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_multi_aff_to_str(
3686 __isl_keep isl_multi_aff *aff);
3687 __isl_give char *isl_union_pw_aff_to_str(
3688 __isl_keep isl_union_pw_aff *upa);
3689 __isl_give char *isl_union_pw_multi_aff_to_str(
3690 __isl_keep isl_union_pw_multi_aff *upma);
3691 __isl_give char *isl_multi_union_pw_aff_to_str(
3692 __isl_keep isl_multi_union_pw_aff *mupa);
3696 =head3 Unary Properties
3702 The following functions test whether the given set or relation
3703 contains any integer points. The ``plain'' variants do not perform
3704 any computations, but simply check if the given set or relation
3705 is already known to be empty.
3707 isl_bool isl_basic_set_plain_is_empty(
3708 __isl_keep isl_basic_set *bset);
3709 isl_bool isl_basic_set_is_empty(
3710 __isl_keep isl_basic_set *bset);
3711 isl_bool isl_set_plain_is_empty(
3712 __isl_keep isl_set *set);
3713 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3714 isl_bool isl_union_set_is_empty(
3715 __isl_keep isl_union_set *uset);
3716 isl_bool isl_basic_map_plain_is_empty(
3717 __isl_keep isl_basic_map *bmap);
3718 isl_bool isl_basic_map_is_empty(
3719 __isl_keep isl_basic_map *bmap);
3720 isl_bool isl_map_plain_is_empty(
3721 __isl_keep isl_map *map);
3722 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3723 isl_bool isl_union_map_is_empty(
3724 __isl_keep isl_union_map *umap);
3726 =item * Universality
3728 isl_bool isl_basic_set_plain_is_universe(
3729 __isl_keep isl_basic_set *bset);
3730 isl_bool isl_basic_set_is_universe(
3731 __isl_keep isl_basic_set *bset);
3732 isl_bool isl_basic_map_plain_is_universe(
3733 __isl_keep isl_basic_map *bmap);
3734 isl_bool isl_basic_map_is_universe(
3735 __isl_keep isl_basic_map *bmap);
3736 isl_bool isl_set_plain_is_universe(
3737 __isl_keep isl_set *set);
3738 isl_bool isl_map_plain_is_universe(
3739 __isl_keep isl_map *map);
3741 =item * Single-valuedness
3743 #include <isl/set.h>
3744 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3746 #include <isl/map.h>
3747 isl_bool isl_basic_map_is_single_valued(
3748 __isl_keep isl_basic_map *bmap);
3749 isl_bool isl_map_plain_is_single_valued(
3750 __isl_keep isl_map *map);
3751 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3753 #include <isl/union_map.h>
3754 isl_bool isl_union_map_is_single_valued(
3755 __isl_keep isl_union_map *umap);
3759 isl_bool isl_map_plain_is_injective(
3760 __isl_keep isl_map *map);
3761 isl_bool isl_map_is_injective(
3762 __isl_keep isl_map *map);
3763 isl_bool isl_union_map_plain_is_injective(
3764 __isl_keep isl_union_map *umap);
3765 isl_bool isl_union_map_is_injective(
3766 __isl_keep isl_union_map *umap);
3770 isl_bool isl_map_is_bijective(
3771 __isl_keep isl_map *map);
3772 isl_bool isl_union_map_is_bijective(
3773 __isl_keep isl_union_map *umap);
3777 The following functions test whether the given relation
3778 only maps elements to themselves.
3780 #include <isl/map.h>
3781 isl_bool isl_map_is_identity(
3782 __isl_keep isl_map *map);
3784 #include <isl/union_map.h>
3785 isl_bool isl_union_map_is_identity(
3786 __isl_keep isl_union_map *umap);
3790 __isl_give isl_val *
3791 isl_basic_map_plain_get_val_if_fixed(
3792 __isl_keep isl_basic_map *bmap,
3793 enum isl_dim_type type, unsigned pos);
3794 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3795 __isl_keep isl_set *set,
3796 enum isl_dim_type type, unsigned pos);
3797 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3798 __isl_keep isl_map *map,
3799 enum isl_dim_type type, unsigned pos);
3801 If the set or relation obviously lies on a hyperplane where the given dimension
3802 has a fixed value, then return that value.
3803 Otherwise return NaN.
3807 isl_stat isl_set_dim_residue_class_val(
3808 __isl_keep isl_set *set,
3809 int pos, __isl_give isl_val **modulo,
3810 __isl_give isl_val **residue);
3812 Check if the values of the given set dimension are equal to a fixed
3813 value modulo some integer value. If so, assign the modulo to C<*modulo>
3814 and the fixed value to C<*residue>. If the given dimension attains only
3815 a single value, then assign C<0> to C<*modulo> and the fixed value to
3817 If the dimension does not attain only a single value and if no modulo
3818 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3822 To check whether the description of a set, relation or function depends
3823 on one or more given dimensions,
3824 the following functions can be used.
3826 #include <isl/constraint.h>
3827 isl_bool isl_constraint_involves_dims(
3828 __isl_keep isl_constraint *constraint,
3829 enum isl_dim_type type, unsigned first, unsigned n);
3831 #include <isl/set.h>
3832 isl_bool isl_basic_set_involves_dims(
3833 __isl_keep isl_basic_set *bset,
3834 enum isl_dim_type type, unsigned first, unsigned n);
3835 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3836 enum isl_dim_type type, unsigned first, unsigned n);
3838 #include <isl/map.h>
3839 isl_bool isl_basic_map_involves_dims(
3840 __isl_keep isl_basic_map *bmap,
3841 enum isl_dim_type type, unsigned first, unsigned n);
3842 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3843 enum isl_dim_type type, unsigned first, unsigned n);
3845 #include <isl/union_map.h>
3846 isl_bool isl_union_map_involves_dims(
3847 __isl_keep isl_union_map *umap,
3848 enum isl_dim_type type, unsigned first, unsigned n);
3850 #include <isl/aff.h>
3851 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3852 enum isl_dim_type type, unsigned first, unsigned n);
3853 isl_bool isl_pw_aff_involves_dims(
3854 __isl_keep isl_pw_aff *pwaff,
3855 enum isl_dim_type type, unsigned first, unsigned n);
3856 isl_bool isl_multi_aff_involves_dims(
3857 __isl_keep isl_multi_aff *ma,
3858 enum isl_dim_type type, unsigned first, unsigned n);
3859 isl_bool isl_multi_pw_aff_involves_dims(
3860 __isl_keep isl_multi_pw_aff *mpa,
3861 enum isl_dim_type type, unsigned first, unsigned n);
3863 #include <isl/polynomial.h>
3864 isl_bool isl_qpolynomial_involves_dims(
3865 __isl_keep isl_qpolynomial *qp,
3866 enum isl_dim_type type, unsigned first, unsigned n);
3868 Similarly, the following functions can be used to check whether
3869 a given dimension is involved in any lower or upper bound.
3871 #include <isl/set.h>
3872 isl_bool isl_set_dim_has_any_lower_bound(
3873 __isl_keep isl_set *set,
3874 enum isl_dim_type type, unsigned pos);
3875 isl_bool isl_set_dim_has_any_upper_bound(
3876 __isl_keep isl_set *set,
3877 enum isl_dim_type type, unsigned pos);
3879 Note that these functions return true even if there is a bound on
3880 the dimension on only some of the basic sets of C<set>.
3881 To check if they have a bound for all of the basic sets in C<set>,
3882 use the following functions instead.
3884 #include <isl/set.h>
3885 isl_bool isl_set_dim_has_lower_bound(
3886 __isl_keep isl_set *set,
3887 enum isl_dim_type type, unsigned pos);
3888 isl_bool isl_set_dim_has_upper_bound(
3889 __isl_keep isl_set *set,
3890 enum isl_dim_type type, unsigned pos);
3894 To check whether a set is a parameter domain, use this function:
3896 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3897 isl_bool isl_union_set_is_params(
3898 __isl_keep isl_union_set *uset);
3902 The following functions check whether the space of the given
3903 (basic) set or relation range is a wrapped relation.
3905 #include <isl/space.h>
3906 isl_bool isl_space_is_wrapping(
3907 __isl_keep isl_space *space);
3908 isl_bool isl_space_domain_is_wrapping(
3909 __isl_keep isl_space *space);
3910 isl_bool isl_space_range_is_wrapping(
3911 __isl_keep isl_space *space);
3913 #include <isl/set.h>
3914 isl_bool isl_basic_set_is_wrapping(
3915 __isl_keep isl_basic_set *bset);
3916 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3918 #include <isl/map.h>
3919 isl_bool isl_map_domain_is_wrapping(
3920 __isl_keep isl_map *map);
3921 isl_bool isl_map_range_is_wrapping(
3922 __isl_keep isl_map *map);
3924 #include <isl/val.h>
3925 isl_bool isl_multi_val_range_is_wrapping(
3926 __isl_keep isl_multi_val *mv);
3928 #include <isl/aff.h>
3929 isl_bool isl_multi_aff_range_is_wrapping(
3930 __isl_keep isl_multi_aff *ma);
3931 isl_bool isl_multi_pw_aff_range_is_wrapping(
3932 __isl_keep isl_multi_pw_aff *mpa);
3933 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3934 __isl_keep isl_multi_union_pw_aff *mupa);
3936 The input to C<isl_space_is_wrapping> should
3937 be the space of a set, while that of
3938 C<isl_space_domain_is_wrapping> and
3939 C<isl_space_range_is_wrapping> should be the space of a relation.
3941 =item * Internal Product
3943 isl_bool isl_basic_map_can_zip(
3944 __isl_keep isl_basic_map *bmap);
3945 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
3947 Check whether the product of domain and range of the given relation
3949 i.e., whether both domain and range are nested relations.
3953 #include <isl/space.h>
3954 isl_bool isl_space_can_curry(
3955 __isl_keep isl_space *space);
3957 #include <isl/map.h>
3958 isl_bool isl_basic_map_can_curry(
3959 __isl_keep isl_basic_map *bmap);
3960 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
3962 Check whether the domain of the (basic) relation is a wrapped relation.
3964 #include <isl/space.h>
3965 __isl_give isl_space *isl_space_uncurry(
3966 __isl_take isl_space *space);
3968 #include <isl/map.h>
3969 isl_bool isl_basic_map_can_uncurry(
3970 __isl_keep isl_basic_map *bmap);
3971 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
3973 Check whether the range of the (basic) relation is a wrapped relation.
3975 #include <isl/space.h>
3976 isl_bool isl_space_can_range_curry(
3977 __isl_keep isl_space *space);
3979 #include <isl/map.h>
3980 isl_bool isl_map_can_range_curry(
3981 __isl_keep isl_map *map);
3983 Check whether the domain of the relation wrapped in the range of
3984 the input is itself a wrapped relation.
3986 =item * Special Values
3988 #include <isl/aff.h>
3989 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
3990 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3991 isl_bool isl_multi_pw_aff_is_cst(
3992 __isl_keep isl_multi_pw_aff *mpa);
3994 Check whether the given expression is a constant.
3996 #include <isl/aff.h>
3997 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
3998 isl_bool isl_pw_aff_involves_nan(
3999 __isl_keep isl_pw_aff *pa);
4001 #include <isl/polynomial.h>
4002 isl_bool isl_qpolynomial_fold_is_nan(
4003 __isl_keep isl_qpolynomial_fold *fold);
4005 Check whether the given expression is equal to or involves NaN.
4007 #include <isl/aff.h>
4008 isl_bool isl_aff_plain_is_zero(
4009 __isl_keep isl_aff *aff);
4011 Check whether the affine expression is obviously zero.
4015 =head3 Binary Properties
4021 The following functions check whether two objects
4022 represent the same set, relation or function.
4023 The C<plain> variants only return true if the objects
4024 are obviously the same. That is, they may return false
4025 even if the objects are the same, but they will never
4026 return true if the objects are not the same.
4028 #include <isl/set.h>
4029 isl_bool isl_basic_set_plain_is_equal(
4030 __isl_keep isl_basic_set *bset1,
4031 __isl_keep isl_basic_set *bset2);
4032 isl_bool isl_basic_set_is_equal(
4033 __isl_keep isl_basic_set *bset1,
4034 __isl_keep isl_basic_set *bset2);
4035 isl_bool isl_set_plain_is_equal(
4036 __isl_keep isl_set *set1,
4037 __isl_keep isl_set *set2);
4038 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4039 __isl_keep isl_set *set2);
4041 #include <isl/map.h>
4042 isl_bool isl_basic_map_is_equal(
4043 __isl_keep isl_basic_map *bmap1,
4044 __isl_keep isl_basic_map *bmap2);
4045 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4046 __isl_keep isl_map *map2);
4047 isl_bool isl_map_plain_is_equal(
4048 __isl_keep isl_map *map1,
4049 __isl_keep isl_map *map2);
4051 #include <isl/union_set.h>
4052 isl_bool isl_union_set_is_equal(
4053 __isl_keep isl_union_set *uset1,
4054 __isl_keep isl_union_set *uset2);
4056 #include <isl/union_map.h>
4057 isl_bool isl_union_map_is_equal(
4058 __isl_keep isl_union_map *umap1,
4059 __isl_keep isl_union_map *umap2);
4061 #include <isl/aff.h>
4062 isl_bool isl_aff_plain_is_equal(
4063 __isl_keep isl_aff *aff1,
4064 __isl_keep isl_aff *aff2);
4065 isl_bool isl_multi_aff_plain_is_equal(
4066 __isl_keep isl_multi_aff *maff1,
4067 __isl_keep isl_multi_aff *maff2);
4068 isl_bool isl_pw_aff_plain_is_equal(
4069 __isl_keep isl_pw_aff *pwaff1,
4070 __isl_keep isl_pw_aff *pwaff2);
4071 isl_bool isl_pw_multi_aff_plain_is_equal(
4072 __isl_keep isl_pw_multi_aff *pma1,
4073 __isl_keep isl_pw_multi_aff *pma2);
4074 isl_bool isl_multi_pw_aff_plain_is_equal(
4075 __isl_keep isl_multi_pw_aff *mpa1,
4076 __isl_keep isl_multi_pw_aff *mpa2);
4077 isl_bool isl_multi_pw_aff_is_equal(
4078 __isl_keep isl_multi_pw_aff *mpa1,
4079 __isl_keep isl_multi_pw_aff *mpa2);
4080 isl_bool isl_union_pw_aff_plain_is_equal(
4081 __isl_keep isl_union_pw_aff *upa1,
4082 __isl_keep isl_union_pw_aff *upa2);
4083 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4084 __isl_keep isl_union_pw_multi_aff *upma1,
4085 __isl_keep isl_union_pw_multi_aff *upma2);
4086 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4087 __isl_keep isl_multi_union_pw_aff *mupa1,
4088 __isl_keep isl_multi_union_pw_aff *mupa2);
4090 #include <isl/polynomial.h>
4091 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4092 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4093 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4094 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4095 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4096 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4098 =item * Disjointness
4100 #include <isl/set.h>
4101 isl_bool isl_basic_set_is_disjoint(
4102 __isl_keep isl_basic_set *bset1,
4103 __isl_keep isl_basic_set *bset2);
4104 isl_bool isl_set_plain_is_disjoint(
4105 __isl_keep isl_set *set1,
4106 __isl_keep isl_set *set2);
4107 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4108 __isl_keep isl_set *set2);
4110 #include <isl/map.h>
4111 isl_bool isl_basic_map_is_disjoint(
4112 __isl_keep isl_basic_map *bmap1,
4113 __isl_keep isl_basic_map *bmap2);
4114 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4115 __isl_keep isl_map *map2);
4117 #include <isl/union_set.h>
4118 isl_bool isl_union_set_is_disjoint(
4119 __isl_keep isl_union_set *uset1,
4120 __isl_keep isl_union_set *uset2);
4122 #include <isl/union_map.h>
4123 isl_bool isl_union_map_is_disjoint(
4124 __isl_keep isl_union_map *umap1,
4125 __isl_keep isl_union_map *umap2);
4129 isl_bool isl_basic_set_is_subset(
4130 __isl_keep isl_basic_set *bset1,
4131 __isl_keep isl_basic_set *bset2);
4132 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4133 __isl_keep isl_set *set2);
4134 isl_bool isl_set_is_strict_subset(
4135 __isl_keep isl_set *set1,
4136 __isl_keep isl_set *set2);
4137 isl_bool isl_union_set_is_subset(
4138 __isl_keep isl_union_set *uset1,
4139 __isl_keep isl_union_set *uset2);
4140 isl_bool isl_union_set_is_strict_subset(
4141 __isl_keep isl_union_set *uset1,
4142 __isl_keep isl_union_set *uset2);
4143 isl_bool isl_basic_map_is_subset(
4144 __isl_keep isl_basic_map *bmap1,
4145 __isl_keep isl_basic_map *bmap2);
4146 isl_bool isl_basic_map_is_strict_subset(
4147 __isl_keep isl_basic_map *bmap1,
4148 __isl_keep isl_basic_map *bmap2);
4149 isl_bool isl_map_is_subset(
4150 __isl_keep isl_map *map1,
4151 __isl_keep isl_map *map2);
4152 isl_bool isl_map_is_strict_subset(
4153 __isl_keep isl_map *map1,
4154 __isl_keep isl_map *map2);
4155 isl_bool isl_union_map_is_subset(
4156 __isl_keep isl_union_map *umap1,
4157 __isl_keep isl_union_map *umap2);
4158 isl_bool isl_union_map_is_strict_subset(
4159 __isl_keep isl_union_map *umap1,
4160 __isl_keep isl_union_map *umap2);
4162 Check whether the first argument is a (strict) subset of the
4167 Every comparison function returns a negative value if the first
4168 argument is considered smaller than the second, a positive value
4169 if the first argument is considered greater and zero if the two
4170 constraints are considered the same by the comparison criterion.
4172 #include <isl/constraint.h>
4173 int isl_constraint_plain_cmp(
4174 __isl_keep isl_constraint *c1,
4175 __isl_keep isl_constraint *c2);
4177 This function is useful for sorting C<isl_constraint>s.
4178 The order depends on the internal representation of the inputs.
4179 The order is fixed over different calls to the function (assuming
4180 the internal representation of the inputs has not changed), but may
4181 change over different versions of C<isl>.
4183 #include <isl/constraint.h>
4184 int isl_constraint_cmp_last_non_zero(
4185 __isl_keep isl_constraint *c1,
4186 __isl_keep isl_constraint *c2);
4188 This function can be used to sort constraints that live in the same
4189 local space. Constraints that involve ``earlier'' dimensions or
4190 that have a smaller coefficient for the shared latest dimension
4191 are considered smaller than other constraints.
4192 This function only defines a B<partial> order.
4194 #include <isl/set.h>
4195 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4196 __isl_keep isl_set *set2);
4198 This function is useful for sorting C<isl_set>s.
4199 The order depends on the internal representation of the inputs.
4200 The order is fixed over different calls to the function (assuming
4201 the internal representation of the inputs has not changed), but may
4202 change over different versions of C<isl>.
4204 #include <isl/aff.h>
4205 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4206 __isl_keep isl_pw_aff *pa2);
4208 The function C<isl_pw_aff_plain_cmp> can be used to sort
4209 C<isl_pw_aff>s. The order is not strictly defined.
4210 The current order sorts expressions that only involve
4211 earlier dimensions before those that involve later dimensions.
4215 =head2 Unary Operations
4221 __isl_give isl_set *isl_set_complement(
4222 __isl_take isl_set *set);
4223 __isl_give isl_map *isl_map_complement(
4224 __isl_take isl_map *map);
4228 #include <isl/space.h>
4229 __isl_give isl_space *isl_space_reverse(
4230 __isl_take isl_space *space);
4232 #include <isl/map.h>
4233 __isl_give isl_basic_map *isl_basic_map_reverse(
4234 __isl_take isl_basic_map *bmap);
4235 __isl_give isl_map *isl_map_reverse(
4236 __isl_take isl_map *map);
4238 #include <isl/union_map.h>
4239 __isl_give isl_union_map *isl_union_map_reverse(
4240 __isl_take isl_union_map *umap);
4244 #include <isl/space.h>
4245 __isl_give isl_space *isl_space_domain(
4246 __isl_take isl_space *space);
4247 __isl_give isl_space *isl_space_range(
4248 __isl_take isl_space *space);
4249 __isl_give isl_space *isl_space_params(
4250 __isl_take isl_space *space);
4252 #include <isl/local_space.h>
4253 __isl_give isl_local_space *isl_local_space_domain(
4254 __isl_take isl_local_space *ls);
4255 __isl_give isl_local_space *isl_local_space_range(
4256 __isl_take isl_local_space *ls);
4258 #include <isl/set.h>
4259 __isl_give isl_basic_set *isl_basic_set_project_out(
4260 __isl_take isl_basic_set *bset,
4261 enum isl_dim_type type, unsigned first, unsigned n);
4262 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4263 enum isl_dim_type type, unsigned first, unsigned n);
4264 __isl_give isl_basic_set *isl_basic_set_params(
4265 __isl_take isl_basic_set *bset);
4266 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4268 #include <isl/map.h>
4269 __isl_give isl_basic_map *isl_basic_map_project_out(
4270 __isl_take isl_basic_map *bmap,
4271 enum isl_dim_type type, unsigned first, unsigned n);
4272 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4273 enum isl_dim_type type, unsigned first, unsigned n);
4274 __isl_give isl_basic_set *isl_basic_map_domain(
4275 __isl_take isl_basic_map *bmap);
4276 __isl_give isl_basic_set *isl_basic_map_range(
4277 __isl_take isl_basic_map *bmap);
4278 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4279 __isl_give isl_set *isl_map_domain(
4280 __isl_take isl_map *bmap);
4281 __isl_give isl_set *isl_map_range(
4282 __isl_take isl_map *map);
4284 #include <isl/union_set.h>
4285 __isl_give isl_union_set *isl_union_set_project_out(
4286 __isl_take isl_union_set *uset,
4287 enum isl_dim_type type,
4288 unsigned first, unsigned n);
4289 __isl_give isl_set *isl_union_set_params(
4290 __isl_take isl_union_set *uset);
4292 The function C<isl_union_set_project_out> can only project out
4295 #include <isl/union_map.h>
4296 __isl_give isl_union_map *isl_union_map_project_out(
4297 __isl_take isl_union_map *umap,
4298 enum isl_dim_type type, unsigned first, unsigned n);
4299 __isl_give isl_set *isl_union_map_params(
4300 __isl_take isl_union_map *umap);
4301 __isl_give isl_union_set *isl_union_map_domain(
4302 __isl_take isl_union_map *umap);
4303 __isl_give isl_union_set *isl_union_map_range(
4304 __isl_take isl_union_map *umap);
4306 The function C<isl_union_map_project_out> can only project out
4309 #include <isl/aff.h>
4310 __isl_give isl_aff *isl_aff_project_domain_on_params(
4311 __isl_take isl_aff *aff);
4312 __isl_give isl_pw_multi_aff *
4313 isl_pw_multi_aff_project_domain_on_params(
4314 __isl_take isl_pw_multi_aff *pma);
4315 __isl_give isl_set *isl_pw_aff_domain(
4316 __isl_take isl_pw_aff *pwaff);
4317 __isl_give isl_set *isl_pw_multi_aff_domain(
4318 __isl_take isl_pw_multi_aff *pma);
4319 __isl_give isl_set *isl_multi_pw_aff_domain(
4320 __isl_take isl_multi_pw_aff *mpa);
4321 __isl_give isl_union_set *isl_union_pw_aff_domain(
4322 __isl_take isl_union_pw_aff *upa);
4323 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4324 __isl_take isl_union_pw_multi_aff *upma);
4325 __isl_give isl_union_set *
4326 isl_multi_union_pw_aff_domain(
4327 __isl_take isl_multi_union_pw_aff *mupa);
4328 __isl_give isl_set *isl_pw_aff_params(
4329 __isl_take isl_pw_aff *pwa);
4331 The function C<isl_multi_union_pw_aff_domain> requires its
4332 input to have at least one set dimension.
4334 #include <isl/polynomial.h>
4335 __isl_give isl_qpolynomial *
4336 isl_qpolynomial_project_domain_on_params(
4337 __isl_take isl_qpolynomial *qp);
4338 __isl_give isl_pw_qpolynomial *
4339 isl_pw_qpolynomial_project_domain_on_params(
4340 __isl_take isl_pw_qpolynomial *pwqp);
4341 __isl_give isl_pw_qpolynomial_fold *
4342 isl_pw_qpolynomial_fold_project_domain_on_params(
4343 __isl_take isl_pw_qpolynomial_fold *pwf);
4344 __isl_give isl_set *isl_pw_qpolynomial_domain(
4345 __isl_take isl_pw_qpolynomial *pwqp);
4346 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4347 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4348 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4349 __isl_take isl_union_pw_qpolynomial *upwqp);
4351 #include <isl/space.h>
4352 __isl_give isl_space *isl_space_domain_map(
4353 __isl_take isl_space *space);
4354 __isl_give isl_space *isl_space_range_map(
4355 __isl_take isl_space *space);
4357 #include <isl/map.h>
4358 __isl_give isl_map *isl_set_wrapped_domain_map(
4359 __isl_take isl_set *set);
4360 __isl_give isl_basic_map *isl_basic_map_domain_map(
4361 __isl_take isl_basic_map *bmap);
4362 __isl_give isl_basic_map *isl_basic_map_range_map(
4363 __isl_take isl_basic_map *bmap);
4364 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4365 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4367 #include <isl/union_map.h>
4368 __isl_give isl_union_map *isl_union_map_domain_map(
4369 __isl_take isl_union_map *umap);
4370 __isl_give isl_union_pw_multi_aff *
4371 isl_union_map_domain_map_union_pw_multi_aff(
4372 __isl_take isl_union_map *umap);
4373 __isl_give isl_union_map *isl_union_map_range_map(
4374 __isl_take isl_union_map *umap);
4375 __isl_give isl_union_map *
4376 isl_union_set_wrapped_domain_map(
4377 __isl_take isl_union_set *uset);
4379 The functions above construct a (basic, regular or union) relation
4380 that maps (a wrapped version of) the input relation to its domain or range.
4381 C<isl_set_wrapped_domain_map> maps the input set to the domain
4382 of its wrapped relation.
4386 __isl_give isl_basic_set *isl_basic_set_eliminate(
4387 __isl_take isl_basic_set *bset,
4388 enum isl_dim_type type,
4389 unsigned first, unsigned n);
4390 __isl_give isl_set *isl_set_eliminate(
4391 __isl_take isl_set *set, enum isl_dim_type type,
4392 unsigned first, unsigned n);
4393 __isl_give isl_basic_map *isl_basic_map_eliminate(
4394 __isl_take isl_basic_map *bmap,
4395 enum isl_dim_type type,
4396 unsigned first, unsigned n);
4397 __isl_give isl_map *isl_map_eliminate(
4398 __isl_take isl_map *map, enum isl_dim_type type,
4399 unsigned first, unsigned n);
4401 Eliminate the coefficients for the given dimensions from the constraints,
4402 without removing the dimensions.
4404 =item * Constructing a set from a parameter domain
4406 A zero-dimensional space or (basic) set can be constructed
4407 on a given parameter domain using the following functions.
4409 #include <isl/space.h>
4410 __isl_give isl_space *isl_space_set_from_params(
4411 __isl_take isl_space *space);
4413 #include <isl/set.h>
4414 __isl_give isl_basic_set *isl_basic_set_from_params(
4415 __isl_take isl_basic_set *bset);
4416 __isl_give isl_set *isl_set_from_params(
4417 __isl_take isl_set *set);
4419 =item * Constructing a relation from one or two sets
4421 Create a relation with the given set(s) as domain and/or range.
4422 If only the domain or the range is specified, then
4423 the range or domain of the created relation is a zero-dimensional
4424 flat anonymous space.
4426 #include <isl/space.h>
4427 __isl_give isl_space *isl_space_from_domain(
4428 __isl_take isl_space *space);
4429 __isl_give isl_space *isl_space_from_range(
4430 __isl_take isl_space *space);
4431 __isl_give isl_space *isl_space_map_from_set(
4432 __isl_take isl_space *space);
4433 __isl_give isl_space *isl_space_map_from_domain_and_range(
4434 __isl_take isl_space *domain,
4435 __isl_take isl_space *range);
4437 #include <isl/local_space.h>
4438 __isl_give isl_local_space *isl_local_space_from_domain(
4439 __isl_take isl_local_space *ls);
4441 #include <isl/map.h>
4442 __isl_give isl_map *isl_map_from_domain(
4443 __isl_take isl_set *set);
4444 __isl_give isl_map *isl_map_from_range(
4445 __isl_take isl_set *set);
4447 #include <isl/union_map.h>
4448 __isl_give isl_union_map *
4449 isl_union_map_from_domain_and_range(
4450 __isl_take isl_union_set *domain,
4451 __isl_take isl_union_set *range);
4453 #include <isl/val.h>
4454 __isl_give isl_multi_val *isl_multi_val_from_range(
4455 __isl_take isl_multi_val *mv);
4457 #include <isl/aff.h>
4458 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4459 __isl_take isl_multi_aff *ma);
4460 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4461 __isl_take isl_pw_aff *pwa);
4462 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4463 __isl_take isl_multi_pw_aff *mpa);
4464 __isl_give isl_multi_union_pw_aff *
4465 isl_multi_union_pw_aff_from_range(
4466 __isl_take isl_multi_union_pw_aff *mupa);
4467 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4468 __isl_take isl_set *set);
4469 __isl_give isl_union_pw_multi_aff *
4470 isl_union_pw_multi_aff_from_domain(
4471 __isl_take isl_union_set *uset);
4475 #include <isl/set.h>
4476 __isl_give isl_basic_set *isl_basic_set_fix_si(
4477 __isl_take isl_basic_set *bset,
4478 enum isl_dim_type type, unsigned pos, int value);
4479 __isl_give isl_basic_set *isl_basic_set_fix_val(
4480 __isl_take isl_basic_set *bset,
4481 enum isl_dim_type type, unsigned pos,
4482 __isl_take isl_val *v);
4483 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4484 enum isl_dim_type type, unsigned pos, int value);
4485 __isl_give isl_set *isl_set_fix_val(
4486 __isl_take isl_set *set,
4487 enum isl_dim_type type, unsigned pos,
4488 __isl_take isl_val *v);
4490 #include <isl/map.h>
4491 __isl_give isl_basic_map *isl_basic_map_fix_si(
4492 __isl_take isl_basic_map *bmap,
4493 enum isl_dim_type type, unsigned pos, int value);
4494 __isl_give isl_basic_map *isl_basic_map_fix_val(
4495 __isl_take isl_basic_map *bmap,
4496 enum isl_dim_type type, unsigned pos,
4497 __isl_take isl_val *v);
4498 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4499 enum isl_dim_type type, unsigned pos, int value);
4500 __isl_give isl_map *isl_map_fix_val(
4501 __isl_take isl_map *map,
4502 enum isl_dim_type type, unsigned pos,
4503 __isl_take isl_val *v);
4505 #include <isl/aff.h>
4506 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4507 __isl_take isl_pw_multi_aff *pma,
4508 enum isl_dim_type type, unsigned pos, int value);
4510 #include <isl/polynomial.h>
4511 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4512 __isl_take isl_pw_qpolynomial *pwqp,
4513 enum isl_dim_type type, unsigned n,
4514 __isl_take isl_val *v);
4516 Intersect the set, relation or function domain
4517 with the hyperplane where the given
4518 dimension has the fixed given value.
4520 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4521 __isl_take isl_basic_map *bmap,
4522 enum isl_dim_type type, unsigned pos, int value);
4523 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4524 __isl_take isl_basic_map *bmap,
4525 enum isl_dim_type type, unsigned pos, int value);
4526 __isl_give isl_set *isl_set_lower_bound_si(
4527 __isl_take isl_set *set,
4528 enum isl_dim_type type, unsigned pos, int value);
4529 __isl_give isl_set *isl_set_lower_bound_val(
4530 __isl_take isl_set *set,
4531 enum isl_dim_type type, unsigned pos,
4532 __isl_take isl_val *value);
4533 __isl_give isl_map *isl_map_lower_bound_si(
4534 __isl_take isl_map *map,
4535 enum isl_dim_type type, unsigned pos, int value);
4536 __isl_give isl_set *isl_set_upper_bound_si(
4537 __isl_take isl_set *set,
4538 enum isl_dim_type type, unsigned pos, int value);
4539 __isl_give isl_set *isl_set_upper_bound_val(
4540 __isl_take isl_set *set,
4541 enum isl_dim_type type, unsigned pos,
4542 __isl_take isl_val *value);
4543 __isl_give isl_map *isl_map_upper_bound_si(
4544 __isl_take isl_map *map,
4545 enum isl_dim_type type, unsigned pos, int value);
4547 Intersect the set or relation with the half-space where the given
4548 dimension has a value bounded by the fixed given integer value.
4550 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4551 enum isl_dim_type type1, int pos1,
4552 enum isl_dim_type type2, int pos2);
4553 __isl_give isl_basic_map *isl_basic_map_equate(
4554 __isl_take isl_basic_map *bmap,
4555 enum isl_dim_type type1, int pos1,
4556 enum isl_dim_type type2, int pos2);
4557 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4558 enum isl_dim_type type1, int pos1,
4559 enum isl_dim_type type2, int pos2);
4561 Intersect the set or relation with the hyperplane where the given
4562 dimensions are equal to each other.
4564 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4565 enum isl_dim_type type1, int pos1,
4566 enum isl_dim_type type2, int pos2);
4568 Intersect the relation with the hyperplane where the given
4569 dimensions have opposite values.
4571 __isl_give isl_map *isl_map_order_le(
4572 __isl_take isl_map *map,
4573 enum isl_dim_type type1, int pos1,
4574 enum isl_dim_type type2, int pos2);
4575 __isl_give isl_basic_map *isl_basic_map_order_ge(
4576 __isl_take isl_basic_map *bmap,
4577 enum isl_dim_type type1, int pos1,
4578 enum isl_dim_type type2, int pos2);
4579 __isl_give isl_map *isl_map_order_ge(
4580 __isl_take isl_map *map,
4581 enum isl_dim_type type1, int pos1,
4582 enum isl_dim_type type2, int pos2);
4583 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4584 enum isl_dim_type type1, int pos1,
4585 enum isl_dim_type type2, int pos2);
4586 __isl_give isl_basic_map *isl_basic_map_order_gt(
4587 __isl_take isl_basic_map *bmap,
4588 enum isl_dim_type type1, int pos1,
4589 enum isl_dim_type type2, int pos2);
4590 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4591 enum isl_dim_type type1, int pos1,
4592 enum isl_dim_type type2, int pos2);
4594 Intersect the relation with the half-space where the given
4595 dimensions satisfy the given ordering.
4599 #include <isl/aff.h>
4600 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4601 __isl_take isl_aff *aff);
4602 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4603 __isl_take isl_aff *aff);
4604 __isl_give isl_set *isl_pw_aff_pos_set(
4605 __isl_take isl_pw_aff *pa);
4606 __isl_give isl_set *isl_pw_aff_nonneg_set(
4607 __isl_take isl_pw_aff *pwaff);
4608 __isl_give isl_set *isl_pw_aff_zero_set(
4609 __isl_take isl_pw_aff *pwaff);
4610 __isl_give isl_set *isl_pw_aff_non_zero_set(
4611 __isl_take isl_pw_aff *pwaff);
4612 __isl_give isl_union_set *
4613 isl_union_pw_aff_zero_union_set(
4614 __isl_take isl_union_pw_aff *upa);
4615 __isl_give isl_union_set *
4616 isl_multi_union_pw_aff_zero_union_set(
4617 __isl_take isl_multi_union_pw_aff *mupa);
4619 The function C<isl_aff_neg_basic_set> returns a basic set
4620 containing those elements in the domain space
4621 of C<aff> where C<aff> is negative.
4622 The function C<isl_pw_aff_nonneg_set> returns a set
4623 containing those elements in the domain
4624 of C<pwaff> where C<pwaff> is non-negative.
4625 The function C<isl_multi_union_pw_aff_zero_union_set>
4626 returns a union set containing those elements
4627 in the domains of its elements where they are all zero.
4631 __isl_give isl_map *isl_set_identity(
4632 __isl_take isl_set *set);
4633 __isl_give isl_union_map *isl_union_set_identity(
4634 __isl_take isl_union_set *uset);
4635 __isl_give isl_union_pw_multi_aff *
4636 isl_union_set_identity_union_pw_multi_aff(
4637 __isl_take isl_union_set *uset);
4639 Construct an identity relation on the given (union) set.
4641 =item * Function Extraction
4643 A piecewise quasi affine expression that is equal to 1 on a set
4644 and 0 outside the set can be created using the following function.
4646 #include <isl/aff.h>
4647 __isl_give isl_pw_aff *isl_set_indicator_function(
4648 __isl_take isl_set *set);
4650 A piecewise multiple quasi affine expression can be extracted
4651 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4652 and the C<isl_map> is single-valued.
4653 In case of a conversion from an C<isl_union_map>
4654 to an C<isl_union_pw_multi_aff>, these properties need to hold
4655 in each domain space.
4656 A conversion to a C<isl_multi_union_pw_aff> additionally
4657 requires that the input is non-empty and involves only a single
4660 #include <isl/aff.h>
4661 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4662 __isl_take isl_set *set);
4663 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4664 __isl_take isl_map *map);
4666 __isl_give isl_union_pw_multi_aff *
4667 isl_union_pw_multi_aff_from_union_set(
4668 __isl_take isl_union_set *uset);
4669 __isl_give isl_union_pw_multi_aff *
4670 isl_union_pw_multi_aff_from_union_map(
4671 __isl_take isl_union_map *umap);
4673 __isl_give isl_multi_union_pw_aff *
4674 isl_multi_union_pw_aff_from_union_map(
4675 __isl_take isl_union_map *umap);
4679 __isl_give isl_basic_set *isl_basic_map_deltas(
4680 __isl_take isl_basic_map *bmap);
4681 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4682 __isl_give isl_union_set *isl_union_map_deltas(
4683 __isl_take isl_union_map *umap);
4685 These functions return a (basic) set containing the differences
4686 between image elements and corresponding domain elements in the input.
4688 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4689 __isl_take isl_basic_map *bmap);
4690 __isl_give isl_map *isl_map_deltas_map(
4691 __isl_take isl_map *map);
4692 __isl_give isl_union_map *isl_union_map_deltas_map(
4693 __isl_take isl_union_map *umap);
4695 The functions above construct a (basic, regular or union) relation
4696 that maps (a wrapped version of) the input relation to its delta set.
4700 Simplify the representation of a set, relation or functions by trying
4701 to combine pairs of basic sets or relations into a single
4702 basic set or relation.
4704 #include <isl/set.h>
4705 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4707 #include <isl/map.h>
4708 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4710 #include <isl/union_set.h>
4711 __isl_give isl_union_set *isl_union_set_coalesce(
4712 __isl_take isl_union_set *uset);
4714 #include <isl/union_map.h>
4715 __isl_give isl_union_map *isl_union_map_coalesce(
4716 __isl_take isl_union_map *umap);
4718 #include <isl/aff.h>
4719 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4720 __isl_take isl_pw_aff *pwqp);
4721 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4722 __isl_take isl_pw_multi_aff *pma);
4723 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4724 __isl_take isl_multi_pw_aff *mpa);
4725 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4726 __isl_take isl_union_pw_aff *upa);
4727 __isl_give isl_union_pw_multi_aff *
4728 isl_union_pw_multi_aff_coalesce(
4729 __isl_take isl_union_pw_multi_aff *upma);
4730 __isl_give isl_multi_union_pw_aff *
4731 isl_multi_union_pw_aff_coalesce(
4732 __isl_take isl_multi_union_pw_aff *aff);
4734 #include <isl/polynomial.h>
4735 __isl_give isl_pw_qpolynomial_fold *
4736 isl_pw_qpolynomial_fold_coalesce(
4737 __isl_take isl_pw_qpolynomial_fold *pwf);
4738 __isl_give isl_union_pw_qpolynomial *
4739 isl_union_pw_qpolynomial_coalesce(
4740 __isl_take isl_union_pw_qpolynomial *upwqp);
4741 __isl_give isl_union_pw_qpolynomial_fold *
4742 isl_union_pw_qpolynomial_fold_coalesce(
4743 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4745 One of the methods for combining pairs of basic sets or relations
4746 can result in coefficients that are much larger than those that appear
4747 in the constraints of the input. By default, the coefficients are
4748 not allowed to grow larger, but this can be changed by unsetting
4749 the following option.
4751 isl_stat isl_options_set_coalesce_bounded_wrapping(
4752 isl_ctx *ctx, int val);
4753 int isl_options_get_coalesce_bounded_wrapping(
4756 =item * Detecting equalities
4758 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4759 __isl_take isl_basic_set *bset);
4760 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4761 __isl_take isl_basic_map *bmap);
4762 __isl_give isl_set *isl_set_detect_equalities(
4763 __isl_take isl_set *set);
4764 __isl_give isl_map *isl_map_detect_equalities(
4765 __isl_take isl_map *map);
4766 __isl_give isl_union_set *isl_union_set_detect_equalities(
4767 __isl_take isl_union_set *uset);
4768 __isl_give isl_union_map *isl_union_map_detect_equalities(
4769 __isl_take isl_union_map *umap);
4771 Simplify the representation of a set or relation by detecting implicit
4774 =item * Removing redundant constraints
4776 #include <isl/set.h>
4777 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4778 __isl_take isl_basic_set *bset);
4779 __isl_give isl_set *isl_set_remove_redundancies(
4780 __isl_take isl_set *set);
4782 #include <isl/union_set.h>
4783 __isl_give isl_union_set *
4784 isl_union_set_remove_redundancies(
4785 __isl_take isl_union_set *uset);
4787 #include <isl/map.h>
4788 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4789 __isl_take isl_basic_map *bmap);
4790 __isl_give isl_map *isl_map_remove_redundancies(
4791 __isl_take isl_map *map);
4793 #include <isl/union_map.h>
4794 __isl_give isl_union_map *
4795 isl_union_map_remove_redundancies(
4796 __isl_take isl_union_map *umap);
4800 __isl_give isl_basic_set *isl_set_convex_hull(
4801 __isl_take isl_set *set);
4802 __isl_give isl_basic_map *isl_map_convex_hull(
4803 __isl_take isl_map *map);
4805 If the input set or relation has any existentially quantified
4806 variables, then the result of these operations is currently undefined.
4810 #include <isl/set.h>
4811 __isl_give isl_basic_set *
4812 isl_set_unshifted_simple_hull(
4813 __isl_take isl_set *set);
4814 __isl_give isl_basic_set *isl_set_simple_hull(
4815 __isl_take isl_set *set);
4816 __isl_give isl_basic_set *
4817 isl_set_unshifted_simple_hull_from_set_list(
4818 __isl_take isl_set *set,
4819 __isl_take isl_set_list *list);
4821 #include <isl/map.h>
4822 __isl_give isl_basic_map *
4823 isl_map_unshifted_simple_hull(
4824 __isl_take isl_map *map);
4825 __isl_give isl_basic_map *isl_map_simple_hull(
4826 __isl_take isl_map *map);
4827 __isl_give isl_basic_map *
4828 isl_map_unshifted_simple_hull_from_map_list(
4829 __isl_take isl_map *map,
4830 __isl_take isl_map_list *list);
4832 #include <isl/union_map.h>
4833 __isl_give isl_union_map *isl_union_map_simple_hull(
4834 __isl_take isl_union_map *umap);
4836 These functions compute a single basic set or relation
4837 that contains the whole input set or relation.
4838 In particular, the output is described by translates
4839 of the constraints describing the basic sets or relations in the input.
4840 In case of C<isl_set_unshifted_simple_hull>, only the original
4841 constraints are used, without any translation.
4842 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4843 C<isl_map_unshifted_simple_hull_from_map_list>, the
4844 constraints are taken from the elements of the second argument.
4848 (See \autoref{s:simple hull}.)
4854 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4855 __isl_take isl_basic_set *bset);
4856 __isl_give isl_basic_set *isl_set_affine_hull(
4857 __isl_take isl_set *set);
4858 __isl_give isl_union_set *isl_union_set_affine_hull(
4859 __isl_take isl_union_set *uset);
4860 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4861 __isl_take isl_basic_map *bmap);
4862 __isl_give isl_basic_map *isl_map_affine_hull(
4863 __isl_take isl_map *map);
4864 __isl_give isl_union_map *isl_union_map_affine_hull(
4865 __isl_take isl_union_map *umap);
4867 In case of union sets and relations, the affine hull is computed
4870 =item * Polyhedral hull
4872 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4873 __isl_take isl_set *set);
4874 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4875 __isl_take isl_map *map);
4876 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4877 __isl_take isl_union_set *uset);
4878 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4879 __isl_take isl_union_map *umap);
4881 These functions compute a single basic set or relation
4882 not involving any existentially quantified variables
4883 that contains the whole input set or relation.
4884 In case of union sets and relations, the polyhedral hull is computed
4887 =item * Other approximations
4889 #include <isl/set.h>
4890 __isl_give isl_basic_set *
4891 isl_basic_set_drop_constraints_involving_dims(
4892 __isl_take isl_basic_set *bset,
4893 enum isl_dim_type type,
4894 unsigned first, unsigned n);
4895 __isl_give isl_basic_set *
4896 isl_basic_set_drop_constraints_not_involving_dims(
4897 __isl_take isl_basic_set *bset,
4898 enum isl_dim_type type,
4899 unsigned first, unsigned n);
4900 __isl_give isl_set *
4901 isl_set_drop_constraints_involving_dims(
4902 __isl_take isl_set *set,
4903 enum isl_dim_type type,
4904 unsigned first, unsigned n);
4906 #include <isl/map.h>
4907 __isl_give isl_basic_map *
4908 isl_basic_map_drop_constraints_involving_dims(
4909 __isl_take isl_basic_map *bmap,
4910 enum isl_dim_type type,
4911 unsigned first, unsigned n);
4912 __isl_give isl_basic_map *
4913 isl_basic_map_drop_constraints_not_involving_dims(
4914 __isl_take isl_basic_map *bmap,
4915 enum isl_dim_type type,
4916 unsigned first, unsigned n);
4917 __isl_give isl_map *
4918 isl_map_drop_constraints_involving_dims(
4919 __isl_take isl_map *map,
4920 enum isl_dim_type type,
4921 unsigned first, unsigned n);
4923 These functions drop any constraints (not) involving the specified dimensions.
4924 Note that the result depends on the representation of the input.
4926 #include <isl/polynomial.h>
4927 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4928 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4929 __isl_give isl_union_pw_qpolynomial *
4930 isl_union_pw_qpolynomial_to_polynomial(
4931 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4933 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4934 the polynomial will be an overapproximation. If C<sign> is negative,
4935 it will be an underapproximation. If C<sign> is zero, the approximation
4936 will lie somewhere in between.
4940 __isl_give isl_basic_set *isl_basic_set_sample(
4941 __isl_take isl_basic_set *bset);
4942 __isl_give isl_basic_set *isl_set_sample(
4943 __isl_take isl_set *set);
4944 __isl_give isl_basic_map *isl_basic_map_sample(
4945 __isl_take isl_basic_map *bmap);
4946 __isl_give isl_basic_map *isl_map_sample(
4947 __isl_take isl_map *map);
4949 If the input (basic) set or relation is non-empty, then return
4950 a singleton subset of the input. Otherwise, return an empty set.
4952 =item * Optimization
4954 #include <isl/ilp.h>
4955 __isl_give isl_val *isl_basic_set_max_val(
4956 __isl_keep isl_basic_set *bset,
4957 __isl_keep isl_aff *obj);
4958 __isl_give isl_val *isl_set_min_val(
4959 __isl_keep isl_set *set,
4960 __isl_keep isl_aff *obj);
4961 __isl_give isl_val *isl_set_max_val(
4962 __isl_keep isl_set *set,
4963 __isl_keep isl_aff *obj);
4965 Compute the minimum or maximum of the integer affine expression C<obj>
4966 over the points in C<set>, returning the result in C<opt>.
4967 The result is C<NULL> in case of an error, the optimal value in case
4968 there is one, negative infinity or infinity if the problem is unbounded and
4969 NaN if the problem is empty.
4971 =item * Parametric optimization
4973 __isl_give isl_pw_aff *isl_set_dim_min(
4974 __isl_take isl_set *set, int pos);
4975 __isl_give isl_pw_aff *isl_set_dim_max(
4976 __isl_take isl_set *set, int pos);
4977 __isl_give isl_pw_aff *isl_map_dim_max(
4978 __isl_take isl_map *map, int pos);
4980 Compute the minimum or maximum of the given set or output dimension
4981 as a function of the parameters (and input dimensions), but independently
4982 of the other set or output dimensions.
4983 For lexicographic optimization, see L<"Lexicographic Optimization">.
4987 The following functions compute either the set of (rational) coefficient
4988 values of valid constraints for the given set or the set of (rational)
4989 values satisfying the constraints with coefficients from the given set.
4990 Internally, these two sets of functions perform essentially the
4991 same operations, except that the set of coefficients is assumed to
4992 be a cone, while the set of values may be any polyhedron.
4993 The current implementation is based on the Farkas lemma and
4994 Fourier-Motzkin elimination, but this may change or be made optional
4995 in future. In particular, future implementations may use different
4996 dualization algorithms or skip the elimination step.
4998 __isl_give isl_basic_set *isl_basic_set_coefficients(
4999 __isl_take isl_basic_set *bset);
5000 __isl_give isl_basic_set *isl_set_coefficients(
5001 __isl_take isl_set *set);
5002 __isl_give isl_union_set *isl_union_set_coefficients(
5003 __isl_take isl_union_set *bset);
5004 __isl_give isl_basic_set *isl_basic_set_solutions(
5005 __isl_take isl_basic_set *bset);
5006 __isl_give isl_basic_set *isl_set_solutions(
5007 __isl_take isl_set *set);
5008 __isl_give isl_union_set *isl_union_set_solutions(
5009 __isl_take isl_union_set *bset);
5013 __isl_give isl_map *isl_map_fixed_power_val(
5014 __isl_take isl_map *map,
5015 __isl_take isl_val *exp);
5016 __isl_give isl_union_map *
5017 isl_union_map_fixed_power_val(
5018 __isl_take isl_union_map *umap,
5019 __isl_take isl_val *exp);
5021 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5022 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5023 of C<map> is computed.
5025 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5027 __isl_give isl_union_map *isl_union_map_power(
5028 __isl_take isl_union_map *umap, int *exact);
5030 Compute a parametric representation for all positive powers I<k> of C<map>.
5031 The result maps I<k> to a nested relation corresponding to the
5032 I<k>th power of C<map>.
5033 The result may be an overapproximation. If the result is known to be exact,
5034 then C<*exact> is set to C<1>.
5036 =item * Transitive closure
5038 __isl_give isl_map *isl_map_transitive_closure(
5039 __isl_take isl_map *map, int *exact);
5040 __isl_give isl_union_map *isl_union_map_transitive_closure(
5041 __isl_take isl_union_map *umap, int *exact);
5043 Compute the transitive closure 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 * Reaching path lengths
5049 __isl_give isl_map *isl_map_reaching_path_lengths(
5050 __isl_take isl_map *map, int *exact);
5052 Compute a relation that maps each element in the range of C<map>
5053 to the lengths of all paths composed of edges in C<map> that
5054 end up in the given element.
5055 The result may be an overapproximation. If the result is known to be exact,
5056 then C<*exact> is set to C<1>.
5057 To compute the I<maximal> path length, the resulting relation
5058 should be postprocessed by C<isl_map_lexmax>.
5059 In particular, if the input relation is a dependence relation
5060 (mapping sources to sinks), then the maximal path length corresponds
5061 to the free schedule.
5062 Note, however, that C<isl_map_lexmax> expects the maximum to be
5063 finite, so if the path lengths are unbounded (possibly due to
5064 the overapproximation), then you will get an error message.
5068 #include <isl/space.h>
5069 __isl_give isl_space *isl_space_wrap(
5070 __isl_take isl_space *space);
5071 __isl_give isl_space *isl_space_unwrap(
5072 __isl_take isl_space *space);
5074 #include <isl/local_space.h>
5075 __isl_give isl_local_space *isl_local_space_wrap(
5076 __isl_take isl_local_space *ls);
5078 #include <isl/set.h>
5079 __isl_give isl_basic_map *isl_basic_set_unwrap(
5080 __isl_take isl_basic_set *bset);
5081 __isl_give isl_map *isl_set_unwrap(
5082 __isl_take isl_set *set);
5084 #include <isl/map.h>
5085 __isl_give isl_basic_set *isl_basic_map_wrap(
5086 __isl_take isl_basic_map *bmap);
5087 __isl_give isl_set *isl_map_wrap(
5088 __isl_take isl_map *map);
5090 #include <isl/union_set.h>
5091 __isl_give isl_union_map *isl_union_set_unwrap(
5092 __isl_take isl_union_set *uset);
5094 #include <isl/union_map.h>
5095 __isl_give isl_union_set *isl_union_map_wrap(
5096 __isl_take isl_union_map *umap);
5098 The input to C<isl_space_unwrap> should
5099 be the space of a set, while that of
5100 C<isl_space_wrap> should be the space of a relation.
5101 Conversely, the output of C<isl_space_unwrap> is the space
5102 of a relation, while that of C<isl_space_wrap> is the space of a set.
5106 Remove any internal structure of domain (and range) of the given
5107 set or relation. If there is any such internal structure in the input,
5108 then the name of the space is also removed.
5110 #include <isl/local_space.h>
5111 __isl_give isl_local_space *
5112 isl_local_space_flatten_domain(
5113 __isl_take isl_local_space *ls);
5114 __isl_give isl_local_space *
5115 isl_local_space_flatten_range(
5116 __isl_take isl_local_space *ls);
5118 #include <isl/set.h>
5119 __isl_give isl_basic_set *isl_basic_set_flatten(
5120 __isl_take isl_basic_set *bset);
5121 __isl_give isl_set *isl_set_flatten(
5122 __isl_take isl_set *set);
5124 #include <isl/map.h>
5125 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5126 __isl_take isl_basic_map *bmap);
5127 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5128 __isl_take isl_basic_map *bmap);
5129 __isl_give isl_map *isl_map_flatten_range(
5130 __isl_take isl_map *map);
5131 __isl_give isl_map *isl_map_flatten_domain(
5132 __isl_take isl_map *map);
5133 __isl_give isl_basic_map *isl_basic_map_flatten(
5134 __isl_take isl_basic_map *bmap);
5135 __isl_give isl_map *isl_map_flatten(
5136 __isl_take isl_map *map);
5138 #include <isl/val.h>
5139 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5140 __isl_take isl_multi_val *mv);
5142 #include <isl/aff.h>
5143 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5144 __isl_take isl_multi_aff *ma);
5145 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5146 __isl_take isl_multi_aff *ma);
5147 __isl_give isl_multi_pw_aff *
5148 isl_multi_pw_aff_flatten_range(
5149 __isl_take isl_multi_pw_aff *mpa);
5150 __isl_give isl_multi_union_pw_aff *
5151 isl_multi_union_pw_aff_flatten_range(
5152 __isl_take isl_multi_union_pw_aff *mupa);
5154 #include <isl/map.h>
5155 __isl_give isl_map *isl_set_flatten_map(
5156 __isl_take isl_set *set);
5158 The function above constructs a relation
5159 that maps the input set to a flattened version of the set.
5163 Lift the input set to a space with extra dimensions corresponding
5164 to the existentially quantified variables in the input.
5165 In particular, the result lives in a wrapped map where the domain
5166 is the original space and the range corresponds to the original
5167 existentially quantified variables.
5169 #include <isl/set.h>
5170 __isl_give isl_basic_set *isl_basic_set_lift(
5171 __isl_take isl_basic_set *bset);
5172 __isl_give isl_set *isl_set_lift(
5173 __isl_take isl_set *set);
5174 __isl_give isl_union_set *isl_union_set_lift(
5175 __isl_take isl_union_set *uset);
5177 Given a local space that contains the existentially quantified
5178 variables of a set, a basic relation that, when applied to
5179 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5180 can be constructed using the following function.
5182 #include <isl/local_space.h>
5183 __isl_give isl_basic_map *isl_local_space_lifting(
5184 __isl_take isl_local_space *ls);
5186 #include <isl/aff.h>
5187 __isl_give isl_multi_aff *isl_multi_aff_lift(
5188 __isl_take isl_multi_aff *maff,
5189 __isl_give isl_local_space **ls);
5191 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5192 then it is assigned the local space that lies at the basis of
5193 the lifting applied.
5195 =item * Internal Product
5197 #include <isl/space.h>
5198 __isl_give isl_space *isl_space_zip(
5199 __isl_take isl_space *space);
5201 #include <isl/map.h>
5202 __isl_give isl_basic_map *isl_basic_map_zip(
5203 __isl_take isl_basic_map *bmap);
5204 __isl_give isl_map *isl_map_zip(
5205 __isl_take isl_map *map);
5207 #include <isl/union_map.h>
5208 __isl_give isl_union_map *isl_union_map_zip(
5209 __isl_take isl_union_map *umap);
5211 Given a relation with nested relations for domain and range,
5212 interchange the range of the domain with the domain of the range.
5216 #include <isl/space.h>
5217 __isl_give isl_space *isl_space_curry(
5218 __isl_take isl_space *space);
5219 __isl_give isl_space *isl_space_uncurry(
5220 __isl_take isl_space *space);
5222 #include <isl/map.h>
5223 __isl_give isl_basic_map *isl_basic_map_curry(
5224 __isl_take isl_basic_map *bmap);
5225 __isl_give isl_basic_map *isl_basic_map_uncurry(
5226 __isl_take isl_basic_map *bmap);
5227 __isl_give isl_map *isl_map_curry(
5228 __isl_take isl_map *map);
5229 __isl_give isl_map *isl_map_uncurry(
5230 __isl_take isl_map *map);
5232 #include <isl/union_map.h>
5233 __isl_give isl_union_map *isl_union_map_curry(
5234 __isl_take isl_union_map *umap);
5235 __isl_give isl_union_map *isl_union_map_uncurry(
5236 __isl_take isl_union_map *umap);
5238 Given a relation with a nested relation for domain,
5239 the C<curry> functions
5240 move the range of the nested relation out of the domain
5241 and use it as the domain of a nested relation in the range,
5242 with the original range as range of this nested relation.
5243 The C<uncurry> functions perform the inverse operation.
5245 #include <isl/space.h>
5246 __isl_give isl_space *isl_space_range_curry(
5247 __isl_take isl_space *space);
5249 #include <isl/map.h>
5250 __isl_give isl_map *isl_map_range_curry(
5251 __isl_take isl_map *map);
5253 #include <isl/union_map.h>
5254 __isl_give isl_union_map *isl_union_map_range_curry(
5255 __isl_take isl_union_map *umap);
5257 These functions apply the currying to the relation that
5258 is nested inside the range of the input.
5260 =item * Aligning parameters
5262 Change the order of the parameters of the given set, relation
5264 such that the first parameters match those of C<model>.
5265 This may involve the introduction of extra parameters.
5266 All parameters need to be named.
5268 #include <isl/space.h>
5269 __isl_give isl_space *isl_space_align_params(
5270 __isl_take isl_space *space1,
5271 __isl_take isl_space *space2)
5273 #include <isl/set.h>
5274 __isl_give isl_basic_set *isl_basic_set_align_params(
5275 __isl_take isl_basic_set *bset,
5276 __isl_take isl_space *model);
5277 __isl_give isl_set *isl_set_align_params(
5278 __isl_take isl_set *set,
5279 __isl_take isl_space *model);
5281 #include <isl/map.h>
5282 __isl_give isl_basic_map *isl_basic_map_align_params(
5283 __isl_take isl_basic_map *bmap,
5284 __isl_take isl_space *model);
5285 __isl_give isl_map *isl_map_align_params(
5286 __isl_take isl_map *map,
5287 __isl_take isl_space *model);
5289 #include <isl/val.h>
5290 __isl_give isl_multi_val *isl_multi_val_align_params(
5291 __isl_take isl_multi_val *mv,
5292 __isl_take isl_space *model);
5294 #include <isl/aff.h>
5295 __isl_give isl_aff *isl_aff_align_params(
5296 __isl_take isl_aff *aff,
5297 __isl_take isl_space *model);
5298 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5299 __isl_take isl_multi_aff *multi,
5300 __isl_take isl_space *model);
5301 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5302 __isl_take isl_pw_aff *pwaff,
5303 __isl_take isl_space *model);
5304 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5305 __isl_take isl_pw_multi_aff *pma,
5306 __isl_take isl_space *model);
5307 __isl_give isl_union_pw_aff *
5308 isl_union_pw_aff_align_params(
5309 __isl_take isl_union_pw_aff *upa,
5310 __isl_take isl_space *model);
5311 __isl_give isl_union_pw_multi_aff *
5312 isl_union_pw_multi_aff_align_params(
5313 __isl_take isl_union_pw_multi_aff *upma,
5314 __isl_take isl_space *model);
5315 __isl_give isl_multi_union_pw_aff *
5316 isl_multi_union_pw_aff_align_params(
5317 __isl_take isl_multi_union_pw_aff *mupa,
5318 __isl_take isl_space *model);
5320 #include <isl/polynomial.h>
5321 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5322 __isl_take isl_qpolynomial *qp,
5323 __isl_take isl_space *model);
5325 =item * Unary Arithmetic Operations
5327 #include <isl/set.h>
5328 __isl_give isl_set *isl_set_neg(
5329 __isl_take isl_set *set);
5330 #include <isl/map.h>
5331 __isl_give isl_map *isl_map_neg(
5332 __isl_take isl_map *map);
5334 C<isl_set_neg> constructs a set containing the opposites of
5335 the elements in its argument.
5336 The domain of the result of C<isl_map_neg> is the same
5337 as the domain of its argument. The corresponding range
5338 elements are the opposites of the corresponding range
5339 elements in the argument.
5341 #include <isl/val.h>
5342 __isl_give isl_multi_val *isl_multi_val_neg(
5343 __isl_take isl_multi_val *mv);
5345 #include <isl/aff.h>
5346 __isl_give isl_aff *isl_aff_neg(
5347 __isl_take isl_aff *aff);
5348 __isl_give isl_multi_aff *isl_multi_aff_neg(
5349 __isl_take isl_multi_aff *ma);
5350 __isl_give isl_pw_aff *isl_pw_aff_neg(
5351 __isl_take isl_pw_aff *pwaff);
5352 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5353 __isl_take isl_pw_multi_aff *pma);
5354 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5355 __isl_take isl_multi_pw_aff *mpa);
5356 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5357 __isl_take isl_union_pw_aff *upa);
5358 __isl_give isl_union_pw_multi_aff *
5359 isl_union_pw_multi_aff_neg(
5360 __isl_take isl_union_pw_multi_aff *upma);
5361 __isl_give isl_multi_union_pw_aff *
5362 isl_multi_union_pw_aff_neg(
5363 __isl_take isl_multi_union_pw_aff *mupa);
5364 __isl_give isl_aff *isl_aff_ceil(
5365 __isl_take isl_aff *aff);
5366 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5367 __isl_take isl_pw_aff *pwaff);
5368 __isl_give isl_aff *isl_aff_floor(
5369 __isl_take isl_aff *aff);
5370 __isl_give isl_multi_aff *isl_multi_aff_floor(
5371 __isl_take isl_multi_aff *ma);
5372 __isl_give isl_pw_aff *isl_pw_aff_floor(
5373 __isl_take isl_pw_aff *pwaff);
5374 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5375 __isl_take isl_union_pw_aff *upa);
5376 __isl_give isl_multi_union_pw_aff *
5377 isl_multi_union_pw_aff_floor(
5378 __isl_take isl_multi_union_pw_aff *mupa);
5380 #include <isl/aff.h>
5381 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5382 __isl_take isl_pw_aff_list *list);
5383 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5384 __isl_take isl_pw_aff_list *list);
5386 #include <isl/polynomial.h>
5387 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5388 __isl_take isl_qpolynomial *qp);
5389 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5390 __isl_take isl_pw_qpolynomial *pwqp);
5391 __isl_give isl_union_pw_qpolynomial *
5392 isl_union_pw_qpolynomial_neg(
5393 __isl_take isl_union_pw_qpolynomial *upwqp);
5394 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5395 __isl_take isl_qpolynomial *qp,
5397 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5398 __isl_take isl_pw_qpolynomial *pwqp,
5403 The following functions evaluate a function in a point.
5405 #include <isl/polynomial.h>
5406 __isl_give isl_val *isl_pw_qpolynomial_eval(
5407 __isl_take isl_pw_qpolynomial *pwqp,
5408 __isl_take isl_point *pnt);
5409 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5410 __isl_take isl_pw_qpolynomial_fold *pwf,
5411 __isl_take isl_point *pnt);
5412 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5413 __isl_take isl_union_pw_qpolynomial *upwqp,
5414 __isl_take isl_point *pnt);
5415 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5416 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5417 __isl_take isl_point *pnt);
5419 =item * Dimension manipulation
5421 It is usually not advisable to directly change the (input or output)
5422 space of a set or a relation as this removes the name and the internal
5423 structure of the space. However, the functions below can be useful
5424 to add new parameters, assuming
5425 C<isl_set_align_params> and C<isl_map_align_params>
5428 #include <isl/space.h>
5429 __isl_give isl_space *isl_space_add_dims(
5430 __isl_take isl_space *space,
5431 enum isl_dim_type type, unsigned n);
5432 __isl_give isl_space *isl_space_insert_dims(
5433 __isl_take isl_space *space,
5434 enum isl_dim_type type, unsigned pos, unsigned n);
5435 __isl_give isl_space *isl_space_drop_dims(
5436 __isl_take isl_space *space,
5437 enum isl_dim_type type, unsigned first, unsigned n);
5438 __isl_give isl_space *isl_space_move_dims(
5439 __isl_take isl_space *space,
5440 enum isl_dim_type dst_type, unsigned dst_pos,
5441 enum isl_dim_type src_type, unsigned src_pos,
5444 #include <isl/local_space.h>
5445 __isl_give isl_local_space *isl_local_space_add_dims(
5446 __isl_take isl_local_space *ls,
5447 enum isl_dim_type type, unsigned n);
5448 __isl_give isl_local_space *isl_local_space_insert_dims(
5449 __isl_take isl_local_space *ls,
5450 enum isl_dim_type type, unsigned first, unsigned n);
5451 __isl_give isl_local_space *isl_local_space_drop_dims(
5452 __isl_take isl_local_space *ls,
5453 enum isl_dim_type type, unsigned first, unsigned n);
5455 #include <isl/set.h>
5456 __isl_give isl_basic_set *isl_basic_set_add_dims(
5457 __isl_take isl_basic_set *bset,
5458 enum isl_dim_type type, unsigned n);
5459 __isl_give isl_set *isl_set_add_dims(
5460 __isl_take isl_set *set,
5461 enum isl_dim_type type, unsigned n);
5462 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5463 __isl_take isl_basic_set *bset,
5464 enum isl_dim_type type, unsigned pos,
5466 __isl_give isl_set *isl_set_insert_dims(
5467 __isl_take isl_set *set,
5468 enum isl_dim_type type, unsigned pos, unsigned n);
5469 __isl_give isl_basic_set *isl_basic_set_move_dims(
5470 __isl_take isl_basic_set *bset,
5471 enum isl_dim_type dst_type, unsigned dst_pos,
5472 enum isl_dim_type src_type, unsigned src_pos,
5474 __isl_give isl_set *isl_set_move_dims(
5475 __isl_take isl_set *set,
5476 enum isl_dim_type dst_type, unsigned dst_pos,
5477 enum isl_dim_type src_type, unsigned src_pos,
5480 #include <isl/map.h>
5481 __isl_give isl_basic_map *isl_basic_map_add_dims(
5482 __isl_take isl_basic_map *bmap,
5483 enum isl_dim_type type, unsigned n);
5484 __isl_give isl_map *isl_map_add_dims(
5485 __isl_take isl_map *map,
5486 enum isl_dim_type type, unsigned n);
5487 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5488 __isl_take isl_basic_map *bmap,
5489 enum isl_dim_type type, unsigned pos,
5491 __isl_give isl_map *isl_map_insert_dims(
5492 __isl_take isl_map *map,
5493 enum isl_dim_type type, unsigned pos, unsigned n);
5494 __isl_give isl_basic_map *isl_basic_map_move_dims(
5495 __isl_take isl_basic_map *bmap,
5496 enum isl_dim_type dst_type, unsigned dst_pos,
5497 enum isl_dim_type src_type, unsigned src_pos,
5499 __isl_give isl_map *isl_map_move_dims(
5500 __isl_take isl_map *map,
5501 enum isl_dim_type dst_type, unsigned dst_pos,
5502 enum isl_dim_type src_type, unsigned src_pos,
5505 #include <isl/val.h>
5506 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5507 __isl_take isl_multi_val *mv,
5508 enum isl_dim_type type, unsigned first, unsigned n);
5509 __isl_give isl_multi_val *isl_multi_val_add_dims(
5510 __isl_take isl_multi_val *mv,
5511 enum isl_dim_type type, unsigned n);
5512 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5513 __isl_take isl_multi_val *mv,
5514 enum isl_dim_type type, unsigned first, unsigned n);
5516 #include <isl/aff.h>
5517 __isl_give isl_aff *isl_aff_insert_dims(
5518 __isl_take isl_aff *aff,
5519 enum isl_dim_type type, unsigned first, unsigned n);
5520 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5521 __isl_take isl_multi_aff *ma,
5522 enum isl_dim_type type, unsigned first, unsigned n);
5523 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5524 __isl_take isl_pw_aff *pwaff,
5525 enum isl_dim_type type, unsigned first, unsigned n);
5526 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5527 __isl_take isl_multi_pw_aff *mpa,
5528 enum isl_dim_type type, unsigned first, unsigned n);
5529 __isl_give isl_aff *isl_aff_add_dims(
5530 __isl_take isl_aff *aff,
5531 enum isl_dim_type type, unsigned n);
5532 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5533 __isl_take isl_multi_aff *ma,
5534 enum isl_dim_type type, unsigned n);
5535 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5536 __isl_take isl_pw_aff *pwaff,
5537 enum isl_dim_type type, unsigned n);
5538 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5539 __isl_take isl_multi_pw_aff *mpa,
5540 enum isl_dim_type type, unsigned n);
5541 __isl_give isl_aff *isl_aff_drop_dims(
5542 __isl_take isl_aff *aff,
5543 enum isl_dim_type type, unsigned first, unsigned n);
5544 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5545 __isl_take isl_multi_aff *maff,
5546 enum isl_dim_type type, unsigned first, unsigned n);
5547 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5548 __isl_take isl_pw_aff *pwaff,
5549 enum isl_dim_type type, unsigned first, unsigned n);
5550 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5551 __isl_take isl_pw_multi_aff *pma,
5552 enum isl_dim_type type, unsigned first, unsigned n);
5553 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5554 __isl_take isl_union_pw_aff *upa,
5555 enum isl_dim_type type, unsigned first, unsigned n);
5556 __isl_give isl_union_pw_multi_aff *
5557 isl_union_pw_multi_aff_drop_dims(
5558 __isl_take isl_union_pw_multi_aff *upma,
5559 enum isl_dim_type type,
5560 unsigned first, unsigned n);
5561 __isl_give isl_multi_union_pw_aff *
5562 isl_multi_union_pw_aff_drop_dims(
5563 __isl_take isl_multi_union_pw_aff *mupa,
5564 enum isl_dim_type type, unsigned first,
5566 __isl_give isl_aff *isl_aff_move_dims(
5567 __isl_take isl_aff *aff,
5568 enum isl_dim_type dst_type, unsigned dst_pos,
5569 enum isl_dim_type src_type, unsigned src_pos,
5571 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5572 __isl_take isl_multi_aff *ma,
5573 enum isl_dim_type dst_type, unsigned dst_pos,
5574 enum isl_dim_type src_type, unsigned src_pos,
5576 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5577 __isl_take isl_pw_aff *pa,
5578 enum isl_dim_type dst_type, unsigned dst_pos,
5579 enum isl_dim_type src_type, unsigned src_pos,
5581 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5582 __isl_take isl_multi_pw_aff *pma,
5583 enum isl_dim_type dst_type, unsigned dst_pos,
5584 enum isl_dim_type src_type, unsigned src_pos,
5587 #include <isl/polynomial.h>
5588 __isl_give isl_union_pw_qpolynomial *
5589 isl_union_pw_qpolynomial_drop_dims(
5590 __isl_take isl_union_pw_qpolynomial *upwqp,
5591 enum isl_dim_type type,
5592 unsigned first, unsigned n);
5593 __isl_give isl_union_pw_qpolynomial_fold *
5594 isl_union_pw_qpolynomial_fold_drop_dims(
5595 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5596 enum isl_dim_type type,
5597 unsigned first, unsigned n);
5599 The operations on union expressions can only manipulate parameters.
5603 =head2 Binary Operations
5605 The two arguments of a binary operation not only need to live
5606 in the same C<isl_ctx>, they currently also need to have
5607 the same (number of) parameters.
5609 =head3 Basic Operations
5613 =item * Intersection
5615 #include <isl/local_space.h>
5616 __isl_give isl_local_space *isl_local_space_intersect(
5617 __isl_take isl_local_space *ls1,
5618 __isl_take isl_local_space *ls2);
5620 #include <isl/set.h>
5621 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5622 __isl_take isl_basic_set *bset1,
5623 __isl_take isl_basic_set *bset2);
5624 __isl_give isl_basic_set *isl_basic_set_intersect(
5625 __isl_take isl_basic_set *bset1,
5626 __isl_take isl_basic_set *bset2);
5627 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5628 __isl_take struct isl_basic_set_list *list);
5629 __isl_give isl_set *isl_set_intersect_params(
5630 __isl_take isl_set *set,
5631 __isl_take isl_set *params);
5632 __isl_give isl_set *isl_set_intersect(
5633 __isl_take isl_set *set1,
5634 __isl_take isl_set *set2);
5636 #include <isl/map.h>
5637 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5638 __isl_take isl_basic_map *bmap,
5639 __isl_take isl_basic_set *bset);
5640 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5641 __isl_take isl_basic_map *bmap,
5642 __isl_take isl_basic_set *bset);
5643 __isl_give isl_basic_map *isl_basic_map_intersect(
5644 __isl_take isl_basic_map *bmap1,
5645 __isl_take isl_basic_map *bmap2);
5646 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5647 __isl_take isl_basic_map_list *list);
5648 __isl_give isl_map *isl_map_intersect_params(
5649 __isl_take isl_map *map,
5650 __isl_take isl_set *params);
5651 __isl_give isl_map *isl_map_intersect_domain(
5652 __isl_take isl_map *map,
5653 __isl_take isl_set *set);
5654 __isl_give isl_map *isl_map_intersect_range(
5655 __isl_take isl_map *map,
5656 __isl_take isl_set *set);
5657 __isl_give isl_map *isl_map_intersect(
5658 __isl_take isl_map *map1,
5659 __isl_take isl_map *map2);
5661 #include <isl/union_set.h>
5662 __isl_give isl_union_set *isl_union_set_intersect_params(
5663 __isl_take isl_union_set *uset,
5664 __isl_take isl_set *set);
5665 __isl_give isl_union_set *isl_union_set_intersect(
5666 __isl_take isl_union_set *uset1,
5667 __isl_take isl_union_set *uset2);
5669 #include <isl/union_map.h>
5670 __isl_give isl_union_map *isl_union_map_intersect_params(
5671 __isl_take isl_union_map *umap,
5672 __isl_take isl_set *set);
5673 __isl_give isl_union_map *isl_union_map_intersect_domain(
5674 __isl_take isl_union_map *umap,
5675 __isl_take isl_union_set *uset);
5676 __isl_give isl_union_map *isl_union_map_intersect_range(
5677 __isl_take isl_union_map *umap,
5678 __isl_take isl_union_set *uset);
5679 __isl_give isl_union_map *isl_union_map_intersect(
5680 __isl_take isl_union_map *umap1,
5681 __isl_take isl_union_map *umap2);
5683 #include <isl/aff.h>
5684 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5685 __isl_take isl_pw_aff *pa,
5686 __isl_take isl_set *set);
5687 __isl_give isl_multi_pw_aff *
5688 isl_multi_pw_aff_intersect_domain(
5689 __isl_take isl_multi_pw_aff *mpa,
5690 __isl_take isl_set *domain);
5691 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5692 __isl_take isl_pw_multi_aff *pma,
5693 __isl_take isl_set *set);
5694 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5695 __isl_take isl_union_pw_aff *upa,
5696 __isl_take isl_union_set *uset);
5697 __isl_give isl_union_pw_multi_aff *
5698 isl_union_pw_multi_aff_intersect_domain(
5699 __isl_take isl_union_pw_multi_aff *upma,
5700 __isl_take isl_union_set *uset);
5701 __isl_give isl_multi_union_pw_aff *
5702 isl_multi_union_pw_aff_intersect_domain(
5703 __isl_take isl_multi_union_pw_aff *mupa,
5704 __isl_take isl_union_set *uset);
5705 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5706 __isl_take isl_pw_aff *pa,
5707 __isl_take isl_set *set);
5708 __isl_give isl_multi_pw_aff *
5709 isl_multi_pw_aff_intersect_params(
5710 __isl_take isl_multi_pw_aff *mpa,
5711 __isl_take isl_set *set);
5712 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5713 __isl_take isl_pw_multi_aff *pma,
5714 __isl_take isl_set *set);
5715 __isl_give isl_union_pw_aff *
5716 isl_union_pw_aff_intersect_params(
5717 __isl_take isl_union_pw_aff *upa,
5718 __isl_give isl_union_pw_multi_aff *
5719 isl_union_pw_multi_aff_intersect_params(
5720 __isl_take isl_union_pw_multi_aff *upma,
5721 __isl_take isl_set *set);
5722 __isl_give isl_multi_union_pw_aff *
5723 isl_multi_union_pw_aff_intersect_params(
5724 __isl_take isl_multi_union_pw_aff *mupa,
5725 __isl_take isl_set *params);
5726 isl_multi_union_pw_aff_intersect_range(
5727 __isl_take isl_multi_union_pw_aff *mupa,
5728 __isl_take isl_set *set);
5730 #include <isl/polynomial.h>
5731 __isl_give isl_pw_qpolynomial *
5732 isl_pw_qpolynomial_intersect_domain(
5733 __isl_take isl_pw_qpolynomial *pwpq,
5734 __isl_take isl_set *set);
5735 __isl_give isl_union_pw_qpolynomial *
5736 isl_union_pw_qpolynomial_intersect_domain(
5737 __isl_take isl_union_pw_qpolynomial *upwpq,
5738 __isl_take isl_union_set *uset);
5739 __isl_give isl_union_pw_qpolynomial_fold *
5740 isl_union_pw_qpolynomial_fold_intersect_domain(
5741 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5742 __isl_take isl_union_set *uset);
5743 __isl_give isl_pw_qpolynomial *
5744 isl_pw_qpolynomial_intersect_params(
5745 __isl_take isl_pw_qpolynomial *pwpq,
5746 __isl_take isl_set *set);
5747 __isl_give isl_pw_qpolynomial_fold *
5748 isl_pw_qpolynomial_fold_intersect_params(
5749 __isl_take isl_pw_qpolynomial_fold *pwf,
5750 __isl_take isl_set *set);
5751 __isl_give isl_union_pw_qpolynomial *
5752 isl_union_pw_qpolynomial_intersect_params(
5753 __isl_take isl_union_pw_qpolynomial *upwpq,
5754 __isl_take isl_set *set);
5755 __isl_give isl_union_pw_qpolynomial_fold *
5756 isl_union_pw_qpolynomial_fold_intersect_params(
5757 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5758 __isl_take isl_set *set);
5760 The second argument to the C<_params> functions needs to be
5761 a parametric (basic) set. For the other functions, a parametric set
5762 for either argument is only allowed if the other argument is
5763 a parametric set as well.
5764 The list passed to C<isl_basic_set_list_intersect> needs to have
5765 at least one element and all elements need to live in the same space.
5766 The function C<isl_multi_union_pw_aff_intersect_range>
5767 restricts the input function to those shared domain elements
5768 that map to the specified range.
5772 #include <isl/set.h>
5773 __isl_give isl_set *isl_basic_set_union(
5774 __isl_take isl_basic_set *bset1,
5775 __isl_take isl_basic_set *bset2);
5776 __isl_give isl_set *isl_set_union(
5777 __isl_take isl_set *set1,
5778 __isl_take isl_set *set2);
5779 __isl_give isl_set *isl_set_list_union(
5780 __isl_take isl_set_list *list);
5782 #include <isl/map.h>
5783 __isl_give isl_map *isl_basic_map_union(
5784 __isl_take isl_basic_map *bmap1,
5785 __isl_take isl_basic_map *bmap2);
5786 __isl_give isl_map *isl_map_union(
5787 __isl_take isl_map *map1,
5788 __isl_take isl_map *map2);
5790 #include <isl/union_set.h>
5791 __isl_give isl_union_set *isl_union_set_union(
5792 __isl_take isl_union_set *uset1,
5793 __isl_take isl_union_set *uset2);
5794 __isl_give isl_union_set *isl_union_set_list_union(
5795 __isl_take isl_union_set_list *list);
5797 #include <isl/union_map.h>
5798 __isl_give isl_union_map *isl_union_map_union(
5799 __isl_take isl_union_map *umap1,
5800 __isl_take isl_union_map *umap2);
5802 The list passed to C<isl_set_list_union> needs to have
5803 at least one element and all elements need to live in the same space.
5805 =item * Set difference
5807 #include <isl/set.h>
5808 __isl_give isl_set *isl_set_subtract(
5809 __isl_take isl_set *set1,
5810 __isl_take isl_set *set2);
5812 #include <isl/map.h>
5813 __isl_give isl_map *isl_map_subtract(
5814 __isl_take isl_map *map1,
5815 __isl_take isl_map *map2);
5816 __isl_give isl_map *isl_map_subtract_domain(
5817 __isl_take isl_map *map,
5818 __isl_take isl_set *dom);
5819 __isl_give isl_map *isl_map_subtract_range(
5820 __isl_take isl_map *map,
5821 __isl_take isl_set *dom);
5823 #include <isl/union_set.h>
5824 __isl_give isl_union_set *isl_union_set_subtract(
5825 __isl_take isl_union_set *uset1,
5826 __isl_take isl_union_set *uset2);
5828 #include <isl/union_map.h>
5829 __isl_give isl_union_map *isl_union_map_subtract(
5830 __isl_take isl_union_map *umap1,
5831 __isl_take isl_union_map *umap2);
5832 __isl_give isl_union_map *isl_union_map_subtract_domain(
5833 __isl_take isl_union_map *umap,
5834 __isl_take isl_union_set *dom);
5835 __isl_give isl_union_map *isl_union_map_subtract_range(
5836 __isl_take isl_union_map *umap,
5837 __isl_take isl_union_set *dom);
5839 #include <isl/aff.h>
5840 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5841 __isl_take isl_pw_aff *pa,
5842 __isl_take isl_set *set);
5843 __isl_give isl_pw_multi_aff *
5844 isl_pw_multi_aff_subtract_domain(
5845 __isl_take isl_pw_multi_aff *pma,
5846 __isl_take isl_set *set);
5847 __isl_give isl_union_pw_aff *
5848 isl_union_pw_aff_subtract_domain(
5849 __isl_take isl_union_pw_aff *upa,
5850 __isl_take isl_union_set *uset);
5851 __isl_give isl_union_pw_multi_aff *
5852 isl_union_pw_multi_aff_subtract_domain(
5853 __isl_take isl_union_pw_multi_aff *upma,
5854 __isl_take isl_set *set);
5856 #include <isl/polynomial.h>
5857 __isl_give isl_pw_qpolynomial *
5858 isl_pw_qpolynomial_subtract_domain(
5859 __isl_take isl_pw_qpolynomial *pwpq,
5860 __isl_take isl_set *set);
5861 __isl_give isl_pw_qpolynomial_fold *
5862 isl_pw_qpolynomial_fold_subtract_domain(
5863 __isl_take isl_pw_qpolynomial_fold *pwf,
5864 __isl_take isl_set *set);
5865 __isl_give isl_union_pw_qpolynomial *
5866 isl_union_pw_qpolynomial_subtract_domain(
5867 __isl_take isl_union_pw_qpolynomial *upwpq,
5868 __isl_take isl_union_set *uset);
5869 __isl_give isl_union_pw_qpolynomial_fold *
5870 isl_union_pw_qpolynomial_fold_subtract_domain(
5871 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5872 __isl_take isl_union_set *uset);
5876 #include <isl/space.h>
5877 __isl_give isl_space *isl_space_join(
5878 __isl_take isl_space *left,
5879 __isl_take isl_space *right);
5881 #include <isl/map.h>
5882 __isl_give isl_basic_set *isl_basic_set_apply(
5883 __isl_take isl_basic_set *bset,
5884 __isl_take isl_basic_map *bmap);
5885 __isl_give isl_set *isl_set_apply(
5886 __isl_take isl_set *set,
5887 __isl_take isl_map *map);
5888 __isl_give isl_union_set *isl_union_set_apply(
5889 __isl_take isl_union_set *uset,
5890 __isl_take isl_union_map *umap);
5891 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5892 __isl_take isl_basic_map *bmap1,
5893 __isl_take isl_basic_map *bmap2);
5894 __isl_give isl_basic_map *isl_basic_map_apply_range(
5895 __isl_take isl_basic_map *bmap1,
5896 __isl_take isl_basic_map *bmap2);
5897 __isl_give isl_map *isl_map_apply_domain(
5898 __isl_take isl_map *map1,
5899 __isl_take isl_map *map2);
5900 __isl_give isl_map *isl_map_apply_range(
5901 __isl_take isl_map *map1,
5902 __isl_take isl_map *map2);
5904 #include <isl/union_map.h>
5905 __isl_give isl_union_map *isl_union_map_apply_domain(
5906 __isl_take isl_union_map *umap1,
5907 __isl_take isl_union_map *umap2);
5908 __isl_give isl_union_map *isl_union_map_apply_range(
5909 __isl_take isl_union_map *umap1,
5910 __isl_take isl_union_map *umap2);
5912 #include <isl/aff.h>
5913 __isl_give isl_union_pw_aff *
5914 isl_multi_union_pw_aff_apply_aff(
5915 __isl_take isl_multi_union_pw_aff *mupa,
5916 __isl_take isl_aff *aff);
5917 __isl_give isl_union_pw_aff *
5918 isl_multi_union_pw_aff_apply_pw_aff(
5919 __isl_take isl_multi_union_pw_aff *mupa,
5920 __isl_take isl_pw_aff *pa);
5921 __isl_give isl_multi_union_pw_aff *
5922 isl_multi_union_pw_aff_apply_multi_aff(
5923 __isl_take isl_multi_union_pw_aff *mupa,
5924 __isl_take isl_multi_aff *ma);
5925 __isl_give isl_multi_union_pw_aff *
5926 isl_multi_union_pw_aff_apply_pw_multi_aff(
5927 __isl_take isl_multi_union_pw_aff *mupa,
5928 __isl_take isl_pw_multi_aff *pma);
5930 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5931 over the shared domain of the elements of the input. The dimension is
5932 required to be greater than zero.
5933 The C<isl_multi_union_pw_aff> argument of
5934 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5935 but only if the range of the C<isl_multi_aff> argument
5936 is also zero-dimensional.
5937 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5939 #include <isl/polynomial.h>
5940 __isl_give isl_pw_qpolynomial_fold *
5941 isl_set_apply_pw_qpolynomial_fold(
5942 __isl_take isl_set *set,
5943 __isl_take isl_pw_qpolynomial_fold *pwf,
5945 __isl_give isl_pw_qpolynomial_fold *
5946 isl_map_apply_pw_qpolynomial_fold(
5947 __isl_take isl_map *map,
5948 __isl_take isl_pw_qpolynomial_fold *pwf,
5950 __isl_give isl_union_pw_qpolynomial_fold *
5951 isl_union_set_apply_union_pw_qpolynomial_fold(
5952 __isl_take isl_union_set *uset,
5953 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5955 __isl_give isl_union_pw_qpolynomial_fold *
5956 isl_union_map_apply_union_pw_qpolynomial_fold(
5957 __isl_take isl_union_map *umap,
5958 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5961 The functions taking a map
5962 compose the given map with the given piecewise quasipolynomial reduction.
5963 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5964 over all elements in the intersection of the range of the map
5965 and the domain of the piecewise quasipolynomial reduction
5966 as a function of an element in the domain of the map.
5967 The functions taking a set compute a bound over all elements in the
5968 intersection of the set and the domain of the
5969 piecewise quasipolynomial reduction.
5973 #include <isl/set.h>
5974 __isl_give isl_basic_set *
5975 isl_basic_set_preimage_multi_aff(
5976 __isl_take isl_basic_set *bset,
5977 __isl_take isl_multi_aff *ma);
5978 __isl_give isl_set *isl_set_preimage_multi_aff(
5979 __isl_take isl_set *set,
5980 __isl_take isl_multi_aff *ma);
5981 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5982 __isl_take isl_set *set,
5983 __isl_take isl_pw_multi_aff *pma);
5984 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5985 __isl_take isl_set *set,
5986 __isl_take isl_multi_pw_aff *mpa);
5988 #include <isl/union_set.h>
5989 __isl_give isl_union_set *
5990 isl_union_set_preimage_multi_aff(
5991 __isl_take isl_union_set *uset,
5992 __isl_take isl_multi_aff *ma);
5993 __isl_give isl_union_set *
5994 isl_union_set_preimage_pw_multi_aff(
5995 __isl_take isl_union_set *uset,
5996 __isl_take isl_pw_multi_aff *pma);
5997 __isl_give isl_union_set *
5998 isl_union_set_preimage_union_pw_multi_aff(
5999 __isl_take isl_union_set *uset,
6000 __isl_take isl_union_pw_multi_aff *upma);
6002 #include <isl/map.h>
6003 __isl_give isl_basic_map *
6004 isl_basic_map_preimage_domain_multi_aff(
6005 __isl_take isl_basic_map *bmap,
6006 __isl_take isl_multi_aff *ma);
6007 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6008 __isl_take isl_map *map,
6009 __isl_take isl_multi_aff *ma);
6010 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6011 __isl_take isl_map *map,
6012 __isl_take isl_multi_aff *ma);
6013 __isl_give isl_map *
6014 isl_map_preimage_domain_pw_multi_aff(
6015 __isl_take isl_map *map,
6016 __isl_take isl_pw_multi_aff *pma);
6017 __isl_give isl_map *
6018 isl_map_preimage_range_pw_multi_aff(
6019 __isl_take isl_map *map,
6020 __isl_take isl_pw_multi_aff *pma);
6021 __isl_give isl_map *
6022 isl_map_preimage_domain_multi_pw_aff(
6023 __isl_take isl_map *map,
6024 __isl_take isl_multi_pw_aff *mpa);
6025 __isl_give isl_basic_map *
6026 isl_basic_map_preimage_range_multi_aff(
6027 __isl_take isl_basic_map *bmap,
6028 __isl_take isl_multi_aff *ma);
6030 #include <isl/union_map.h>
6031 __isl_give isl_union_map *
6032 isl_union_map_preimage_domain_multi_aff(
6033 __isl_take isl_union_map *umap,
6034 __isl_take isl_multi_aff *ma);
6035 __isl_give isl_union_map *
6036 isl_union_map_preimage_range_multi_aff(
6037 __isl_take isl_union_map *umap,
6038 __isl_take isl_multi_aff *ma);
6039 __isl_give isl_union_map *
6040 isl_union_map_preimage_domain_pw_multi_aff(
6041 __isl_take isl_union_map *umap,
6042 __isl_take isl_pw_multi_aff *pma);
6043 __isl_give isl_union_map *
6044 isl_union_map_preimage_range_pw_multi_aff(
6045 __isl_take isl_union_map *umap,
6046 __isl_take isl_pw_multi_aff *pma);
6047 __isl_give isl_union_map *
6048 isl_union_map_preimage_domain_union_pw_multi_aff(
6049 __isl_take isl_union_map *umap,
6050 __isl_take isl_union_pw_multi_aff *upma);
6051 __isl_give isl_union_map *
6052 isl_union_map_preimage_range_union_pw_multi_aff(
6053 __isl_take isl_union_map *umap,
6054 __isl_take isl_union_pw_multi_aff *upma);
6056 These functions compute the preimage of the given set or map domain/range under
6057 the given function. In other words, the expression is plugged
6058 into the set description or into the domain/range of the map.
6062 #include <isl/aff.h>
6063 __isl_give isl_aff *isl_aff_pullback_aff(
6064 __isl_take isl_aff *aff1,
6065 __isl_take isl_aff *aff2);
6066 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6067 __isl_take isl_aff *aff,
6068 __isl_take isl_multi_aff *ma);
6069 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6070 __isl_take isl_pw_aff *pa,
6071 __isl_take isl_multi_aff *ma);
6072 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6073 __isl_take isl_pw_aff *pa,
6074 __isl_take isl_pw_multi_aff *pma);
6075 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6076 __isl_take isl_pw_aff *pa,
6077 __isl_take isl_multi_pw_aff *mpa);
6078 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6079 __isl_take isl_multi_aff *ma1,
6080 __isl_take isl_multi_aff *ma2);
6081 __isl_give isl_pw_multi_aff *
6082 isl_pw_multi_aff_pullback_multi_aff(
6083 __isl_take isl_pw_multi_aff *pma,
6084 __isl_take isl_multi_aff *ma);
6085 __isl_give isl_multi_pw_aff *
6086 isl_multi_pw_aff_pullback_multi_aff(
6087 __isl_take isl_multi_pw_aff *mpa,
6088 __isl_take isl_multi_aff *ma);
6089 __isl_give isl_pw_multi_aff *
6090 isl_pw_multi_aff_pullback_pw_multi_aff(
6091 __isl_take isl_pw_multi_aff *pma1,
6092 __isl_take isl_pw_multi_aff *pma2);
6093 __isl_give isl_multi_pw_aff *
6094 isl_multi_pw_aff_pullback_pw_multi_aff(
6095 __isl_take isl_multi_pw_aff *mpa,
6096 __isl_take isl_pw_multi_aff *pma);
6097 __isl_give isl_multi_pw_aff *
6098 isl_multi_pw_aff_pullback_multi_pw_aff(
6099 __isl_take isl_multi_pw_aff *mpa1,
6100 __isl_take isl_multi_pw_aff *mpa2);
6101 __isl_give isl_union_pw_aff *
6102 isl_union_pw_aff_pullback_union_pw_multi_aff(
6103 __isl_take isl_union_pw_aff *upa,
6104 __isl_take isl_union_pw_multi_aff *upma);
6105 __isl_give isl_union_pw_multi_aff *
6106 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6107 __isl_take isl_union_pw_multi_aff *upma1,
6108 __isl_take isl_union_pw_multi_aff *upma2);
6109 __isl_give isl_multi_union_pw_aff *
6110 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6111 __isl_take isl_multi_union_pw_aff *mupa,
6112 __isl_take isl_union_pw_multi_aff *upma);
6114 These functions precompose the first expression by the second function.
6115 In other words, the second function is plugged
6116 into the first expression.
6120 #include <isl/aff.h>
6121 __isl_give isl_basic_set *isl_aff_le_basic_set(
6122 __isl_take isl_aff *aff1,
6123 __isl_take isl_aff *aff2);
6124 __isl_give isl_set *isl_aff_le_set(
6125 __isl_take isl_aff *aff1,
6126 __isl_take isl_aff *aff2);
6127 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6128 __isl_take isl_aff *aff1,
6129 __isl_take isl_aff *aff2);
6130 __isl_give isl_set *isl_aff_ge_set(
6131 __isl_take isl_aff *aff1,
6132 __isl_take isl_aff *aff2);
6133 __isl_give isl_set *isl_pw_aff_eq_set(
6134 __isl_take isl_pw_aff *pwaff1,
6135 __isl_take isl_pw_aff *pwaff2);
6136 __isl_give isl_set *isl_pw_aff_ne_set(
6137 __isl_take isl_pw_aff *pwaff1,
6138 __isl_take isl_pw_aff *pwaff2);
6139 __isl_give isl_set *isl_pw_aff_le_set(
6140 __isl_take isl_pw_aff *pwaff1,
6141 __isl_take isl_pw_aff *pwaff2);
6142 __isl_give isl_set *isl_pw_aff_lt_set(
6143 __isl_take isl_pw_aff *pwaff1,
6144 __isl_take isl_pw_aff *pwaff2);
6145 __isl_give isl_set *isl_pw_aff_ge_set(
6146 __isl_take isl_pw_aff *pwaff1,
6147 __isl_take isl_pw_aff *pwaff2);
6148 __isl_give isl_set *isl_pw_aff_gt_set(
6149 __isl_take isl_pw_aff *pwaff1,
6150 __isl_take isl_pw_aff *pwaff2);
6152 __isl_give isl_set *isl_multi_aff_lex_le_set(
6153 __isl_take isl_multi_aff *ma1,
6154 __isl_take isl_multi_aff *ma2);
6155 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6156 __isl_take isl_multi_aff *ma1,
6157 __isl_take isl_multi_aff *ma2);
6158 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6159 __isl_take isl_multi_aff *ma1,
6160 __isl_take isl_multi_aff *ma2);
6161 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6162 __isl_take isl_multi_aff *ma1,
6163 __isl_take isl_multi_aff *ma2);
6165 __isl_give isl_set *isl_pw_aff_list_eq_set(
6166 __isl_take isl_pw_aff_list *list1,
6167 __isl_take isl_pw_aff_list *list2);
6168 __isl_give isl_set *isl_pw_aff_list_ne_set(
6169 __isl_take isl_pw_aff_list *list1,
6170 __isl_take isl_pw_aff_list *list2);
6171 __isl_give isl_set *isl_pw_aff_list_le_set(
6172 __isl_take isl_pw_aff_list *list1,
6173 __isl_take isl_pw_aff_list *list2);
6174 __isl_give isl_set *isl_pw_aff_list_lt_set(
6175 __isl_take isl_pw_aff_list *list1,
6176 __isl_take isl_pw_aff_list *list2);
6177 __isl_give isl_set *isl_pw_aff_list_ge_set(
6178 __isl_take isl_pw_aff_list *list1,
6179 __isl_take isl_pw_aff_list *list2);
6180 __isl_give isl_set *isl_pw_aff_list_gt_set(
6181 __isl_take isl_pw_aff_list *list1,
6182 __isl_take isl_pw_aff_list *list2);
6184 The function C<isl_aff_ge_basic_set> returns a basic set
6185 containing those elements in the shared space
6186 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6187 The function C<isl_pw_aff_ge_set> returns a set
6188 containing those elements in the shared domain
6189 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6190 greater than or equal to C<pwaff2>.
6191 The function C<isl_multi_aff_lex_le_set> returns a set
6192 containing those elements in the shared domain space
6193 where C<ma1> is lexicographically smaller than or
6195 The functions operating on C<isl_pw_aff_list> apply the corresponding
6196 C<isl_pw_aff> function to each pair of elements in the two lists.
6198 #include <isl/aff.h>
6199 __isl_give isl_map *isl_pw_aff_eq_map(
6200 __isl_take isl_pw_aff *pa1,
6201 __isl_take isl_pw_aff *pa2);
6202 __isl_give isl_map *isl_pw_aff_lt_map(
6203 __isl_take isl_pw_aff *pa1,
6204 __isl_take isl_pw_aff *pa2);
6205 __isl_give isl_map *isl_pw_aff_gt_map(
6206 __isl_take isl_pw_aff *pa1,
6207 __isl_take isl_pw_aff *pa2);
6209 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6210 __isl_take isl_multi_pw_aff *mpa1,
6211 __isl_take isl_multi_pw_aff *mpa2);
6212 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6213 __isl_take isl_multi_pw_aff *mpa1,
6214 __isl_take isl_multi_pw_aff *mpa2);
6215 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6216 __isl_take isl_multi_pw_aff *mpa1,
6217 __isl_take isl_multi_pw_aff *mpa2);
6219 These functions return a map between domain elements of the arguments
6220 where the function values satisfy the given relation.
6222 #include <isl/union_map.h>
6223 __isl_give isl_union_map *
6224 isl_union_map_eq_at_multi_union_pw_aff(
6225 __isl_take isl_union_map *umap,
6226 __isl_take isl_multi_union_pw_aff *mupa);
6227 __isl_give isl_union_map *
6228 isl_union_map_lex_lt_at_multi_union_pw_aff(
6229 __isl_take isl_union_map *umap,
6230 __isl_take isl_multi_union_pw_aff *mupa);
6231 __isl_give isl_union_map *
6232 isl_union_map_lex_gt_at_multi_union_pw_aff(
6233 __isl_take isl_union_map *umap,
6234 __isl_take isl_multi_union_pw_aff *mupa);
6236 These functions select the subset of elements in the union map
6237 that have an equal or lexicographically smaller function value.
6239 =item * Cartesian Product
6241 #include <isl/space.h>
6242 __isl_give isl_space *isl_space_product(
6243 __isl_take isl_space *space1,
6244 __isl_take isl_space *space2);
6245 __isl_give isl_space *isl_space_domain_product(
6246 __isl_take isl_space *space1,
6247 __isl_take isl_space *space2);
6248 __isl_give isl_space *isl_space_range_product(
6249 __isl_take isl_space *space1,
6250 __isl_take isl_space *space2);
6253 C<isl_space_product>, C<isl_space_domain_product>
6254 and C<isl_space_range_product> take pairs or relation spaces and
6255 produce a single relations space, where either the domain, the range
6256 or both domain and range are wrapped spaces of relations between
6257 the domains and/or ranges of the input spaces.
6258 If the product is only constructed over the domain or the range
6259 then the ranges or the domains of the inputs should be the same.
6260 The function C<isl_space_product> also accepts a pair of set spaces,
6261 in which case it returns a wrapped space of a relation between the
6264 #include <isl/set.h>
6265 __isl_give isl_set *isl_set_product(
6266 __isl_take isl_set *set1,
6267 __isl_take isl_set *set2);
6269 #include <isl/map.h>
6270 __isl_give isl_basic_map *isl_basic_map_domain_product(
6271 __isl_take isl_basic_map *bmap1,
6272 __isl_take isl_basic_map *bmap2);
6273 __isl_give isl_basic_map *isl_basic_map_range_product(
6274 __isl_take isl_basic_map *bmap1,
6275 __isl_take isl_basic_map *bmap2);
6276 __isl_give isl_basic_map *isl_basic_map_product(
6277 __isl_take isl_basic_map *bmap1,
6278 __isl_take isl_basic_map *bmap2);
6279 __isl_give isl_map *isl_map_domain_product(
6280 __isl_take isl_map *map1,
6281 __isl_take isl_map *map2);
6282 __isl_give isl_map *isl_map_range_product(
6283 __isl_take isl_map *map1,
6284 __isl_take isl_map *map2);
6285 __isl_give isl_map *isl_map_product(
6286 __isl_take isl_map *map1,
6287 __isl_take isl_map *map2);
6289 #include <isl/union_set.h>
6290 __isl_give isl_union_set *isl_union_set_product(
6291 __isl_take isl_union_set *uset1,
6292 __isl_take isl_union_set *uset2);
6294 #include <isl/union_map.h>
6295 __isl_give isl_union_map *isl_union_map_domain_product(
6296 __isl_take isl_union_map *umap1,
6297 __isl_take isl_union_map *umap2);
6298 __isl_give isl_union_map *isl_union_map_range_product(
6299 __isl_take isl_union_map *umap1,
6300 __isl_take isl_union_map *umap2);
6301 __isl_give isl_union_map *isl_union_map_product(
6302 __isl_take isl_union_map *umap1,
6303 __isl_take isl_union_map *umap2);
6305 #include <isl/val.h>
6306 __isl_give isl_multi_val *isl_multi_val_range_product(
6307 __isl_take isl_multi_val *mv1,
6308 __isl_take isl_multi_val *mv2);
6309 __isl_give isl_multi_val *isl_multi_val_product(
6310 __isl_take isl_multi_val *mv1,
6311 __isl_take isl_multi_val *mv2);
6313 #include <isl/aff.h>
6314 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6315 __isl_take isl_multi_aff *ma1,
6316 __isl_take isl_multi_aff *ma2);
6317 __isl_give isl_multi_aff *isl_multi_aff_product(
6318 __isl_take isl_multi_aff *ma1,
6319 __isl_take isl_multi_aff *ma2);
6320 __isl_give isl_multi_pw_aff *
6321 isl_multi_pw_aff_range_product(
6322 __isl_take isl_multi_pw_aff *mpa1,
6323 __isl_take isl_multi_pw_aff *mpa2);
6324 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6325 __isl_take isl_multi_pw_aff *mpa1,
6326 __isl_take isl_multi_pw_aff *mpa2);
6327 __isl_give isl_pw_multi_aff *
6328 isl_pw_multi_aff_range_product(
6329 __isl_take isl_pw_multi_aff *pma1,
6330 __isl_take isl_pw_multi_aff *pma2);
6331 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6332 __isl_take isl_pw_multi_aff *pma1,
6333 __isl_take isl_pw_multi_aff *pma2);
6334 __isl_give isl_multi_union_pw_aff *
6335 isl_multi_union_pw_aff_range_product(
6336 __isl_take isl_multi_union_pw_aff *mupa1,
6337 __isl_take isl_multi_union_pw_aff *mupa2);
6339 The above functions compute the cross product of the given
6340 sets, relations or functions. The domains and ranges of the results
6341 are wrapped maps between domains and ranges of the inputs.
6342 To obtain a ``flat'' product, use the following functions
6345 #include <isl/set.h>
6346 __isl_give isl_basic_set *isl_basic_set_flat_product(
6347 __isl_take isl_basic_set *bset1,
6348 __isl_take isl_basic_set *bset2);
6349 __isl_give isl_set *isl_set_flat_product(
6350 __isl_take isl_set *set1,
6351 __isl_take isl_set *set2);
6353 #include <isl/map.h>
6354 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6355 __isl_take isl_basic_map *bmap1,
6356 __isl_take isl_basic_map *bmap2);
6357 __isl_give isl_map *isl_map_flat_domain_product(
6358 __isl_take isl_map *map1,
6359 __isl_take isl_map *map2);
6360 __isl_give isl_map *isl_map_flat_range_product(
6361 __isl_take isl_map *map1,
6362 __isl_take isl_map *map2);
6363 __isl_give isl_basic_map *isl_basic_map_flat_product(
6364 __isl_take isl_basic_map *bmap1,
6365 __isl_take isl_basic_map *bmap2);
6366 __isl_give isl_map *isl_map_flat_product(
6367 __isl_take isl_map *map1,
6368 __isl_take isl_map *map2);
6370 #include <isl/union_map.h>
6371 __isl_give isl_union_map *
6372 isl_union_map_flat_domain_product(
6373 __isl_take isl_union_map *umap1,
6374 __isl_take isl_union_map *umap2);
6375 __isl_give isl_union_map *
6376 isl_union_map_flat_range_product(
6377 __isl_take isl_union_map *umap1,
6378 __isl_take isl_union_map *umap2);
6380 #include <isl/val.h>
6381 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6382 __isl_take isl_multi_val *mv1,
6383 __isl_take isl_multi_aff *mv2);
6385 #include <isl/aff.h>
6386 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6387 __isl_take isl_multi_aff *ma1,
6388 __isl_take isl_multi_aff *ma2);
6389 __isl_give isl_pw_multi_aff *
6390 isl_pw_multi_aff_flat_range_product(
6391 __isl_take isl_pw_multi_aff *pma1,
6392 __isl_take isl_pw_multi_aff *pma2);
6393 __isl_give isl_multi_pw_aff *
6394 isl_multi_pw_aff_flat_range_product(
6395 __isl_take isl_multi_pw_aff *mpa1,
6396 __isl_take isl_multi_pw_aff *mpa2);
6397 __isl_give isl_union_pw_multi_aff *
6398 isl_union_pw_multi_aff_flat_range_product(
6399 __isl_take isl_union_pw_multi_aff *upma1,
6400 __isl_take isl_union_pw_multi_aff *upma2);
6401 __isl_give isl_multi_union_pw_aff *
6402 isl_multi_union_pw_aff_flat_range_product(
6403 __isl_take isl_multi_union_pw_aff *mupa1,
6404 __isl_take isl_multi_union_pw_aff *mupa2);
6406 #include <isl/space.h>
6407 __isl_give isl_space *isl_space_factor_domain(
6408 __isl_take isl_space *space);
6409 __isl_give isl_space *isl_space_factor_range(
6410 __isl_take isl_space *space);
6411 __isl_give isl_space *isl_space_domain_factor_domain(
6412 __isl_take isl_space *space);
6413 __isl_give isl_space *isl_space_domain_factor_range(
6414 __isl_take isl_space *space);
6415 __isl_give isl_space *isl_space_range_factor_domain(
6416 __isl_take isl_space *space);
6417 __isl_give isl_space *isl_space_range_factor_range(
6418 __isl_take isl_space *space);
6420 The functions C<isl_space_range_factor_domain> and
6421 C<isl_space_range_factor_range> extract the two arguments from
6422 the result of a call to C<isl_space_range_product>.
6424 The arguments of a call to a product can be extracted
6425 from the result using the following functions.
6427 #include <isl/map.h>
6428 __isl_give isl_map *isl_map_factor_domain(
6429 __isl_take isl_map *map);
6430 __isl_give isl_map *isl_map_factor_range(
6431 __isl_take isl_map *map);
6432 __isl_give isl_map *isl_map_domain_factor_domain(
6433 __isl_take isl_map *map);
6434 __isl_give isl_map *isl_map_domain_factor_range(
6435 __isl_take isl_map *map);
6436 __isl_give isl_map *isl_map_range_factor_domain(
6437 __isl_take isl_map *map);
6438 __isl_give isl_map *isl_map_range_factor_range(
6439 __isl_take isl_map *map);
6441 #include <isl/union_map.h>
6442 __isl_give isl_union_map *isl_union_map_factor_domain(
6443 __isl_take isl_union_map *umap);
6444 __isl_give isl_union_map *isl_union_map_factor_range(
6445 __isl_take isl_union_map *umap);
6446 __isl_give isl_union_map *
6447 isl_union_map_domain_factor_domain(
6448 __isl_take isl_union_map *umap);
6449 __isl_give isl_union_map *
6450 isl_union_map_domain_factor_range(
6451 __isl_take isl_union_map *umap);
6452 __isl_give isl_union_map *
6453 isl_union_map_range_factor_domain(
6454 __isl_take isl_union_map *umap);
6455 __isl_give isl_union_map *
6456 isl_union_map_range_factor_range(
6457 __isl_take isl_union_map *umap);
6459 #include <isl/val.h>
6460 __isl_give isl_multi_val *isl_multi_val_factor_range(
6461 __isl_take isl_multi_val *mv);
6462 __isl_give isl_multi_val *
6463 isl_multi_val_range_factor_domain(
6464 __isl_take isl_multi_val *mv);
6465 __isl_give isl_multi_val *
6466 isl_multi_val_range_factor_range(
6467 __isl_take isl_multi_val *mv);
6469 #include <isl/aff.h>
6470 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6471 __isl_take isl_multi_aff *ma);
6472 __isl_give isl_multi_aff *
6473 isl_multi_aff_range_factor_domain(
6474 __isl_take isl_multi_aff *ma);
6475 __isl_give isl_multi_aff *
6476 isl_multi_aff_range_factor_range(
6477 __isl_take isl_multi_aff *ma);
6478 __isl_give isl_multi_pw_aff *
6479 isl_multi_pw_aff_factor_range(
6480 __isl_take isl_multi_pw_aff *mpa);
6481 __isl_give isl_multi_pw_aff *
6482 isl_multi_pw_aff_range_factor_domain(
6483 __isl_take isl_multi_pw_aff *mpa);
6484 __isl_give isl_multi_pw_aff *
6485 isl_multi_pw_aff_range_factor_range(
6486 __isl_take isl_multi_pw_aff *mpa);
6487 __isl_give isl_multi_union_pw_aff *
6488 isl_multi_union_pw_aff_factor_range(
6489 __isl_take isl_multi_union_pw_aff *mupa);
6490 __isl_give isl_multi_union_pw_aff *
6491 isl_multi_union_pw_aff_range_factor_domain(
6492 __isl_take isl_multi_union_pw_aff *mupa);
6493 __isl_give isl_multi_union_pw_aff *
6494 isl_multi_union_pw_aff_range_factor_range(
6495 __isl_take isl_multi_union_pw_aff *mupa);
6497 The splice functions are a generalization of the flat product functions,
6498 where the second argument may be inserted at any position inside
6499 the first argument rather than being placed at the end.
6500 The functions C<isl_multi_val_factor_range>,
6501 C<isl_multi_aff_factor_range>,
6502 C<isl_multi_pw_aff_factor_range> and
6503 C<isl_multi_union_pw_aff_factor_range>
6504 take functions that live in a set space.
6506 #include <isl/val.h>
6507 __isl_give isl_multi_val *isl_multi_val_range_splice(
6508 __isl_take isl_multi_val *mv1, unsigned pos,
6509 __isl_take isl_multi_val *mv2);
6511 #include <isl/aff.h>
6512 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6513 __isl_take isl_multi_aff *ma1, unsigned pos,
6514 __isl_take isl_multi_aff *ma2);
6515 __isl_give isl_multi_aff *isl_multi_aff_splice(
6516 __isl_take isl_multi_aff *ma1,
6517 unsigned in_pos, unsigned out_pos,
6518 __isl_take isl_multi_aff *ma2);
6519 __isl_give isl_multi_pw_aff *
6520 isl_multi_pw_aff_range_splice(
6521 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6522 __isl_take isl_multi_pw_aff *mpa2);
6523 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6524 __isl_take isl_multi_pw_aff *mpa1,
6525 unsigned in_pos, unsigned out_pos,
6526 __isl_take isl_multi_pw_aff *mpa2);
6527 __isl_give isl_multi_union_pw_aff *
6528 isl_multi_union_pw_aff_range_splice(
6529 __isl_take isl_multi_union_pw_aff *mupa1,
6531 __isl_take isl_multi_union_pw_aff *mupa2);
6533 =item * Simplification
6535 When applied to a set or relation,
6536 the gist operation returns a set or relation that has the
6537 same intersection with the context as the input set or relation.
6538 Any implicit equality in the intersection is made explicit in the result,
6539 while all inequalities that are redundant with respect to the intersection
6541 In case of union sets and relations, the gist operation is performed
6544 When applied to a function,
6545 the gist operation applies the set gist operation to each of
6546 the cells in the domain of the input piecewise expression.
6547 The context is also exploited
6548 to simplify the expression associated to each cell.
6550 #include <isl/set.h>
6551 __isl_give isl_basic_set *isl_basic_set_gist(
6552 __isl_take isl_basic_set *bset,
6553 __isl_take isl_basic_set *context);
6554 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6555 __isl_take isl_set *context);
6556 __isl_give isl_set *isl_set_gist_params(
6557 __isl_take isl_set *set,
6558 __isl_take isl_set *context);
6560 #include <isl/map.h>
6561 __isl_give isl_basic_map *isl_basic_map_gist(
6562 __isl_take isl_basic_map *bmap,
6563 __isl_take isl_basic_map *context);
6564 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6565 __isl_take isl_basic_map *bmap,
6566 __isl_take isl_basic_set *context);
6567 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6568 __isl_take isl_map *context);
6569 __isl_give isl_map *isl_map_gist_params(
6570 __isl_take isl_map *map,
6571 __isl_take isl_set *context);
6572 __isl_give isl_map *isl_map_gist_domain(
6573 __isl_take isl_map *map,
6574 __isl_take isl_set *context);
6575 __isl_give isl_map *isl_map_gist_range(
6576 __isl_take isl_map *map,
6577 __isl_take isl_set *context);
6579 #include <isl/union_set.h>
6580 __isl_give isl_union_set *isl_union_set_gist(
6581 __isl_take isl_union_set *uset,
6582 __isl_take isl_union_set *context);
6583 __isl_give isl_union_set *isl_union_set_gist_params(
6584 __isl_take isl_union_set *uset,
6585 __isl_take isl_set *set);
6587 #include <isl/union_map.h>
6588 __isl_give isl_union_map *isl_union_map_gist(
6589 __isl_take isl_union_map *umap,
6590 __isl_take isl_union_map *context);
6591 __isl_give isl_union_map *isl_union_map_gist_params(
6592 __isl_take isl_union_map *umap,
6593 __isl_take isl_set *set);
6594 __isl_give isl_union_map *isl_union_map_gist_domain(
6595 __isl_take isl_union_map *umap,
6596 __isl_take isl_union_set *uset);
6597 __isl_give isl_union_map *isl_union_map_gist_range(
6598 __isl_take isl_union_map *umap,
6599 __isl_take isl_union_set *uset);
6601 #include <isl/aff.h>
6602 __isl_give isl_aff *isl_aff_gist_params(
6603 __isl_take isl_aff *aff,
6604 __isl_take isl_set *context);
6605 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6606 __isl_take isl_set *context);
6607 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6608 __isl_take isl_multi_aff *maff,
6609 __isl_take isl_set *context);
6610 __isl_give isl_multi_aff *isl_multi_aff_gist(
6611 __isl_take isl_multi_aff *maff,
6612 __isl_take isl_set *context);
6613 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6614 __isl_take isl_pw_aff *pwaff,
6615 __isl_take isl_set *context);
6616 __isl_give isl_pw_aff *isl_pw_aff_gist(
6617 __isl_take isl_pw_aff *pwaff,
6618 __isl_take isl_set *context);
6619 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6620 __isl_take isl_pw_multi_aff *pma,
6621 __isl_take isl_set *set);
6622 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6623 __isl_take isl_pw_multi_aff *pma,
6624 __isl_take isl_set *set);
6625 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6626 __isl_take isl_multi_pw_aff *mpa,
6627 __isl_take isl_set *set);
6628 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6629 __isl_take isl_multi_pw_aff *mpa,
6630 __isl_take isl_set *set);
6631 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6632 __isl_take isl_union_pw_aff *upa,
6633 __isl_take isl_union_set *context);
6634 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6635 __isl_take isl_union_pw_aff *upa,
6636 __isl_take isl_set *context);
6637 __isl_give isl_union_pw_multi_aff *
6638 isl_union_pw_multi_aff_gist_params(
6639 __isl_take isl_union_pw_multi_aff *upma,
6640 __isl_take isl_set *context);
6641 __isl_give isl_union_pw_multi_aff *
6642 isl_union_pw_multi_aff_gist(
6643 __isl_take isl_union_pw_multi_aff *upma,
6644 __isl_take isl_union_set *context);
6645 __isl_give isl_multi_union_pw_aff *
6646 isl_multi_union_pw_aff_gist_params(
6647 __isl_take isl_multi_union_pw_aff *aff,
6648 __isl_take isl_set *context);
6649 __isl_give isl_multi_union_pw_aff *
6650 isl_multi_union_pw_aff_gist(
6651 __isl_take isl_multi_union_pw_aff *aff,
6652 __isl_take isl_union_set *context);
6654 #include <isl/polynomial.h>
6655 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6656 __isl_take isl_qpolynomial *qp,
6657 __isl_take isl_set *context);
6658 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6659 __isl_take isl_qpolynomial *qp,
6660 __isl_take isl_set *context);
6661 __isl_give isl_qpolynomial_fold *
6662 isl_qpolynomial_fold_gist_params(
6663 __isl_take isl_qpolynomial_fold *fold,
6664 __isl_take isl_set *context);
6665 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6666 __isl_take isl_qpolynomial_fold *fold,
6667 __isl_take isl_set *context);
6668 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6669 __isl_take isl_pw_qpolynomial *pwqp,
6670 __isl_take isl_set *context);
6671 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6672 __isl_take isl_pw_qpolynomial *pwqp,
6673 __isl_take isl_set *context);
6674 __isl_give isl_pw_qpolynomial_fold *
6675 isl_pw_qpolynomial_fold_gist(
6676 __isl_take isl_pw_qpolynomial_fold *pwf,
6677 __isl_take isl_set *context);
6678 __isl_give isl_pw_qpolynomial_fold *
6679 isl_pw_qpolynomial_fold_gist_params(
6680 __isl_take isl_pw_qpolynomial_fold *pwf,
6681 __isl_take isl_set *context);
6682 __isl_give isl_union_pw_qpolynomial *
6683 isl_union_pw_qpolynomial_gist_params(
6684 __isl_take isl_union_pw_qpolynomial *upwqp,
6685 __isl_take isl_set *context);
6686 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6687 __isl_take isl_union_pw_qpolynomial *upwqp,
6688 __isl_take isl_union_set *context);
6689 __isl_give isl_union_pw_qpolynomial_fold *
6690 isl_union_pw_qpolynomial_fold_gist(
6691 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6692 __isl_take isl_union_set *context);
6693 __isl_give isl_union_pw_qpolynomial_fold *
6694 isl_union_pw_qpolynomial_fold_gist_params(
6695 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6696 __isl_take isl_set *context);
6698 =item * Binary Arithmetic Operations
6700 #include <isl/set.h>
6701 __isl_give isl_set *isl_set_sum(
6702 __isl_take isl_set *set1,
6703 __isl_take isl_set *set2);
6704 #include <isl/map.h>
6705 __isl_give isl_map *isl_map_sum(
6706 __isl_take isl_map *map1,
6707 __isl_take isl_map *map2);
6709 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6710 i.e., the set containing the sums of pairs of elements from
6711 C<set1> and C<set2>.
6712 The domain of the result of C<isl_map_sum> is the intersection
6713 of the domains of its two arguments. The corresponding range
6714 elements are the sums of the corresponding range elements
6715 in the two arguments.
6717 #include <isl/val.h>
6718 __isl_give isl_multi_val *isl_multi_val_add(
6719 __isl_take isl_multi_val *mv1,
6720 __isl_take isl_multi_val *mv2);
6721 __isl_give isl_multi_val *isl_multi_val_sub(
6722 __isl_take isl_multi_val *mv1,
6723 __isl_take isl_multi_val *mv2);
6725 #include <isl/aff.h>
6726 __isl_give isl_aff *isl_aff_add(
6727 __isl_take isl_aff *aff1,
6728 __isl_take isl_aff *aff2);
6729 __isl_give isl_multi_aff *isl_multi_aff_add(
6730 __isl_take isl_multi_aff *maff1,
6731 __isl_take isl_multi_aff *maff2);
6732 __isl_give isl_pw_aff *isl_pw_aff_add(
6733 __isl_take isl_pw_aff *pwaff1,
6734 __isl_take isl_pw_aff *pwaff2);
6735 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6736 __isl_take isl_multi_pw_aff *mpa1,
6737 __isl_take isl_multi_pw_aff *mpa2);
6738 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6739 __isl_take isl_pw_multi_aff *pma1,
6740 __isl_take isl_pw_multi_aff *pma2);
6741 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6742 __isl_take isl_union_pw_aff *upa1,
6743 __isl_take isl_union_pw_aff *upa2);
6744 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6745 __isl_take isl_union_pw_multi_aff *upma1,
6746 __isl_take isl_union_pw_multi_aff *upma2);
6747 __isl_give isl_multi_union_pw_aff *
6748 isl_multi_union_pw_aff_add(
6749 __isl_take isl_multi_union_pw_aff *mupa1,
6750 __isl_take isl_multi_union_pw_aff *mupa2);
6751 __isl_give isl_pw_aff *isl_pw_aff_min(
6752 __isl_take isl_pw_aff *pwaff1,
6753 __isl_take isl_pw_aff *pwaff2);
6754 __isl_give isl_pw_aff *isl_pw_aff_max(
6755 __isl_take isl_pw_aff *pwaff1,
6756 __isl_take isl_pw_aff *pwaff2);
6757 __isl_give isl_aff *isl_aff_sub(
6758 __isl_take isl_aff *aff1,
6759 __isl_take isl_aff *aff2);
6760 __isl_give isl_multi_aff *isl_multi_aff_sub(
6761 __isl_take isl_multi_aff *ma1,
6762 __isl_take isl_multi_aff *ma2);
6763 __isl_give isl_pw_aff *isl_pw_aff_sub(
6764 __isl_take isl_pw_aff *pwaff1,
6765 __isl_take isl_pw_aff *pwaff2);
6766 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6767 __isl_take isl_multi_pw_aff *mpa1,
6768 __isl_take isl_multi_pw_aff *mpa2);
6769 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6770 __isl_take isl_pw_multi_aff *pma1,
6771 __isl_take isl_pw_multi_aff *pma2);
6772 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6773 __isl_take isl_union_pw_aff *upa1,
6774 __isl_take isl_union_pw_aff *upa2);
6775 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6776 __isl_take isl_union_pw_multi_aff *upma1,
6777 __isl_take isl_union_pw_multi_aff *upma2);
6778 __isl_give isl_multi_union_pw_aff *
6779 isl_multi_union_pw_aff_sub(
6780 __isl_take isl_multi_union_pw_aff *mupa1,
6781 __isl_take isl_multi_union_pw_aff *mupa2);
6783 C<isl_aff_sub> subtracts the second argument from the first.
6785 #include <isl/polynomial.h>
6786 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6787 __isl_take isl_qpolynomial *qp1,
6788 __isl_take isl_qpolynomial *qp2);
6789 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6790 __isl_take isl_pw_qpolynomial *pwqp1,
6791 __isl_take isl_pw_qpolynomial *pwqp2);
6792 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6793 __isl_take isl_pw_qpolynomial *pwqp1,
6794 __isl_take isl_pw_qpolynomial *pwqp2);
6795 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6796 __isl_take isl_pw_qpolynomial_fold *pwf1,
6797 __isl_take isl_pw_qpolynomial_fold *pwf2);
6798 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6799 __isl_take isl_union_pw_qpolynomial *upwqp1,
6800 __isl_take isl_union_pw_qpolynomial *upwqp2);
6801 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6802 __isl_take isl_qpolynomial *qp1,
6803 __isl_take isl_qpolynomial *qp2);
6804 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6805 __isl_take isl_pw_qpolynomial *pwqp1,
6806 __isl_take isl_pw_qpolynomial *pwqp2);
6807 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6808 __isl_take isl_union_pw_qpolynomial *upwqp1,
6809 __isl_take isl_union_pw_qpolynomial *upwqp2);
6810 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6811 __isl_take isl_pw_qpolynomial_fold *pwf1,
6812 __isl_take isl_pw_qpolynomial_fold *pwf2);
6813 __isl_give isl_union_pw_qpolynomial_fold *
6814 isl_union_pw_qpolynomial_fold_fold(
6815 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6816 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6818 #include <isl/aff.h>
6819 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6820 __isl_take isl_pw_aff *pwaff1,
6821 __isl_take isl_pw_aff *pwaff2);
6822 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6823 __isl_take isl_pw_multi_aff *pma1,
6824 __isl_take isl_pw_multi_aff *pma2);
6825 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6826 __isl_take isl_union_pw_aff *upa1,
6827 __isl_take isl_union_pw_aff *upa2);
6828 __isl_give isl_union_pw_multi_aff *
6829 isl_union_pw_multi_aff_union_add(
6830 __isl_take isl_union_pw_multi_aff *upma1,
6831 __isl_take isl_union_pw_multi_aff *upma2);
6832 __isl_give isl_multi_union_pw_aff *
6833 isl_multi_union_pw_aff_union_add(
6834 __isl_take isl_multi_union_pw_aff *mupa1,
6835 __isl_take isl_multi_union_pw_aff *mupa2);
6836 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6837 __isl_take isl_pw_aff *pwaff1,
6838 __isl_take isl_pw_aff *pwaff2);
6839 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6840 __isl_take isl_pw_aff *pwaff1,
6841 __isl_take isl_pw_aff *pwaff2);
6843 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6844 expression with a domain that is the union of those of C<pwaff1> and
6845 C<pwaff2> and such that on each cell, the quasi-affine expression is
6846 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6847 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6848 associated expression is the defined one.
6849 This in contrast to the C<isl_pw_aff_max> function, which is
6850 only defined on the shared definition domain of the arguments.
6852 #include <isl/val.h>
6853 __isl_give isl_multi_val *isl_multi_val_add_val(
6854 __isl_take isl_multi_val *mv,
6855 __isl_take isl_val *v);
6856 __isl_give isl_multi_val *isl_multi_val_mod_val(
6857 __isl_take isl_multi_val *mv,
6858 __isl_take isl_val *v);
6859 __isl_give isl_multi_val *isl_multi_val_scale_val(
6860 __isl_take isl_multi_val *mv,
6861 __isl_take isl_val *v);
6862 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6863 __isl_take isl_multi_val *mv,
6864 __isl_take isl_val *v);
6866 #include <isl/aff.h>
6867 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6868 __isl_take isl_val *mod);
6869 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6870 __isl_take isl_pw_aff *pa,
6871 __isl_take isl_val *mod);
6872 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6873 __isl_take isl_union_pw_aff *upa,
6874 __isl_take isl_val *f);
6875 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6876 __isl_take isl_val *v);
6877 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6878 __isl_take isl_multi_aff *ma,
6879 __isl_take isl_val *v);
6880 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6881 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6882 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6883 __isl_take isl_multi_pw_aff *mpa,
6884 __isl_take isl_val *v);
6885 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6886 __isl_take isl_pw_multi_aff *pma,
6887 __isl_take isl_val *v);
6888 __isl_give isl_union_pw_multi_aff *
6889 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6890 __isl_take isl_union_pw_aff *upa,
6891 __isl_take isl_val *f);
6892 isl_union_pw_multi_aff_scale_val(
6893 __isl_take isl_union_pw_multi_aff *upma,
6894 __isl_take isl_val *val);
6895 __isl_give isl_multi_union_pw_aff *
6896 isl_multi_union_pw_aff_scale_val(
6897 __isl_take isl_multi_union_pw_aff *mupa,
6898 __isl_take isl_val *v);
6899 __isl_give isl_aff *isl_aff_scale_down_ui(
6900 __isl_take isl_aff *aff, unsigned f);
6901 __isl_give isl_aff *isl_aff_scale_down_val(
6902 __isl_take isl_aff *aff, __isl_take isl_val *v);
6903 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6904 __isl_take isl_multi_aff *ma,
6905 __isl_take isl_val *v);
6906 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6907 __isl_take isl_pw_aff *pa,
6908 __isl_take isl_val *f);
6909 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6910 __isl_take isl_multi_pw_aff *mpa,
6911 __isl_take isl_val *v);
6912 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6913 __isl_take isl_pw_multi_aff *pma,
6914 __isl_take isl_val *v);
6915 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6916 __isl_take isl_union_pw_aff *upa,
6917 __isl_take isl_val *v);
6918 __isl_give isl_union_pw_multi_aff *
6919 isl_union_pw_multi_aff_scale_down_val(
6920 __isl_take isl_union_pw_multi_aff *upma,
6921 __isl_take isl_val *val);
6922 __isl_give isl_multi_union_pw_aff *
6923 isl_multi_union_pw_aff_scale_down_val(
6924 __isl_take isl_multi_union_pw_aff *mupa,
6925 __isl_take isl_val *v);
6927 #include <isl/polynomial.h>
6928 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6929 __isl_take isl_qpolynomial *qp,
6930 __isl_take isl_val *v);
6931 __isl_give isl_qpolynomial_fold *
6932 isl_qpolynomial_fold_scale_val(
6933 __isl_take isl_qpolynomial_fold *fold,
6934 __isl_take isl_val *v);
6935 __isl_give isl_pw_qpolynomial *
6936 isl_pw_qpolynomial_scale_val(
6937 __isl_take isl_pw_qpolynomial *pwqp,
6938 __isl_take isl_val *v);
6939 __isl_give isl_pw_qpolynomial_fold *
6940 isl_pw_qpolynomial_fold_scale_val(
6941 __isl_take isl_pw_qpolynomial_fold *pwf,
6942 __isl_take isl_val *v);
6943 __isl_give isl_union_pw_qpolynomial *
6944 isl_union_pw_qpolynomial_scale_val(
6945 __isl_take isl_union_pw_qpolynomial *upwqp,
6946 __isl_take isl_val *v);
6947 __isl_give isl_union_pw_qpolynomial_fold *
6948 isl_union_pw_qpolynomial_fold_scale_val(
6949 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6950 __isl_take isl_val *v);
6951 __isl_give isl_qpolynomial *
6952 isl_qpolynomial_scale_down_val(
6953 __isl_take isl_qpolynomial *qp,
6954 __isl_take isl_val *v);
6955 __isl_give isl_qpolynomial_fold *
6956 isl_qpolynomial_fold_scale_down_val(
6957 __isl_take isl_qpolynomial_fold *fold,
6958 __isl_take isl_val *v);
6959 __isl_give isl_pw_qpolynomial *
6960 isl_pw_qpolynomial_scale_down_val(
6961 __isl_take isl_pw_qpolynomial *pwqp,
6962 __isl_take isl_val *v);
6963 __isl_give isl_pw_qpolynomial_fold *
6964 isl_pw_qpolynomial_fold_scale_down_val(
6965 __isl_take isl_pw_qpolynomial_fold *pwf,
6966 __isl_take isl_val *v);
6967 __isl_give isl_union_pw_qpolynomial *
6968 isl_union_pw_qpolynomial_scale_down_val(
6969 __isl_take isl_union_pw_qpolynomial *upwqp,
6970 __isl_take isl_val *v);
6971 __isl_give isl_union_pw_qpolynomial_fold *
6972 isl_union_pw_qpolynomial_fold_scale_down_val(
6973 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6974 __isl_take isl_val *v);
6976 #include <isl/val.h>
6977 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6978 __isl_take isl_multi_val *mv1,
6979 __isl_take isl_multi_val *mv2);
6980 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6981 __isl_take isl_multi_val *mv1,
6982 __isl_take isl_multi_val *mv2);
6983 __isl_give isl_multi_val *
6984 isl_multi_val_scale_down_multi_val(
6985 __isl_take isl_multi_val *mv1,
6986 __isl_take isl_multi_val *mv2);
6988 #include <isl/aff.h>
6989 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6990 __isl_take isl_multi_aff *ma,
6991 __isl_take isl_multi_val *mv);
6992 __isl_give isl_multi_union_pw_aff *
6993 isl_multi_union_pw_aff_mod_multi_val(
6994 __isl_take isl_multi_union_pw_aff *upma,
6995 __isl_take isl_multi_val *mv);
6996 __isl_give isl_multi_pw_aff *
6997 isl_multi_pw_aff_mod_multi_val(
6998 __isl_take isl_multi_pw_aff *mpa,
6999 __isl_take isl_multi_val *mv);
7000 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7001 __isl_take isl_multi_aff *ma,
7002 __isl_take isl_multi_val *mv);
7003 __isl_give isl_pw_multi_aff *
7004 isl_pw_multi_aff_scale_multi_val(
7005 __isl_take isl_pw_multi_aff *pma,
7006 __isl_take isl_multi_val *mv);
7007 __isl_give isl_multi_pw_aff *
7008 isl_multi_pw_aff_scale_multi_val(
7009 __isl_take isl_multi_pw_aff *mpa,
7010 __isl_take isl_multi_val *mv);
7011 __isl_give isl_multi_union_pw_aff *
7012 isl_multi_union_pw_aff_scale_multi_val(
7013 __isl_take isl_multi_union_pw_aff *mupa,
7014 __isl_take isl_multi_val *mv);
7015 __isl_give isl_union_pw_multi_aff *
7016 isl_union_pw_multi_aff_scale_multi_val(
7017 __isl_take isl_union_pw_multi_aff *upma,
7018 __isl_take isl_multi_val *mv);
7019 __isl_give isl_multi_aff *
7020 isl_multi_aff_scale_down_multi_val(
7021 __isl_take isl_multi_aff *ma,
7022 __isl_take isl_multi_val *mv);
7023 __isl_give isl_multi_pw_aff *
7024 isl_multi_pw_aff_scale_down_multi_val(
7025 __isl_take isl_multi_pw_aff *mpa,
7026 __isl_take isl_multi_val *mv);
7027 __isl_give isl_multi_union_pw_aff *
7028 isl_multi_union_pw_aff_scale_down_multi_val(
7029 __isl_take isl_multi_union_pw_aff *mupa,
7030 __isl_take isl_multi_val *mv);
7032 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7033 by the corresponding elements of C<mv>.
7035 #include <isl/aff.h>
7036 __isl_give isl_aff *isl_aff_mul(
7037 __isl_take isl_aff *aff1,
7038 __isl_take isl_aff *aff2);
7039 __isl_give isl_aff *isl_aff_div(
7040 __isl_take isl_aff *aff1,
7041 __isl_take isl_aff *aff2);
7042 __isl_give isl_pw_aff *isl_pw_aff_mul(
7043 __isl_take isl_pw_aff *pwaff1,
7044 __isl_take isl_pw_aff *pwaff2);
7045 __isl_give isl_pw_aff *isl_pw_aff_div(
7046 __isl_take isl_pw_aff *pa1,
7047 __isl_take isl_pw_aff *pa2);
7048 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7049 __isl_take isl_pw_aff *pa1,
7050 __isl_take isl_pw_aff *pa2);
7051 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7052 __isl_take isl_pw_aff *pa1,
7053 __isl_take isl_pw_aff *pa2);
7055 When multiplying two affine expressions, at least one of the two needs
7056 to be a constant. Similarly, when dividing an affine expression by another,
7057 the second expression needs to be a constant.
7058 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7059 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7062 #include <isl/polynomial.h>
7063 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7064 __isl_take isl_qpolynomial *qp1,
7065 __isl_take isl_qpolynomial *qp2);
7066 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7067 __isl_take isl_pw_qpolynomial *pwqp1,
7068 __isl_take isl_pw_qpolynomial *pwqp2);
7069 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7070 __isl_take isl_union_pw_qpolynomial *upwqp1,
7071 __isl_take isl_union_pw_qpolynomial *upwqp2);
7075 =head3 Lexicographic Optimization
7077 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7078 the following functions
7079 compute a set that contains the lexicographic minimum or maximum
7080 of the elements in C<set> (or C<bset>) for those values of the parameters
7081 that satisfy C<dom>.
7082 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7083 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7085 In other words, the union of the parameter values
7086 for which the result is non-empty and of C<*empty>
7089 #include <isl/set.h>
7090 __isl_give isl_set *isl_basic_set_partial_lexmin(
7091 __isl_take isl_basic_set *bset,
7092 __isl_take isl_basic_set *dom,
7093 __isl_give isl_set **empty);
7094 __isl_give isl_set *isl_basic_set_partial_lexmax(
7095 __isl_take isl_basic_set *bset,
7096 __isl_take isl_basic_set *dom,
7097 __isl_give isl_set **empty);
7098 __isl_give isl_set *isl_set_partial_lexmin(
7099 __isl_take isl_set *set, __isl_take isl_set *dom,
7100 __isl_give isl_set **empty);
7101 __isl_give isl_set *isl_set_partial_lexmax(
7102 __isl_take isl_set *set, __isl_take isl_set *dom,
7103 __isl_give isl_set **empty);
7105 Given a (basic) set C<set> (or C<bset>), the following functions simply
7106 return a set containing the lexicographic minimum or maximum
7107 of the elements in C<set> (or C<bset>).
7108 In case of union sets, the optimum is computed per space.
7110 #include <isl/set.h>
7111 __isl_give isl_set *isl_basic_set_lexmin(
7112 __isl_take isl_basic_set *bset);
7113 __isl_give isl_set *isl_basic_set_lexmax(
7114 __isl_take isl_basic_set *bset);
7115 __isl_give isl_set *isl_set_lexmin(
7116 __isl_take isl_set *set);
7117 __isl_give isl_set *isl_set_lexmax(
7118 __isl_take isl_set *set);
7119 __isl_give isl_union_set *isl_union_set_lexmin(
7120 __isl_take isl_union_set *uset);
7121 __isl_give isl_union_set *isl_union_set_lexmax(
7122 __isl_take isl_union_set *uset);
7124 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7125 the following functions
7126 compute a relation that maps each element of C<dom>
7127 to the single lexicographic minimum or maximum
7128 of the elements that are associated to that same
7129 element in C<map> (or C<bmap>).
7130 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7131 that contains the elements in C<dom> that do not map
7132 to any elements in C<map> (or C<bmap>).
7133 In other words, the union of the domain of the result and of C<*empty>
7136 #include <isl/map.h>
7137 __isl_give isl_map *isl_basic_map_partial_lexmax(
7138 __isl_take isl_basic_map *bmap,
7139 __isl_take isl_basic_set *dom,
7140 __isl_give isl_set **empty);
7141 __isl_give isl_map *isl_basic_map_partial_lexmin(
7142 __isl_take isl_basic_map *bmap,
7143 __isl_take isl_basic_set *dom,
7144 __isl_give isl_set **empty);
7145 __isl_give isl_map *isl_map_partial_lexmax(
7146 __isl_take isl_map *map, __isl_take isl_set *dom,
7147 __isl_give isl_set **empty);
7148 __isl_give isl_map *isl_map_partial_lexmin(
7149 __isl_take isl_map *map, __isl_take isl_set *dom,
7150 __isl_give isl_set **empty);
7152 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7153 return a map mapping each element in the domain of
7154 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7155 of all elements associated to that element.
7156 In case of union relations, the optimum is computed per space.
7158 #include <isl/map.h>
7159 __isl_give isl_map *isl_basic_map_lexmin(
7160 __isl_take isl_basic_map *bmap);
7161 __isl_give isl_map *isl_basic_map_lexmax(
7162 __isl_take isl_basic_map *bmap);
7163 __isl_give isl_map *isl_map_lexmin(
7164 __isl_take isl_map *map);
7165 __isl_give isl_map *isl_map_lexmax(
7166 __isl_take isl_map *map);
7167 __isl_give isl_union_map *isl_union_map_lexmin(
7168 __isl_take isl_union_map *umap);
7169 __isl_give isl_union_map *isl_union_map_lexmax(
7170 __isl_take isl_union_map *umap);
7172 The following functions return their result in the form of
7173 a piecewise multi-affine expression,
7174 but are otherwise equivalent to the corresponding functions
7175 returning a basic set or relation.
7177 #include <isl/set.h>
7178 __isl_give isl_pw_multi_aff *
7179 isl_basic_set_partial_lexmin_pw_multi_aff(
7180 __isl_take isl_basic_set *bset,
7181 __isl_take isl_basic_set *dom,
7182 __isl_give isl_set **empty);
7183 __isl_give isl_pw_multi_aff *
7184 isl_basic_set_partial_lexmax_pw_multi_aff(
7185 __isl_take isl_basic_set *bset,
7186 __isl_take isl_basic_set *dom,
7187 __isl_give isl_set **empty);
7188 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7189 __isl_take isl_set *set);
7190 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7191 __isl_take isl_set *set);
7193 #include <isl/map.h>
7194 __isl_give isl_pw_multi_aff *
7195 isl_basic_map_lexmin_pw_multi_aff(
7196 __isl_take isl_basic_map *bmap);
7197 __isl_give isl_pw_multi_aff *
7198 isl_basic_map_partial_lexmin_pw_multi_aff(
7199 __isl_take isl_basic_map *bmap,
7200 __isl_take isl_basic_set *dom,
7201 __isl_give isl_set **empty);
7202 __isl_give isl_pw_multi_aff *
7203 isl_basic_map_partial_lexmax_pw_multi_aff(
7204 __isl_take isl_basic_map *bmap,
7205 __isl_take isl_basic_set *dom,
7206 __isl_give isl_set **empty);
7207 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7208 __isl_take isl_map *map);
7209 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7210 __isl_take isl_map *map);
7212 The following functions return the lexicographic minimum or maximum
7213 on the shared domain of the inputs and the single defined function
7214 on those parts of the domain where only a single function is defined.
7216 #include <isl/aff.h>
7217 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7218 __isl_take isl_pw_multi_aff *pma1,
7219 __isl_take isl_pw_multi_aff *pma2);
7220 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7221 __isl_take isl_pw_multi_aff *pma1,
7222 __isl_take isl_pw_multi_aff *pma2);
7224 =head2 Ternary Operations
7226 #include <isl/aff.h>
7227 __isl_give isl_pw_aff *isl_pw_aff_cond(
7228 __isl_take isl_pw_aff *cond,
7229 __isl_take isl_pw_aff *pwaff_true,
7230 __isl_take isl_pw_aff *pwaff_false);
7232 The function C<isl_pw_aff_cond> performs a conditional operator
7233 and returns an expression that is equal to C<pwaff_true>
7234 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7235 where C<cond> is zero.
7239 Lists are defined over several element types, including
7240 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7241 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7242 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7243 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7244 Here we take lists of C<isl_set>s as an example.
7245 Lists can be created, copied, modified and freed using the following functions.
7247 #include <isl/set.h>
7248 __isl_give isl_set_list *isl_set_list_from_set(
7249 __isl_take isl_set *el);
7250 __isl_give isl_set_list *isl_set_list_alloc(
7251 isl_ctx *ctx, int n);
7252 __isl_give isl_set_list *isl_set_list_copy(
7253 __isl_keep isl_set_list *list);
7254 __isl_give isl_set_list *isl_set_list_insert(
7255 __isl_take isl_set_list *list, unsigned pos,
7256 __isl_take isl_set *el);
7257 __isl_give isl_set_list *isl_set_list_add(
7258 __isl_take isl_set_list *list,
7259 __isl_take isl_set *el);
7260 __isl_give isl_set_list *isl_set_list_drop(
7261 __isl_take isl_set_list *list,
7262 unsigned first, unsigned n);
7263 __isl_give isl_set_list *isl_set_list_set_set(
7264 __isl_take isl_set_list *list, int index,
7265 __isl_take isl_set *set);
7266 __isl_give isl_set_list *isl_set_list_concat(
7267 __isl_take isl_set_list *list1,
7268 __isl_take isl_set_list *list2);
7269 __isl_give isl_set_list *isl_set_list_sort(
7270 __isl_take isl_set_list *list,
7271 int (*cmp)(__isl_keep isl_set *a,
7272 __isl_keep isl_set *b, void *user),
7274 __isl_null isl_set_list *isl_set_list_free(
7275 __isl_take isl_set_list *list);
7277 C<isl_set_list_alloc> creates an empty list with an initial capacity
7278 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7279 add elements to a list, increasing its capacity as needed.
7280 C<isl_set_list_from_set> creates a list with a single element.
7282 Lists can be inspected using the following functions.
7284 #include <isl/set.h>
7285 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7286 __isl_give isl_set *isl_set_list_get_set(
7287 __isl_keep isl_set_list *list, int index);
7288 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7289 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7291 isl_stat isl_set_list_foreach_scc(
7292 __isl_keep isl_set_list *list,
7293 isl_bool (*follows)(__isl_keep isl_set *a,
7294 __isl_keep isl_set *b, void *user),
7296 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7299 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7300 strongly connected components of the graph with as vertices the elements
7301 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7302 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
7303 should return C<-1> on error.
7305 Lists can be printed using
7307 #include <isl/set.h>
7308 __isl_give isl_printer *isl_printer_print_set_list(
7309 __isl_take isl_printer *p,
7310 __isl_keep isl_set_list *list);
7312 =head2 Associative arrays
7314 Associative arrays map isl objects of a specific type to isl objects
7315 of some (other) specific type. They are defined for several pairs
7316 of types, including (C<isl_map>, C<isl_basic_set>),
7317 (C<isl_id>, C<isl_ast_expr>),
7318 (C<isl_id>, C<isl_id>) and
7319 (C<isl_id>, C<isl_pw_aff>).
7320 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7323 Associative arrays can be created, copied and freed using
7324 the following functions.
7326 #include <isl/id_to_ast_expr.h>
7327 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7328 isl_ctx *ctx, int min_size);
7329 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7330 __isl_keep isl_id_to_ast_expr *id2expr);
7331 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7332 __isl_take isl_id_to_ast_expr *id2expr);
7334 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7335 to specify the expected size of the associative array.
7336 The associative array will be grown automatically as needed.
7338 Associative arrays can be inspected using the following functions.
7340 #include <isl/id_to_ast_expr.h>
7341 __isl_give isl_maybe_isl_ast_expr
7342 isl_id_to_ast_expr_try_get(
7343 __isl_keep isl_id_to_ast_expr *id2expr,
7344 __isl_keep isl_id *key);
7345 isl_bool isl_id_to_ast_expr_has(
7346 __isl_keep isl_id_to_ast_expr *id2expr,
7347 __isl_keep isl_id *key);
7348 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7349 __isl_keep isl_id_to_ast_expr *id2expr,
7350 __isl_take isl_id *key);
7351 isl_stat isl_id_to_ast_expr_foreach(
7352 __isl_keep isl_id_to_ast_expr *id2expr,
7353 isl_stat (*fn)(__isl_take isl_id *key,
7354 __isl_take isl_ast_expr *val, void *user),
7357 The function C<isl_id_to_ast_expr_try_get> returns a structure
7358 containing two elements, C<valid> and C<value>.
7359 If there is a value associated to the key, then C<valid>
7360 is set to C<isl_bool_true> and C<value> contains a copy of
7361 the associated value. Otherwise C<value> is C<NULL> and
7362 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7363 on whether some error has occurred or there simply is no associated value.
7364 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7365 in the structure and
7366 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7368 Associative arrays can be modified using the following functions.
7370 #include <isl/id_to_ast_expr.h>
7371 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7372 __isl_take isl_id_to_ast_expr *id2expr,
7373 __isl_take isl_id *key,
7374 __isl_take isl_ast_expr *val);
7375 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7376 __isl_take isl_id_to_ast_expr *id2expr,
7377 __isl_take isl_id *key);
7379 Associative arrays can be printed using the following function.
7381 #include <isl/id_to_ast_expr.h>
7382 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7383 __isl_take isl_printer *p,
7384 __isl_keep isl_id_to_ast_expr *id2expr);
7388 Vectors can be created, copied and freed using the following functions.
7390 #include <isl/vec.h>
7391 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7393 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7394 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7396 Note that the elements of a newly created vector may have arbitrary values.
7397 The elements can be changed and inspected using the following functions.
7399 int isl_vec_size(__isl_keep isl_vec *vec);
7400 __isl_give isl_val *isl_vec_get_element_val(
7401 __isl_keep isl_vec *vec, int pos);
7402 __isl_give isl_vec *isl_vec_set_element_si(
7403 __isl_take isl_vec *vec, int pos, int v);
7404 __isl_give isl_vec *isl_vec_set_element_val(
7405 __isl_take isl_vec *vec, int pos,
7406 __isl_take isl_val *v);
7407 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7409 __isl_give isl_vec *isl_vec_set_val(
7410 __isl_take isl_vec *vec, __isl_take isl_val *v);
7411 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7412 __isl_keep isl_vec *vec2, int pos);
7414 C<isl_vec_get_element> will return a negative value if anything went wrong.
7415 In that case, the value of C<*v> is undefined.
7417 The following function can be used to concatenate two vectors.
7419 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7420 __isl_take isl_vec *vec2);
7424 Matrices can be created, copied and freed using the following functions.
7426 #include <isl/mat.h>
7427 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7428 unsigned n_row, unsigned n_col);
7429 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7430 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7432 Note that the elements of a newly created matrix may have arbitrary values.
7433 The elements can be changed and inspected using the following functions.
7435 int isl_mat_rows(__isl_keep isl_mat *mat);
7436 int isl_mat_cols(__isl_keep isl_mat *mat);
7437 __isl_give isl_val *isl_mat_get_element_val(
7438 __isl_keep isl_mat *mat, int row, int col);
7439 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7440 int row, int col, int v);
7441 __isl_give isl_mat *isl_mat_set_element_val(
7442 __isl_take isl_mat *mat, int row, int col,
7443 __isl_take isl_val *v);
7445 C<isl_mat_get_element> will return a negative value if anything went wrong.
7446 In that case, the value of C<*v> is undefined.
7448 The following function can be used to compute the (right) inverse
7449 of a matrix, i.e., a matrix such that the product of the original
7450 and the inverse (in that order) is a multiple of the identity matrix.
7451 The input matrix is assumed to be of full row-rank.
7453 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7455 The following function can be used to compute the (right) kernel
7456 (or null space) of a matrix, i.e., a matrix such that the product of
7457 the original and the kernel (in that order) is the zero matrix.
7459 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7461 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7463 The following functions determine
7464 an upper or lower bound on a quasipolynomial over its domain.
7466 __isl_give isl_pw_qpolynomial_fold *
7467 isl_pw_qpolynomial_bound(
7468 __isl_take isl_pw_qpolynomial *pwqp,
7469 enum isl_fold type, int *tight);
7471 __isl_give isl_union_pw_qpolynomial_fold *
7472 isl_union_pw_qpolynomial_bound(
7473 __isl_take isl_union_pw_qpolynomial *upwqp,
7474 enum isl_fold type, int *tight);
7476 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7477 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7478 is the returned bound is known be tight, i.e., for each value
7479 of the parameters there is at least
7480 one element in the domain that reaches the bound.
7481 If the domain of C<pwqp> is not wrapping, then the bound is computed
7482 over all elements in that domain and the result has a purely parametric
7483 domain. If the domain of C<pwqp> is wrapping, then the bound is
7484 computed over the range of the wrapped relation. The domain of the
7485 wrapped relation becomes the domain of the result.
7487 =head2 Parametric Vertex Enumeration
7489 The parametric vertex enumeration described in this section
7490 is mainly intended to be used internally and by the C<barvinok>
7493 #include <isl/vertices.h>
7494 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7495 __isl_keep isl_basic_set *bset);
7497 The function C<isl_basic_set_compute_vertices> performs the
7498 actual computation of the parametric vertices and the chamber
7499 decomposition and store the result in an C<isl_vertices> object.
7500 This information can be queried by either iterating over all
7501 the vertices or iterating over all the chambers or cells
7502 and then iterating over all vertices that are active on the chamber.
7504 isl_stat isl_vertices_foreach_vertex(
7505 __isl_keep isl_vertices *vertices,
7506 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7507 void *user), void *user);
7509 isl_stat isl_vertices_foreach_cell(
7510 __isl_keep isl_vertices *vertices,
7511 isl_stat (*fn)(__isl_take isl_cell *cell,
7512 void *user), void *user);
7513 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7514 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7515 void *user), void *user);
7517 Other operations that can be performed on an C<isl_vertices> object are
7520 int isl_vertices_get_n_vertices(
7521 __isl_keep isl_vertices *vertices);
7522 void isl_vertices_free(__isl_take isl_vertices *vertices);
7524 Vertices can be inspected and destroyed using the following functions.
7526 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7527 __isl_give isl_basic_set *isl_vertex_get_domain(
7528 __isl_keep isl_vertex *vertex);
7529 __isl_give isl_multi_aff *isl_vertex_get_expr(
7530 __isl_keep isl_vertex *vertex);
7531 void isl_vertex_free(__isl_take isl_vertex *vertex);
7533 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7534 describing the vertex in terms of the parameters,
7535 while C<isl_vertex_get_domain> returns the activity domain
7538 Chambers can be inspected and destroyed using the following functions.
7540 __isl_give isl_basic_set *isl_cell_get_domain(
7541 __isl_keep isl_cell *cell);
7542 void isl_cell_free(__isl_take isl_cell *cell);
7544 =head1 Polyhedral Compilation Library
7546 This section collects functionality in C<isl> that has been specifically
7547 designed for use during polyhedral compilation.
7549 =head2 Schedule Trees
7551 A schedule tree is a structured representation of a schedule,
7552 assigning a relative order to a set of domain elements.
7553 The relative order expressed by the schedule tree is
7554 defined recursively. In particular, the order between
7555 two domain elements is determined by the node that is closest
7556 to the root that refers to both elements and that orders them apart.
7557 Each node in the tree is of one of several types.
7558 The root node is always of type C<isl_schedule_node_domain>
7559 (or C<isl_schedule_node_extension>)
7560 and it describes the (extra) domain elements to which the schedule applies.
7561 The other types of nodes are as follows.
7565 =item C<isl_schedule_node_band>
7567 A band of schedule dimensions. Each schedule dimension is represented
7568 by a union piecewise quasi-affine expression. If this expression
7569 assigns a different value to two domain elements, while all previous
7570 schedule dimensions in the same band assign them the same value,
7571 then the two domain elements are ordered according to these two
7573 Each expression is required to be total in the domain elements
7574 that reach the band node.
7576 =item C<isl_schedule_node_expansion>
7578 An expansion node maps each of the domain elements that reach the node
7579 to one or more domain elements. The image of this mapping forms
7580 the set of domain elements that reach the child of the expansion node.
7581 The function that maps each of the expanded domain elements
7582 to the original domain element from which it was expanded
7583 is called the contraction.
7585 =item C<isl_schedule_node_filter>
7587 A filter node does not impose any ordering, but rather intersects
7588 the set of domain elements that the current subtree refers to
7589 with a given union set. The subtree of the filter node only
7590 refers to domain elements in the intersection.
7591 A filter node is typically only used a child of a sequence or
7594 =item C<isl_schedule_node_leaf>
7596 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7598 =item C<isl_schedule_node_mark>
7600 A mark node can be used to attach any kind of information to a subtree
7601 of the schedule tree.
7603 =item C<isl_schedule_node_sequence>
7605 A sequence node has one or more children, each of which is a filter node.
7606 The filters on these filter nodes form a partition of
7607 the domain elements that the current subtree refers to.
7608 If two domain elements appear in distinct filters then the sequence
7609 node orders them according to the child positions of the corresponding
7612 =item C<isl_schedule_node_set>
7614 A set node is similar to a sequence node, except that
7615 it expresses that domain elements appearing in distinct filters
7616 may have any order. The order of the children of a set node
7617 is therefore also immaterial.
7621 The following node types are only supported by the AST generator.
7625 =item C<isl_schedule_node_context>
7627 The context describes constraints on the parameters and
7628 the schedule dimensions of outer
7629 bands that the AST generator may assume to hold. It is also the only
7630 kind of node that may introduce additional parameters.
7631 The space of the context is that of the flat product of the outer
7632 band nodes. In particular, if there are no outer band nodes, then
7633 this space is the unnamed zero-dimensional space.
7634 Since a context node references the outer band nodes, any tree
7635 containing a context node is considered to be anchored.
7637 =item C<isl_schedule_node_extension>
7639 An extension node instructs the AST generator to add additional
7640 domain elements that need to be scheduled.
7641 The additional domain elements are described by the range of
7642 the extension map in terms of the outer schedule dimensions,
7643 i.e., the flat product of the outer band nodes.
7644 Note that domain elements are added whenever the AST generator
7645 reaches the extension node, meaning that there are still some
7646 active domain elements for which an AST needs to be generated.
7647 The conditions under which some domain elements are still active
7648 may however not be completely described by the outer AST nodes
7649 generated at that point.
7651 An extension node may also appear as the root of a schedule tree,
7652 when it is intended to be inserted into another tree
7653 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7654 In this case, the domain of the extension node should
7655 correspond to the flat product of the outer band nodes
7656 in this other schedule tree at the point where the extension tree
7659 =item C<isl_schedule_node_guard>
7661 The guard describes constraints on the parameters and
7662 the schedule dimensions of outer
7663 bands that need to be enforced by the outer nodes
7664 in the generated AST.
7665 The space of the guard is that of the flat product of the outer
7666 band nodes. In particular, if there are no outer band nodes, then
7667 this space is the unnamed zero-dimensional space.
7668 Since a guard node references the outer band nodes, any tree
7669 containing a guard node is considered to be anchored.
7673 Except for the C<isl_schedule_node_context> nodes,
7674 none of the nodes may introduce any parameters that were not
7675 already present in the root domain node.
7677 A schedule tree is encapsulated in an C<isl_schedule> object.
7678 The simplest such objects, those with a tree consisting of single domain node,
7679 can be created using the following functions with either an empty
7680 domain or a given domain.
7682 #include <isl/schedule.h>
7683 __isl_give isl_schedule *isl_schedule_empty(
7684 __isl_take isl_space *space);
7685 __isl_give isl_schedule *isl_schedule_from_domain(
7686 __isl_take isl_union_set *domain);
7688 The function C<isl_schedule_constraints_compute_schedule> described
7689 in L</"Scheduling"> can also be used to construct schedules.
7691 C<isl_schedule> objects may be copied and freed using the following functions.
7693 #include <isl/schedule.h>
7694 __isl_give isl_schedule *isl_schedule_copy(
7695 __isl_keep isl_schedule *sched);
7696 __isl_null isl_schedule *isl_schedule_free(
7697 __isl_take isl_schedule *sched);
7699 The following functions checks whether two C<isl_schedule> objects
7700 are obviously the same.
7702 #include <isl/schedule.h>
7703 isl_bool isl_schedule_plain_is_equal(
7704 __isl_keep isl_schedule *schedule1,
7705 __isl_keep isl_schedule *schedule2);
7707 The domain of the schedule, i.e., the domain described by the root node,
7708 can be obtained using the following function.
7710 #include <isl/schedule.h>
7711 __isl_give isl_union_set *isl_schedule_get_domain(
7712 __isl_keep isl_schedule *schedule);
7714 An extra top-level band node (right underneath the domain node) can
7715 be introduced into the schedule using the following function.
7716 The schedule tree is assumed not to have any anchored nodes.
7718 #include <isl/schedule.h>
7719 __isl_give isl_schedule *
7720 isl_schedule_insert_partial_schedule(
7721 __isl_take isl_schedule *schedule,
7722 __isl_take isl_multi_union_pw_aff *partial);
7724 A top-level context node (right underneath the domain node) can
7725 be introduced into the schedule using the following function.
7727 #include <isl/schedule.h>
7728 __isl_give isl_schedule *isl_schedule_insert_context(
7729 __isl_take isl_schedule *schedule,
7730 __isl_take isl_set *context)
7732 A top-level guard node (right underneath the domain node) can
7733 be introduced into the schedule using the following function.
7735 #include <isl/schedule.h>
7736 __isl_give isl_schedule *isl_schedule_insert_guard(
7737 __isl_take isl_schedule *schedule,
7738 __isl_take isl_set *guard)
7740 A schedule that combines two schedules either in the given
7741 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7742 or an C<isl_schedule_node_set> node,
7743 can be created using the following functions.
7745 #include <isl/schedule.h>
7746 __isl_give isl_schedule *isl_schedule_sequence(
7747 __isl_take isl_schedule *schedule1,
7748 __isl_take isl_schedule *schedule2);
7749 __isl_give isl_schedule *isl_schedule_set(
7750 __isl_take isl_schedule *schedule1,
7751 __isl_take isl_schedule *schedule2);
7753 The domains of the two input schedules need to be disjoint.
7755 The following function can be used to restrict the domain
7756 of a schedule with a domain node as root to be a subset of the given union set.
7757 This operation may remove nodes in the tree that have become
7760 #include <isl/schedule.h>
7761 __isl_give isl_schedule *isl_schedule_intersect_domain(
7762 __isl_take isl_schedule *schedule,
7763 __isl_take isl_union_set *domain);
7765 The following function can be used to simplify the domain
7766 of a schedule with a domain node as root with respect to the given
7769 #include <isl/schedule.h>
7770 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7771 __isl_take isl_schedule *schedule,
7772 __isl_take isl_set *context);
7774 The following function resets the user pointers on all parameter
7775 and tuple identifiers referenced by the nodes of the given schedule.
7777 #include <isl/schedule.h>
7778 __isl_give isl_schedule *isl_schedule_reset_user(
7779 __isl_take isl_schedule *schedule);
7781 The following function aligns the parameters of all nodes
7782 in the given schedule to the given space.
7784 #include <isl/schedule.h>
7785 __isl_give isl_schedule *isl_schedule_align_params(
7786 __isl_take isl_schedule *schedule,
7787 __isl_take isl_space *space);
7789 The following function allows the user to plug in a given function
7790 in the iteration domains. The input schedule is not allowed to contain
7791 any expansion nodes.
7793 #include <isl/schedule.h>
7794 __isl_give isl_schedule *
7795 isl_schedule_pullback_union_pw_multi_aff(
7796 __isl_take isl_schedule *schedule,
7797 __isl_take isl_union_pw_multi_aff *upma);
7799 An C<isl_union_map> representation of the schedule can be obtained
7800 from an C<isl_schedule> using the following function.
7802 #include <isl/schedule.h>
7803 __isl_give isl_union_map *isl_schedule_get_map(
7804 __isl_keep isl_schedule *sched);
7806 The resulting relation encodes the same relative ordering as
7807 the schedule by mapping the domain elements to a common schedule space.
7808 If the schedule_separate_components option is set, then the order
7809 of the children of a set node is explicitly encoded in the result.
7810 If the tree contains any expansion nodes, then the relation
7811 is formulated in terms of the expanded domain elements.
7813 Schedules can be read from input using the following functions.
7815 #include <isl/schedule.h>
7816 __isl_give isl_schedule *isl_schedule_read_from_file(
7817 isl_ctx *ctx, FILE *input);
7818 __isl_give isl_schedule *isl_schedule_read_from_str(
7819 isl_ctx *ctx, const char *str);
7821 A representation of the schedule can be printed using
7823 #include <isl/schedule.h>
7824 __isl_give isl_printer *isl_printer_print_schedule(
7825 __isl_take isl_printer *p,
7826 __isl_keep isl_schedule *schedule);
7827 __isl_give char *isl_schedule_to_str(
7828 __isl_keep isl_schedule *schedule);
7830 C<isl_schedule_to_str> prints the schedule in flow format.
7832 The schedule tree can be traversed through the use of
7833 C<isl_schedule_node> objects that point to a particular
7834 position in the schedule tree. Whenever a C<isl_schedule_node>
7835 is use to modify a node in the schedule tree, the original schedule
7836 tree is left untouched and the modifications are performed to a copy
7837 of the tree. The returned C<isl_schedule_node> then points to
7838 this modified copy of the tree.
7840 The root of the schedule tree can be obtained using the following function.
7842 #include <isl/schedule.h>
7843 __isl_give isl_schedule_node *isl_schedule_get_root(
7844 __isl_keep isl_schedule *schedule);
7846 A pointer to a newly created schedule tree with a single domain
7847 node can be created using the following functions.
7849 #include <isl/schedule_node.h>
7850 __isl_give isl_schedule_node *
7851 isl_schedule_node_from_domain(
7852 __isl_take isl_union_set *domain);
7853 __isl_give isl_schedule_node *
7854 isl_schedule_node_from_extension(
7855 __isl_take isl_union_map *extension);
7857 C<isl_schedule_node_from_extension> creates a tree with an extension
7860 Schedule nodes can be copied and freed using the following functions.
7862 #include <isl/schedule_node.h>
7863 __isl_give isl_schedule_node *isl_schedule_node_copy(
7864 __isl_keep isl_schedule_node *node);
7865 __isl_null isl_schedule_node *isl_schedule_node_free(
7866 __isl_take isl_schedule_node *node);
7868 The following functions can be used to check if two schedule
7869 nodes point to the same position in the same schedule.
7871 #include <isl/schedule_node.h>
7872 isl_bool isl_schedule_node_is_equal(
7873 __isl_keep isl_schedule_node *node1,
7874 __isl_keep isl_schedule_node *node2);
7876 The following properties can be obtained from a schedule node.
7878 #include <isl/schedule_node.h>
7879 enum isl_schedule_node_type isl_schedule_node_get_type(
7880 __isl_keep isl_schedule_node *node);
7881 enum isl_schedule_node_type
7882 isl_schedule_node_get_parent_type(
7883 __isl_keep isl_schedule_node *node);
7884 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7885 __isl_keep isl_schedule_node *node);
7887 The function C<isl_schedule_node_get_type> returns the type of
7888 the node, while C<isl_schedule_node_get_parent_type> returns
7889 type of the parent of the node, which is required to exist.
7890 The function C<isl_schedule_node_get_schedule> returns a copy
7891 to the schedule to which the node belongs.
7893 The following functions can be used to move the schedule node
7894 to a different position in the tree or to check if such a position
7897 #include <isl/schedule_node.h>
7898 isl_bool isl_schedule_node_has_parent(
7899 __isl_keep isl_schedule_node *node);
7900 __isl_give isl_schedule_node *isl_schedule_node_parent(
7901 __isl_take isl_schedule_node *node);
7902 __isl_give isl_schedule_node *isl_schedule_node_root(
7903 __isl_take isl_schedule_node *node);
7904 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
7905 __isl_take isl_schedule_node *node,
7907 int isl_schedule_node_n_children(
7908 __isl_keep isl_schedule_node *node);
7909 __isl_give isl_schedule_node *isl_schedule_node_child(
7910 __isl_take isl_schedule_node *node, int pos);
7911 isl_bool isl_schedule_node_has_children(
7912 __isl_keep isl_schedule_node *node);
7913 __isl_give isl_schedule_node *isl_schedule_node_first_child(
7914 __isl_take isl_schedule_node *node);
7915 isl_bool isl_schedule_node_has_previous_sibling(
7916 __isl_keep isl_schedule_node *node);
7917 __isl_give isl_schedule_node *
7918 isl_schedule_node_previous_sibling(
7919 __isl_take isl_schedule_node *node);
7920 isl_bool isl_schedule_node_has_next_sibling(
7921 __isl_keep isl_schedule_node *node);
7922 __isl_give isl_schedule_node *
7923 isl_schedule_node_next_sibling(
7924 __isl_take isl_schedule_node *node);
7926 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
7927 is the node itself, the ancestor of generation 1 is its parent and so on.
7929 It is also possible to query the number of ancestors of a node,
7930 the position of the current node
7931 within the children of its parent, the position of the subtree
7932 containing a node within the children of an ancestor
7933 or to obtain a copy of a given
7934 child without destroying the current node.
7935 Given two nodes that point to the same schedule, their closest
7936 shared ancestor can be obtained using
7937 C<isl_schedule_node_get_shared_ancestor>.
7939 #include <isl/schedule_node.h>
7940 int isl_schedule_node_get_tree_depth(
7941 __isl_keep isl_schedule_node *node);
7942 int isl_schedule_node_get_child_position(
7943 __isl_keep isl_schedule_node *node);
7944 int isl_schedule_node_get_ancestor_child_position(
7945 __isl_keep isl_schedule_node *node,
7946 __isl_keep isl_schedule_node *ancestor);
7947 __isl_give isl_schedule_node *isl_schedule_node_get_child(
7948 __isl_keep isl_schedule_node *node, int pos);
7949 __isl_give isl_schedule_node *
7950 isl_schedule_node_get_shared_ancestor(
7951 __isl_keep isl_schedule_node *node1,
7952 __isl_keep isl_schedule_node *node2);
7954 All nodes in a schedule tree or
7955 all descendants of a specific node (including the node) can be visited
7956 in depth-first pre-order using the following functions.
7958 #include <isl/schedule.h>
7959 isl_stat isl_schedule_foreach_schedule_node_top_down(
7960 __isl_keep isl_schedule *sched,
7961 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7962 void *user), void *user);
7964 #include <isl/schedule_node.h>
7965 isl_stat isl_schedule_node_foreach_descendant_top_down(
7966 __isl_keep isl_schedule_node *node,
7967 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7968 void *user), void *user);
7970 The callback function is slightly different from the usual
7971 callbacks in that it not only indicates success (non-negative result)
7972 or failure (negative result), but also indicates whether the children
7973 of the given node should be visited. In particular, if the callback
7974 returns a positive value, then the children are visited, but if
7975 the callback returns zero, then the children are not visited.
7977 The ancestors of a node in a schedule tree can be visited from
7978 the root down to and including the parent of the node using
7979 the following function.
7981 #include <isl/schedule_node.h>
7982 isl_stat isl_schedule_node_foreach_ancestor_top_down(
7983 __isl_keep isl_schedule_node *node,
7984 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
7985 void *user), void *user);
7987 The following functions allows for a depth-first post-order
7988 traversal of the nodes in a schedule tree or
7989 of the descendants of a specific node (including the node
7990 itself), where the user callback is allowed to modify the
7993 #include <isl/schedule.h>
7994 __isl_give isl_schedule *
7995 isl_schedule_map_schedule_node_bottom_up(
7996 __isl_take isl_schedule *schedule,
7997 __isl_give isl_schedule_node *(*fn)(
7998 __isl_take isl_schedule_node *node,
7999 void *user), void *user);
8001 #include <isl/schedule_node.h>
8002 __isl_give isl_schedule_node *
8003 isl_schedule_node_map_descendant_bottom_up(
8004 __isl_take isl_schedule_node *node,
8005 __isl_give isl_schedule_node *(*fn)(
8006 __isl_take isl_schedule_node *node,
8007 void *user), void *user);
8009 The traversal continues from the node returned by the callback function.
8010 It is the responsibility of the user to ensure that this does not
8011 lead to an infinite loop. It is safest to always return a pointer
8012 to the same position (same ancestors and child positions) as the input node.
8014 The following function removes a node (along with its descendants)
8015 from a schedule tree and returns a pointer to the leaf at the
8016 same position in the updated tree.
8017 It is not allowed to remove the root of a schedule tree or
8018 a child of a set or sequence node.
8020 #include <isl/schedule_node.h>
8021 __isl_give isl_schedule_node *isl_schedule_node_cut(
8022 __isl_take isl_schedule_node *node);
8024 The following function removes a single node
8025 from a schedule tree and returns a pointer to the child
8026 of the node, now located at the position of the original node
8027 or to a leaf node at that position if there was no child.
8028 It is not allowed to remove the root of a schedule tree,
8029 a set or sequence node, a child of a set or sequence node or
8030 a band node with an anchored subtree.
8032 #include <isl/schedule_node.h>
8033 __isl_give isl_schedule_node *isl_schedule_node_delete(
8034 __isl_take isl_schedule_node *node);
8036 Most nodes in a schedule tree only contain local information.
8037 In some cases, however, a node may also refer to outer band nodes.
8038 This means that the position of the node within the tree should
8039 not be changed, or at least that no changes are performed to the
8040 outer band nodes. The following function can be used to test
8041 whether the subtree rooted at a given node contains any such nodes.
8043 #include <isl/schedule_node.h>
8044 isl_bool isl_schedule_node_is_subtree_anchored(
8045 __isl_keep isl_schedule_node *node);
8047 The following function resets the user pointers on all parameter
8048 and tuple identifiers referenced by the given schedule node.
8050 #include <isl/schedule_node.h>
8051 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8052 __isl_take isl_schedule_node *node);
8054 The following function aligns the parameters of the given schedule
8055 node to the given space.
8057 #include <isl/schedule_node.h>
8058 __isl_give isl_schedule_node *
8059 isl_schedule_node_align_params(
8060 __isl_take isl_schedule_node *node,
8061 __isl_take isl_space *space);
8063 Several node types have their own functions for querying
8064 (and in some cases setting) some node type specific properties.
8066 #include <isl/schedule_node.h>
8067 __isl_give isl_space *isl_schedule_node_band_get_space(
8068 __isl_keep isl_schedule_node *node);
8069 __isl_give isl_multi_union_pw_aff *
8070 isl_schedule_node_band_get_partial_schedule(
8071 __isl_keep isl_schedule_node *node);
8072 __isl_give isl_union_map *
8073 isl_schedule_node_band_get_partial_schedule_union_map(
8074 __isl_keep isl_schedule_node *node);
8075 unsigned isl_schedule_node_band_n_member(
8076 __isl_keep isl_schedule_node *node);
8077 isl_bool isl_schedule_node_band_member_get_coincident(
8078 __isl_keep isl_schedule_node *node, int pos);
8079 __isl_give isl_schedule_node *
8080 isl_schedule_node_band_member_set_coincident(
8081 __isl_take isl_schedule_node *node, int pos,
8083 isl_bool isl_schedule_node_band_get_permutable(
8084 __isl_keep isl_schedule_node *node);
8085 __isl_give isl_schedule_node *
8086 isl_schedule_node_band_set_permutable(
8087 __isl_take isl_schedule_node *node, int permutable);
8088 enum isl_ast_loop_type
8089 isl_schedule_node_band_member_get_ast_loop_type(
8090 __isl_keep isl_schedule_node *node, int pos);
8091 __isl_give isl_schedule_node *
8092 isl_schedule_node_band_member_set_ast_loop_type(
8093 __isl_take isl_schedule_node *node, int pos,
8094 enum isl_ast_loop_type type);
8095 __isl_give isl_union_set *
8096 enum isl_ast_loop_type
8097 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8098 __isl_keep isl_schedule_node *node, int pos);
8099 __isl_give isl_schedule_node *
8100 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8101 __isl_take isl_schedule_node *node, int pos,
8102 enum isl_ast_loop_type type);
8103 isl_schedule_node_band_get_ast_build_options(
8104 __isl_keep isl_schedule_node *node);
8105 __isl_give isl_schedule_node *
8106 isl_schedule_node_band_set_ast_build_options(
8107 __isl_take isl_schedule_node *node,
8108 __isl_take isl_union_set *options);
8110 The function C<isl_schedule_node_band_get_space> returns the space
8111 of the partial schedule of the band.
8112 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8113 returns a representation of the partial schedule of the band node
8114 in the form of an C<isl_union_map>.
8115 The coincident and permutable properties are set by
8116 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8118 A scheduling dimension is considered to be ``coincident''
8119 if it satisfies the coincidence constraints within its band.
8120 That is, if the dependence distances of the coincidence
8121 constraints are all zero in that direction (for fixed
8122 iterations of outer bands).
8123 A band is marked permutable if it was produced using the Pluto-like scheduler.
8124 Note that the scheduler may have to resort to a Feautrier style scheduling
8125 step even if the default scheduler is used.
8126 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8127 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8128 For the meaning of these loop AST generation types and the difference
8129 between the regular loop AST generation type and the isolate
8130 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8131 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8132 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8133 may return C<isl_ast_loop_error> if an error occurs.
8134 The AST build options govern how an AST is generated for
8135 the individual schedule dimensions during AST generation.
8136 See L</"AST Generation Options (Schedule Tree)">.
8138 #include <isl/schedule_node.h>
8139 __isl_give isl_set *
8140 isl_schedule_node_context_get_context(
8141 __isl_keep isl_schedule_node *node);
8143 #include <isl/schedule_node.h>
8144 __isl_give isl_union_set *
8145 isl_schedule_node_domain_get_domain(
8146 __isl_keep isl_schedule_node *node);
8148 #include <isl/schedule_node.h>
8149 __isl_give isl_union_map *
8150 isl_schedule_node_expansion_get_expansion(
8151 __isl_keep isl_schedule_node *node);
8152 __isl_give isl_union_pw_multi_aff *
8153 isl_schedule_node_expansion_get_contraction(
8154 __isl_keep isl_schedule_node *node);
8156 #include <isl/schedule_node.h>
8157 __isl_give isl_union_map *
8158 isl_schedule_node_extension_get_extension(
8159 __isl_keep isl_schedule_node *node);
8161 #include <isl/schedule_node.h>
8162 __isl_give isl_union_set *
8163 isl_schedule_node_filter_get_filter(
8164 __isl_keep isl_schedule_node *node);
8166 #include <isl/schedule_node.h>
8167 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8168 __isl_keep isl_schedule_node *node);
8170 #include <isl/schedule_node.h>
8171 __isl_give isl_id *isl_schedule_node_mark_get_id(
8172 __isl_keep isl_schedule_node *node);
8174 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8175 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8176 partial schedules related to the node.
8178 #include <isl/schedule_node.h>
8179 __isl_give isl_multi_union_pw_aff *
8180 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8181 __isl_keep isl_schedule_node *node);
8182 __isl_give isl_union_pw_multi_aff *
8183 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8184 __isl_keep isl_schedule_node *node);
8185 __isl_give isl_union_map *
8186 isl_schedule_node_get_prefix_schedule_union_map(
8187 __isl_keep isl_schedule_node *node);
8188 __isl_give isl_union_map *
8189 isl_schedule_node_get_prefix_schedule_relation(
8190 __isl_keep isl_schedule_node *node);
8191 __isl_give isl_union_map *
8192 isl_schedule_node_get_subtree_schedule_union_map(
8193 __isl_keep isl_schedule_node *node);
8195 In particular, the functions
8196 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8197 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8198 and C<isl_schedule_node_get_prefix_schedule_union_map>
8199 return a relative ordering on the domain elements that reach the given
8200 node determined by its ancestors.
8201 The function C<isl_schedule_node_get_prefix_schedule_relation>
8202 additionally includes the domain constraints in the result.
8203 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8204 returns a representation of the partial schedule defined by the
8205 subtree rooted at the given node.
8206 If the tree contains any expansion nodes, then the subtree schedule
8207 is formulated in terms of the expanded domain elements.
8208 The tree passed to functions returning a prefix schedule
8209 may only contain extension nodes if these would not affect
8210 the result of these functions. That is, if one of the ancestors
8211 is an extension node, then all of the domain elements that were
8212 added by the extension node need to have been filtered out
8213 by filter nodes between the extension node and the input node.
8214 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8215 may not contain in extension nodes in the selected subtree.
8217 The expansion/contraction defined by an entire subtree, combining
8218 the expansions/contractions
8219 on the expansion nodes in the subtree, can be obtained using
8220 the following functions.
8222 #include <isl/schedule_node.h>
8223 __isl_give isl_union_map *
8224 isl_schedule_node_get_subtree_expansion(
8225 __isl_keep isl_schedule_node *node);
8226 __isl_give isl_union_pw_multi_aff *
8227 isl_schedule_node_get_subtree_contraction(
8228 __isl_keep isl_schedule_node *node);
8230 The total number of outer band members of given node, i.e.,
8231 the shared output dimension of the maps in the result
8232 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8233 using the following function.
8235 #include <isl/schedule_node.h>
8236 int isl_schedule_node_get_schedule_depth(
8237 __isl_keep isl_schedule_node *node);
8239 The following functions return the elements that reach the given node
8240 or the union of universes in the spaces that contain these elements.
8242 #include <isl/schedule_node.h>
8243 __isl_give isl_union_set *
8244 isl_schedule_node_get_domain(
8245 __isl_keep isl_schedule_node *node);
8246 __isl_give isl_union_set *
8247 isl_schedule_node_get_universe_domain(
8248 __isl_keep isl_schedule_node *node);
8250 The input tree of C<isl_schedule_node_get_domain>
8251 may only contain extension nodes if these would not affect
8252 the result of this function. That is, if one of the ancestors
8253 is an extension node, then all of the domain elements that were
8254 added by the extension node need to have been filtered out
8255 by filter nodes between the extension node and the input node.
8257 The following functions can be used to introduce additional nodes
8258 in the schedule tree. The new node is introduced at the point
8259 in the tree where the C<isl_schedule_node> points to and
8260 the results points to the new node.
8262 #include <isl/schedule_node.h>
8263 __isl_give isl_schedule_node *
8264 isl_schedule_node_insert_partial_schedule(
8265 __isl_take isl_schedule_node *node,
8266 __isl_take isl_multi_union_pw_aff *schedule);
8268 This function inserts a new band node with (the greatest integer
8269 part of) the given partial schedule.
8270 The subtree rooted at the given node is assumed not to have
8273 #include <isl/schedule_node.h>
8274 __isl_give isl_schedule_node *
8275 isl_schedule_node_insert_context(
8276 __isl_take isl_schedule_node *node,
8277 __isl_take isl_set *context);
8279 This function inserts a new context node with the given context constraints.
8281 #include <isl/schedule_node.h>
8282 __isl_give isl_schedule_node *
8283 isl_schedule_node_insert_filter(
8284 __isl_take isl_schedule_node *node,
8285 __isl_take isl_union_set *filter);
8287 This function inserts a new filter node with the given filter.
8288 If the original node already pointed to a filter node, then the
8289 two filter nodes are merged into one.
8291 #include <isl/schedule_node.h>
8292 __isl_give isl_schedule_node *
8293 isl_schedule_node_insert_guard(
8294 __isl_take isl_schedule_node *node,
8295 __isl_take isl_set *guard);
8297 This function inserts a new guard node with the given guard constraints.
8299 #include <isl/schedule_node.h>
8300 __isl_give isl_schedule_node *
8301 isl_schedule_node_insert_mark(
8302 __isl_take isl_schedule_node *node,
8303 __isl_take isl_id *mark);
8305 This function inserts a new mark node with the give mark identifier.
8307 #include <isl/schedule_node.h>
8308 __isl_give isl_schedule_node *
8309 isl_schedule_node_insert_sequence(
8310 __isl_take isl_schedule_node *node,
8311 __isl_take isl_union_set_list *filters);
8312 __isl_give isl_schedule_node *
8313 isl_schedule_node_insert_set(
8314 __isl_take isl_schedule_node *node,
8315 __isl_take isl_union_set_list *filters);
8317 These functions insert a new sequence or set node with the given
8318 filters as children.
8320 #include <isl/schedule_node.h>
8321 __isl_give isl_schedule_node *isl_schedule_node_group(
8322 __isl_take isl_schedule_node *node,
8323 __isl_take isl_id *group_id);
8325 This function introduces an expansion node in between the current
8326 node and its parent that expands instances of a space with tuple
8327 identifier C<group_id> to the original domain elements that reach
8328 the node. The group instances are identified by the prefix schedule
8329 of those domain elements. The ancestors of the node are adjusted
8330 to refer to the group instances instead of the original domain
8331 elements. The return value points to the same node in the updated
8332 schedule tree as the input node, i.e., to the child of the newly
8333 introduced expansion node. Grouping instances of different statements
8334 ensures that they will be treated as a single statement by the
8335 AST generator up to the point of the expansion node.
8337 The following function can be used to flatten a nested
8340 #include <isl/schedule_node.h>
8341 __isl_give isl_schedule_node *
8342 isl_schedule_node_sequence_splice_child(
8343 __isl_take isl_schedule_node *node, int pos);
8345 That is, given a sequence node C<node> that has another sequence node
8346 in its child at position C<pos> (in particular, the child of that filter
8347 node is a sequence node), attach the children of that other sequence
8348 node as children of C<node>, replacing the original child at position
8351 The partial schedule of a band node can be scaled (down) or reduced using
8352 the following functions.
8354 #include <isl/schedule_node.h>
8355 __isl_give isl_schedule_node *
8356 isl_schedule_node_band_scale(
8357 __isl_take isl_schedule_node *node,
8358 __isl_take isl_multi_val *mv);
8359 __isl_give isl_schedule_node *
8360 isl_schedule_node_band_scale_down(
8361 __isl_take isl_schedule_node *node,
8362 __isl_take isl_multi_val *mv);
8363 __isl_give isl_schedule_node *
8364 isl_schedule_node_band_mod(
8365 __isl_take isl_schedule_node *node,
8366 __isl_take isl_multi_val *mv);
8368 The spaces of the two arguments need to match.
8369 After scaling, the partial schedule is replaced by its greatest
8370 integer part to ensure that the schedule remains integral.
8372 The partial schedule of a band node can be shifted by an
8373 C<isl_multi_union_pw_aff> with a domain that is a superset
8374 of the domain of the partial schedule using
8375 the following function.
8377 #include <isl/schedule_node.h>
8378 __isl_give isl_schedule_node *
8379 isl_schedule_node_band_shift(
8380 __isl_take isl_schedule_node *node,
8381 __isl_take isl_multi_union_pw_aff *shift);
8383 A band node can be tiled using the following function.
8385 #include <isl/schedule_node.h>
8386 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8387 __isl_take isl_schedule_node *node,
8388 __isl_take isl_multi_val *sizes);
8390 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8392 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8393 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8395 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8397 The C<isl_schedule_node_band_tile> function tiles
8398 the band using the given tile sizes inside its schedule.
8399 A new child band node is created to represent the point loops and it is
8400 inserted between the modified band and its children.
8401 The subtree rooted at the given node is assumed not to have
8403 The C<tile_scale_tile_loops> option specifies whether the tile
8404 loops iterators should be scaled by the tile sizes.
8405 If the C<tile_shift_point_loops> option is set, then the point loops
8406 are shifted to start at zero.
8408 A band node can be split into two nested band nodes
8409 using the following function.
8411 #include <isl/schedule_node.h>
8412 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8413 __isl_take isl_schedule_node *node, int pos);
8415 The resulting outer band node contains the first C<pos> dimensions of
8416 the schedule of C<node> while the inner band contains the remaining dimensions.
8417 The schedules of the two band nodes live in anonymous spaces.
8419 A band node can be moved down to the leaves of the subtree rooted
8420 at the band node using the following function.
8422 #include <isl/schedule_node.h>
8423 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8424 __isl_take isl_schedule_node *node);
8426 The subtree rooted at the given node is assumed not to have
8428 The result points to the node in the resulting tree that is in the same
8429 position as the node pointed to by C<node> in the original tree.
8431 #include <isl/schedule_node.h>
8432 __isl_give isl_schedule_node *
8433 isl_schedule_node_order_before(
8434 __isl_take isl_schedule_node *node,
8435 __isl_take isl_union_set *filter);
8436 __isl_give isl_schedule_node *
8437 isl_schedule_node_order_after(
8438 __isl_take isl_schedule_node *node,
8439 __isl_take isl_union_set *filter);
8441 These functions split the domain elements that reach C<node>
8442 into those that satisfy C<filter> and those that do not and
8443 arranges for the elements that do satisfy the filter to be
8444 executed before (in case of C<isl_schedule_node_order_before>)
8445 or after (in case of C<isl_schedule_node_order_after>)
8446 those that do not. The order is imposed by
8447 a sequence node, possibly reusing the grandparent of C<node>
8448 on two copies of the subtree attached to the original C<node>.
8449 Both copies are simplified with respect to their filter.
8451 Return a pointer to the copy of the subtree that does not
8452 satisfy C<filter>. If there is no such copy (because all
8453 reaching domain elements satisfy the filter), then return
8454 the original pointer.
8456 #include <isl/schedule_node.h>
8457 __isl_give isl_schedule_node *
8458 isl_schedule_node_graft_before(
8459 __isl_take isl_schedule_node *node,
8460 __isl_take isl_schedule_node *graft);
8461 __isl_give isl_schedule_node *
8462 isl_schedule_node_graft_after(
8463 __isl_take isl_schedule_node *node,
8464 __isl_take isl_schedule_node *graft);
8466 This function inserts the C<graft> tree into the tree containing C<node>
8467 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8468 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8469 The root node of C<graft>
8470 should be an extension node where the domain of the extension
8471 is the flat product of all outer band nodes of C<node>.
8472 The root node may also be a domain node.
8473 The elements of the domain or the range of the extension may not
8474 intersect with the domain elements that reach "node".
8475 The schedule tree of C<graft> may not be anchored.
8477 The schedule tree of C<node> is modified to include an extension node
8478 corresponding to the root node of C<graft> as a child of the original
8479 parent of C<node>. The original node that C<node> points to and the
8480 child of the root node of C<graft> are attached to this extension node
8481 through a sequence, with appropriate filters and with the child
8482 of C<graft> appearing before or after the original C<node>.
8484 If C<node> already appears inside a sequence that is the child of
8485 an extension node and if the spaces of the new domain elements
8486 do not overlap with those of the original domain elements,
8487 then that extension node is extended with the new extension
8488 rather than introducing a new segment of extension and sequence nodes.
8490 Return a pointer to the same node in the modified tree that
8491 C<node> pointed to in the original tree.
8493 A representation of the schedule node can be printed using
8495 #include <isl/schedule_node.h>
8496 __isl_give isl_printer *isl_printer_print_schedule_node(
8497 __isl_take isl_printer *p,
8498 __isl_keep isl_schedule_node *node);
8499 __isl_give char *isl_schedule_node_to_str(
8500 __isl_keep isl_schedule_node *node);
8502 C<isl_schedule_node_to_str> prints the schedule node in block format.
8504 =head2 Dependence Analysis
8506 C<isl> contains specialized functionality for performing
8507 array dataflow analysis. That is, given a I<sink> access relation
8508 and a collection of possible I<source> access relations,
8509 C<isl> can compute relations that describe
8510 for each iteration of the sink access, which iteration
8511 of which of the source access relations was the last
8512 to access the same data element before the given iteration
8514 The resulting dependence relations map source iterations
8515 to either the corresponding sink iterations or
8516 pairs of corresponding sink iterations and accessed data elements.
8517 To compute standard flow dependences, the sink should be
8518 a read, while the sources should be writes.
8519 If any of the source accesses are marked as being I<may>
8520 accesses, then there will be a dependence from the last
8521 I<must> access B<and> from any I<may> access that follows
8522 this last I<must> access.
8523 In particular, if I<all> sources are I<may> accesses,
8524 then memory based dependence analysis is performed.
8525 If, on the other hand, all sources are I<must> accesses,
8526 then value based dependence analysis is performed.
8528 =head3 High-level Interface
8530 A high-level interface to dependence analysis is provided
8531 by the following function.
8533 #include <isl/flow.h>
8534 __isl_give isl_union_flow *
8535 isl_union_access_info_compute_flow(
8536 __isl_take isl_union_access_info *access);
8538 The input C<isl_union_access_info> object describes the sink
8539 access relations, the source access relations and a schedule,
8540 while the output C<isl_union_flow> object describes
8541 the resulting dependence relations and the subsets of the
8542 sink relations for which no source was found.
8544 An C<isl_union_access_info> is created, modified, copied and freed using
8545 the following functions.
8547 #include <isl/flow.h>
8548 __isl_give isl_union_access_info *
8549 isl_union_access_info_from_sink(
8550 __isl_take isl_union_map *sink);
8551 __isl_give isl_union_access_info *
8552 isl_union_access_info_set_must_source(
8553 __isl_take isl_union_access_info *access,
8554 __isl_take isl_union_map *must_source);
8555 __isl_give isl_union_access_info *
8556 isl_union_access_info_set_may_source(
8557 __isl_take isl_union_access_info *access,
8558 __isl_take isl_union_map *may_source);
8559 __isl_give isl_union_access_info *
8560 isl_union_access_info_set_schedule(
8561 __isl_take isl_union_access_info *access,
8562 __isl_take isl_schedule *schedule);
8563 __isl_give isl_union_access_info *
8564 isl_union_access_info_set_schedule_map(
8565 __isl_take isl_union_access_info *access,
8566 __isl_take isl_union_map *schedule_map);
8567 __isl_give isl_union_access_info *
8568 isl_union_access_info_copy(
8569 __isl_keep isl_union_access_info *access);
8570 __isl_null isl_union_access_info *
8571 isl_union_access_info_free(
8572 __isl_take isl_union_access_info *access);
8574 The may sources set by C<isl_union_access_info_set_may_source>
8575 do not need to include the must sources set by
8576 C<isl_union_access_info_set_must_source> as a subset.
8577 The user is free not to call one (or both) of these functions,
8578 in which case the corresponding set is kept to its empty default.
8579 Similarly, the default schedule initialized by
8580 C<isl_union_access_info_from_sink> is empty.
8581 The current schedule is determined by the last call to either
8582 C<isl_union_access_info_set_schedule> or
8583 C<isl_union_access_info_set_schedule_map>.
8584 The domain of the schedule corresponds to the domains of
8585 the access relations. In particular, the domains of the access
8586 relations are effectively intersected with the domain of the schedule
8587 and only the resulting accesses are considered by the dependence analysis.
8589 A representation of the information contained in an object
8590 of type C<isl_union_access_info> can be obtained using
8592 #include <isl/flow.h>
8593 __isl_give isl_printer *
8594 isl_printer_print_union_access_info(
8595 __isl_take isl_printer *p,
8596 __isl_keep isl_union_access_info *access);
8597 __isl_give char *isl_union_access_info_to_str(
8598 __isl_keep isl_union_access_info *access);
8600 C<isl_union_access_info_to_str> prints the information in flow format.
8602 The output of C<isl_union_access_info_compute_flow> can be examined
8603 and freed using the following functions.
8605 #include <isl/flow.h>
8606 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8607 __isl_keep isl_union_flow *flow);
8608 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8609 __isl_keep isl_union_flow *flow);
8610 __isl_give isl_union_map *
8611 isl_union_flow_get_full_must_dependence(
8612 __isl_keep isl_union_flow *flow);
8613 __isl_give isl_union_map *
8614 isl_union_flow_get_full_may_dependence(
8615 __isl_keep isl_union_flow *flow);
8616 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8617 __isl_keep isl_union_flow *flow);
8618 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8619 __isl_keep isl_union_flow *flow);
8620 __isl_null isl_union_flow *isl_union_flow_free(
8621 __isl_take isl_union_flow *flow);
8623 The relation returned by C<isl_union_flow_get_must_dependence>
8624 relates domain elements of must sources to domain elements of the sink.
8625 The relation returned by C<isl_union_flow_get_may_dependence>
8626 relates domain elements of must or may sources to domain elements of the sink
8627 and includes the previous relation as a subset.
8628 The relation returned by C<isl_union_flow_get_full_must_dependence>
8629 relates domain elements of must sources to pairs of domain elements of the sink
8630 and accessed data elements.
8631 The relation returned by C<isl_union_flow_get_full_may_dependence>
8632 relates domain elements of must or may sources to pairs of
8633 domain elements of the sink and accessed data elements.
8634 This relation includes the previous relation as a subset.
8635 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8636 of the sink relation for which no dependences have been found.
8637 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8638 of the sink relation for which no definite dependences have been found.
8639 That is, it contains those sink access that do not contribute to any
8640 of the elements in the relation returned
8641 by C<isl_union_flow_get_must_dependence>.
8643 A representation of the information contained in an object
8644 of type C<isl_union_flow> can be obtained using
8646 #include <isl/flow.h>
8647 __isl_give isl_printer *isl_printer_print_union_flow(
8648 __isl_take isl_printer *p,
8649 __isl_keep isl_union_flow *flow);
8650 __isl_give char *isl_union_flow_to_str(
8651 __isl_keep isl_union_flow *flow);
8653 C<isl_union_flow_to_str> prints the information in flow format.
8655 =head3 Low-level Interface
8657 A lower-level interface is provided by the following functions.
8659 #include <isl/flow.h>
8661 typedef int (*isl_access_level_before)(void *first, void *second);
8663 __isl_give isl_access_info *isl_access_info_alloc(
8664 __isl_take isl_map *sink,
8665 void *sink_user, isl_access_level_before fn,
8667 __isl_give isl_access_info *isl_access_info_add_source(
8668 __isl_take isl_access_info *acc,
8669 __isl_take isl_map *source, int must,
8671 __isl_null isl_access_info *isl_access_info_free(
8672 __isl_take isl_access_info *acc);
8674 __isl_give isl_flow *isl_access_info_compute_flow(
8675 __isl_take isl_access_info *acc);
8677 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8678 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8679 void *dep_user, void *user),
8681 __isl_give isl_map *isl_flow_get_no_source(
8682 __isl_keep isl_flow *deps, int must);
8683 void isl_flow_free(__isl_take isl_flow *deps);
8685 The function C<isl_access_info_compute_flow> performs the actual
8686 dependence analysis. The other functions are used to construct
8687 the input for this function or to read off the output.
8689 The input is collected in an C<isl_access_info>, which can
8690 be created through a call to C<isl_access_info_alloc>.
8691 The arguments to this functions are the sink access relation
8692 C<sink>, a token C<sink_user> used to identify the sink
8693 access to the user, a callback function for specifying the
8694 relative order of source and sink accesses, and the number
8695 of source access relations that will be added.
8696 The callback function has type C<int (*)(void *first, void *second)>.
8697 The function is called with two user supplied tokens identifying
8698 either a source or the sink and it should return the shared nesting
8699 level and the relative order of the two accesses.
8700 In particular, let I<n> be the number of loops shared by
8701 the two accesses. If C<first> precedes C<second> textually,
8702 then the function should return I<2 * n + 1>; otherwise,
8703 it should return I<2 * n>.
8704 The sources can be added to the C<isl_access_info> by performing
8705 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8706 C<must> indicates whether the source is a I<must> access
8707 or a I<may> access. Note that a multi-valued access relation
8708 should only be marked I<must> if every iteration in the domain
8709 of the relation accesses I<all> elements in its image.
8710 The C<source_user> token is again used to identify
8711 the source access. The range of the source access relation
8712 C<source> should have the same dimension as the range
8713 of the sink access relation.
8714 The C<isl_access_info_free> function should usually not be
8715 called explicitly, because it is called implicitly by
8716 C<isl_access_info_compute_flow>.
8718 The result of the dependence analysis is collected in an
8719 C<isl_flow>. There may be elements of
8720 the sink access for which no preceding source access could be
8721 found or for which all preceding sources are I<may> accesses.
8722 The relations containing these elements can be obtained through
8723 calls to C<isl_flow_get_no_source>, the first with C<must> set
8724 and the second with C<must> unset.
8725 In the case of standard flow dependence analysis,
8726 with the sink a read and the sources I<must> writes,
8727 the first relation corresponds to the reads from uninitialized
8728 array elements and the second relation is empty.
8729 The actual flow dependences can be extracted using
8730 C<isl_flow_foreach>. This function will call the user-specified
8731 callback function C<fn> for each B<non-empty> dependence between
8732 a source and the sink. The callback function is called
8733 with four arguments, the actual flow dependence relation
8734 mapping source iterations to sink iterations, a boolean that
8735 indicates whether it is a I<must> or I<may> dependence, a token
8736 identifying the source and an additional C<void *> with value
8737 equal to the third argument of the C<isl_flow_foreach> call.
8738 A dependence is marked I<must> if it originates from a I<must>
8739 source and if it is not followed by any I<may> sources.
8741 After finishing with an C<isl_flow>, the user should call
8742 C<isl_flow_free> to free all associated memory.
8744 =head3 Interaction with the Low-level Interface
8746 During the dependence analysis, we frequently need to perform
8747 the following operation. Given a relation between sink iterations
8748 and potential source iterations from a particular source domain,
8749 what is the last potential source iteration corresponding to each
8750 sink iteration. It can sometimes be convenient to adjust
8751 the set of potential source iterations before or after each such operation.
8752 The prototypical example is fuzzy array dataflow analysis,
8753 where we need to analyze if, based on data-dependent constraints,
8754 the sink iteration can ever be executed without one or more of
8755 the corresponding potential source iterations being executed.
8756 If so, we can introduce extra parameters and select an unknown
8757 but fixed source iteration from the potential source iterations.
8758 To be able to perform such manipulations, C<isl> provides the following
8761 #include <isl/flow.h>
8763 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8764 __isl_keep isl_map *source_map,
8765 __isl_keep isl_set *sink, void *source_user,
8767 __isl_give isl_access_info *isl_access_info_set_restrict(
8768 __isl_take isl_access_info *acc,
8769 isl_access_restrict fn, void *user);
8771 The function C<isl_access_info_set_restrict> should be called
8772 before calling C<isl_access_info_compute_flow> and registers a callback function
8773 that will be called any time C<isl> is about to compute the last
8774 potential source. The first argument is the (reverse) proto-dependence,
8775 mapping sink iterations to potential source iterations.
8776 The second argument represents the sink iterations for which
8777 we want to compute the last source iteration.
8778 The third argument is the token corresponding to the source
8779 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8780 The callback is expected to return a restriction on either the input or
8781 the output of the operation computing the last potential source.
8782 If the input needs to be restricted then restrictions are needed
8783 for both the source and the sink iterations. The sink iterations
8784 and the potential source iterations will be intersected with these sets.
8785 If the output needs to be restricted then only a restriction on the source
8786 iterations is required.
8787 If any error occurs, the callback should return C<NULL>.
8788 An C<isl_restriction> object can be created, freed and inspected
8789 using the following functions.
8791 #include <isl/flow.h>
8793 __isl_give isl_restriction *isl_restriction_input(
8794 __isl_take isl_set *source_restr,
8795 __isl_take isl_set *sink_restr);
8796 __isl_give isl_restriction *isl_restriction_output(
8797 __isl_take isl_set *source_restr);
8798 __isl_give isl_restriction *isl_restriction_none(
8799 __isl_take isl_map *source_map);
8800 __isl_give isl_restriction *isl_restriction_empty(
8801 __isl_take isl_map *source_map);
8802 __isl_null isl_restriction *isl_restriction_free(
8803 __isl_take isl_restriction *restr);
8805 C<isl_restriction_none> and C<isl_restriction_empty> are special
8806 cases of C<isl_restriction_input>. C<isl_restriction_none>
8807 is essentially equivalent to
8809 isl_restriction_input(isl_set_universe(
8810 isl_space_range(isl_map_get_space(source_map))),
8812 isl_space_domain(isl_map_get_space(source_map))));
8814 whereas C<isl_restriction_empty> is essentially equivalent to
8816 isl_restriction_input(isl_set_empty(
8817 isl_space_range(isl_map_get_space(source_map))),
8819 isl_space_domain(isl_map_get_space(source_map))));
8823 B<The functionality described in this section is fairly new
8824 and may be subject to change.>
8826 #include <isl/schedule.h>
8827 __isl_give isl_schedule *
8828 isl_schedule_constraints_compute_schedule(
8829 __isl_take isl_schedule_constraints *sc);
8831 The function C<isl_schedule_constraints_compute_schedule> can be
8832 used to compute a schedule that satisfies the given schedule constraints.
8833 These schedule constraints include the iteration domain for which
8834 a schedule should be computed and dependences between pairs of
8835 iterations. In particular, these dependences include
8836 I<validity> dependences and I<proximity> dependences.
8837 By default, the algorithm used to construct the schedule is similar
8838 to that of C<Pluto>.
8839 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8841 The generated schedule respects all validity dependences.
8842 That is, all dependence distances over these dependences in the
8843 scheduled space are lexicographically positive.
8845 The default algorithm tries to ensure that the dependence distances
8846 over coincidence constraints are zero and to minimize the
8847 dependence distances over proximity dependences.
8848 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8849 for groups of domains where the dependence distances over validity
8850 dependences have only non-negative values.
8851 Note that when minimizing the maximal dependence distance
8852 over proximity dependences, a single affine expression in the parameters
8853 is constructed that bounds all dependence distances. If no such expression
8854 exists, then the algorithm will fail and resort to an alternative
8855 scheduling algorithm. In particular, this means that adding proximity
8856 dependences may eliminate valid solutions. A typical example where this
8857 phenomenon may occur is when some subset of the proximity dependences
8858 has no restriction on some parameter, forcing the coefficient of that
8859 parameter to be zero, while some other subset forces the dependence
8860 distance to depend on that parameter, requiring the same coefficient
8862 When using Feautrier's algorithm, the coincidence and proximity constraints
8863 are only taken into account during the extension to a
8864 full-dimensional schedule.
8866 An C<isl_schedule_constraints> object can be constructed
8867 and manipulated using the following functions.
8869 #include <isl/schedule.h>
8870 __isl_give isl_schedule_constraints *
8871 isl_schedule_constraints_copy(
8872 __isl_keep isl_schedule_constraints *sc);
8873 __isl_give isl_schedule_constraints *
8874 isl_schedule_constraints_on_domain(
8875 __isl_take isl_union_set *domain);
8876 __isl_give isl_schedule_constraints *
8877 isl_schedule_constraints_set_context(
8878 __isl_take isl_schedule_constraints *sc,
8879 __isl_take isl_set *context);
8880 __isl_give isl_schedule_constraints *
8881 isl_schedule_constraints_set_validity(
8882 __isl_take isl_schedule_constraints *sc,
8883 __isl_take isl_union_map *validity);
8884 __isl_give isl_schedule_constraints *
8885 isl_schedule_constraints_set_coincidence(
8886 __isl_take isl_schedule_constraints *sc,
8887 __isl_take isl_union_map *coincidence);
8888 __isl_give isl_schedule_constraints *
8889 isl_schedule_constraints_set_proximity(
8890 __isl_take isl_schedule_constraints *sc,
8891 __isl_take isl_union_map *proximity);
8892 __isl_give isl_schedule_constraints *
8893 isl_schedule_constraints_set_conditional_validity(
8894 __isl_take isl_schedule_constraints *sc,
8895 __isl_take isl_union_map *condition,
8896 __isl_take isl_union_map *validity);
8897 __isl_null isl_schedule_constraints *
8898 isl_schedule_constraints_free(
8899 __isl_take isl_schedule_constraints *sc);
8901 The initial C<isl_schedule_constraints> object created by
8902 C<isl_schedule_constraints_on_domain> does not impose any constraints.
8903 That is, it has an empty set of dependences.
8904 The function C<isl_schedule_constraints_set_context> allows the user
8905 to specify additional constraints on the parameters that may
8906 be assumed to hold during the construction of the schedule.
8907 The function C<isl_schedule_constraints_set_validity> replaces the
8908 validity dependences, mapping domain elements I<i> to domain
8909 elements that should be scheduled after I<i>.
8910 The function C<isl_schedule_constraints_set_coincidence> replaces the
8911 coincidence dependences, mapping domain elements I<i> to domain
8912 elements that should be scheduled together with I<I>, if possible.
8913 The function C<isl_schedule_constraints_set_proximity> replaces the
8914 proximity dependences, mapping domain elements I<i> to domain
8915 elements that should be scheduled either before I<I>
8916 or as early as possible after I<i>.
8918 The function C<isl_schedule_constraints_set_conditional_validity>
8919 replaces the conditional validity constraints.
8920 A conditional validity constraint is only imposed when any of the corresponding
8921 conditions is satisfied, i.e., when any of them is non-zero.
8922 That is, the scheduler ensures that within each band if the dependence
8923 distances over the condition constraints are not all zero
8924 then all corresponding conditional validity constraints are respected.
8925 A conditional validity constraint corresponds to a condition
8926 if the two are adjacent, i.e., if the domain of one relation intersect
8927 the range of the other relation.
8928 The typical use case of conditional validity constraints is
8929 to allow order constraints between live ranges to be violated
8930 as long as the live ranges themselves are local to the band.
8931 To allow more fine-grained control over which conditions correspond
8932 to which conditional validity constraints, the domains and ranges
8933 of these relations may include I<tags>. That is, the domains and
8934 ranges of those relation may themselves be wrapped relations
8935 where the iteration domain appears in the domain of those wrapped relations
8936 and the range of the wrapped relations can be arbitrarily chosen
8937 by the user. Conditions and conditional validity constraints are only
8938 considered adjacent to each other if the entire wrapped relation matches.
8939 In particular, a relation with a tag will never be considered adjacent
8940 to a relation without a tag.
8942 An C<isl_schedule_constraints> object can be inspected
8943 using the following functions.
8945 #include <isl/schedule.h>
8946 __isl_give isl_union_set *
8947 isl_schedule_constraints_get_domain(
8948 __isl_keep isl_schedule_constraints *sc);
8949 __isl_give isl_union_map *
8950 isl_schedule_constraints_get_validity(
8951 __isl_keep isl_schedule_constraints *sc);
8952 __isl_give isl_union_map *
8953 isl_schedule_constraints_get_coincidence(
8954 __isl_keep isl_schedule_constraints *sc);
8955 __isl_give isl_union_map *
8956 isl_schedule_constraints_get_proximity(
8957 __isl_keep isl_schedule_constraints *sc);
8958 __isl_give isl_union_map *
8959 isl_schedule_constraints_get_conditional_validity(
8960 __isl_keep isl_schedule_constraints *sc);
8961 __isl_give isl_union_map *
8962 isl_schedule_constraints_get_conditional_validity_condition(
8963 __isl_keep isl_schedule_constraints *sc);
8965 The following function computes a schedule directly from
8966 an iteration domain and validity and proximity dependences
8967 and is implemented in terms of the functions described above.
8968 The use of C<isl_union_set_compute_schedule> is discouraged.
8970 #include <isl/schedule.h>
8971 __isl_give isl_schedule *isl_union_set_compute_schedule(
8972 __isl_take isl_union_set *domain,
8973 __isl_take isl_union_map *validity,
8974 __isl_take isl_union_map *proximity);
8976 The generated schedule represents a schedule tree.
8977 For more information on schedule trees, see
8978 L</"Schedule Trees">.
8982 #include <isl/schedule.h>
8983 isl_stat isl_options_set_schedule_max_coefficient(
8984 isl_ctx *ctx, int val);
8985 int isl_options_get_schedule_max_coefficient(
8987 isl_stat isl_options_set_schedule_max_constant_term(
8988 isl_ctx *ctx, int val);
8989 int isl_options_get_schedule_max_constant_term(
8991 isl_stat isl_options_set_schedule_serialize_sccs(
8992 isl_ctx *ctx, int val);
8993 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
8994 isl_stat isl_options_set_schedule_whole_component(
8995 isl_ctx *ctx, int val);
8996 int isl_options_get_schedule_whole_component(
8998 isl_stat isl_options_set_schedule_maximize_band_depth(
8999 isl_ctx *ctx, int val);
9000 int isl_options_get_schedule_maximize_band_depth(
9002 isl_stat isl_options_set_schedule_outer_coincidence(
9003 isl_ctx *ctx, int val);
9004 int isl_options_get_schedule_outer_coincidence(
9006 isl_stat isl_options_set_schedule_split_scaled(
9007 isl_ctx *ctx, int val);
9008 int isl_options_get_schedule_split_scaled(
9010 isl_stat isl_options_set_schedule_algorithm(
9011 isl_ctx *ctx, int val);
9012 int isl_options_get_schedule_algorithm(
9014 isl_stat isl_options_set_schedule_separate_components(
9015 isl_ctx *ctx, int val);
9016 int isl_options_get_schedule_separate_components(
9021 =item * schedule_max_coefficient
9023 This option enforces that the coefficients for variable and parameter
9024 dimensions in the calculated schedule are not larger than the specified value.
9025 This option can significantly increase the speed of the scheduling calculation
9026 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9027 this option does not introduce bounds on the variable or parameter
9030 =item * schedule_max_constant_term
9032 This option enforces that the constant coefficients in the calculated schedule
9033 are not larger than the maximal constant term. This option can significantly
9034 increase the speed of the scheduling calculation and may also prevent fusing of
9035 unrelated dimensions. A value of -1 means that this option does not introduce
9036 bounds on the constant coefficients.
9038 =item * schedule_serialize_sccs
9040 If this option is set, then all strongly connected components
9041 in the dependence graph are serialized as soon as they are detected.
9042 This means in particular that instances of statements will only
9043 appear in the same band node if these statements belong
9044 to the same strongly connected component at the point where
9045 the band node is constructed.
9047 =item * schedule_whole_component
9049 If this option is set, then entire (weakly) connected
9050 components in the dependence graph are scheduled together
9052 Otherwise, each strongly connected component within
9053 such a weakly connected component is first scheduled separately
9054 and then combined with other strongly connected components.
9055 This option has no effect if C<schedule_serialize_sccs> is set.
9057 =item * schedule_maximize_band_depth
9059 If this option is set, then the scheduler tries to maximize
9060 the width of the bands. Wider bands give more possibilities for tiling.
9061 In particular, if the C<schedule_whole_component> option is set,
9062 then bands are split if this might result in wider bands.
9063 Otherwise, the effect of this option is to only allow
9064 strongly connected components to be combined if this does
9065 not reduce the width of the bands.
9066 Note that if the C<schedule_serialize_sccs> options is set, then
9067 the C<schedule_maximize_band_depth> option therefore has no effect.
9069 =item * schedule_maximize_coincidence
9071 This option is only effective if the C<schedule_whole_component>
9072 option is turned off.
9073 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9074 strongly connected components are only combined with each other
9075 if this does not reduce the number of coincident band members.
9077 =item * schedule_outer_coincidence
9079 If this option is set, then we try to construct schedules
9080 where the outermost scheduling dimension in each band
9081 satisfies the coincidence constraints.
9083 =item * schedule_split_scaled
9085 If this option is set, then we try to construct schedules in which the
9086 constant term is split off from the linear part if the linear parts of
9087 the scheduling rows for all nodes in the graphs have a common non-trivial
9089 The constant term is then placed in a separate band and the linear
9092 =item * schedule_algorithm
9094 Selects the scheduling algorithm to be used.
9095 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9096 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9098 =item * schedule_separate_components
9100 If this option is set then the function C<isl_schedule_get_map>
9101 will treat set nodes in the same way as sequence nodes.
9105 =head2 AST Generation
9107 This section describes the C<isl> functionality for generating
9108 ASTs that visit all the elements
9109 in a domain in an order specified by a schedule tree or
9111 In case the schedule given as a C<isl_union_map>, an AST is generated
9112 that visits all the elements in the domain of the C<isl_union_map>
9113 according to the lexicographic order of the corresponding image
9114 element(s). If the range of the C<isl_union_map> consists of
9115 elements in more than one space, then each of these spaces is handled
9116 separately in an arbitrary order.
9117 It should be noted that the schedule tree or the image elements
9118 in a schedule map only specify the I<order>
9119 in which the corresponding domain elements should be visited.
9120 No direct relation between the partial schedule values
9121 or the image elements on the one hand and the loop iterators
9122 in the generated AST on the other hand should be assumed.
9124 Each AST is generated within a build. The initial build
9125 simply specifies the constraints on the parameters (if any)
9126 and can be created, inspected, copied and freed using the following functions.
9128 #include <isl/ast_build.h>
9129 __isl_give isl_ast_build *isl_ast_build_alloc(
9131 __isl_give isl_ast_build *isl_ast_build_from_context(
9132 __isl_take isl_set *set);
9133 __isl_give isl_ast_build *isl_ast_build_copy(
9134 __isl_keep isl_ast_build *build);
9135 __isl_null isl_ast_build *isl_ast_build_free(
9136 __isl_take isl_ast_build *build);
9138 The C<set> argument is usually a parameter set with zero or more parameters.
9139 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9140 this set is required to be a parameter set.
9141 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9142 specify any parameter constraints.
9143 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9144 and L</"Fine-grained Control over AST Generation">.
9145 Finally, the AST itself can be constructed using one of the following
9148 #include <isl/ast_build.h>
9149 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9150 __isl_keep isl_ast_build *build,
9151 __isl_take isl_schedule *schedule);
9152 __isl_give isl_ast_node *
9153 isl_ast_build_node_from_schedule_map(
9154 __isl_keep isl_ast_build *build,
9155 __isl_take isl_union_map *schedule);
9157 =head3 Inspecting the AST
9159 The basic properties of an AST node can be obtained as follows.
9161 #include <isl/ast.h>
9162 enum isl_ast_node_type isl_ast_node_get_type(
9163 __isl_keep isl_ast_node *node);
9165 The type of an AST node is one of
9166 C<isl_ast_node_for>,
9168 C<isl_ast_node_block>,
9169 C<isl_ast_node_mark> or
9170 C<isl_ast_node_user>.
9171 An C<isl_ast_node_for> represents a for node.
9172 An C<isl_ast_node_if> represents an if node.
9173 An C<isl_ast_node_block> represents a compound node.
9174 An C<isl_ast_node_mark> introduces a mark in the AST.
9175 An C<isl_ast_node_user> represents an expression statement.
9176 An expression statement typically corresponds to a domain element, i.e.,
9177 one of the elements that is visited by the AST.
9179 Each type of node has its own additional properties.
9181 #include <isl/ast.h>
9182 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9183 __isl_keep isl_ast_node *node);
9184 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9185 __isl_keep isl_ast_node *node);
9186 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9187 __isl_keep isl_ast_node *node);
9188 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9189 __isl_keep isl_ast_node *node);
9190 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9191 __isl_keep isl_ast_node *node);
9192 isl_bool isl_ast_node_for_is_degenerate(
9193 __isl_keep isl_ast_node *node);
9195 An C<isl_ast_for> is considered degenerate if it is known to execute
9198 #include <isl/ast.h>
9199 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9200 __isl_keep isl_ast_node *node);
9201 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9202 __isl_keep isl_ast_node *node);
9203 isl_bool isl_ast_node_if_has_else(
9204 __isl_keep isl_ast_node *node);
9205 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9206 __isl_keep isl_ast_node *node);
9208 __isl_give isl_ast_node_list *
9209 isl_ast_node_block_get_children(
9210 __isl_keep isl_ast_node *node);
9212 __isl_give isl_id *isl_ast_node_mark_get_id(
9213 __isl_keep isl_ast_node *node);
9214 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9215 __isl_keep isl_ast_node *node);
9217 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9218 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9220 #include <isl/ast.h>
9221 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9222 __isl_keep isl_ast_node *node);
9224 All descendants of a specific node in the AST (including the node itself)
9226 in depth-first pre-order using the following function.
9228 #include <isl/ast.h>
9229 isl_stat isl_ast_node_foreach_descendant_top_down(
9230 __isl_keep isl_ast_node *node,
9231 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9232 void *user), void *user);
9234 The callback function should return C<isl_bool_true> if the children
9235 of the given node should be visited and C<isl_bool_false> if they should not.
9236 It should return C<isl_bool_error> in case of failure, in which case
9237 the entire traversal is aborted.
9239 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9240 the following functions.
9242 #include <isl/ast.h>
9243 enum isl_ast_expr_type isl_ast_expr_get_type(
9244 __isl_keep isl_ast_expr *expr);
9246 The type of an AST expression is one of
9248 C<isl_ast_expr_id> or
9249 C<isl_ast_expr_int>.
9250 An C<isl_ast_expr_op> represents the result of an operation.
9251 An C<isl_ast_expr_id> represents an identifier.
9252 An C<isl_ast_expr_int> represents an integer value.
9254 Each type of expression has its own additional properties.
9256 #include <isl/ast.h>
9257 enum isl_ast_op_type isl_ast_expr_get_op_type(
9258 __isl_keep isl_ast_expr *expr);
9259 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9260 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9261 __isl_keep isl_ast_expr *expr, int pos);
9262 isl_stat isl_ast_expr_foreach_ast_op_type(
9263 __isl_keep isl_ast_expr *expr,
9264 isl_stat (*fn)(enum isl_ast_op_type type,
9265 void *user), void *user);
9266 isl_stat isl_ast_node_foreach_ast_op_type(
9267 __isl_keep isl_ast_node *node,
9268 isl_stat (*fn)(enum isl_ast_op_type type,
9269 void *user), void *user);
9271 C<isl_ast_expr_get_op_type> returns the type of the operation
9272 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9273 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9275 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9276 C<isl_ast_op_type> that appears in C<expr>.
9277 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9278 C<isl_ast_op_type> that appears in C<node>.
9279 The operation type is one of the following.
9283 =item C<isl_ast_op_and>
9285 Logical I<and> of two arguments.
9286 Both arguments can be evaluated.
9288 =item C<isl_ast_op_and_then>
9290 Logical I<and> of two arguments.
9291 The second argument can only be evaluated if the first evaluates to true.
9293 =item C<isl_ast_op_or>
9295 Logical I<or> of two arguments.
9296 Both arguments can be evaluated.
9298 =item C<isl_ast_op_or_else>
9300 Logical I<or> of two arguments.
9301 The second argument can only be evaluated if the first evaluates to false.
9303 =item C<isl_ast_op_max>
9305 Maximum of two or more arguments.
9307 =item C<isl_ast_op_min>
9309 Minimum of two or more arguments.
9311 =item C<isl_ast_op_minus>
9315 =item C<isl_ast_op_add>
9317 Sum of two arguments.
9319 =item C<isl_ast_op_sub>
9321 Difference of two arguments.
9323 =item C<isl_ast_op_mul>
9325 Product of two arguments.
9327 =item C<isl_ast_op_div>
9329 Exact division. That is, the result is known to be an integer.
9331 =item C<isl_ast_op_fdiv_q>
9333 Result of integer division, rounded towards negative
9336 =item C<isl_ast_op_pdiv_q>
9338 Result of integer division, where dividend is known to be non-negative.
9340 =item C<isl_ast_op_pdiv_r>
9342 Remainder of integer division, where dividend is known to be non-negative.
9344 =item C<isl_ast_op_zdiv_r>
9346 Equal to zero iff the remainder on integer division is zero.
9348 =item C<isl_ast_op_cond>
9350 Conditional operator defined on three arguments.
9351 If the first argument evaluates to true, then the result
9352 is equal to the second argument. Otherwise, the result
9353 is equal to the third argument.
9354 The second and third argument may only be evaluated if
9355 the first argument evaluates to true and false, respectively.
9356 Corresponds to C<a ? b : c> in C.
9358 =item C<isl_ast_op_select>
9360 Conditional operator defined on three arguments.
9361 If the first argument evaluates to true, then the result
9362 is equal to the second argument. Otherwise, the result
9363 is equal to the third argument.
9364 The second and third argument may be evaluated independently
9365 of the value of the first argument.
9366 Corresponds to C<a * b + (1 - a) * c> in C.
9368 =item C<isl_ast_op_eq>
9372 =item C<isl_ast_op_le>
9374 Less than or equal relation.
9376 =item C<isl_ast_op_lt>
9380 =item C<isl_ast_op_ge>
9382 Greater than or equal relation.
9384 =item C<isl_ast_op_gt>
9386 Greater than relation.
9388 =item C<isl_ast_op_call>
9391 The number of arguments of the C<isl_ast_expr> is one more than
9392 the number of arguments in the function call, the first argument
9393 representing the function being called.
9395 =item C<isl_ast_op_access>
9398 The number of arguments of the C<isl_ast_expr> is one more than
9399 the number of index expressions in the array access, the first argument
9400 representing the array being accessed.
9402 =item C<isl_ast_op_member>
9405 This operation has two arguments, a structure and the name of
9406 the member of the structure being accessed.
9410 #include <isl/ast.h>
9411 __isl_give isl_id *isl_ast_expr_get_id(
9412 __isl_keep isl_ast_expr *expr);
9414 Return the identifier represented by the AST expression.
9416 #include <isl/ast.h>
9417 __isl_give isl_val *isl_ast_expr_get_val(
9418 __isl_keep isl_ast_expr *expr);
9420 Return the integer represented by the AST expression.
9422 =head3 Properties of ASTs
9424 #include <isl/ast.h>
9425 isl_bool isl_ast_expr_is_equal(
9426 __isl_keep isl_ast_expr *expr1,
9427 __isl_keep isl_ast_expr *expr2);
9429 Check if two C<isl_ast_expr>s are equal to each other.
9431 =head3 Manipulating and printing the AST
9433 AST nodes can be copied and freed using the following functions.
9435 #include <isl/ast.h>
9436 __isl_give isl_ast_node *isl_ast_node_copy(
9437 __isl_keep isl_ast_node *node);
9438 __isl_null isl_ast_node *isl_ast_node_free(
9439 __isl_take isl_ast_node *node);
9441 AST expressions can be copied and freed using the following functions.
9443 #include <isl/ast.h>
9444 __isl_give isl_ast_expr *isl_ast_expr_copy(
9445 __isl_keep isl_ast_expr *expr);
9446 __isl_null isl_ast_expr *isl_ast_expr_free(
9447 __isl_take isl_ast_expr *expr);
9449 New AST expressions can be created either directly or within
9450 the context of an C<isl_ast_build>.
9452 #include <isl/ast.h>
9453 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9454 __isl_take isl_val *v);
9455 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9456 __isl_take isl_id *id);
9457 __isl_give isl_ast_expr *isl_ast_expr_neg(
9458 __isl_take isl_ast_expr *expr);
9459 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9460 __isl_take isl_ast_expr *expr);
9461 __isl_give isl_ast_expr *isl_ast_expr_add(
9462 __isl_take isl_ast_expr *expr1,
9463 __isl_take isl_ast_expr *expr2);
9464 __isl_give isl_ast_expr *isl_ast_expr_sub(
9465 __isl_take isl_ast_expr *expr1,
9466 __isl_take isl_ast_expr *expr2);
9467 __isl_give isl_ast_expr *isl_ast_expr_mul(
9468 __isl_take isl_ast_expr *expr1,
9469 __isl_take isl_ast_expr *expr2);
9470 __isl_give isl_ast_expr *isl_ast_expr_div(
9471 __isl_take isl_ast_expr *expr1,
9472 __isl_take isl_ast_expr *expr2);
9473 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9474 __isl_take isl_ast_expr *expr1,
9475 __isl_take isl_ast_expr *expr2);
9476 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9477 __isl_take isl_ast_expr *expr1,
9478 __isl_take isl_ast_expr *expr2);
9479 __isl_give isl_ast_expr *isl_ast_expr_and(
9480 __isl_take isl_ast_expr *expr1,
9481 __isl_take isl_ast_expr *expr2)
9482 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9483 __isl_take isl_ast_expr *expr1,
9484 __isl_take isl_ast_expr *expr2)
9485 __isl_give isl_ast_expr *isl_ast_expr_or(
9486 __isl_take isl_ast_expr *expr1,
9487 __isl_take isl_ast_expr *expr2)
9488 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9489 __isl_take isl_ast_expr *expr1,
9490 __isl_take isl_ast_expr *expr2)
9491 __isl_give isl_ast_expr *isl_ast_expr_eq(
9492 __isl_take isl_ast_expr *expr1,
9493 __isl_take isl_ast_expr *expr2);
9494 __isl_give isl_ast_expr *isl_ast_expr_le(
9495 __isl_take isl_ast_expr *expr1,
9496 __isl_take isl_ast_expr *expr2);
9497 __isl_give isl_ast_expr *isl_ast_expr_lt(
9498 __isl_take isl_ast_expr *expr1,
9499 __isl_take isl_ast_expr *expr2);
9500 __isl_give isl_ast_expr *isl_ast_expr_ge(
9501 __isl_take isl_ast_expr *expr1,
9502 __isl_take isl_ast_expr *expr2);
9503 __isl_give isl_ast_expr *isl_ast_expr_gt(
9504 __isl_take isl_ast_expr *expr1,
9505 __isl_take isl_ast_expr *expr2);
9506 __isl_give isl_ast_expr *isl_ast_expr_access(
9507 __isl_take isl_ast_expr *array,
9508 __isl_take isl_ast_expr_list *indices);
9509 __isl_give isl_ast_expr *isl_ast_expr_call(
9510 __isl_take isl_ast_expr *function,
9511 __isl_take isl_ast_expr_list *arguments);
9513 The function C<isl_ast_expr_address_of> can be applied to an
9514 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9515 to represent the address of the C<isl_ast_expr_access>. The function
9516 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9517 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9519 #include <isl/ast_build.h>
9520 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9521 __isl_keep isl_ast_build *build,
9522 __isl_take isl_set *set);
9523 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9524 __isl_keep isl_ast_build *build,
9525 __isl_take isl_pw_aff *pa);
9526 __isl_give isl_ast_expr *
9527 isl_ast_build_access_from_pw_multi_aff(
9528 __isl_keep isl_ast_build *build,
9529 __isl_take isl_pw_multi_aff *pma);
9530 __isl_give isl_ast_expr *
9531 isl_ast_build_access_from_multi_pw_aff(
9532 __isl_keep isl_ast_build *build,
9533 __isl_take isl_multi_pw_aff *mpa);
9534 __isl_give isl_ast_expr *
9535 isl_ast_build_call_from_pw_multi_aff(
9536 __isl_keep isl_ast_build *build,
9537 __isl_take isl_pw_multi_aff *pma);
9538 __isl_give isl_ast_expr *
9539 isl_ast_build_call_from_multi_pw_aff(
9540 __isl_keep isl_ast_build *build,
9541 __isl_take isl_multi_pw_aff *mpa);
9544 the domains of C<pa>, C<mpa> and C<pma> should correspond
9545 to the schedule space of C<build>.
9546 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9547 the function being called.
9548 If the accessed space is a nested relation, then it is taken
9549 to represent an access of the member specified by the range
9550 of this nested relation of the structure specified by the domain
9551 of the nested relation.
9553 The following functions can be used to modify an C<isl_ast_expr>.
9555 #include <isl/ast.h>
9556 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9557 __isl_take isl_ast_expr *expr, int pos,
9558 __isl_take isl_ast_expr *arg);
9560 Replace the argument of C<expr> at position C<pos> by C<arg>.
9562 #include <isl/ast.h>
9563 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9564 __isl_take isl_ast_expr *expr,
9565 __isl_take isl_id_to_ast_expr *id2expr);
9567 The function C<isl_ast_expr_substitute_ids> replaces the
9568 subexpressions of C<expr> of type C<isl_ast_expr_id>
9569 by the corresponding expression in C<id2expr>, if there is any.
9572 User specified data can be attached to an C<isl_ast_node> and obtained
9573 from the same C<isl_ast_node> using the following functions.
9575 #include <isl/ast.h>
9576 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9577 __isl_take isl_ast_node *node,
9578 __isl_take isl_id *annotation);
9579 __isl_give isl_id *isl_ast_node_get_annotation(
9580 __isl_keep isl_ast_node *node);
9582 Basic printing can be performed using the following functions.
9584 #include <isl/ast.h>
9585 __isl_give isl_printer *isl_printer_print_ast_expr(
9586 __isl_take isl_printer *p,
9587 __isl_keep isl_ast_expr *expr);
9588 __isl_give isl_printer *isl_printer_print_ast_node(
9589 __isl_take isl_printer *p,
9590 __isl_keep isl_ast_node *node);
9591 __isl_give char *isl_ast_expr_to_str(
9592 __isl_keep isl_ast_expr *expr);
9594 More advanced printing can be performed using the following functions.
9596 #include <isl/ast.h>
9597 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9598 __isl_take isl_printer *p,
9599 enum isl_ast_op_type type,
9600 __isl_keep const char *name);
9601 isl_stat isl_options_set_ast_print_macro_once(
9602 isl_ctx *ctx, int val);
9603 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9604 __isl_give isl_printer *isl_ast_op_type_print_macro(
9605 enum isl_ast_op_type type,
9606 __isl_take isl_printer *p);
9607 __isl_give isl_printer *isl_ast_expr_print_macros(
9608 __isl_keep isl_ast_expr *expr,
9609 __isl_take isl_printer *p);
9610 __isl_give isl_printer *isl_ast_node_print_macros(
9611 __isl_keep isl_ast_node *node,
9612 __isl_take isl_printer *p);
9613 __isl_give isl_printer *isl_ast_node_print(
9614 __isl_keep isl_ast_node *node,
9615 __isl_take isl_printer *p,
9616 __isl_take isl_ast_print_options *options);
9617 __isl_give isl_printer *isl_ast_node_for_print(
9618 __isl_keep isl_ast_node *node,
9619 __isl_take isl_printer *p,
9620 __isl_take isl_ast_print_options *options);
9621 __isl_give isl_printer *isl_ast_node_if_print(
9622 __isl_keep isl_ast_node *node,
9623 __isl_take isl_printer *p,
9624 __isl_take isl_ast_print_options *options);
9626 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9627 C<isl> may print out an AST that makes use of macros such
9628 as C<floord>, C<min> and C<max>.
9629 The names of these macros may be modified by a call
9630 to C<isl_ast_op_type_set_print_name>. The user-specified
9631 names are associated to the printer object.
9632 C<isl_ast_op_type_print_macro> prints out the macro
9633 corresponding to a specific C<isl_ast_op_type>.
9634 If the print-macro-once option is set, then a given macro definition
9635 is only printed once to any given printer object.
9636 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9637 for subexpressions where these macros would be used and prints
9638 out the required macro definitions.
9639 Essentially, C<isl_ast_expr_print_macros> calls
9640 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9641 as function argument.
9642 C<isl_ast_node_print_macros> does the same
9643 for expressions in its C<isl_ast_node> argument.
9644 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9645 C<isl_ast_node_if_print> print an C<isl_ast_node>
9646 in C<ISL_FORMAT_C>, but allow for some extra control
9647 through an C<isl_ast_print_options> object.
9648 This object can be created using the following functions.
9650 #include <isl/ast.h>
9651 __isl_give isl_ast_print_options *
9652 isl_ast_print_options_alloc(isl_ctx *ctx);
9653 __isl_give isl_ast_print_options *
9654 isl_ast_print_options_copy(
9655 __isl_keep isl_ast_print_options *options);
9656 __isl_null isl_ast_print_options *
9657 isl_ast_print_options_free(
9658 __isl_take isl_ast_print_options *options);
9660 __isl_give isl_ast_print_options *
9661 isl_ast_print_options_set_print_user(
9662 __isl_take isl_ast_print_options *options,
9663 __isl_give isl_printer *(*print_user)(
9664 __isl_take isl_printer *p,
9665 __isl_take isl_ast_print_options *options,
9666 __isl_keep isl_ast_node *node, void *user),
9668 __isl_give isl_ast_print_options *
9669 isl_ast_print_options_set_print_for(
9670 __isl_take isl_ast_print_options *options,
9671 __isl_give isl_printer *(*print_for)(
9672 __isl_take isl_printer *p,
9673 __isl_take isl_ast_print_options *options,
9674 __isl_keep isl_ast_node *node, void *user),
9677 The callback set by C<isl_ast_print_options_set_print_user>
9678 is called whenever a node of type C<isl_ast_node_user> needs to
9680 The callback set by C<isl_ast_print_options_set_print_for>
9681 is called whenever a node of type C<isl_ast_node_for> needs to
9683 Note that C<isl_ast_node_for_print> will I<not> call the
9684 callback set by C<isl_ast_print_options_set_print_for> on the node
9685 on which C<isl_ast_node_for_print> is called, but only on nested
9686 nodes of type C<isl_ast_node_for>. It is therefore safe to
9687 call C<isl_ast_node_for_print> from within the callback set by
9688 C<isl_ast_print_options_set_print_for>.
9690 The following option determines the type to be used for iterators
9691 while printing the AST.
9693 isl_stat isl_options_set_ast_iterator_type(
9694 isl_ctx *ctx, const char *val);
9695 const char *isl_options_get_ast_iterator_type(
9698 The AST printer only prints body nodes as blocks if these
9699 blocks cannot be safely omitted.
9700 For example, a C<for> node with one body node will not be
9701 surrounded with braces in C<ISL_FORMAT_C>.
9702 A block will always be printed by setting the following option.
9704 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9706 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9710 #include <isl/ast_build.h>
9711 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9712 isl_ctx *ctx, int val);
9713 int isl_options_get_ast_build_atomic_upper_bound(
9715 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9717 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9718 isl_stat isl_options_set_ast_build_detect_min_max(
9719 isl_ctx *ctx, int val);
9720 int isl_options_get_ast_build_detect_min_max(
9722 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9723 isl_ctx *ctx, int val);
9724 int isl_options_get_ast_build_exploit_nested_bounds(
9726 isl_stat isl_options_set_ast_build_group_coscheduled(
9727 isl_ctx *ctx, int val);
9728 int isl_options_get_ast_build_group_coscheduled(
9730 isl_stat isl_options_set_ast_build_scale_strides(
9731 isl_ctx *ctx, int val);
9732 int isl_options_get_ast_build_scale_strides(
9734 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9736 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9737 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9739 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9743 =item * ast_build_atomic_upper_bound
9745 Generate loop upper bounds that consist of the current loop iterator,
9746 an operator and an expression not involving the iterator.
9747 If this option is not set, then the current loop iterator may appear
9748 several times in the upper bound.
9749 For example, when this option is turned off, AST generation
9752 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9756 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9759 When the option is turned on, the following AST is generated
9761 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9764 =item * ast_build_prefer_pdiv
9766 If this option is turned off, then the AST generation will
9767 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9768 operators, but no C<isl_ast_op_pdiv_q> or
9769 C<isl_ast_op_pdiv_r> operators.
9770 If this option is turned on, then C<isl> will try to convert
9771 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9772 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9774 =item * ast_build_detect_min_max
9776 If this option is turned on, then C<isl> will try and detect
9777 min or max-expressions when building AST expressions from
9778 piecewise affine expressions.
9780 =item * ast_build_exploit_nested_bounds
9782 Simplify conditions based on bounds of nested for loops.
9783 In particular, remove conditions that are implied by the fact
9784 that one or more nested loops have at least one iteration,
9785 meaning that the upper bound is at least as large as the lower bound.
9786 For example, when this option is turned off, AST generation
9789 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
9795 for (int c0 = 0; c0 <= N; c0 += 1)
9796 for (int c1 = 0; c1 <= M; c1 += 1)
9799 When the option is turned on, the following AST is generated
9801 for (int c0 = 0; c0 <= N; c0 += 1)
9802 for (int c1 = 0; c1 <= M; c1 += 1)
9805 =item * ast_build_group_coscheduled
9807 If two domain elements are assigned the same schedule point, then
9808 they may be executed in any order and they may even appear in different
9809 loops. If this options is set, then the AST generator will make
9810 sure that coscheduled domain elements do not appear in separate parts
9811 of the AST. This is useful in case of nested AST generation
9812 if the outer AST generation is given only part of a schedule
9813 and the inner AST generation should handle the domains that are
9814 coscheduled by this initial part of the schedule together.
9815 For example if an AST is generated for a schedule
9817 { A[i] -> [0]; B[i] -> [0] }
9819 then the C<isl_ast_build_set_create_leaf> callback described
9820 below may get called twice, once for each domain.
9821 Setting this option ensures that the callback is only called once
9822 on both domains together.
9824 =item * ast_build_separation_bounds
9826 This option specifies which bounds to use during separation.
9827 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
9828 then all (possibly implicit) bounds on the current dimension will
9829 be used during separation.
9830 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
9831 then only those bounds that are explicitly available will
9832 be used during separation.
9834 =item * ast_build_scale_strides
9836 This option specifies whether the AST generator is allowed
9837 to scale down iterators of strided loops.
9839 =item * ast_build_allow_else
9841 This option specifies whether the AST generator is allowed
9842 to construct if statements with else branches.
9844 =item * ast_build_allow_or
9846 This option specifies whether the AST generator is allowed
9847 to construct if conditions with disjunctions.
9851 =head3 AST Generation Options (Schedule Tree)
9853 In case of AST construction from a schedule tree, the options
9854 that control how an AST is created from the individual schedule
9855 dimensions are stored in the band nodes of the tree
9856 (see L</"Schedule Trees">).
9858 In particular, a schedule dimension can be handled in four
9859 different ways, atomic, separate, unroll or the default.
9860 This loop AST generation type can be set using
9861 C<isl_schedule_node_band_member_set_ast_loop_type>.
9863 the first three can be selected by including a one-dimensional
9864 element with as value the position of the schedule dimension
9865 within the band and as name one of C<atomic>, C<separate>
9866 or C<unroll> in the options
9867 set by C<isl_schedule_node_band_set_ast_build_options>.
9868 Only one of these three may be specified for
9869 any given schedule dimension within a band node.
9870 If none of these is specified, then the default
9871 is used. The meaning of the options is as follows.
9877 When this option is specified, the AST generator will make
9878 sure that a given domains space only appears in a single
9879 loop at the specified level.
9881 For example, for the schedule tree
9883 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9885 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9886 options: "{ atomic[x] }"
9888 the following AST will be generated
9890 for (int c0 = 0; c0 <= 10; c0 += 1) {
9897 On the other hand, for the schedule tree
9899 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9901 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9902 options: "{ separate[x] }"
9904 the following AST will be generated
9908 for (int c0 = 1; c0 <= 9; c0 += 1) {
9915 If neither C<atomic> nor C<separate> is specified, then the AST generator
9916 may produce either of these two results or some intermediate form.
9920 When this option is specified, the AST generator will
9921 split the domain of the specified schedule dimension
9922 into pieces with a fixed set of statements for which
9923 instances need to be executed by the iterations in
9924 the schedule domain part. This option tends to avoid
9925 the generation of guards inside the corresponding loops.
9926 See also the C<atomic> option.
9930 When this option is specified, the AST generator will
9931 I<completely> unroll the corresponding schedule dimension.
9932 It is the responsibility of the user to ensure that such
9933 unrolling is possible.
9934 To obtain a partial unrolling, the user should apply an additional
9935 strip-mining to the schedule and fully unroll the inner schedule
9940 The C<isolate> option is a bit more involved. It allows the user
9941 to isolate a range of schedule dimension values from smaller and
9942 greater values. Additionally, the user may specify a different
9943 atomic/separate/unroll choice for the isolated part and the remaining
9944 parts. The typical use case of the C<isolate> option is to isolate
9945 full tiles from partial tiles.
9946 The part that needs to be isolated may depend on outer schedule dimensions.
9947 The option therefore needs to be able to reference those outer schedule
9948 dimensions. In particular, the space of the C<isolate> option is that
9949 of a wrapped map with as domain the flat product of all outer band nodes
9950 and as range the space of the current band node.
9951 The atomic/separate/unroll choice for the isolated part is determined
9952 by an option that lives in an unnamed wrapped space with as domain
9953 a zero-dimensional C<isolate> space and as range the regular
9954 C<atomic>, C<separate> or C<unroll> space.
9955 This option may also be set directly using
9956 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
9957 The atomic/separate/unroll choice for the remaining part is determined
9958 by the regular C<atomic>, C<separate> or C<unroll> option.
9959 The use of the C<isolate> option causes any tree containing the node
9960 to be considered anchored.
9962 As an example, consider the isolation of full tiles from partial tiles
9963 in a tiling of a triangular domain. The original schedule is as follows.
9965 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9967 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9968 { A[i,j] -> [floor(j/10)] }, \
9969 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9973 for (int c0 = 0; c0 <= 10; c0 += 1)
9974 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9975 for (int c2 = 10 * c0;
9976 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9977 for (int c3 = 10 * c1;
9978 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9981 Isolating the full tiles, we have the following input
9983 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9985 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9986 { A[i,j] -> [floor(j/10)] }, \
9987 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9988 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9989 10a+9+10b+9 <= 100 }"
9994 for (int c0 = 0; c0 <= 8; c0 += 1) {
9995 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9996 for (int c2 = 10 * c0;
9997 c2 <= 10 * c0 + 9; c2 += 1)
9998 for (int c3 = 10 * c1;
9999 c3 <= 10 * c1 + 9; c3 += 1)
10001 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10002 for (int c2 = 10 * c0;
10003 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10004 for (int c3 = 10 * c1;
10005 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10008 for (int c0 = 9; c0 <= 10; c0 += 1)
10009 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10010 for (int c2 = 10 * c0;
10011 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10012 for (int c3 = 10 * c1;
10013 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10017 We may then additionally unroll the innermost loop of the isolated part
10019 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10021 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10022 { A[i,j] -> [floor(j/10)] }, \
10023 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10024 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10025 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10030 for (int c0 = 0; c0 <= 8; c0 += 1) {
10031 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10032 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10034 A(c2, 10 * c1 + 1);
10035 A(c2, 10 * c1 + 2);
10036 A(c2, 10 * c1 + 3);
10037 A(c2, 10 * c1 + 4);
10038 A(c2, 10 * c1 + 5);
10039 A(c2, 10 * c1 + 6);
10040 A(c2, 10 * c1 + 7);
10041 A(c2, 10 * c1 + 8);
10042 A(c2, 10 * c1 + 9);
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)
10061 =head3 AST Generation Options (Schedule Map)
10063 In case of AST construction using
10064 C<isl_ast_build_node_from_schedule_map>, the options
10065 that control how an AST is created from the individual schedule
10066 dimensions are stored in the C<isl_ast_build>.
10067 They can be set using the following function.
10069 #include <isl/ast_build.h>
10070 __isl_give isl_ast_build *
10071 isl_ast_build_set_options(
10072 __isl_take isl_ast_build *control,
10073 __isl_take isl_union_map *options);
10075 The options are encoded in an C<isl_union_map>.
10076 The domain of this union relation refers to the schedule domain,
10077 i.e., the range of the schedule passed
10078 to C<isl_ast_build_node_from_schedule_map>.
10079 In the case of nested AST generation (see L</"Nested AST Generation">),
10080 the domain of C<options> should refer to the extra piece of the schedule.
10081 That is, it should be equal to the range of the wrapped relation in the
10082 range of the schedule.
10083 The range of the options can consist of elements in one or more spaces,
10084 the names of which determine the effect of the option.
10085 The values of the range typically also refer to the schedule dimension
10086 to which the option applies. In case of nested AST generation
10087 (see L</"Nested AST Generation">), these values refer to the position
10088 of the schedule dimension within the innermost AST generation.
10089 The constraints on the domain elements of
10090 the option should only refer to this dimension and earlier dimensions.
10091 We consider the following spaces.
10095 =item C<separation_class>
10097 B<This option has been deprecated. Use the isolate option on
10098 schedule trees instead.>
10100 This space is a wrapped relation between two one dimensional spaces.
10101 The input space represents the schedule dimension to which the option
10102 applies and the output space represents the separation class.
10103 While constructing a loop corresponding to the specified schedule
10104 dimension(s), the AST generator will try to generate separate loops
10105 for domain elements that are assigned different classes.
10106 If only some of the elements are assigned a class, then those elements
10107 that are not assigned any class will be treated as belonging to a class
10108 that is separate from the explicitly assigned classes.
10109 The typical use case for this option is to separate full tiles from
10111 The other options, described below, are applied after the separation
10114 As an example, consider the separation into full and partial tiles
10115 of a tiling of a triangular domain.
10116 Take, for example, the domain
10118 { A[i,j] : 0 <= i,j and i + j <= 100 }
10120 and a tiling into tiles of 10 by 10. The input to the AST generator
10121 is then the schedule
10123 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10126 Without any options, the following AST is generated
10128 for (int c0 = 0; c0 <= 10; c0 += 1)
10129 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10130 for (int c2 = 10 * c0;
10131 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10133 for (int c3 = 10 * c1;
10134 c3 <= min(10 * c1 + 9, -c2 + 100);
10138 Separation into full and partial tiles can be obtained by assigning
10139 a class, say C<0>, to the full tiles. The full tiles are represented by those
10140 values of the first and second schedule dimensions for which there are
10141 values of the third and fourth dimensions to cover an entire tile.
10142 That is, we need to specify the following option
10144 { [a,b,c,d] -> separation_class[[0]->[0]] :
10145 exists b': 0 <= 10a,10b' and
10146 10a+9+10b'+9 <= 100;
10147 [a,b,c,d] -> separation_class[[1]->[0]] :
10148 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10150 which simplifies to
10152 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10153 a >= 0 and b >= 0 and b <= 8 - a;
10154 [a, b, c, d] -> separation_class[[0] -> [0]] :
10155 a >= 0 and a <= 8 }
10157 With this option, the generated AST is as follows
10160 for (int c0 = 0; c0 <= 8; c0 += 1) {
10161 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10162 for (int c2 = 10 * c0;
10163 c2 <= 10 * c0 + 9; c2 += 1)
10164 for (int c3 = 10 * c1;
10165 c3 <= 10 * c1 + 9; c3 += 1)
10167 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10168 for (int c2 = 10 * c0;
10169 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10171 for (int c3 = 10 * c1;
10172 c3 <= min(-c2 + 100, 10 * c1 + 9);
10176 for (int c0 = 9; c0 <= 10; c0 += 1)
10177 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10178 for (int c2 = 10 * c0;
10179 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10181 for (int c3 = 10 * c1;
10182 c3 <= min(10 * c1 + 9, -c2 + 100);
10189 This is a single-dimensional space representing the schedule dimension(s)
10190 to which ``separation'' should be applied. Separation tries to split
10191 a loop into several pieces if this can avoid the generation of guards
10193 See also the C<atomic> option.
10197 This is a single-dimensional space representing the schedule dimension(s)
10198 for which the domains should be considered ``atomic''. That is, the
10199 AST generator will make sure that any given domain space will only appear
10200 in a single loop at the specified level.
10202 Consider the following schedule
10204 { a[i] -> [i] : 0 <= i < 10;
10205 b[i] -> [i+1] : 0 <= i < 10 }
10207 If the following option is specified
10209 { [i] -> separate[x] }
10211 then the following AST will be generated
10215 for (int c0 = 1; c0 <= 9; c0 += 1) {
10222 If, on the other hand, the following option is specified
10224 { [i] -> atomic[x] }
10226 then the following AST will be generated
10228 for (int c0 = 0; c0 <= 10; c0 += 1) {
10235 If neither C<atomic> nor C<separate> is specified, then the AST generator
10236 may produce either of these two results or some intermediate form.
10240 This is a single-dimensional space representing the schedule dimension(s)
10241 that should be I<completely> unrolled.
10242 To obtain a partial unrolling, the user should apply an additional
10243 strip-mining to the schedule and fully unroll the inner loop.
10247 =head3 Fine-grained Control over AST Generation
10249 Besides specifying the constraints on the parameters,
10250 an C<isl_ast_build> object can be used to control
10251 various aspects of the AST generation process.
10252 In case of AST construction using
10253 C<isl_ast_build_node_from_schedule_map>,
10254 the most prominent way of control is through ``options'',
10255 as explained above.
10257 Additional control is available through the following functions.
10259 #include <isl/ast_build.h>
10260 __isl_give isl_ast_build *
10261 isl_ast_build_set_iterators(
10262 __isl_take isl_ast_build *control,
10263 __isl_take isl_id_list *iterators);
10265 The function C<isl_ast_build_set_iterators> allows the user to
10266 specify a list of iterator C<isl_id>s to be used as iterators.
10267 If the input schedule is injective, then
10268 the number of elements in this list should be as large as the dimension
10269 of the schedule space, but no direct correspondence should be assumed
10270 between dimensions and elements.
10271 If the input schedule is not injective, then an additional number
10272 of C<isl_id>s equal to the largest dimension of the input domains
10274 If the number of provided C<isl_id>s is insufficient, then additional
10275 names are automatically generated.
10277 #include <isl/ast_build.h>
10278 __isl_give isl_ast_build *
10279 isl_ast_build_set_create_leaf(
10280 __isl_take isl_ast_build *control,
10281 __isl_give isl_ast_node *(*fn)(
10282 __isl_take isl_ast_build *build,
10283 void *user), void *user);
10286 C<isl_ast_build_set_create_leaf> function allows for the
10287 specification of a callback that should be called whenever the AST
10288 generator arrives at an element of the schedule domain.
10289 The callback should return an AST node that should be inserted
10290 at the corresponding position of the AST. The default action (when
10291 the callback is not set) is to continue generating parts of the AST to scan
10292 all the domain elements associated to the schedule domain element
10293 and to insert user nodes, ``calling'' the domain element, for each of them.
10294 The C<build> argument contains the current state of the C<isl_ast_build>.
10295 To ease nested AST generation (see L</"Nested AST Generation">),
10296 all control information that is
10297 specific to the current AST generation such as the options and
10298 the callbacks has been removed from this C<isl_ast_build>.
10299 The callback would typically return the result of a nested
10300 AST generation or a
10301 user defined node created using the following function.
10303 #include <isl/ast.h>
10304 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10305 __isl_take isl_ast_expr *expr);
10307 #include <isl/ast_build.h>
10308 __isl_give isl_ast_build *
10309 isl_ast_build_set_at_each_domain(
10310 __isl_take isl_ast_build *build,
10311 __isl_give isl_ast_node *(*fn)(
10312 __isl_take isl_ast_node *node,
10313 __isl_keep isl_ast_build *build,
10314 void *user), void *user);
10315 __isl_give isl_ast_build *
10316 isl_ast_build_set_before_each_for(
10317 __isl_take isl_ast_build *build,
10318 __isl_give isl_id *(*fn)(
10319 __isl_keep isl_ast_build *build,
10320 void *user), void *user);
10321 __isl_give isl_ast_build *
10322 isl_ast_build_set_after_each_for(
10323 __isl_take isl_ast_build *build,
10324 __isl_give isl_ast_node *(*fn)(
10325 __isl_take isl_ast_node *node,
10326 __isl_keep isl_ast_build *build,
10327 void *user), void *user);
10328 __isl_give isl_ast_build *
10329 isl_ast_build_set_before_each_mark(
10330 __isl_take isl_ast_build *build,
10331 isl_stat (*fn)(__isl_keep isl_id *mark,
10332 __isl_keep isl_ast_build *build,
10333 void *user), void *user);
10334 __isl_give isl_ast_build *
10335 isl_ast_build_set_after_each_mark(
10336 __isl_take isl_ast_build *build,
10337 __isl_give isl_ast_node *(*fn)(
10338 __isl_take isl_ast_node *node,
10339 __isl_keep isl_ast_build *build,
10340 void *user), void *user);
10342 The callback set by C<isl_ast_build_set_at_each_domain> will
10343 be called for each domain AST node.
10344 The callbacks set by C<isl_ast_build_set_before_each_for>
10345 and C<isl_ast_build_set_after_each_for> will be called
10346 for each for AST node. The first will be called in depth-first
10347 pre-order, while the second will be called in depth-first post-order.
10348 Since C<isl_ast_build_set_before_each_for> is called before the for
10349 node is actually constructed, it is only passed an C<isl_ast_build>.
10350 The returned C<isl_id> will be added as an annotation (using
10351 C<isl_ast_node_set_annotation>) to the constructed for node.
10352 In particular, if the user has also specified an C<after_each_for>
10353 callback, then the annotation can be retrieved from the node passed to
10354 that callback using C<isl_ast_node_get_annotation>.
10355 The callbacks set by C<isl_ast_build_set_before_each_mark>
10356 and C<isl_ast_build_set_after_each_mark> will be called for each
10357 mark AST node that is created, i.e., for each mark schedule node
10358 in the input schedule tree. The first will be called in depth-first
10359 pre-order, while the second will be called in depth-first post-order.
10360 Since the callback set by C<isl_ast_build_set_before_each_mark>
10361 is called before the mark AST node is actually constructed, it is passed
10362 the identifier of the mark node.
10363 All callbacks should C<NULL> (or -1) on failure.
10364 The given C<isl_ast_build> can be used to create new
10365 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10366 or C<isl_ast_build_call_from_pw_multi_aff>.
10368 =head3 Nested AST Generation
10370 C<isl> allows the user to create an AST within the context
10371 of another AST. These nested ASTs are created using the
10372 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10373 the outer AST. The C<build> argument should be an C<isl_ast_build>
10374 passed to a callback set by
10375 C<isl_ast_build_set_create_leaf>.
10376 The space of the range of the C<schedule> argument should refer
10377 to this build. In particular, the space should be a wrapped
10378 relation and the domain of this wrapped relation should be the
10379 same as that of the range of the schedule returned by
10380 C<isl_ast_build_get_schedule> below.
10381 In practice, the new schedule is typically
10382 created by calling C<isl_union_map_range_product> on the old schedule
10383 and some extra piece of the schedule.
10384 The space of the schedule domain is also available from
10385 the C<isl_ast_build>.
10387 #include <isl/ast_build.h>
10388 __isl_give isl_union_map *isl_ast_build_get_schedule(
10389 __isl_keep isl_ast_build *build);
10390 __isl_give isl_space *isl_ast_build_get_schedule_space(
10391 __isl_keep isl_ast_build *build);
10392 __isl_give isl_ast_build *isl_ast_build_restrict(
10393 __isl_take isl_ast_build *build,
10394 __isl_take isl_set *set);
10396 The C<isl_ast_build_get_schedule> function returns a (partial)
10397 schedule for the domains elements for which part of the AST still needs to
10398 be generated in the current build.
10399 In particular, the domain elements are mapped to those iterations of the loops
10400 enclosing the current point of the AST generation inside which
10401 the domain elements are executed.
10402 No direct correspondence between
10403 the input schedule and this schedule should be assumed.
10404 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10405 to create a set for C<isl_ast_build_restrict> to intersect
10406 with the current build. In particular, the set passed to
10407 C<isl_ast_build_restrict> can have additional parameters.
10408 The ids of the set dimensions in the space returned by
10409 C<isl_ast_build_get_schedule_space> correspond to the
10410 iterators of the already generated loops.
10411 The user should not rely on the ids of the output dimensions
10412 of the relations in the union relation returned by
10413 C<isl_ast_build_get_schedule> having any particular value.
10415 =head1 Applications
10417 Although C<isl> is mainly meant to be used as a library,
10418 it also contains some basic applications that use some
10419 of the functionality of C<isl>.
10420 The input may be specified in either the L<isl format>
10421 or the L<PolyLib format>.
10423 =head2 C<isl_polyhedron_sample>
10425 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10426 an integer element of the polyhedron, if there is any.
10427 The first column in the output is the denominator and is always
10428 equal to 1. If the polyhedron contains no integer points,
10429 then a vector of length zero is printed.
10433 C<isl_pip> takes the same input as the C<example> program
10434 from the C<piplib> distribution, i.e., a set of constraints
10435 on the parameters, a line containing only -1 and finally a set
10436 of constraints on a parametric polyhedron.
10437 The coefficients of the parameters appear in the last columns
10438 (but before the final constant column).
10439 The output is the lexicographic minimum of the parametric polyhedron.
10440 As C<isl> currently does not have its own output format, the output
10441 is just a dump of the internal state.
10443 =head2 C<isl_polyhedron_minimize>
10445 C<isl_polyhedron_minimize> computes the minimum of some linear
10446 or affine objective function over the integer points in a polyhedron.
10447 If an affine objective function
10448 is given, then the constant should appear in the last column.
10450 =head2 C<isl_polytope_scan>
10452 Given a polytope, C<isl_polytope_scan> prints
10453 all integer points in the polytope.
10455 =head2 C<isl_codegen>
10457 Given a schedule, a context set and an options relation,
10458 C<isl_codegen> prints out an AST that scans the domain elements
10459 of the schedule in the order of their image(s) taking into account
10460 the constraints in the context set.