7679 the schedule dimensions of outer
7680 bands that need to be enforced by the outer nodes
7681 in the generated AST.
7682 The space of the guard is that of the flat product of the outer
7683 band nodes. In particular, if there are no outer band nodes, then
7684 this space is the unnamed zero-dimensional space.
7685 Since a guard node references the outer band nodes, any tree
7686 containing a guard node is considered to be anchored.
7690 Except for the C<isl_schedule_node_context> nodes,
7691 none of the nodes may introduce any parameters that were not
7692 already present in the root domain node.
7694 A schedule tree is encapsulated in an C<isl_schedule> object.
7695 The simplest such objects, those with a tree consisting of single domain node,
7696 can be created using the following functions with either an empty
7697 domain or a given domain.
7699 #include <isl/schedule.h>
7700 __isl_give isl_schedule *isl_schedule_empty(
7701 __isl_take isl_space *space);
7702 __isl_give isl_schedule *isl_schedule_from_domain(
7703 __isl_take isl_union_set *domain);
7705 The function C<isl_schedule_constraints_compute_schedule> described
7706 in L</"Scheduling"> can also be used to construct schedules.
7708 C<isl_schedule> objects may be copied and freed using the following functions.
7710 #include <isl/schedule.h>
7711 __isl_give isl_schedule *isl_schedule_copy(
7712 __isl_keep isl_schedule *sched);
7713 __isl_null isl_schedule *isl_schedule_free(
7714 __isl_take isl_schedule *sched);
7716 The following functions checks whether two C<isl_schedule> objects
7717 are obviously the same.
7719 #include <isl/schedule.h>
7720 isl_bool isl_schedule_plain_is_equal(
7721 __isl_keep isl_schedule *schedule1,
7722 __isl_keep isl_schedule *schedule2);
7724 The domain of the schedule, i.e., the domain described by the root node,
7725 can be obtained using the following function.
7727 #include <isl/schedule.h>
7728 __isl_give isl_union_set *isl_schedule_get_domain(
7729 __isl_keep isl_schedule *schedule);
7731 An extra top-level band node (right underneath the domain node) can
7732 be introduced into the schedule using the following function.
7733 The schedule tree is assumed not to have any anchored nodes.
7735 #include <isl/schedule.h>
7736 __isl_give isl_schedule *
7737 isl_schedule_insert_partial_schedule(
7738 __isl_take isl_schedule *schedule,
7739 __isl_take isl_multi_union_pw_aff *partial);
7741 A top-level context node (right underneath the domain node) can
7742 be introduced into the schedule using the following function.
7744 #include <isl/schedule.h>
7745 __isl_give isl_schedule *isl_schedule_insert_context(
7746 __isl_take isl_schedule *schedule,
7747 __isl_take isl_set *context)
7749 A top-level guard node (right underneath the domain node) can
7750 be introduced into the schedule using the following function.
7752 #include <isl/schedule.h>
7753 __isl_give isl_schedule *isl_schedule_insert_guard(
7754 __isl_take isl_schedule *schedule,
7755 __isl_take isl_set *guard)
7757 A schedule that combines two schedules either in the given
7758 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7759 or an C<isl_schedule_node_set> node,
7760 can be created using the following functions.
7762 #include <isl/schedule.h>
7763 __isl_give isl_schedule *isl_schedule_sequence(
7764 __isl_take isl_schedule *schedule1,
7765 __isl_take isl_schedule *schedule2);
7766 __isl_give isl_schedule *isl_schedule_set(
7767 __isl_take isl_schedule *schedule1,
7768 __isl_take isl_schedule *schedule2);
7770 The domains of the two input schedules need to be disjoint.
7772 The following function can be used to restrict the domain
7773 of a schedule with a domain node as root to be a subset of the given union set.
7774 This operation may remove nodes in the tree that have become
7777 #include <isl/schedule.h>
7778 __isl_give isl_schedule *isl_schedule_intersect_domain(
7779 __isl_take isl_schedule *schedule,
7780 __isl_take isl_union_set *domain);
7782 The following function can be used to simplify the domain
7783 of a schedule with a domain node as root with respect to the given
7786 #include <isl/schedule.h>
7787 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7788 __isl_take isl_schedule *schedule,
7789 __isl_take isl_set *context);
7791 The following function resets the user pointers on all parameter
7792 and tuple identifiers referenced by the nodes of the given schedule.
7794 #include <isl/schedule.h>
7795 __isl_give isl_schedule *isl_schedule_reset_user(
7796 __isl_take isl_schedule *schedule);
7798 The following function aligns the parameters of all nodes
7799 in the given schedule to the given space.
7801 #include <isl/schedule.h>
7802 __isl_give isl_schedule *isl_schedule_align_params(
7803 __isl_take isl_schedule *schedule,
7804 __isl_take isl_space *space);
7806 The following function allows the user to plug in a given function
7807 in the iteration domains. The input schedule is not allowed to contain
7808 any expansion nodes.
7810 #include <isl/schedule.h>
7811 __isl_give isl_schedule *
7812 isl_schedule_pullback_union_pw_multi_aff(
7813 __isl_take isl_schedule *schedule,
7814 __isl_take isl_union_pw_multi_aff *upma);
7816 The following function can be used to plug in the schedule C<expansion>
7817 in the leaves of C<schedule>, where C<contraction> describes how
7818 the domain elements of C<expansion> map to the domain elements
7819 at the original leaves of C<schedule>.
7820 The resulting schedule will contain expansion nodes, unless
7821 C<contraction> is an identity function.
7823 #include <isl/schedule.h>
7824 __isl_give isl_schedule *isl_schedule_expand(
7825 __isl_take isl_schedule *schedule,
7826 __isl_take isl_union_pw_multi_aff *contraction,
7827 __isl_take isl_schedule *expansion);
7829 An C<isl_union_map> representation of the schedule can be obtained
7830 from an C<isl_schedule> using the following function.
7832 #include <isl/schedule.h>
7833 __isl_give isl_union_map *isl_schedule_get_map(
7834 __isl_keep isl_schedule *sched);
7836 The resulting relation encodes the same relative ordering as
7837 the schedule by mapping the domain elements to a common schedule space.
7838 If the schedule_separate_components option is set, then the order
7839 of the children of a set node is explicitly encoded in the result.
7840 If the tree contains any expansion nodes, then the relation
7841 is formulated in terms of the expanded domain elements.
7843 Schedules can be read from input using the following functions.
7845 #include <isl/schedule.h>
7846 __isl_give isl_schedule *isl_schedule_read_from_file(
7847 isl_ctx *ctx, FILE *input);
7848 __isl_give isl_schedule *isl_schedule_read_from_str(
7849 isl_ctx *ctx, const char *str);
7851 A representation of the schedule can be printed using
7853 #include <isl/schedule.h>
7854 __isl_give isl_printer *isl_printer_print_schedule(
7855 __isl_take isl_printer *p,
7856 __isl_keep isl_schedule *schedule);
7857 __isl_give char *isl_schedule_to_str(
7858 __isl_keep isl_schedule *schedule);
7860 C<isl_schedule_to_str> prints the schedule in flow format.
7862 The schedule tree can be traversed through the use of
7863 C<isl_schedule_node> objects that point to a particular
7864 position in the schedule tree. Whenever a C<isl_schedule_node>
7865 is use to modify a node in the schedule tree, the original schedule
7866 tree is left untouched and the modifications are performed to a copy
7867 of the tree. The returned C<isl_schedule_node> then points to
7868 this modified copy of the tree.
7870 The root of the schedule tree can be obtained using the following function.
7872 #include <isl/schedule.h>
7873 __isl_give isl_schedule_node *isl_schedule_get_root(
7874 __isl_keep isl_schedule *schedule);
7876 A pointer to a newly created schedule tree with a single domain
7877 node can be created using the following functions.
7879 #include <isl/schedule_node.h>
7880 __isl_give isl_schedule_node *
7881 isl_schedule_node_from_domain(
7882 __isl_take isl_union_set *domain);
7883 __isl_give isl_schedule_node *
7884 isl_schedule_node_from_extension(
7885 __isl_take isl_union_map *extension);
7887 C<isl_schedule_node_from_extension> creates a tree with an extension
7890 Schedule nodes can be copied and freed using the following functions.
7892 #include <isl/schedule_node.h>
7893 __isl_give isl_schedule_node *isl_schedule_node_copy(
7894 __isl_keep isl_schedule_node *node);
7895 __isl_null isl_schedule_node *isl_schedule_node_free(
7896 __isl_take isl_schedule_node *node);
7898 The following functions can be used to check if two schedule
7899 nodes point to the same position in the same schedule.
7901 #include <isl/schedule_node.h>
7902 isl_bool isl_schedule_node_is_equal(
7903 __isl_keep isl_schedule_node *node1,
7904 __isl_keep isl_schedule_node *node2);
7906 The following properties can be obtained from a schedule node.
7908 #include <isl/schedule_node.h>
7909 enum isl_schedule_node_type isl_schedule_node_get_type(
7910 __isl_keep isl_schedule_node *node);
7911 enum isl_schedule_node_type
7912 isl_schedule_node_get_parent_type(
7913 __isl_keep isl_schedule_node *node);
7914 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7915 __isl_keep isl_schedule_node *node);
7917 The function C<isl_schedule_node_get_type> returns the type of
7918 the node, while C<isl_schedule_node_get_parent_type> returns
7919 type of the parent of the node, which is required to exist.
7920 The function C<isl_schedule_node_get_schedule> returns a copy
7921 to the schedule to which the node belongs.
7923 The following functions can be used to move the schedule node
7924 to a different position in the tree or to check if such a position
7927 #include <isl/schedule_node.h>
7928 isl_bool isl_schedule_node_has_parent(
7929 __isl_keep isl_schedule_node *node);
7930 __isl_give isl_schedule_node *isl_schedule_node_parent(
7931 __isl_take isl_schedule_node *node);
7932 __isl_give isl_schedule_node *isl_schedule_node_root(
7933 __isl_take isl_schedule_node *node);
7934 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
7935 __isl_take isl_schedule_node *node,
7937 int isl_schedule_node_n_children(
7938 __isl_keep isl_schedule_node *node);
7939 __isl_give isl_schedule_node *isl_schedule_node_child(
7940 __isl_take isl_schedule_node *node, int pos);
7941 isl_bool isl_schedule_node_has_children(
7942 __isl_keep isl_schedule_node *node);
7943 __isl_give isl_schedule_node *isl_schedule_node_first_child(
7944 __isl_take isl_schedule_node *node);
7945 isl_bool isl_schedule_node_has_previous_sibling(
7946 __isl_keep isl_schedule_node *node);
7947 __isl_give isl_schedule_node *
7948 isl_schedule_node_previous_sibling(
7949 __isl_take isl_schedule_node *node);
7950 isl_bool isl_schedule_node_has_next_sibling(
7951 __isl_keep isl_schedule_node *node);
7952 __isl_give isl_schedule_node *
7953 isl_schedule_node_next_sibling(
7954 __isl_take isl_schedule_node *node);
7956 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
7957 is the node itself, the ancestor of generation 1 is its parent and so on.
7959 It is also possible to query the number of ancestors of a node,
7960 the position of the current node
7961 within the children of its parent, the position of the subtree
7962 containing a node within the children of an ancestor
7963 or to obtain a copy of a given
7964 child without destroying the current node.
7965 Given two nodes that point to the same schedule, their closest
7966 shared ancestor can be obtained using
7967 C<isl_schedule_node_get_shared_ancestor>.
7969 #include <isl/schedule_node.h>
7970 int isl_schedule_node_get_tree_depth(
7971 __isl_keep isl_schedule_node *node);
7972 int isl_schedule_node_get_child_position(
7973 __isl_keep isl_schedule_node *node);
7974 int isl_schedule_node_get_ancestor_child_position(
7975 __isl_keep isl_schedule_node *node,
7976 __isl_keep isl_schedule_node *ancestor);
7977 __isl_give isl_schedule_node *isl_schedule_node_get_child(
7978 __isl_keep isl_schedule_node *node, int pos);
7979 __isl_give isl_schedule_node *
7980 isl_schedule_node_get_shared_ancestor(
7981 __isl_keep isl_schedule_node *node1,
7982 __isl_keep isl_schedule_node *node2);
7984 All nodes in a schedule tree or
7985 all descendants of a specific node (including the node) can be visited
7986 in depth-first pre-order using the following functions.
7988 #include <isl/schedule.h>
7989 isl_stat isl_schedule_foreach_schedule_node_top_down(
7990 __isl_keep isl_schedule *sched,
7991 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7992 void *user), void *user);
7994 #include <isl/schedule_node.h>
7995 isl_stat isl_schedule_node_foreach_descendant_top_down(
7996 __isl_keep isl_schedule_node *node,
7997 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7998 void *user), void *user);
8000 The callback function is slightly different from the usual
8001 callbacks in that it not only indicates success (non-negative result)
8002 or failure (negative result), but also indicates whether the children
8003 of the given node should be visited. In particular, if the callback
8004 returns a positive value, then the children are visited, but if
8005 the callback returns zero, then the children are not visited.
8007 The ancestors of a node in a schedule tree can be visited from
8008 the root down to and including the parent of the node using
8009 the following function.
8011 #include <isl/schedule_node.h>
8012 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8013 __isl_keep isl_schedule_node *node,
8014 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8015 void *user), void *user);
8017 The following functions allows for a depth-first post-order
8018 traversal of the nodes in a schedule tree or
8019 of the descendants of a specific node (including the node
8020 itself), where the user callback is allowed to modify the
8023 #include <isl/schedule.h>
8024 __isl_give isl_schedule *
8025 isl_schedule_map_schedule_node_bottom_up(
8026 __isl_take isl_schedule *schedule,
8027 __isl_give isl_schedule_node *(*fn)(
8028 __isl_take isl_schedule_node *node,
8029 void *user), void *user);
8031 #include <isl/schedule_node.h>
8032 __isl_give isl_schedule_node *
8033 isl_schedule_node_map_descendant_bottom_up(
8034 __isl_take isl_schedule_node *node,
8035 __isl_give isl_schedule_node *(*fn)(
8036 __isl_take isl_schedule_node *node,
8037 void *user), void *user);
8039 The traversal continues from the node returned by the callback function.
8040 It is the responsibility of the user to ensure that this does not
8041 lead to an infinite loop. It is safest to always return a pointer
8042 to the same position (same ancestors and child positions) as the input node.
8044 The following function removes a node (along with its descendants)
8045 from a schedule tree and returns a pointer to the leaf at the
8046 same position in the updated tree.
8047 It is not allowed to remove the root of a schedule tree or
8048 a child of a set or sequence node.
8050 #include <isl/schedule_node.h>
8051 __isl_give isl_schedule_node *isl_schedule_node_cut(
8052 __isl_take isl_schedule_node *node);
8054 The following function removes a single node
8055 from a schedule tree and returns a pointer to the child
8056 of the node, now located at the position of the original node
8057 or to a leaf node at that position if there was no child.
8058 It is not allowed to remove the root of a schedule tree,
8059 a set or sequence node, a child of a set or sequence node or
8060 a band node with an anchored subtree.
8062 #include <isl/schedule_node.h>
8063 __isl_give isl_schedule_node *isl_schedule_node_delete(
8064 __isl_take isl_schedule_node *node);
8066 Most nodes in a schedule tree only contain local information.
8067 In some cases, however, a node may also refer to outer band nodes.
8068 This means that the position of the node within the tree should
8069 not be changed, or at least that no changes are performed to the
8070 outer band nodes. The following function can be used to test
8071 whether the subtree rooted at a given node contains any such nodes.
8073 #include <isl/schedule_node.h>
8074 isl_bool isl_schedule_node_is_subtree_anchored(
8075 __isl_keep isl_schedule_node *node);
8077 The following function resets the user pointers on all parameter
8078 and tuple identifiers referenced by the given schedule node.
8080 #include <isl/schedule_node.h>
8081 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8082 __isl_take isl_schedule_node *node);
8084 The following function aligns the parameters of the given schedule
8085 node to the given space.
8087 #include <isl/schedule_node.h>
8088 __isl_give isl_schedule_node *
8089 isl_schedule_node_align_params(
8090 __isl_take isl_schedule_node *node,
8091 __isl_take isl_space *space);
8093 Several node types have their own functions for querying
8094 (and in some cases setting) some node type specific properties.
8096 #include <isl/schedule_node.h>
8097 __isl_give isl_space *isl_schedule_node_band_get_space(
8098 __isl_keep isl_schedule_node *node);
8099 __isl_give isl_multi_union_pw_aff *
8100 isl_schedule_node_band_get_partial_schedule(
8101 __isl_keep isl_schedule_node *node);
8102 __isl_give isl_union_map *
8103 isl_schedule_node_band_get_partial_schedule_union_map(
8104 __isl_keep isl_schedule_node *node);
8105 unsigned isl_schedule_node_band_n_member(
8106 __isl_keep isl_schedule_node *node);
8107 isl_bool isl_schedule_node_band_member_get_coincident(
8108 __isl_keep isl_schedule_node *node, int pos);
8109 __isl_give isl_schedule_node *
8110 isl_schedule_node_band_member_set_coincident(
8111 __isl_take isl_schedule_node *node, int pos,
8113 isl_bool isl_schedule_node_band_get_permutable(
8114 __isl_keep isl_schedule_node *node);
8115 __isl_give isl_schedule_node *
8116 isl_schedule_node_band_set_permutable(
8117 __isl_take isl_schedule_node *node, int permutable);
8118 enum isl_ast_loop_type
8119 isl_schedule_node_band_member_get_ast_loop_type(
8120 __isl_keep isl_schedule_node *node, int pos);
8121 __isl_give isl_schedule_node *
8122 isl_schedule_node_band_member_set_ast_loop_type(
8123 __isl_take isl_schedule_node *node, int pos,
8124 enum isl_ast_loop_type type);
8125 __isl_give isl_union_set *
8126 enum isl_ast_loop_type
8127 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8128 __isl_keep isl_schedule_node *node, int pos);
8129 __isl_give isl_schedule_node *
8130 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8131 __isl_take isl_schedule_node *node, int pos,
8132 enum isl_ast_loop_type type);
8133 isl_schedule_node_band_get_ast_build_options(
8134 __isl_keep isl_schedule_node *node);
8135 __isl_give isl_schedule_node *
8136 isl_schedule_node_band_set_ast_build_options(
8137 __isl_take isl_schedule_node *node,
8138 __isl_take isl_union_set *options);
8140 The function C<isl_schedule_node_band_get_space> returns the space
8141 of the partial schedule of the band.
8142 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8143 returns a representation of the partial schedule of the band node
8144 in the form of an C<isl_union_map>.
8145 The coincident and permutable properties are set by
8146 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8148 A scheduling dimension is considered to be ``coincident''
8149 if it satisfies the coincidence constraints within its band.
8150 That is, if the dependence distances of the coincidence
8151 constraints are all zero in that direction (for fixed
8152 iterations of outer bands).
8153 A band is marked permutable if it was produced using the Pluto-like scheduler.
8154 Note that the scheduler may have to resort to a Feautrier style scheduling
8155 step even if the default scheduler is used.
8156 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8157 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8158 For the meaning of these loop AST generation types and the difference
8159 between the regular loop AST generation type and the isolate
8160 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8161 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8162 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8163 may return C<isl_ast_loop_error> if an error occurs.
8164 The AST build options govern how an AST is generated for
8165 the individual schedule dimensions during AST generation.
8166 See L</"AST Generation Options (Schedule Tree)">.
8168 #include <isl/schedule_node.h>
8169 __isl_give isl_set *
8170 isl_schedule_node_context_get_context(
8171 __isl_keep isl_schedule_node *node);
8173 #include <isl/schedule_node.h>
8174 __isl_give isl_union_set *
8175 isl_schedule_node_domain_get_domain(
8176 __isl_keep isl_schedule_node *node);
8178 #include <isl/schedule_node.h>
8179 __isl_give isl_union_map *
8180 isl_schedule_node_expansion_get_expansion(
8181 __isl_keep isl_schedule_node *node);
8182 __isl_give isl_union_pw_multi_aff *
8183 isl_schedule_node_expansion_get_contraction(
8184 __isl_keep isl_schedule_node *node);
8186 #include <isl/schedule_node.h>
8187 __isl_give isl_union_map *
8188 isl_schedule_node_extension_get_extension(
8189 __isl_keep isl_schedule_node *node);
8191 #include <isl/schedule_node.h>
8192 __isl_give isl_union_set *
8193 isl_schedule_node_filter_get_filter(
8194 __isl_keep isl_schedule_node *node);
8196 #include <isl/schedule_node.h>
8197 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8198 __isl_keep isl_schedule_node *node);
8200 #include <isl/schedule_node.h>
8201 __isl_give isl_id *isl_schedule_node_mark_get_id(
8202 __isl_keep isl_schedule_node *node);
8204 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8205 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8206 partial schedules related to the node.
8208 #include <isl/schedule_node.h>
8209 __isl_give isl_multi_union_pw_aff *
8210 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8211 __isl_keep isl_schedule_node *node);
8212 __isl_give isl_union_pw_multi_aff *
8213 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8214 __isl_keep isl_schedule_node *node);
8215 __isl_give isl_union_map *
8216 isl_schedule_node_get_prefix_schedule_union_map(
8217 __isl_keep isl_schedule_node *node);
8218 __isl_give isl_union_map *
8219 isl_schedule_node_get_prefix_schedule_relation(
8220 __isl_keep isl_schedule_node *node);
8221 __isl_give isl_union_map *
8222 isl_schedule_node_get_subtree_schedule_union_map(
8223 __isl_keep isl_schedule_node *node);
8225 In particular, the functions
8226 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8227 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8228 and C<isl_schedule_node_get_prefix_schedule_union_map>
8229 return a relative ordering on the domain elements that reach the given
8230 node determined by its ancestors.
8231 The function C<isl_schedule_node_get_prefix_schedule_relation>
8232 additionally includes the domain constraints in the result.
8233 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8234 returns a representation of the partial schedule defined by the
8235 subtree rooted at the given node.
8236 If the tree contains any expansion nodes, then the subtree schedule
8237 is formulated in terms of the expanded domain elements.
8238 The tree passed to functions returning a prefix schedule
8239 may only contain extension nodes if these would not affect
8240 the result of these functions. That is, if one of the ancestors
8241 is an extension node, then all of the domain elements that were
8242 added by the extension node need to have been filtered out
8243 by filter nodes between the extension node and the input node.
8244 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8245 may not contain in extension nodes in the selected subtree.
8247 The expansion/contraction defined by an entire subtree, combining
8248 the expansions/contractions
8249 on the expansion nodes in the subtree, can be obtained using
8250 the following functions.
8252 #include <isl/schedule_node.h>
8253 __isl_give isl_union_map *
8254 isl_schedule_node_get_subtree_expansion(
8255 __isl_keep isl_schedule_node *node);
8256 __isl_give isl_union_pw_multi_aff *
8257 isl_schedule_node_get_subtree_contraction(
8258 __isl_keep isl_schedule_node *node);
8260 The total number of outer band members of given node, i.e.,
8261 the shared output dimension of the maps in the result
8262 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8263 using the following function.
8265 #include <isl/schedule_node.h>
8266 int isl_schedule_node_get_schedule_depth(
8267 __isl_keep isl_schedule_node *node);
8269 The following functions return the elements that reach the given node
8270 or the union of universes in the spaces that contain these elements.
8272 #include <isl/schedule_node.h>
8273 __isl_give isl_union_set *
8274 isl_schedule_node_get_domain(
8275 __isl_keep isl_schedule_node *node);
8276 __isl_give isl_union_set *
8277 isl_schedule_node_get_universe_domain(
8278 __isl_keep isl_schedule_node *node);
8280 The input tree of C<isl_schedule_node_get_domain>
8281 may only contain extension nodes if these would not affect
8282 the result of this function. That is, if one of the ancestors
8283 is an extension node, then all of the domain elements that were
8284 added by the extension node need to have been filtered out
8285 by filter nodes between the extension node and the input node.
8287 The following functions can be used to introduce additional nodes
8288 in the schedule tree. The new node is introduced at the point
8289 in the tree where the C<isl_schedule_node> points to and
8290 the results points to the new node.
8292 #include <isl/schedule_node.h>
8293 __isl_give isl_schedule_node *
8294 isl_schedule_node_insert_partial_schedule(
8295 __isl_take isl_schedule_node *node,
8296 __isl_take isl_multi_union_pw_aff *schedule);
8298 This function inserts a new band node with (the greatest integer
8299 part of) the given partial schedule.
8300 The subtree rooted at the given node is assumed not to have
8303 #include <isl/schedule_node.h>
8304 __isl_give isl_schedule_node *
8305 isl_schedule_node_insert_context(
8306 __isl_take isl_schedule_node *node,
8307 __isl_take isl_set *context);
8309 This function inserts a new context node with the given context constraints.
8311 #include <isl/schedule_node.h>
8312 __isl_give isl_schedule_node *
8313 isl_schedule_node_insert_filter(
8314 __isl_take isl_schedule_node *node,
8315 __isl_take isl_union_set *filter);
8317 This function inserts a new filter node with the given filter.
8318 If the original node already pointed to a filter node, then the
8319 two filter nodes are merged into one.
8321 #include <isl/schedule_node.h>
8322 __isl_give isl_schedule_node *
8323 isl_schedule_node_insert_guard(
8324 __isl_take isl_schedule_node *node,
8325 __isl_take isl_set *guard);
8327 This function inserts a new guard node with the given guard constraints.
8329 #include <isl/schedule_node.h>
8330 __isl_give isl_schedule_node *
8331 isl_schedule_node_insert_mark(
8332 __isl_take isl_schedule_node *node,
8333 __isl_take isl_id *mark);
8335 This function inserts a new mark node with the give mark identifier.
8337 #include <isl/schedule_node.h>
8338 __isl_give isl_schedule_node *
8339 isl_schedule_node_insert_sequence(
8340 __isl_take isl_schedule_node *node,
8341 __isl_take isl_union_set_list *filters);
8342 __isl_give isl_schedule_node *
8343 isl_schedule_node_insert_set(
8344 __isl_take isl_schedule_node *node,
8345 __isl_take isl_union_set_list *filters);
8347 These functions insert a new sequence or set node with the given
8348 filters as children.
8350 #include <isl/schedule_node.h>
8351 __isl_give isl_schedule_node *isl_schedule_node_group(
8352 __isl_take isl_schedule_node *node,
8353 __isl_take isl_id *group_id);
8355 This function introduces an expansion node in between the current
8356 node and its parent that expands instances of a space with tuple
8357 identifier C<group_id> to the original domain elements that reach
8358 the node. The group instances are identified by the prefix schedule
8359 of those domain elements. The ancestors of the node are adjusted
8360 to refer to the group instances instead of the original domain
8361 elements. The return value points to the same node in the updated
8362 schedule tree as the input node, i.e., to the child of the newly
8363 introduced expansion node. Grouping instances of different statements
8364 ensures that they will be treated as a single statement by the
8365 AST generator up to the point of the expansion node.
8367 The following function can be used to flatten a nested
8370 #include <isl/schedule_node.h>
8371 __isl_give isl_schedule_node *
8372 isl_schedule_node_sequence_splice_child(
8373 __isl_take isl_schedule_node *node, int pos);
8375 That is, given a sequence node C<node> that has another sequence node
8376 in its child at position C<pos> (in particular, the child of that filter
8377 node is a sequence node), attach the children of that other sequence
8378 node as children of C<node>, replacing the original child at position
8381 The partial schedule of a band node can be scaled (down) or reduced using
8382 the following functions.
8384 #include <isl/schedule_node.h>
8385 __isl_give isl_schedule_node *
8386 isl_schedule_node_band_scale(
8387 __isl_take isl_schedule_node *node,
8388 __isl_take isl_multi_val *mv);
8389 __isl_give isl_schedule_node *
8390 isl_schedule_node_band_scale_down(
8391 __isl_take isl_schedule_node *node,
8392 __isl_take isl_multi_val *mv);
8393 __isl_give isl_schedule_node *
8394 isl_schedule_node_band_mod(
8395 __isl_take isl_schedule_node *node,
8396 __isl_take isl_multi_val *mv);
8398 The spaces of the two arguments need to match.
8399 After scaling, the partial schedule is replaced by its greatest
8400 integer part to ensure that the schedule remains integral.
8402 The partial schedule of a band node can be shifted by an
8403 C<isl_multi_union_pw_aff> with a domain that is a superset
8404 of the domain of the partial schedule using
8405 the following function.
8407 #include <isl/schedule_node.h>
8408 __isl_give isl_schedule_node *
8409 isl_schedule_node_band_shift(
8410 __isl_take isl_schedule_node *node,
8411 __isl_take isl_multi_union_pw_aff *shift);
8413 A band node can be tiled using the following function.
8415 #include <isl/schedule_node.h>
8416 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8417 __isl_take isl_schedule_node *node,
8418 __isl_take isl_multi_val *sizes);
8420 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8422 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8423 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8425 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8427 The C<isl_schedule_node_band_tile> function tiles
8428 the band using the given tile sizes inside its schedule.
8429 A new child band node is created to represent the point loops and it is
8430 inserted between the modified band and its children.
8431 The subtree rooted at the given node is assumed not to have
8433 The C<tile_scale_tile_loops> option specifies whether the tile
8434 loops iterators should be scaled by the tile sizes.
8435 If the C<tile_shift_point_loops> option is set, then the point loops
8436 are shifted to start at zero.
8438 A band node can be split into two nested band nodes
8439 using the following function.
8441 #include <isl/schedule_node.h>
8442 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8443 __isl_take isl_schedule_node *node, int pos);
8445 The resulting outer band node contains the first C<pos> dimensions of
8446 the schedule of C<node> while the inner band contains the remaining dimensions.
8447 The schedules of the two band nodes live in anonymous spaces.
8449 A band node can be moved down to the leaves of the subtree rooted
8450 at the band node using the following function.
8452 #include <isl/schedule_node.h>
8453 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8454 __isl_take isl_schedule_node *node);
8456 The subtree rooted at the given node is assumed not to have
8458 The result points to the node in the resulting tree that is in the same
8459 position as the node pointed to by C<node> in the original tree.
8461 #include <isl/schedule_node.h>
8462 __isl_give isl_schedule_node *
8463 isl_schedule_node_order_before(
8464 __isl_take isl_schedule_node *node,
8465 __isl_take isl_union_set *filter);
8466 __isl_give isl_schedule_node *
8467 isl_schedule_node_order_after(
8468 __isl_take isl_schedule_node *node,
8469 __isl_take isl_union_set *filter);
8471 These functions split the domain elements that reach C<node>
8472 into those that satisfy C<filter> and those that do not and
8473 arranges for the elements that do satisfy the filter to be
8474 executed before (in case of C<isl_schedule_node_order_before>)
8475 or after (in case of C<isl_schedule_node_order_after>)
8476 those that do not. The order is imposed by
8477 a sequence node, possibly reusing the grandparent of C<node>
8478 on two copies of the subtree attached to the original C<node>.
8479 Both copies are simplified with respect to their filter.
8481 Return a pointer to the copy of the subtree that does not
8482 satisfy C<filter>. If there is no such copy (because all
8483 reaching domain elements satisfy the filter), then return
8484 the original pointer.
8486 #include <isl/schedule_node.h>
8487 __isl_give isl_schedule_node *
8488 isl_schedule_node_graft_before(
8489 __isl_take isl_schedule_node *node,
8490 __isl_take isl_schedule_node *graft);
8491 __isl_give isl_schedule_node *
8492 isl_schedule_node_graft_after(
8493 __isl_take isl_schedule_node *node,
8494 __isl_take isl_schedule_node *graft);
8496 This function inserts the C<graft> tree into the tree containing C<node>
8497 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8498 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8499 The root node of C<graft>
8500 should be an extension node where the domain of the extension
8501 is the flat product of all outer band nodes of C<node>.
8502 The root node may also be a domain node.
8503 The elements of the domain or the range of the extension may not
8504 intersect with the domain elements that reach "node".
8505 The schedule tree of C<graft> may not be anchored.
8507 The schedule tree of C<node> is modified to include an extension node
8508 corresponding to the root node of C<graft> as a child of the original
8509 parent of C<node>. The original node that C<node> points to and the
8510 child of the root node of C<graft> are attached to this extension node
8511 through a sequence, with appropriate filters and with the child
8512 of C<graft> appearing before or after the original C<node>.
8514 If C<node> already appears inside a sequence that is the child of
8515 an extension node and if the spaces of the new domain elements
8516 do not overlap with those of the original domain elements,
8517 then that extension node is extended with the new extension
8518 rather than introducing a new segment of extension and sequence nodes.
8520 Return a pointer to the same node in the modified tree that
8521 C<node> pointed to in the original tree.
8523 A representation of the schedule node can be printed using
8525 #include <isl/schedule_node.h>
8526 __isl_give isl_printer *isl_printer_print_schedule_node(
8527 __isl_take isl_printer *p,
8528 __isl_keep isl_schedule_node *node);
8529 __isl_give char *isl_schedule_node_to_str(
8530 __isl_keep isl_schedule_node *node);
8532 C<isl_schedule_node_to_str> prints the schedule node in block format.
8534 =head2 Dependence Analysis
8536 C<isl> contains specialized functionality for performing
8537 array dataflow analysis. That is, given a I<sink> access relation
8538 and a collection of possible I<source> access relations,
8539 C<isl> can compute relations that describe
8540 for each iteration of the sink access, which iteration
8541 of which of the source access relations was the last
8542 to access the same data element before the given iteration
8544 The resulting dependence relations map source iterations
8545 to either the corresponding sink iterations or
8546 pairs of corresponding sink iterations and accessed data elements.
8547 To compute standard flow dependences, the sink should be
8548 a read, while the sources should be writes.
8549 If any of the source accesses are marked as being I<may>
8550 accesses, then there will be a dependence from the last
8551 I<must> access B<and> from any I<may> access that follows
8552 this last I<must> access.
8553 In particular, if I<all> sources are I<may> accesses,
8554 then memory based dependence analysis is performed.
8555 If, on the other hand, all sources are I<must> accesses,
8556 then value based dependence analysis is performed.
8558 =head3 High-level Interface
8560 A high-level interface to dependence analysis is provided
8561 by the following function.
8563 #include <isl/flow.h>
8564 __isl_give isl_union_flow *
8565 isl_union_access_info_compute_flow(
8566 __isl_take isl_union_access_info *access);
8568 The input C<isl_union_access_info> object describes the sink
8569 access relations, the source access relations and a schedule,
8570 while the output C<isl_union_flow> object describes
8571 the resulting dependence relations and the subsets of the
8572 sink relations for which no source was found.
8574 An C<isl_union_access_info> is created, modified, copied and freed using
8575 the following functions.
8577 #include <isl/flow.h>
8578 __isl_give isl_union_access_info *
8579 isl_union_access_info_from_sink(
8580 __isl_take isl_union_map *sink);
8581 __isl_give isl_union_access_info *
8582 isl_union_access_info_set_must_source(
8583 __isl_take isl_union_access_info *access,
8584 __isl_take isl_union_map *must_source);
8585 __isl_give isl_union_access_info *
8586 isl_union_access_info_set_may_source(
8587 __isl_take isl_union_access_info *access,
8588 __isl_take isl_union_map *may_source);
8589 __isl_give isl_union_access_info *
8590 isl_union_access_info_set_schedule(
8591 __isl_take isl_union_access_info *access,
8592 __isl_take isl_schedule *schedule);
8593 __isl_give isl_union_access_info *
8594 isl_union_access_info_set_schedule_map(
8595 __isl_take isl_union_access_info *access,
8596 __isl_take isl_union_map *schedule_map);
8597 __isl_give isl_union_access_info *
8598 isl_union_access_info_copy(
8599 __isl_keep isl_union_access_info *access);
8600 __isl_null isl_union_access_info *
8601 isl_union_access_info_free(
8602 __isl_take isl_union_access_info *access);
8604 The may sources set by C<isl_union_access_info_set_may_source>
8605 do not need to include the must sources set by
8606 C<isl_union_access_info_set_must_source> as a subset.
8607 The user is free not to call one (or both) of these functions,
8608 in which case the corresponding set is kept to its empty default.
8609 Similarly, the default schedule initialized by
8610 C<isl_union_access_info_from_sink> is empty.
8611 The current schedule is determined by the last call to either
8612 C<isl_union_access_info_set_schedule> or
8613 C<isl_union_access_info_set_schedule_map>.
8614 The domain of the schedule corresponds to the domains of
8615 the access relations. In particular, the domains of the access
8616 relations are effectively intersected with the domain of the schedule
8617 and only the resulting accesses are considered by the dependence analysis.
8619 A representation of the information contained in an object
8620 of type C<isl_union_access_info> can be obtained using
8622 #include <isl/flow.h>
8623 __isl_give isl_printer *
8624 isl_printer_print_union_access_info(
8625 __isl_take isl_printer *p,
8626 __isl_keep isl_union_access_info *access);
8627 __isl_give char *isl_union_access_info_to_str(
8628 __isl_keep isl_union_access_info *access);
8630 C<isl_union_access_info_to_str> prints the information in flow format.
8632 The output of C<isl_union_access_info_compute_flow> can be examined
8633 and freed using the following functions.
8635 #include <isl/flow.h>
8636 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8637 __isl_keep isl_union_flow *flow);
8638 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8639 __isl_keep isl_union_flow *flow);
8640 __isl_give isl_union_map *
8641 isl_union_flow_get_full_must_dependence(
8642 __isl_keep isl_union_flow *flow);
8643 __isl_give isl_union_map *
8644 isl_union_flow_get_full_may_dependence(
8645 __isl_keep isl_union_flow *flow);
8646 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8647 __isl_keep isl_union_flow *flow);
8648 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8649 __isl_keep isl_union_flow *flow);
8650 __isl_null isl_union_flow *isl_union_flow_free(
8651 __isl_take isl_union_flow *flow);
8653 The relation returned by C<isl_union_flow_get_must_dependence>
8654 relates domain elements of must sources to domain elements of the sink.
8655 The relation returned by C<isl_union_flow_get_may_dependence>
8656 relates domain elements of must or may sources to domain elements of the sink
8657 and includes the previous relation as a subset.
8658 The relation returned by C<isl_union_flow_get_full_must_dependence>
8659 relates domain elements of must sources to pairs of domain elements of the sink
8660 and accessed data elements.
8661 The relation returned by C<isl_union_flow_get_full_may_dependence>
8662 relates domain elements of must or may sources to pairs of
8663 domain elements of the sink and accessed data elements.
8664 This relation includes the previous relation as a subset.
8665 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8666 of the sink relation for which no dependences have been found.
8667 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8668 of the sink relation for which no definite dependences have been found.
8669 That is, it contains those sink access that do not contribute to any
8670 of the elements in the relation returned
8671 by C<isl_union_flow_get_must_dependence>.
8673 A representation of the information contained in an object
8674 of type C<isl_union_flow> can be obtained using
8676 #include <isl/flow.h>
8677 __isl_give isl_printer *isl_printer_print_union_flow(
8678 __isl_take isl_printer *p,
8679 __isl_keep isl_union_flow *flow);
8680 __isl_give char *isl_union_flow_to_str(
8681 __isl_keep isl_union_flow *flow);
8683 C<isl_union_flow_to_str> prints the information in flow format.
8685 =head3 Low-level Interface
8687 A lower-level interface is provided by the following functions.
8689 #include <isl/flow.h>
8691 typedef int (*isl_access_level_before)(void *first, void *second);
8693 __isl_give isl_access_info *isl_access_info_alloc(
8694 __isl_take isl_map *sink,
8695 void *sink_user, isl_access_level_before fn,
8697 __isl_give isl_access_info *isl_access_info_add_source(
8698 __isl_take isl_access_info *acc,
8699 __isl_take isl_map *source, int must,
8701 __isl_null isl_access_info *isl_access_info_free(
8702 __isl_take isl_access_info *acc);
8704 __isl_give isl_flow *isl_access_info_compute_flow(
8705 __isl_take isl_access_info *acc);
8707 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8708 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8709 void *dep_user, void *user),
8711 __isl_give isl_map *isl_flow_get_no_source(
8712 __isl_keep isl_flow *deps, int must);
8713 void isl_flow_free(__isl_take isl_flow *deps);
8715 The function C<isl_access_info_compute_flow> performs the actual
8716 dependence analysis. The other functions are used to construct
8717 the input for this function or to read off the output.
8719 The input is collected in an C<isl_access_info>, which can
8720 be created through a call to C<isl_access_info_alloc>.
8721 The arguments to this functions are the sink access relation
8722 C<sink>, a token C<sink_user> used to identify the sink
8723 access to the user, a callback function for specifying the
8724 relative order of source and sink accesses, and the number
8725 of source access relations that will be added.
8726 The callback function has type C<int (*)(void *first, void *second)>.
8727 The function is called with two user supplied tokens identifying
8728 either a source or the sink and it should return the shared nesting
8729 level and the relative order of the two accesses.
8730 In particular, let I<n> be the number of loops shared by
8731 the two accesses. If C<first> precedes C<second> textually,
8732 then the function should return I<2 * n + 1>; otherwise,
8733 it should return I<2 * n>.
8734 The sources can be added to the C<isl_access_info> by performing
8735 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8736 C<must> indicates whether the source is a I<must> access
8737 or a I<may> access. Note that a multi-valued access relation
8738 should only be marked I<must> if every iteration in the domain
8739 of the relation accesses I<all> elements in its image.
8740 The C<source_user> token is again used to identify
8741 the source access. The range of the source access relation
8742 C<source> should have the same dimension as the range
8743 of the sink access relation.
8744 The C<isl_access_info_free> function should usually not be
8745 called explicitly, because it is called implicitly by
8746 C<isl_access_info_compute_flow>.
8748 The result of the dependence analysis is collected in an
8749 C<isl_flow>. There may be elements of
8750 the sink access for which no preceding source access could be
8751 found or for which all preceding sources are I<may> accesses.
8752 The relations containing these elements can be obtained through
8753 calls to C<isl_flow_get_no_source>, the first with C<must> set
8754 and the second with C<must> unset.
8755 In the case of standard flow dependence analysis,
8756 with the sink a read and the sources I<must> writes,
8757 the first relation corresponds to the reads from uninitialized
8758 array elements and the second relation is empty.
8759 The actual flow dependences can be extracted using
8760 C<isl_flow_foreach>. This function will call the user-specified
8761 callback function C<fn> for each B<non-empty> dependence between
8762 a source and the sink. The callback function is called
8763 with four arguments, the actual flow dependence relation
8764 mapping source iterations to sink iterations, a boolean that
8765 indicates whether it is a I<must> or I<may> dependence, a token
8766 identifying the source and an additional C<void *> with value
8767 equal to the third argument of the C<isl_flow_foreach> call.
8768 A dependence is marked I<must> if it originates from a I<must>
8769 source and if it is not followed by any I<may> sources.
8771 After finishing with an C<isl_flow>, the user should call
8772 C<isl_flow_free> to free all associated memory.
8774 =head3 Interaction with the Low-level Interface
8776 During the dependence analysis, we frequently need to perform
8777 the following operation. Given a relation between sink iterations
8778 and potential source iterations from a particular source domain,
8779 what is the last potential source iteration corresponding to each
8780 sink iteration. It can sometimes be convenient to adjust
8781 the set of potential source iterations before or after each such operation.
8782 The prototypical example is fuzzy array dataflow analysis,
8783 where we need to analyze if, based on data-dependent constraints,
8784 the sink iteration can ever be executed without one or more of
8785 the corresponding potential source iterations being executed.
8786 If so, we can introduce extra parameters and select an unknown
8787 but fixed source iteration from the potential source iterations.
8788 To be able to perform such manipulations, C<isl> provides the following
8791 #include <isl/flow.h>
8793 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8794 __isl_keep isl_map *source_map,
8795 __isl_keep isl_set *sink, void *source_user,
8797 __isl_give isl_access_info *isl_access_info_set_restrict(
8798 __isl_take isl_access_info *acc,
8799 isl_access_restrict fn, void *user);
8801 The function C<isl_access_info_set_restrict> should be called
8802 before calling C<isl_access_info_compute_flow> and registers a callback function
8803 that will be called any time C<isl> is about to compute the last
8804 potential source. The first argument is the (reverse) proto-dependence,
8805 mapping sink iterations to potential source iterations.
8806 The second argument represents the sink iterations for which
8807 we want to compute the last source iteration.
8808 The third argument is the token corresponding to the source
8809 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8810 The callback is expected to return a restriction on either the input or
8811 the output of the operation computing the last potential source.
8812 If the input needs to be restricted then restrictions are needed
8813 for both the source and the sink iterations. The sink iterations
8814 and the potential source iterations will be intersected with these sets.
8815 If the output needs to be restricted then only a restriction on the source
8816 iterations is required.
8817 If any error occurs, the callback should return C<NULL>.
8818 An C<isl_restriction> object can be created, freed and inspected
8819 using the following functions.
8821 #include <isl/flow.h>
8823 __isl_give isl_restriction *isl_restriction_input(
8824 __isl_take isl_set *source_restr,
8825 __isl_take isl_set *sink_restr);
8826 __isl_give isl_restriction *isl_restriction_output(
8827 __isl_take isl_set *source_restr);
8828 __isl_give isl_restriction *isl_restriction_none(
8829 __isl_take isl_map *source_map);
8830 __isl_give isl_restriction *isl_restriction_empty(
8831 __isl_take isl_map *source_map);
8832 __isl_null isl_restriction *isl_restriction_free(
8833 __isl_take isl_restriction *restr);
8835 C<isl_restriction_none> and C<isl_restriction_empty> are special
8836 cases of C<isl_restriction_input>. C<isl_restriction_none>
8837 is essentially equivalent to
8839 isl_restriction_input(isl_set_universe(
8840 isl_space_range(isl_map_get_space(source_map))),
8842 isl_space_domain(isl_map_get_space(source_map))));
8844 whereas C<isl_restriction_empty> is essentially equivalent to
8846 isl_restriction_input(isl_set_empty(
8847 isl_space_range(isl_map_get_space(source_map))),
8849 isl_space_domain(isl_map_get_space(source_map))));
8853 B<The functionality described in this section is fairly new
8854 and may be subject to change.>
8856 #include <isl/schedule.h>
8857 __isl_give isl_schedule *
8858 isl_schedule_constraints_compute_schedule(
8859 __isl_take isl_schedule_constraints *sc);
8861 The function C<isl_schedule_constraints_compute_schedule> can be
8862 used to compute a schedule that satisfies the given schedule constraints.
8863 These schedule constraints include the iteration domain for which
8864 a schedule should be computed and dependences between pairs of
8865 iterations. In particular, these dependences include
8866 I<validity> dependences and I<proximity> dependences.
8867 By default, the algorithm used to construct the schedule is similar
8868 to that of C<Pluto>.
8869 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8871 The generated schedule respects all validity dependences.
8872 That is, all dependence distances over these dependences in the
8873 scheduled space are lexicographically positive.
8875 The default algorithm tries to ensure that the dependence distances
8876 over coincidence constraints are zero and to minimize the
8877 dependence distances over proximity dependences.
8878 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8879 for groups of domains where the dependence distances over validity
8880 dependences have only non-negative values.
8881 Note that when minimizing the maximal dependence distance
8882 over proximity dependences, a single affine expression in the parameters
8883 is constructed that bounds all dependence distances. If no such expression
8884 exists, then the algorithm will fail and resort to an alternative
8885 scheduling algorithm. In particular, this means that adding proximity
8886 dependences may eliminate valid solutions. A typical example where this
8887 phenomenon may occur is when some subset of the proximity dependences
8888 has no restriction on some parameter, forcing the coefficient of that
8889 parameter to be zero, while some other subset forces the dependence
8890 distance to depend on that parameter, requiring the same coefficient
8892 When using Feautrier's algorithm, the coincidence and proximity constraints
8893 are only taken into account during the extension to a
8894 full-dimensional schedule.
8896 An C<isl_schedule_constraints> object can be constructed
8897 and manipulated using the following functions.
8899 #include <isl/schedule.h>
8900 __isl_give isl_schedule_constraints *
8901 isl_schedule_constraints_copy(
8902 __isl_keep isl_schedule_constraints *sc);
8903 __isl_give isl_schedule_constraints *
8904 isl_schedule_constraints_on_domain(
8905 __isl_take isl_union_set *domain);
8906 __isl_give isl_schedule_constraints *
8907 isl_schedule_constraints_set_context(
8908 __isl_take isl_schedule_constraints *sc,
8909 __isl_take isl_set *context);
8910 __isl_give isl_schedule_constraints *
8911 isl_schedule_constraints_set_validity(
8912 __isl_take isl_schedule_constraints *sc,
8913 __isl_take isl_union_map *validity);
8914 __isl_give isl_schedule_constraints *
8915 isl_schedule_constraints_set_coincidence(
8916 __isl_take isl_schedule_constraints *sc,
8917 __isl_take isl_union_map *coincidence);
8918 __isl_give isl_schedule_constraints *
8919 isl_schedule_constraints_set_proximity(
8920 __isl_take isl_schedule_constraints *sc,
8921 __isl_take isl_union_map *proximity);
8922 __isl_give isl_schedule_constraints *
8923 isl_schedule_constraints_set_conditional_validity(
8924 __isl_take isl_schedule_constraints *sc,
8925 __isl_take isl_union_map *condition,
8926 __isl_take isl_union_map *validity);
8927 __isl_give isl_schedule_constraints *
8928 isl_schedule_constraints_apply(
8929 __isl_take isl_schedule_constraints *sc,
8930 __isl_take isl_union_map *umap);
8931 __isl_null isl_schedule_constraints *
8932 isl_schedule_constraints_free(
8933 __isl_take isl_schedule_constraints *sc);
8935 The initial C<isl_schedule_constraints> object created by
8936 C<isl_schedule_constraints_on_domain> does not impose any constraints.
8937 That is, it has an empty set of dependences.
8938 The function C<isl_schedule_constraints_set_context> allows the user
8939 to specify additional constraints on the parameters that may
8940 be assumed to hold during the construction of the schedule.
8941 The function C<isl_schedule_constraints_set_validity> replaces the
8942 validity dependences, mapping domain elements I<i> to domain
8943 elements that should be scheduled after I<i>.
8944 The function C<isl_schedule_constraints_set_coincidence> replaces the
8945 coincidence dependences, mapping domain elements I<i> to domain
8946 elements that should be scheduled together with I<I>, if possible.
8947 The function C<isl_schedule_constraints_set_proximity> replaces the
8948 proximity dependences, mapping domain elements I<i> to domain
8949 elements that should be scheduled either before I<I>
8950 or as early as possible after I<i>.
8952 The function C<isl_schedule_constraints_set_conditional_validity>
8953 replaces the conditional validity constraints.
8954 A conditional validity constraint is only imposed when any of the corresponding
8955 conditions is satisfied, i.e., when any of them is non-zero.
8956 That is, the scheduler ensures that within each band if the dependence
8957 distances over the condition constraints are not all zero
8958 then all corresponding conditional validity constraints are respected.
8959 A conditional validity constraint corresponds to a condition
8960 if the two are adjacent, i.e., if the domain of one relation intersect
8961 the range of the other relation.
8962 The typical use case of conditional validity constraints is
8963 to allow order constraints between live ranges to be violated
8964 as long as the live ranges themselves are local to the band.
8965 To allow more fine-grained control over which conditions correspond
8966 to which conditional validity constraints, the domains and ranges
8967 of these relations may include I<tags>. That is, the domains and
8968 ranges of those relation may themselves be wrapped relations
8969 where the iteration domain appears in the domain of those wrapped relations
8970 and the range of the wrapped relations can be arbitrarily chosen
8971 by the user. Conditions and conditional validity constraints are only
8972 considered adjacent to each other if the entire wrapped relation matches.
8973 In particular, a relation with a tag will never be considered adjacent
8974 to a relation without a tag.
8976 The function C<isl_schedule_constraints_compute_schedule> takes
8977 schedule constraints that are defined on some set of domain elements
8978 and transforms them to schedule constraints on the elements
8979 to which these domain elements are mapped by the given transformation.
8981 An C<isl_schedule_constraints> object can be inspected
8982 using the following functions.
8984 #include <isl/schedule.h>
8985 __isl_give isl_union_set *
8986 isl_schedule_constraints_get_domain(
8987 __isl_keep isl_schedule_constraints *sc);
8988 __isl_give isl_union_map *
8989 isl_schedule_constraints_get_validity(
8990 __isl_keep isl_schedule_constraints *sc);
8991 __isl_give isl_union_map *
8992 isl_schedule_constraints_get_coincidence(
8993 __isl_keep isl_schedule_constraints *sc);
8994 __isl_give isl_union_map *
8995 isl_schedule_constraints_get_proximity(
8996 __isl_keep isl_schedule_constraints *sc);
8997 __isl_give isl_union_map *
8998 isl_schedule_constraints_get_conditional_validity(
8999 __isl_keep isl_schedule_constraints *sc);
9000 __isl_give isl_union_map *
9001 isl_schedule_constraints_get_conditional_validity_condition(
9002 __isl_keep isl_schedule_constraints *sc);
9004 The following function computes a schedule directly from
9005 an iteration domain and validity and proximity dependences
9006 and is implemented in terms of the functions described above.
9007 The use of C<isl_union_set_compute_schedule> is discouraged.
9009 #include <isl/schedule.h>
9010 __isl_give isl_schedule *isl_union_set_compute_schedule(
9011 __isl_take isl_union_set *domain,
9012 __isl_take isl_union_map *validity,
9013 __isl_take isl_union_map *proximity);
9015 The generated schedule represents a schedule tree.
9016 For more information on schedule trees, see
9017 L</"Schedule Trees">.
9021 #include <isl/schedule.h>
9022 isl_stat isl_options_set_schedule_max_coefficient(
9023 isl_ctx *ctx, int val);
9024 int isl_options_get_schedule_max_coefficient(
9026 isl_stat isl_options_set_schedule_max_constant_term(
9027 isl_ctx *ctx, int val);
9028 int isl_options_get_schedule_max_constant_term(
9030 isl_stat isl_options_set_schedule_serialize_sccs(
9031 isl_ctx *ctx, int val);
9032 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9033 isl_stat isl_options_set_schedule_whole_component(
9034 isl_ctx *ctx, int val);
9035 int isl_options_get_schedule_whole_component(
9037 isl_stat isl_options_set_schedule_maximize_band_depth(
9038 isl_ctx *ctx, int val);
9039 int isl_options_get_schedule_maximize_band_depth(
9041 isl_stat isl_options_set_schedule_maximize_coincidence(
9042 isl_ctx *ctx, int val);
9043 int isl_options_get_schedule_maximize_coincidence(
9045 isl_stat isl_options_set_schedule_outer_coincidence(
9046 isl_ctx *ctx, int val);
9047 int isl_options_get_schedule_outer_coincidence(
9049 isl_stat isl_options_set_schedule_split_scaled(
9050 isl_ctx *ctx, int val);
9051 int isl_options_get_schedule_split_scaled(
9053 isl_stat isl_options_set_schedule_algorithm(
9054 isl_ctx *ctx, int val);
9055 int isl_options_get_schedule_algorithm(
9057 isl_stat isl_options_set_schedule_separate_components(
9058 isl_ctx *ctx, int val);
9059 int isl_options_get_schedule_separate_components(
9064 =item * schedule_max_coefficient
9066 This option enforces that the coefficients for variable and parameter
9067 dimensions in the calculated schedule are not larger than the specified value.
9068 This option can significantly increase the speed of the scheduling calculation
9069 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9070 this option does not introduce bounds on the variable or parameter
9073 =item * schedule_max_constant_term
9075 This option enforces that the constant coefficients in the calculated schedule
9076 are not larger than the maximal constant term. This option can significantly
9077 increase the speed of the scheduling calculation and may also prevent fusing of
9078 unrelated dimensions. A value of -1 means that this option does not introduce
9079 bounds on the constant coefficients.
9081 =item * schedule_serialize_sccs
9083 If this option is set, then all strongly connected components
9084 in the dependence graph are serialized as soon as they are detected.
9085 This means in particular that instances of statements will only
9086 appear in the same band node if these statements belong
9087 to the same strongly connected component at the point where
9088 the band node is constructed.
9090 =item * schedule_whole_component
9092 If this option is set, then entire (weakly) connected
9093 components in the dependence graph are scheduled together
9095 Otherwise, each strongly connected component within
9096 such a weakly connected component is first scheduled separately
9097 and then combined with other strongly connected components.
9098 This option has no effect if C<schedule_serialize_sccs> is set.
9100 =item * schedule_maximize_band_depth
9102 If this option is set, then the scheduler tries to maximize
9103 the width of the bands. Wider bands give more possibilities for tiling.
9104 In particular, if the C<schedule_whole_component> option is set,
9105 then bands are split if this might result in wider bands.
9106 Otherwise, the effect of this option is to only allow
9107 strongly connected components to be combined if this does
9108 not reduce the width of the bands.
9109 Note that if the C<schedule_serialize_sccs> options is set, then
9110 the C<schedule_maximize_band_depth> option therefore has no effect.
9112 =item * schedule_maximize_coincidence
9114 This option is only effective if the C<schedule_whole_component>
9115 option is turned off.
9116 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9117 strongly connected components are only combined with each other
9118 if this does not reduce the number of coincident band members.
9120 =item * schedule_outer_coincidence
9122 If this option is set, then we try to construct schedules
9123 where the outermost scheduling dimension in each band
9124 satisfies the coincidence constraints.
9126 =item * schedule_split_scaled
9128 If this option is set, then we try to construct schedules in which the
9129 constant term is split off from the linear part if the linear parts of
9130 the scheduling rows for all nodes in the graphs have a common non-trivial
9132 The constant term is then placed in a separate band and the linear
9135 =item * schedule_algorithm
9137 Selects the scheduling algorithm to be used.
9138 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9139 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9141 =item * schedule_separate_components
9143 If this option is set then the function C<isl_schedule_get_map>
9144 will treat set nodes in the same way as sequence nodes.
9148 =head2 AST Generation
9150 This section describes the C<isl> functionality for generating
9151 ASTs that visit all the elements
9152 in a domain in an order specified by a schedule tree or
9154 In case the schedule given as a C<isl_union_map>, an AST is generated
9155 that visits all the elements in the domain of the C<isl_union_map>
9156 according to the lexicographic order of the corresponding image
9157 element(s). If the range of the C<isl_union_map> consists of
9158 elements in more than one space, then each of these spaces is handled
9159 separately in an arbitrary order.
9160 It should be noted that the schedule tree or the image elements
9161 in a schedule map only specify the I<order>
9162 in which the corresponding domain elements should be visited.
9163 No direct relation between the partial schedule values
9164 or the image elements on the one hand and the loop iterators
9165 in the generated AST on the other hand should be assumed.
9167 Each AST is generated within a build. The initial build
9168 simply specifies the constraints on the parameters (if any)
9169 and can be created, inspected, copied and freed using the following functions.
9171 #include <isl/ast_build.h>
9172 __isl_give isl_ast_build *isl_ast_build_alloc(
9174 __isl_give isl_ast_build *isl_ast_build_from_context(
9175 __isl_take isl_set *set);
9176 __isl_give isl_ast_build *isl_ast_build_copy(
9177 __isl_keep isl_ast_build *build);
9178 __isl_null isl_ast_build *isl_ast_build_free(
9179 __isl_take isl_ast_build *build);
9181 The C<set> argument is usually a parameter set with zero or more parameters.
9182 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9183 this set is required to be a parameter set.
9184 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9185 specify any parameter constraints.
9186 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9187 and L</"Fine-grained Control over AST Generation">.
9188 Finally, the AST itself can be constructed using one of the following
9191 #include <isl/ast_build.h>
9192 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9193 __isl_keep isl_ast_build *build,
9194 __isl_take isl_schedule *schedule);
9195 __isl_give isl_ast_node *
9196 isl_ast_build_node_from_schedule_map(
9197 __isl_keep isl_ast_build *build,
9198 __isl_take isl_union_map *schedule);
9200 =head3 Inspecting the AST
9202 The basic properties of an AST node can be obtained as follows.
9204 #include <isl/ast.h>
9205 enum isl_ast_node_type isl_ast_node_get_type(
9206 __isl_keep isl_ast_node *node);
9208 The type of an AST node is one of
9209 C<isl_ast_node_for>,
9211 C<isl_ast_node_block>,
9212 C<isl_ast_node_mark> or
9213 C<isl_ast_node_user>.
9214 An C<isl_ast_node_for> represents a for node.
9215 An C<isl_ast_node_if> represents an if node.
9216 An C<isl_ast_node_block> represents a compound node.
9217 An C<isl_ast_node_mark> introduces a mark in the AST.
9218 An C<isl_ast_node_user> represents an expression statement.
9219 An expression statement typically corresponds to a domain element, i.e.,
9220 one of the elements that is visited by the AST.
9222 Each type of node has its own additional properties.
9224 #include <isl/ast.h>
9225 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9226 __isl_keep isl_ast_node *node);
9227 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9228 __isl_keep isl_ast_node *node);
9229 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9230 __isl_keep isl_ast_node *node);
9231 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9232 __isl_keep isl_ast_node *node);
9233 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9234 __isl_keep isl_ast_node *node);
9235 isl_bool isl_ast_node_for_is_degenerate(
9236 __isl_keep isl_ast_node *node);
9238 An C<isl_ast_for> is considered degenerate if it is known to execute
9241 #include <isl/ast.h>
9242 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9243 __isl_keep isl_ast_node *node);
9244 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9245 __isl_keep isl_ast_node *node);
9246 isl_bool isl_ast_node_if_has_else(
9247 __isl_keep isl_ast_node *node);
9248 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9249 __isl_keep isl_ast_node *node);
9251 __isl_give isl_ast_node_list *
9252 isl_ast_node_block_get_children(
9253 __isl_keep isl_ast_node *node);
9255 __isl_give isl_id *isl_ast_node_mark_get_id(
9256 __isl_keep isl_ast_node *node);
9257 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9258 __isl_keep isl_ast_node *node);
9260 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9261 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9263 #include <isl/ast.h>
9264 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9265 __isl_keep isl_ast_node *node);
9267 All descendants of a specific node in the AST (including the node itself)
9269 in depth-first pre-order using the following function.
9271 #include <isl/ast.h>
9272 isl_stat isl_ast_node_foreach_descendant_top_down(
9273 __isl_keep isl_ast_node *node,
9274 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9275 void *user), void *user);
9277 The callback function should return C<isl_bool_true> if the children
9278 of the given node should be visited and C<isl_bool_false> if they should not.
9279 It should return C<isl_bool_error> in case of failure, in which case
9280 the entire traversal is aborted.
9282 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9283 the following functions.
9285 #include <isl/ast.h>
9286 enum isl_ast_expr_type isl_ast_expr_get_type(
9287 __isl_keep isl_ast_expr *expr);
9289 The type of an AST expression is one of
9291 C<isl_ast_expr_id> or
9292 C<isl_ast_expr_int>.
9293 An C<isl_ast_expr_op> represents the result of an operation.
9294 An C<isl_ast_expr_id> represents an identifier.
9295 An C<isl_ast_expr_int> represents an integer value.
9297 Each type of expression has its own additional properties.
9299 #include <isl/ast.h>
9300 enum isl_ast_op_type isl_ast_expr_get_op_type(
9301 __isl_keep isl_ast_expr *expr);
9302 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9303 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9304 __isl_keep isl_ast_expr *expr, int pos);
9305 isl_stat isl_ast_expr_foreach_ast_op_type(
9306 __isl_keep isl_ast_expr *expr,
9307 isl_stat (*fn)(enum isl_ast_op_type type,
9308 void *user), void *user);
9309 isl_stat isl_ast_node_foreach_ast_op_type(
9310 __isl_keep isl_ast_node *node,
9311 isl_stat (*fn)(enum isl_ast_op_type type,
9312 void *user), void *user);
9314 C<isl_ast_expr_get_op_type> returns the type of the operation
9315 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9316 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9318 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9319 C<isl_ast_op_type> that appears in C<expr>.
9320 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9321 C<isl_ast_op_type> that appears in C<node>.
9322 The operation type is one of the following.
9326 =item C<isl_ast_op_and>
9328 Logical I<and> of two arguments.
9329 Both arguments can be evaluated.
9331 =item C<isl_ast_op_and_then>
9333 Logical I<and> of two arguments.
9334 The second argument can only be evaluated if the first evaluates to true.
9336 =item C<isl_ast_op_or>
9338 Logical I<or> of two arguments.
9339 Both arguments can be evaluated.
9341 =item C<isl_ast_op_or_else>
9343 Logical I<or> of two arguments.
9344 The second argument can only be evaluated if the first evaluates to false.
9346 =item C<isl_ast_op_max>
9348 Maximum of two or more arguments.
9350 =item C<isl_ast_op_min>
9352 Minimum of two or more arguments.
9354 =item C<isl_ast_op_minus>
9358 =item C<isl_ast_op_add>
9360 Sum of two arguments.
9362 =item C<isl_ast_op_sub>
9364 Difference of two arguments.
9366 =item C<isl_ast_op_mul>
9368 Product of two arguments.
9370 =item C<isl_ast_op_div>
9372 Exact division. That is, the result is known to be an integer.
9374 =item C<isl_ast_op_fdiv_q>
9376 Result of integer division, rounded towards negative
9379 =item C<isl_ast_op_pdiv_q>
9381 Result of integer division, where dividend is known to be non-negative.
9383 =item C<isl_ast_op_pdiv_r>
9385 Remainder of integer division, where dividend is known to be non-negative.
9387 =item C<isl_ast_op_zdiv_r>
9389 Equal to zero iff the remainder on integer division is zero.
9391 =item C<isl_ast_op_cond>
9393 Conditional operator defined on three arguments.
9394 If the first argument evaluates to true, then the result
9395 is equal to the second argument. Otherwise, the result
9396 is equal to the third argument.
9397 The second and third argument may only be evaluated if
9398 the first argument evaluates to true and false, respectively.
9399 Corresponds to C<a ? b : c> in C.
9401 =item C<isl_ast_op_select>
9403 Conditional operator defined on three arguments.
9404 If the first argument evaluates to true, then the result
9405 is equal to the second argument. Otherwise, the result
9406 is equal to the third argument.
9407 The second and third argument may be evaluated independently
9408 of the value of the first argument.
9409 Corresponds to C<a * b + (1 - a) * c> in C.
9411 =item C<isl_ast_op_eq>
9415 =item C<isl_ast_op_le>
9417 Less than or equal relation.
9419 =item C<isl_ast_op_lt>
9423 =item C<isl_ast_op_ge>
9425 Greater than or equal relation.
9427 =item C<isl_ast_op_gt>
9429 Greater than relation.
9431 =item C<isl_ast_op_call>
9434 The number of arguments of the C<isl_ast_expr> is one more than
9435 the number of arguments in the function call, the first argument
9436 representing the function being called.
9438 =item C<isl_ast_op_access>
9441 The number of arguments of the C<isl_ast_expr> is one more than
9442 the number of index expressions in the array access, the first argument
9443 representing the array being accessed.
9445 =item C<isl_ast_op_member>
9448 This operation has two arguments, a structure and the name of
9449 the member of the structure being accessed.
9453 #include <isl/ast.h>
9454 __isl_give isl_id *isl_ast_expr_get_id(
9455 __isl_keep isl_ast_expr *expr);
9457 Return the identifier represented by the AST expression.
9459 #include <isl/ast.h>
9460 __isl_give isl_val *isl_ast_expr_get_val(
9461 __isl_keep isl_ast_expr *expr);
9463 Return the integer represented by the AST expression.
9465 =head3 Properties of ASTs
9467 #include <isl/ast.h>
9468 isl_bool isl_ast_expr_is_equal(
9469 __isl_keep isl_ast_expr *expr1,
9470 __isl_keep isl_ast_expr *expr2);
9472 Check if two C<isl_ast_expr>s are equal to each other.
9474 =head3 Manipulating and printing the AST
9476 AST nodes can be copied and freed using the following functions.
9478 #include <isl/ast.h>
9479 __isl_give isl_ast_node *isl_ast_node_copy(
9480 __isl_keep isl_ast_node *node);
9481 __isl_null isl_ast_node *isl_ast_node_free(
9482 __isl_take isl_ast_node *node);
9484 AST expressions can be copied and freed using the following functions.
9486 #include <isl/ast.h>
9487 __isl_give isl_ast_expr *isl_ast_expr_copy(
9488 __isl_keep isl_ast_expr *expr);
9489 __isl_null isl_ast_expr *isl_ast_expr_free(
9490 __isl_take isl_ast_expr *expr);
9492 New AST expressions can be created either directly or within
9493 the context of an C<isl_ast_build>.
9495 #include <isl/ast.h>
9496 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9497 __isl_take isl_val *v);
9498 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9499 __isl_take isl_id *id);
9500 __isl_give isl_ast_expr *isl_ast_expr_neg(
9501 __isl_take isl_ast_expr *expr);
9502 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9503 __isl_take isl_ast_expr *expr);
9504 __isl_give isl_ast_expr *isl_ast_expr_add(
9505 __isl_take isl_ast_expr *expr1,
9506 __isl_take isl_ast_expr *expr2);
9507 __isl_give isl_ast_expr *isl_ast_expr_sub(
9508 __isl_take isl_ast_expr *expr1,
9509 __isl_take isl_ast_expr *expr2);
9510 __isl_give isl_ast_expr *isl_ast_expr_mul(
9511 __isl_take isl_ast_expr *expr1,
9512 __isl_take isl_ast_expr *expr2);
9513 __isl_give isl_ast_expr *isl_ast_expr_div(
9514 __isl_take isl_ast_expr *expr1,
9515 __isl_take isl_ast_expr *expr2);
9516 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9517 __isl_take isl_ast_expr *expr1,
9518 __isl_take isl_ast_expr *expr2);
9519 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9520 __isl_take isl_ast_expr *expr1,
9521 __isl_take isl_ast_expr *expr2);
9522 __isl_give isl_ast_expr *isl_ast_expr_and(
9523 __isl_take isl_ast_expr *expr1,
9524 __isl_take isl_ast_expr *expr2)
9525 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9526 __isl_take isl_ast_expr *expr1,
9527 __isl_take isl_ast_expr *expr2)
9528 __isl_give isl_ast_expr *isl_ast_expr_or(
9529 __isl_take isl_ast_expr *expr1,
9530 __isl_take isl_ast_expr *expr2)
9531 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9532 __isl_take isl_ast_expr *expr1,
9533 __isl_take isl_ast_expr *expr2)
9534 __isl_give isl_ast_expr *isl_ast_expr_eq(
9535 __isl_take isl_ast_expr *expr1,
9536 __isl_take isl_ast_expr *expr2);
9537 __isl_give isl_ast_expr *isl_ast_expr_le(
9538 __isl_take isl_ast_expr *expr1,
9539 __isl_take isl_ast_expr *expr2);
9540 __isl_give isl_ast_expr *isl_ast_expr_lt(
9541 __isl_take isl_ast_expr *expr1,
9542 __isl_take isl_ast_expr *expr2);
9543 __isl_give isl_ast_expr *isl_ast_expr_ge(
9544 __isl_take isl_ast_expr *expr1,
9545 __isl_take isl_ast_expr *expr2);
9546 __isl_give isl_ast_expr *isl_ast_expr_gt(
9547 __isl_take isl_ast_expr *expr1,
9548 __isl_take isl_ast_expr *expr2);
9549 __isl_give isl_ast_expr *isl_ast_expr_access(
9550 __isl_take isl_ast_expr *array,
9551 __isl_take isl_ast_expr_list *indices);
9552 __isl_give isl_ast_expr *isl_ast_expr_call(
9553 __isl_take isl_ast_expr *function,
9554 __isl_take isl_ast_expr_list *arguments);
9556 The function C<isl_ast_expr_address_of> can be applied to an
9557 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9558 to represent the address of the C<isl_ast_expr_access>. The function
9559 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9560 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9562 #include <isl/ast_build.h>
9563 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9564 __isl_keep isl_ast_build *build,
9565 __isl_take isl_set *set);
9566 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9567 __isl_keep isl_ast_build *build,
9568 __isl_take isl_pw_aff *pa);
9569 __isl_give isl_ast_expr *
9570 isl_ast_build_access_from_pw_multi_aff(
9571 __isl_keep isl_ast_build *build,
9572 __isl_take isl_pw_multi_aff *pma);
9573 __isl_give isl_ast_expr *
9574 isl_ast_build_access_from_multi_pw_aff(
9575 __isl_keep isl_ast_build *build,
9576 __isl_take isl_multi_pw_aff *mpa);
9577 __isl_give isl_ast_expr *
9578 isl_ast_build_call_from_pw_multi_aff(
9579 __isl_keep isl_ast_build *build,
9580 __isl_take isl_pw_multi_aff *pma);
9581 __isl_give isl_ast_expr *
9582 isl_ast_build_call_from_multi_pw_aff(
9583 __isl_keep isl_ast_build *build,
9584 __isl_take isl_multi_pw_aff *mpa);
9587 the domains of C<pa>, C<mpa> and C<pma> should correspond
9588 to the schedule space of C<build>.
9589 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9590 the function being called.
9591 If the accessed space is a nested relation, then it is taken
9592 to represent an access of the member specified by the range
9593 of this nested relation of the structure specified by the domain
9594 of the nested relation.
9596 The following functions can be used to modify an C<isl_ast_expr>.
9598 #include <isl/ast.h>
9599 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9600 __isl_take isl_ast_expr *expr, int pos,
9601 __isl_take isl_ast_expr *arg);
9603 Replace the argument of C<expr> at position C<pos> by C<arg>.
9605 #include <isl/ast.h>
9606 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9607 __isl_take isl_ast_expr *expr,
9608 __isl_take isl_id_to_ast_expr *id2expr);
9610 The function C<isl_ast_expr_substitute_ids> replaces the
9611 subexpressions of C<expr> of type C<isl_ast_expr_id>
9612 by the corresponding expression in C<id2expr>, if there is any.
9615 User specified data can be attached to an C<isl_ast_node> and obtained
9616 from the same C<isl_ast_node> using the following functions.
9618 #include <isl/ast.h>
9619 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9620 __isl_take isl_ast_node *node,
9621 __isl_take isl_id *annotation);
9622 __isl_give isl_id *isl_ast_node_get_annotation(
9623 __isl_keep isl_ast_node *node);
9625 Basic printing can be performed using the following functions.
9627 #include <isl/ast.h>
9628 __isl_give isl_printer *isl_printer_print_ast_expr(
9629 __isl_take isl_printer *p,
9630 __isl_keep isl_ast_expr *expr);
9631 __isl_give isl_printer *isl_printer_print_ast_node(
9632 __isl_take isl_printer *p,
9633 __isl_keep isl_ast_node *node);
9634 __isl_give char *isl_ast_expr_to_str(
9635 __isl_keep isl_ast_expr *expr);
9637 More advanced printing can be performed using the following functions.
9639 #include <isl/ast.h>
9640 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9641 __isl_take isl_printer *p,
9642 enum isl_ast_op_type type,
9643 __isl_keep const char *name);
9644 isl_stat isl_options_set_ast_print_macro_once(
9645 isl_ctx *ctx, int val);
9646 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9647 __isl_give isl_printer *isl_ast_op_type_print_macro(
9648 enum isl_ast_op_type type,
9649 __isl_take isl_printer *p);
9650 __isl_give isl_printer *isl_ast_expr_print_macros(
9651 __isl_keep isl_ast_expr *expr,
9652 __isl_take isl_printer *p);
9653 __isl_give isl_printer *isl_ast_node_print_macros(
9654 __isl_keep isl_ast_node *node,
9655 __isl_take isl_printer *p);
9656 __isl_give isl_printer *isl_ast_node_print(
9657 __isl_keep isl_ast_node *node,
9658 __isl_take isl_printer *p,
9659 __isl_take isl_ast_print_options *options);
9660 __isl_give isl_printer *isl_ast_node_for_print(
9661 __isl_keep isl_ast_node *node,
9662 __isl_take isl_printer *p,
9663 __isl_take isl_ast_print_options *options);
9664 __isl_give isl_printer *isl_ast_node_if_print(
9665 __isl_keep isl_ast_node *node,
9666 __isl_take isl_printer *p,
9667 __isl_take isl_ast_print_options *options);
9669 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9670 C<isl> may print out an AST that makes use of macros such
9671 as C<floord>, C<min> and C<max>.
9672 The names of these macros may be modified by a call
9673 to C<isl_ast_op_type_set_print_name>. The user-specified
9674 names are associated to the printer object.
9675 C<isl_ast_op_type_print_macro> prints out the macro
9676 corresponding to a specific C<isl_ast_op_type>.
9677 If the print-macro-once option is set, then a given macro definition
9678 is only printed once to any given printer object.
9679 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9680 for subexpressions where these macros would be used and prints
9681 out the required macro definitions.
9682 Essentially, C<isl_ast_expr_print_macros> calls
9683 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9684 as function argument.
9685 C<isl_ast_node_print_macros> does the same
9686 for expressions in its C<isl_ast_node> argument.
9687 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9688 C<isl_ast_node_if_print> print an C<isl_ast_node>
9689 in C<ISL_FORMAT_C>, but allow for some extra control
9690 through an C<isl_ast_print_options> object.
9691 This object can be created using the following functions.
9693 #include <isl/ast.h>
9694 __isl_give isl_ast_print_options *
9695 isl_ast_print_options_alloc(isl_ctx *ctx);
9696 __isl_give isl_ast_print_options *
9697 isl_ast_print_options_copy(
9698 __isl_keep isl_ast_print_options *options);
9699 __isl_null isl_ast_print_options *
9700 isl_ast_print_options_free(
9701 __isl_take isl_ast_print_options *options);
9703 __isl_give isl_ast_print_options *
9704 isl_ast_print_options_set_print_user(
9705 __isl_take isl_ast_print_options *options,
9706 __isl_give isl_printer *(*print_user)(
9707 __isl_take isl_printer *p,
9708 __isl_take isl_ast_print_options *options,
9709 __isl_keep isl_ast_node *node, void *user),
9711 __isl_give isl_ast_print_options *
9712 isl_ast_print_options_set_print_for(
9713 __isl_take isl_ast_print_options *options,
9714 __isl_give isl_printer *(*print_for)(
9715 __isl_take isl_printer *p,
9716 __isl_take isl_ast_print_options *options,
9717 __isl_keep isl_ast_node *node, void *user),
9720 The callback set by C<isl_ast_print_options_set_print_user>
9721 is called whenever a node of type C<isl_ast_node_user> needs to
9723 The callback set by C<isl_ast_print_options_set_print_for>
9724 is called whenever a node of type C<isl_ast_node_for> needs to
9726 Note that C<isl_ast_node_for_print> will I<not> call the
9727 callback set by C<isl_ast_print_options_set_print_for> on the node
9728 on which C<isl_ast_node_for_print> is called, but only on nested
9729 nodes of type C<isl_ast_node_for>. It is therefore safe to
9730 call C<isl_ast_node_for_print> from within the callback set by
9731 C<isl_ast_print_options_set_print_for>.
9733 The following option determines the type to be used for iterators
9734 while printing the AST.
9736 isl_stat isl_options_set_ast_iterator_type(
9737 isl_ctx *ctx, const char *val);
9738 const char *isl_options_get_ast_iterator_type(
9741 The AST printer only prints body nodes as blocks if these
9742 blocks cannot be safely omitted.
9743 For example, a C<for> node with one body node will not be
9744 surrounded with braces in C<ISL_FORMAT_C>.
9745 A block will always be printed by setting the following option.
9747 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9749 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9753 #include <isl/ast_build.h>
9754 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9755 isl_ctx *ctx, int val);
9756 int isl_options_get_ast_build_atomic_upper_bound(
9758 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9760 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9761 isl_stat isl_options_set_ast_build_detect_min_max(
9762 isl_ctx *ctx, int val);
9763 int isl_options_get_ast_build_detect_min_max(
9765 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9766 isl_ctx *ctx, int val);
9767 int isl_options_get_ast_build_exploit_nested_bounds(
9769 isl_stat isl_options_set_ast_build_group_coscheduled(
9770 isl_ctx *ctx, int val);
9771 int isl_options_get_ast_build_group_coscheduled(
9773 isl_stat isl_options_set_ast_build_scale_strides(
9774 isl_ctx *ctx, int val);
9775 int isl_options_get_ast_build_scale_strides(
9777 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9779 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9780 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9782 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9786 =item * ast_build_atomic_upper_bound
9788 Generate loop upper bounds that consist of the current loop iterator,
9789 an operator and an expression not involving the iterator.
9790 If this option is not set, then the current loop iterator may appear
9791 several times in the upper bound.
9792 For example, when this option is turned off, AST generation
9795 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9799 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9802 When the option is turned on, the following AST is generated
9804 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9807 =item * ast_build_prefer_pdiv
9809 If this option is turned off, then the AST generation will
9810 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9811 operators, but no C<isl_ast_op_pdiv_q> or
9812 C<isl_ast_op_pdiv_r> operators.
9813 If this option is turned on, then C<isl> will try to convert
9814 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9815 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9817 =item * ast_build_detect_min_max
9819 If this option is turned on, then C<isl> will try and detect
9820 min or max-expressions when building AST expressions from
9821 piecewise affine expressions.
9823 =item * ast_build_exploit_nested_bounds
9825 Simplify conditions based on bounds of nested for loops.
9826 In particular, remove conditions that are implied by the fact
9827 that one or more nested loops have at least one iteration,
9828 meaning that the upper bound is at least as large as the lower bound.
9829 For example, when this option is turned off, AST generation
9832 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
9838 for (int c0 = 0; c0 <= N; c0 += 1)
9839 for (int c1 = 0; c1 <= M; c1 += 1)
9842 When the option is turned on, the following AST is generated
9844 for (int c0 = 0; c0 <= N; c0 += 1)
9845 for (int c1 = 0; c1 <= M; c1 += 1)
9848 =item * ast_build_group_coscheduled
9850 If two domain elements are assigned the same schedule point, then
9851 they may be executed in any order and they may even appear in different
9852 loops. If this options is set, then the AST generator will make
9853 sure that coscheduled domain elements do not appear in separate parts
9854 of the AST. This is useful in case of nested AST generation
9855 if the outer AST generation is given only part of a schedule
9856 and the inner AST generation should handle the domains that are
9857 coscheduled by this initial part of the schedule together.
9858 For example if an AST is generated for a schedule
9860 { A[i] -> [0]; B[i] -> [0] }
9862 then the C<isl_ast_build_set_create_leaf> callback described
9863 below may get called twice, once for each domain.
9864 Setting this option ensures that the callback is only called once
9865 on both domains together.
9867 =item * ast_build_separation_bounds
9869 This option specifies which bounds to use during separation.
9870 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
9871 then all (possibly implicit) bounds on the current dimension will
9872 be used during separation.
9873 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
9874 then only those bounds that are explicitly available will
9875 be used during separation.
9877 =item * ast_build_scale_strides
9879 This option specifies whether the AST generator is allowed
9880 to scale down iterators of strided loops.
9882 =item * ast_build_allow_else
9884 This option specifies whether the AST generator is allowed
9885 to construct if statements with else branches.
9887 =item * ast_build_allow_or
9889 This option specifies whether the AST generator is allowed
9890 to construct if conditions with disjunctions.
9894 =head3 AST Generation Options (Schedule Tree)
9896 In case of AST construction from a schedule tree, the options
9897 that control how an AST is created from the individual schedule
9898 dimensions are stored in the band nodes of the tree
9899 (see L</"Schedule Trees">).
9901 In particular, a schedule dimension can be handled in four
9902 different ways, atomic, separate, unroll or the default.
9903 This loop AST generation type can be set using
9904 C<isl_schedule_node_band_member_set_ast_loop_type>.
9906 the first three can be selected by including a one-dimensional
9907 element with as value the position of the schedule dimension
9908 within the band and as name one of C<atomic>, C<separate>
9909 or C<unroll> in the options
9910 set by C<isl_schedule_node_band_set_ast_build_options>.
9911 Only one of these three may be specified for
9912 any given schedule dimension within a band node.
9913 If none of these is specified, then the default
9914 is used. The meaning of the options is as follows.
9920 When this option is specified, the AST generator will make
9921 sure that a given domains space only appears in a single
9922 loop at the specified level.
9924 For example, for the schedule tree
9926 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9928 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9929 options: "{ atomic[x] }"
9931 the following AST will be generated
9933 for (int c0 = 0; c0 <= 10; c0 += 1) {
9940 On the other hand, for the schedule tree
9942 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9944 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9945 options: "{ separate[x] }"
9947 the following AST will be generated
9951 for (int c0 = 1; c0 <= 9; c0 += 1) {
9958 If neither C<atomic> nor C<separate> is specified, then the AST generator
9959 may produce either of these two results or some intermediate form.
9963 When this option is specified, the AST generator will
9964 split the domain of the specified schedule dimension
9965 into pieces with a fixed set of statements for which
9966 instances need to be executed by the iterations in
9967 the schedule domain part. This option tends to avoid
9968 the generation of guards inside the corresponding loops.
9969 See also the C<atomic> option.
9973 When this option is specified, the AST generator will
9974 I<completely> unroll the corresponding schedule dimension.
9975 It is the responsibility of the user to ensure that such
9976 unrolling is possible.
9977 To obtain a partial unrolling, the user should apply an additional
9978 strip-mining to the schedule and fully unroll the inner schedule
9983 The C<isolate> option is a bit more involved. It allows the user
9984 to isolate a range of schedule dimension values from smaller and
9985 greater values. Additionally, the user may specify a different
9986 atomic/separate/unroll choice for the isolated part and the remaining
9987 parts. The typical use case of the C<isolate> option is to isolate
9988 full tiles from partial tiles.
9989 The part that needs to be isolated may depend on outer schedule dimensions.
9990 The option therefore needs to be able to reference those outer schedule
9991 dimensions. In particular, the space of the C<isolate> option is that
9992 of a wrapped map with as domain the flat product of all outer band nodes
9993 and as range the space of the current band node.
9994 The atomic/separate/unroll choice for the isolated part is determined
9995 by an option that lives in an unnamed wrapped space with as domain
9996 a zero-dimensional C<isolate> space and as range the regular
9997 C<atomic>, C<separate> or C<unroll> space.
9998 This option may also be set directly using
9999 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10000 The atomic/separate/unroll choice for the remaining part is determined
10001 by the regular C<atomic>, C<separate> or C<unroll> option.
10002 The use of the C<isolate> option causes any tree containing the node
10003 to be considered anchored.
10005 As an example, consider the isolation of full tiles from partial tiles
10006 in a tiling of a triangular domain. The original schedule is as follows.
10008 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10010 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10011 { A[i,j] -> [floor(j/10)] }, \
10012 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10016 for (int c0 = 0; c0 <= 10; c0 += 1)
10017 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10018 for (int c2 = 10 * c0;
10019 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10020 for (int c3 = 10 * c1;
10021 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10024 Isolating the full tiles, we have the following input
10026 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10028 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10029 { A[i,j] -> [floor(j/10)] }, \
10030 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10031 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10032 10a+9+10b+9 <= 100 }"
10037 for (int c0 = 0; c0 <= 8; c0 += 1) {
10038 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10039 for (int c2 = 10 * c0;
10040 c2 <= 10 * c0 + 9; c2 += 1)
10041 for (int c3 = 10 * c1;
10042 c3 <= 10 * c1 + 9; c3 += 1)
10044 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10045 for (int c2 = 10 * c0;
10046 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10047 for (int c3 = 10 * c1;
10048 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10051 for (int c0 = 9; c0 <= 10; c0 += 1)
10052 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10053 for (int c2 = 10 * c0;
10054 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10055 for (int c3 = 10 * c1;
10056 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10060 We may then additionally unroll the innermost loop of the isolated part
10062 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10064 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10065 { A[i,j] -> [floor(j/10)] }, \
10066 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10067 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10068 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10073 for (int c0 = 0; c0 <= 8; c0 += 1) {
10074 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10075 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10077 A(c2, 10 * c1 + 1);
10078 A(c2, 10 * c1 + 2);
10079 A(c2, 10 * c1 + 3);
10080 A(c2, 10 * c1 + 4);
10081 A(c2, 10 * c1 + 5);
10082 A(c2, 10 * c1 + 6);
10083 A(c2, 10 * c1 + 7);
10084 A(c2, 10 * c1 + 8);
10085 A(c2, 10 * c1 + 9);
10087 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10088 for (int c2 = 10 * c0;
10089 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10090 for (int c3 = 10 * c1;
10091 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10094 for (int c0 = 9; c0 <= 10; c0 += 1)
10095 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10096 for (int c2 = 10 * c0;
10097 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10098 for (int c3 = 10 * c1;
10099 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10104 =head3 AST Generation Options (Schedule Map)
10106 In case of AST construction using
10107 C<isl_ast_build_node_from_schedule_map>, the options
10108 that control how an AST is created from the individual schedule
10109 dimensions are stored in the C<isl_ast_build>.
10110 They can be set using the following function.
10112 #include <isl/ast_build.h>
10113 __isl_give isl_ast_build *
10114 isl_ast_build_set_options(
10115 __isl_take isl_ast_build *control,
10116 __isl_take isl_union_map *options);
10118 The options are encoded in an C<isl_union_map>.
10119 The domain of this union relation refers to the schedule domain,
10120 i.e., the range of the schedule passed
10121 to C<isl_ast_build_node_from_schedule_map>.
10122 In the case of nested AST generation (see L</"Nested AST Generation">),
10123 the domain of C<options> should refer to the extra piece of the schedule.
10124 That is, it should be equal to the range of the wrapped relation in the
10125 range of the schedule.
10126 The range of the options can consist of elements in one or more spaces,
10127 the names of which determine the effect of the option.
10128 The values of the range typically also refer to the schedule dimension
10129 to which the option applies. In case of nested AST generation
10130 (see L</"Nested AST Generation">), these values refer to the position
10131 of the schedule dimension within the innermost AST generation.
10132 The constraints on the domain elements of
10133 the option should only refer to this dimension and earlier dimensions.
10134 We consider the following spaces.
10138 =item C<separation_class>
10140 B<This option has been deprecated. Use the isolate option on
10141 schedule trees instead.>
10143 This space is a wrapped relation between two one dimensional spaces.
10144 The input space represents the schedule dimension to which the option
10145 applies and the output space represents the separation class.
10146 While constructing a loop corresponding to the specified schedule
10147 dimension(s), the AST generator will try to generate separate loops
10148 for domain elements that are assigned different classes.
10149 If only some of the elements are assigned a class, then those elements
10150 that are not assigned any class will be treated as belonging to a class
10151 that is separate from the explicitly assigned classes.
10152 The typical use case for this option is to separate full tiles from
10154 The other options, described below, are applied after the separation
10157 As an example, consider the separation into full and partial tiles
10158 of a tiling of a triangular domain.
10159 Take, for example, the domain
10161 { A[i,j] : 0 <= i,j and i + j <= 100 }
10163 and a tiling into tiles of 10 by 10. The input to the AST generator
10164 is then the schedule
10166 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10169 Without any options, the following AST is generated
10171 for (int c0 = 0; c0 <= 10; c0 += 1)
10172 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10173 for (int c2 = 10 * c0;
10174 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10176 for (int c3 = 10 * c1;
10177 c3 <= min(10 * c1 + 9, -c2 + 100);
10181 Separation into full and partial tiles can be obtained by assigning
10182 a class, say C<0>, to the full tiles. The full tiles are represented by those
10183 values of the first and second schedule dimensions for which there are
10184 values of the third and fourth dimensions to cover an entire tile.
10185 That is, we need to specify the following option
10187 { [a,b,c,d] -> separation_class[[0]->[0]] :
10188 exists b': 0 <= 10a,10b' and
10189 10a+9+10b'+9 <= 100;
10190 [a,b,c,d] -> separation_class[[1]->[0]] :
10191 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10193 which simplifies to
10195 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10196 a >= 0 and b >= 0 and b <= 8 - a;
10197 [a, b, c, d] -> separation_class[[0] -> [0]] :
10198 a >= 0 and a <= 8 }
10200 With this option, the generated AST is as follows
10203 for (int c0 = 0; c0 <= 8; c0 += 1) {
10204 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10205 for (int c2 = 10 * c0;
10206 c2 <= 10 * c0 + 9; c2 += 1)
10207 for (int c3 = 10 * c1;
10208 c3 <= 10 * c1 + 9; c3 += 1)
10210 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10211 for (int c2 = 10 * c0;
10212 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10214 for (int c3 = 10 * c1;
10215 c3 <= min(-c2 + 100, 10 * c1 + 9);
10219 for (int c0 = 9; c0 <= 10; c0 += 1)
10220 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10221 for (int c2 = 10 * c0;
10222 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10224 for (int c3 = 10 * c1;
10225 c3 <= min(10 * c1 + 9, -c2 + 100);
10232 This is a single-dimensional space representing the schedule dimension(s)
10233 to which ``separation'' should be applied. Separation tries to split
10234 a loop into several pieces if this can avoid the generation of guards
10236 See also the C<atomic> option.
10240 This is a single-dimensional space representing the schedule dimension(s)
10241 for which the domains should be considered ``atomic''. That is, the
10242 AST generator will make sure that any given domain space will only appear
10243 in a single loop at the specified level.
10245 Consider the following schedule
10247 { a[i] -> [i] : 0 <= i < 10;
10248 b[i] -> [i+1] : 0 <= i < 10 }
10250 If the following option is specified
10252 { [i] -> separate[x] }
10254 then the following AST will be generated
10258 for (int c0 = 1; c0 <= 9; c0 += 1) {
10265 If, on the other hand, the following option is specified
10267 { [i] -> atomic[x] }
10269 then the following AST will be generated
10271 for (int c0 = 0; c0 <= 10; c0 += 1) {
10278 If neither C<atomic> nor C<separate> is specified, then the AST generator
10279 may produce either of these two results or some intermediate form.
10283 This is a single-dimensional space representing the schedule dimension(s)
10284 that should be I<completely> unrolled.
10285 To obtain a partial unrolling, the user should apply an additional
10286 strip-mining to the schedule and fully unroll the inner loop.
10290 =head3 Fine-grained Control over AST Generation
10292 Besides specifying the constraints on the parameters,
10293 an C<isl_ast_build> object can be used to control
10294 various aspects of the AST generation process.
10295 In case of AST construction using
10296 C<isl_ast_build_node_from_schedule_map>,
10297 the most prominent way of control is through ``options'',
10298 as explained above.
10300 Additional control is available through the following functions.
10302 #include <isl/ast_build.h>
10303 __isl_give isl_ast_build *
10304 isl_ast_build_set_iterators(
10305 __isl_take isl_ast_build *control,
10306 __isl_take isl_id_list *iterators);
10308 The function C<isl_ast_build_set_iterators> allows the user to
10309 specify a list of iterator C<isl_id>s to be used as iterators.
10310 If the input schedule is injective, then
10311 the number of elements in this list should be as large as the dimension
10312 of the schedule space, but no direct correspondence should be assumed
10313 between dimensions and elements.
10314 If the input schedule is not injective, then an additional number
10315 of C<isl_id>s equal to the largest dimension of the input domains
10317 If the number of provided C<isl_id>s is insufficient, then additional
10318 names are automatically generated.
10320 #include <isl/ast_build.h>
10321 __isl_give isl_ast_build *
10322 isl_ast_build_set_create_leaf(
10323 __isl_take isl_ast_build *control,
10324 __isl_give isl_ast_node *(*fn)(
10325 __isl_take isl_ast_build *build,
10326 void *user), void *user);
10329 C<isl_ast_build_set_create_leaf> function allows for the
10330 specification of a callback that should be called whenever the AST
10331 generator arrives at an element of the schedule domain.
10332 The callback should return an AST node that should be inserted
10333 at the corresponding position of the AST. The default action (when
10334 the callback is not set) is to continue generating parts of the AST to scan
10335 all the domain elements associated to the schedule domain element
10336 and to insert user nodes, ``calling'' the domain element, for each of them.
10337 The C<build> argument contains the current state of the C<isl_ast_build>.
10338 To ease nested AST generation (see L</"Nested AST Generation">),
10339 all control information that is
10340 specific to the current AST generation such as the options and
10341 the callbacks has been removed from this C<isl_ast_build>.
10342 The callback would typically return the result of a nested
10343 AST generation or a
10344 user defined node created using the following function.
10346 #include <isl/ast.h>
10347 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10348 __isl_take isl_ast_expr *expr);
10350 #include <isl/ast_build.h>
10351 __isl_give isl_ast_build *
10352 isl_ast_build_set_at_each_domain(
10353 __isl_take isl_ast_build *build,
10354 __isl_give isl_ast_node *(*fn)(
10355 __isl_take isl_ast_node *node,
10356 __isl_keep isl_ast_build *build,
10357 void *user), void *user);
10358 __isl_give isl_ast_build *
10359 isl_ast_build_set_before_each_for(
10360 __isl_take isl_ast_build *build,
10361 __isl_give isl_id *(*fn)(
10362 __isl_keep isl_ast_build *build,
10363 void *user), void *user);
10364 __isl_give isl_ast_build *
10365 isl_ast_build_set_after_each_for(
10366 __isl_take isl_ast_build *build,
10367 __isl_give isl_ast_node *(*fn)(
10368 __isl_take isl_ast_node *node,
10369 __isl_keep isl_ast_build *build,
10370 void *user), void *user);
10371 __isl_give isl_ast_build *
10372 isl_ast_build_set_before_each_mark(
10373 __isl_take isl_ast_build *build,
10374 isl_stat (*fn)(__isl_keep isl_id *mark,
10375 __isl_keep isl_ast_build *build,
10376 void *user), void *user);
10377 __isl_give isl_ast_build *
10378 isl_ast_build_set_after_each_mark(
10379 __isl_take isl_ast_build *build,
10380 __isl_give isl_ast_node *(*fn)(
10381 __isl_take isl_ast_node *node,
10382 __isl_keep isl_ast_build *build,
10383 void *user), void *user);
10385 The callback set by C<isl_ast_build_set_at_each_domain> will
10386 be called for each domain AST node.
10387 The callbacks set by C<isl_ast_build_set_before_each_for>
10388 and C<isl_ast_build_set_after_each_for> will be called
10389 for each for AST node. The first will be called in depth-first
10390 pre-order, while the second will be called in depth-first post-order.
10391 Since C<isl_ast_build_set_before_each_for> is called before the for
10392 node is actually constructed, it is only passed an C<isl_ast_build>.
10393 The returned C<isl_id> will be added as an annotation (using
10394 C<isl_ast_node_set_annotation>) to the constructed for node.
10395 In particular, if the user has also specified an C<after_each_for>
10396 callback, then the annotation can be retrieved from the node passed to
10397 that callback using C<isl_ast_node_get_annotation>.
10398 The callbacks set by C<isl_ast_build_set_before_each_mark>
10399 and C<isl_ast_build_set_after_each_mark> will be called for each
10400 mark AST node that is created, i.e., for each mark schedule node
10401 in the input schedule tree. The first will be called in depth-first
10402 pre-order, while the second will be called in depth-first post-order.
10403 Since the callback set by C<isl_ast_build_set_before_each_mark>
10404 is called before the mark AST node is actually constructed, it is passed
10405 the identifier of the mark node.
10406 All callbacks should C<NULL> (or -1) on failure.
10407 The given C<isl_ast_build> can be used to create new
10408 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10409 or C<isl_ast_build_call_from_pw_multi_aff>.
10411 =head3 Nested AST Generation
10413 C<isl> allows the user to create an AST within the context
10414 of another AST. These nested ASTs are created using the
10415 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10416 the outer AST. The C<build> argument should be an C<isl_ast_build>
10417 passed to a callback set by
10418 C<isl_ast_build_set_create_leaf>.
10419 The space of the range of the C<schedule> argument should refer
10420 to this build. In particular, the space should be a wrapped
10421 relation and the domain of this wrapped relation should be the
10422 same as that of the range of the schedule returned by
10423 C<isl_ast_build_get_schedule> below.
10424 In practice, the new schedule is typically
10425 created by calling C<isl_union_map_range_product> on the old schedule
10426 and some extra piece of the schedule.
10427 The space of the schedule domain is also available from
10428 the C<isl_ast_build>.
10430 #include <isl/ast_build.h>
10431 __isl_give isl_union_map *isl_ast_build_get_schedule(
10432 __isl_keep isl_ast_build *build);
10433 __isl_give isl_space *isl_ast_build_get_schedule_space(
10434 __isl_keep isl_ast_build *build);
10435 __isl_give isl_ast_build *isl_ast_build_restrict(
10436 __isl_take isl_ast_build *build,
10437 __isl_take isl_set *set);
10439 The C<isl_ast_build_get_schedule> function returns a (partial)
10440 schedule for the domains elements for which part of the AST still needs to
10441 be generated in the current build.
10442 In particular, the domain elements are mapped to those iterations of the loops
10443 enclosing the current point of the AST generation inside which
10444 the domain elements are executed.
10445 No direct correspondence between
10446 the input schedule and this schedule should be assumed.
10447 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10448 to create a set for C<isl_ast_build_restrict> to intersect
10449 with the current build. In particular, the set passed to
10450 C<isl_ast_build_restrict> can have additional parameters.
10451 The ids of the set dimensions in the space returned by
10452 C<isl_ast_build_get_schedule_space> correspond to the
10453 iterators of the already generated loops.
10454 The user should not rely on the ids of the output dimensions
10455 of the relations in the union relation returned by
10456 C<isl_ast_build_get_schedule> having any particular value.
10458 =head1 Applications
10460 Although C<isl> is mainly meant to be used as a library,
10461 it also contains some basic applications that use some
10462 of the functionality of C<isl>.
10463 The input may be specified in either the L<isl format>
10464 or the L<PolyLib format>.
10466 =head2 C<isl_polyhedron_sample>
10468 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10469 an integer element of the polyhedron, if there is any.
10470 The first column in the output is the denominator and is always
10471 equal to 1. If the polyhedron contains no integer points,
10472 then a vector of length zero is printed.
10476 C<isl_pip> takes the same input as the C<example> program
10477 from the C<piplib> distribution, i.e., a set of constraints
10478 on the parameters, a line containing only -1 and finally a set
10479 of constraints on a parametric polyhedron.
10480 The coefficients of the parameters appear in the last columns
10481 (but before the final constant column).
10482 The output is the lexicographic minimum of the parametric polyhedron.
10483 As C<isl> currently does not have its own output format, the output
10484 is just a dump of the internal state.
10486 =head2 C<isl_polyhedron_minimize>
10488 C<isl_polyhedron_minimize> computes the minimum of some linear
10489 or affine objective function over the integer points in a polyhedron.
10490 If an affine objective function
10491 is given, then the constant should appear in the last column.
10493 =head2 C<isl_polytope_scan>
10495 Given a polytope, C<isl_polytope_scan> prints
10496 all integer points in the polytope.
10498 =head2 C<isl_codegen>
10500 Given a schedule, a context set and an options relation,
10501 C<isl_codegen> prints out an AST that scans the domain elements
10502 of the schedule in the order of their image(s) taking into account
10503 the constraints in the context set.