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 function tests 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);
3786 __isl_give isl_val *
3787 isl_basic_map_plain_get_val_if_fixed(
3788 __isl_keep isl_basic_map *bmap,
3789 enum isl_dim_type type, unsigned pos);
3790 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3791 __isl_keep isl_set *set,
3792 enum isl_dim_type type, unsigned pos);
3793 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3794 __isl_keep isl_map *map,
3795 enum isl_dim_type type, unsigned pos);
3797 If the set or relation obviously lies on a hyperplane where the given dimension
3798 has a fixed value, then return that value.
3799 Otherwise return NaN.
3803 isl_stat isl_set_dim_residue_class_val(
3804 __isl_keep isl_set *set,
3805 int pos, __isl_give isl_val **modulo,
3806 __isl_give isl_val **residue);
3808 Check if the values of the given set dimension are equal to a fixed
3809 value modulo some integer value. If so, assign the modulo to C<*modulo>
3810 and the fixed value to C<*residue>. If the given dimension attains only
3811 a single value, then assign C<0> to C<*modulo> and the fixed value to
3813 If the dimension does not attain only a single value and if no modulo
3814 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3818 To check whether the description of a set, relation or function depends
3819 on one or more given dimensions,
3820 the following functions can be used.
3822 #include <isl/constraint.h>
3823 isl_bool isl_constraint_involves_dims(
3824 __isl_keep isl_constraint *constraint,
3825 enum isl_dim_type type, unsigned first, unsigned n);
3827 #include <isl/set.h>
3828 isl_bool isl_basic_set_involves_dims(
3829 __isl_keep isl_basic_set *bset,
3830 enum isl_dim_type type, unsigned first, unsigned n);
3831 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3832 enum isl_dim_type type, unsigned first, unsigned n);
3834 #include <isl/map.h>
3835 isl_bool isl_basic_map_involves_dims(
3836 __isl_keep isl_basic_map *bmap,
3837 enum isl_dim_type type, unsigned first, unsigned n);
3838 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3839 enum isl_dim_type type, unsigned first, unsigned n);
3841 #include <isl/union_map.h>
3842 isl_bool isl_union_map_involves_dims(
3843 __isl_keep isl_union_map *umap,
3844 enum isl_dim_type type, unsigned first, unsigned n);
3846 #include <isl/aff.h>
3847 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3848 enum isl_dim_type type, unsigned first, unsigned n);
3849 isl_bool isl_pw_aff_involves_dims(
3850 __isl_keep isl_pw_aff *pwaff,
3851 enum isl_dim_type type, unsigned first, unsigned n);
3852 isl_bool isl_multi_aff_involves_dims(
3853 __isl_keep isl_multi_aff *ma,
3854 enum isl_dim_type type, unsigned first, unsigned n);
3855 isl_bool isl_multi_pw_aff_involves_dims(
3856 __isl_keep isl_multi_pw_aff *mpa,
3857 enum isl_dim_type type, unsigned first, unsigned n);
3859 #include <isl/polynomial.h>
3860 isl_bool isl_qpolynomial_involves_dims(
3861 __isl_keep isl_qpolynomial *qp,
3862 enum isl_dim_type type, unsigned first, unsigned n);
3864 Similarly, the following functions can be used to check whether
3865 a given dimension is involved in any lower or upper bound.
3867 #include <isl/set.h>
3868 isl_bool isl_set_dim_has_any_lower_bound(
3869 __isl_keep isl_set *set,
3870 enum isl_dim_type type, unsigned pos);
3871 isl_bool isl_set_dim_has_any_upper_bound(
3872 __isl_keep isl_set *set,
3873 enum isl_dim_type type, unsigned pos);
3875 Note that these functions return true even if there is a bound on
3876 the dimension on only some of the basic sets of C<set>.
3877 To check if they have a bound for all of the basic sets in C<set>,
3878 use the following functions instead.
3880 #include <isl/set.h>
3881 isl_bool isl_set_dim_has_lower_bound(
3882 __isl_keep isl_set *set,
3883 enum isl_dim_type type, unsigned pos);
3884 isl_bool isl_set_dim_has_upper_bound(
3885 __isl_keep isl_set *set,
3886 enum isl_dim_type type, unsigned pos);
3890 To check whether a set is a parameter domain, use this function:
3892 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3893 isl_bool isl_union_set_is_params(
3894 __isl_keep isl_union_set *uset);
3898 The following functions check whether the space of the given
3899 (basic) set or relation range is a wrapped relation.
3901 #include <isl/space.h>
3902 isl_bool isl_space_is_wrapping(
3903 __isl_keep isl_space *space);
3904 isl_bool isl_space_domain_is_wrapping(
3905 __isl_keep isl_space *space);
3906 isl_bool isl_space_range_is_wrapping(
3907 __isl_keep isl_space *space);
3909 #include <isl/set.h>
3910 isl_bool isl_basic_set_is_wrapping(
3911 __isl_keep isl_basic_set *bset);
3912 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3914 #include <isl/map.h>
3915 isl_bool isl_map_domain_is_wrapping(
3916 __isl_keep isl_map *map);
3917 isl_bool isl_map_range_is_wrapping(
3918 __isl_keep isl_map *map);
3920 #include <isl/val.h>
3921 isl_bool isl_multi_val_range_is_wrapping(
3922 __isl_keep isl_multi_val *mv);
3924 #include <isl/aff.h>
3925 isl_bool isl_multi_aff_range_is_wrapping(
3926 __isl_keep isl_multi_aff *ma);
3927 isl_bool isl_multi_pw_aff_range_is_wrapping(
3928 __isl_keep isl_multi_pw_aff *mpa);
3929 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3930 __isl_keep isl_multi_union_pw_aff *mupa);
3932 The input to C<isl_space_is_wrapping> should
3933 be the space of a set, while that of
3934 C<isl_space_domain_is_wrapping> and
3935 C<isl_space_range_is_wrapping> should be the space of a relation.
3937 =item * Internal Product
3939 isl_bool isl_basic_map_can_zip(
3940 __isl_keep isl_basic_map *bmap);
3941 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
3943 Check whether the product of domain and range of the given relation
3945 i.e., whether both domain and range are nested relations.
3949 #include <isl/space.h>
3950 isl_bool isl_space_can_curry(
3951 __isl_keep isl_space *space);
3953 #include <isl/map.h>
3954 isl_bool isl_basic_map_can_curry(
3955 __isl_keep isl_basic_map *bmap);
3956 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
3958 Check whether the domain of the (basic) relation is a wrapped relation.
3960 #include <isl/space.h>
3961 __isl_give isl_space *isl_space_uncurry(
3962 __isl_take isl_space *space);
3964 #include <isl/map.h>
3965 isl_bool isl_basic_map_can_uncurry(
3966 __isl_keep isl_basic_map *bmap);
3967 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
3969 Check whether the range of the (basic) relation is a wrapped relation.
3971 #include <isl/space.h>
3972 isl_bool isl_space_can_range_curry(
3973 __isl_keep isl_space *space);
3975 #include <isl/map.h>
3976 isl_bool isl_map_can_range_curry(
3977 __isl_keep isl_map *map);
3979 Check whether the domain of the relation wrapped in the range of
3980 the input is itself a wrapped relation.
3982 =item * Special Values
3984 #include <isl/aff.h>
3985 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
3986 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3987 isl_bool isl_multi_pw_aff_is_cst(
3988 __isl_keep isl_multi_pw_aff *mpa);
3990 Check whether the given expression is a constant.
3992 #include <isl/aff.h>
3993 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
3994 isl_bool isl_pw_aff_involves_nan(
3995 __isl_keep isl_pw_aff *pa);
3997 #include <isl/polynomial.h>
3998 isl_bool isl_qpolynomial_fold_is_nan(
3999 __isl_keep isl_qpolynomial_fold *fold);
4001 Check whether the given expression is equal to or involves NaN.
4003 #include <isl/aff.h>
4004 isl_bool isl_aff_plain_is_zero(
4005 __isl_keep isl_aff *aff);
4007 Check whether the affine expression is obviously zero.
4011 =head3 Binary Properties
4017 The following functions check whether two objects
4018 represent the same set, relation or function.
4019 The C<plain> variants only return true if the objects
4020 are obviously the same. That is, they may return false
4021 even if the objects are the same, but they will never
4022 return true if the objects are not the same.
4024 #include <isl/set.h>
4025 isl_bool isl_basic_set_plain_is_equal(
4026 __isl_keep isl_basic_set *bset1,
4027 __isl_keep isl_basic_set *bset2);
4028 isl_bool isl_basic_set_is_equal(
4029 __isl_keep isl_basic_set *bset1,
4030 __isl_keep isl_basic_set *bset2);
4031 isl_bool isl_set_plain_is_equal(
4032 __isl_keep isl_set *set1,
4033 __isl_keep isl_set *set2);
4034 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4035 __isl_keep isl_set *set2);
4037 #include <isl/map.h>
4038 isl_bool isl_basic_map_is_equal(
4039 __isl_keep isl_basic_map *bmap1,
4040 __isl_keep isl_basic_map *bmap2);
4041 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4042 __isl_keep isl_map *map2);
4043 isl_bool isl_map_plain_is_equal(
4044 __isl_keep isl_map *map1,
4045 __isl_keep isl_map *map2);
4047 #include <isl/union_set.h>
4048 isl_bool isl_union_set_is_equal(
4049 __isl_keep isl_union_set *uset1,
4050 __isl_keep isl_union_set *uset2);
4052 #include <isl/union_map.h>
4053 isl_bool isl_union_map_is_equal(
4054 __isl_keep isl_union_map *umap1,
4055 __isl_keep isl_union_map *umap2);
4057 #include <isl/aff.h>
4058 isl_bool isl_aff_plain_is_equal(
4059 __isl_keep isl_aff *aff1,
4060 __isl_keep isl_aff *aff2);
4061 isl_bool isl_multi_aff_plain_is_equal(
4062 __isl_keep isl_multi_aff *maff1,
4063 __isl_keep isl_multi_aff *maff2);
4064 isl_bool isl_pw_aff_plain_is_equal(
4065 __isl_keep isl_pw_aff *pwaff1,
4066 __isl_keep isl_pw_aff *pwaff2);
4067 isl_bool isl_pw_multi_aff_plain_is_equal(
4068 __isl_keep isl_pw_multi_aff *pma1,
4069 __isl_keep isl_pw_multi_aff *pma2);
4070 isl_bool isl_multi_pw_aff_plain_is_equal(
4071 __isl_keep isl_multi_pw_aff *mpa1,
4072 __isl_keep isl_multi_pw_aff *mpa2);
4073 isl_bool isl_multi_pw_aff_is_equal(
4074 __isl_keep isl_multi_pw_aff *mpa1,
4075 __isl_keep isl_multi_pw_aff *mpa2);
4076 isl_bool isl_union_pw_aff_plain_is_equal(
4077 __isl_keep isl_union_pw_aff *upa1,
4078 __isl_keep isl_union_pw_aff *upa2);
4079 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4080 __isl_keep isl_union_pw_multi_aff *upma1,
4081 __isl_keep isl_union_pw_multi_aff *upma2);
4082 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4083 __isl_keep isl_multi_union_pw_aff *mupa1,
4084 __isl_keep isl_multi_union_pw_aff *mupa2);
4086 #include <isl/polynomial.h>
4087 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4088 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4089 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4090 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4091 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4092 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4094 =item * Disjointness
4096 #include <isl/set.h>
4097 isl_bool isl_basic_set_is_disjoint(
4098 __isl_keep isl_basic_set *bset1,
4099 __isl_keep isl_basic_set *bset2);
4100 isl_bool isl_set_plain_is_disjoint(
4101 __isl_keep isl_set *set1,
4102 __isl_keep isl_set *set2);
4103 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4104 __isl_keep isl_set *set2);
4106 #include <isl/map.h>
4107 isl_bool isl_basic_map_is_disjoint(
4108 __isl_keep isl_basic_map *bmap1,
4109 __isl_keep isl_basic_map *bmap2);
4110 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4111 __isl_keep isl_map *map2);
4113 #include <isl/union_set.h>
4114 isl_bool isl_union_set_is_disjoint(
4115 __isl_keep isl_union_set *uset1,
4116 __isl_keep isl_union_set *uset2);
4118 #include <isl/union_map.h>
4119 isl_bool isl_union_map_is_disjoint(
4120 __isl_keep isl_union_map *umap1,
4121 __isl_keep isl_union_map *umap2);
4125 isl_bool isl_basic_set_is_subset(
4126 __isl_keep isl_basic_set *bset1,
4127 __isl_keep isl_basic_set *bset2);
4128 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4129 __isl_keep isl_set *set2);
4130 isl_bool isl_set_is_strict_subset(
4131 __isl_keep isl_set *set1,
4132 __isl_keep isl_set *set2);
4133 isl_bool isl_union_set_is_subset(
4134 __isl_keep isl_union_set *uset1,
4135 __isl_keep isl_union_set *uset2);
4136 isl_bool isl_union_set_is_strict_subset(
4137 __isl_keep isl_union_set *uset1,
4138 __isl_keep isl_union_set *uset2);
4139 isl_bool isl_basic_map_is_subset(
4140 __isl_keep isl_basic_map *bmap1,
4141 __isl_keep isl_basic_map *bmap2);
4142 isl_bool isl_basic_map_is_strict_subset(
4143 __isl_keep isl_basic_map *bmap1,
4144 __isl_keep isl_basic_map *bmap2);
4145 isl_bool isl_map_is_subset(
4146 __isl_keep isl_map *map1,
4147 __isl_keep isl_map *map2);
4148 isl_bool isl_map_is_strict_subset(
4149 __isl_keep isl_map *map1,
4150 __isl_keep isl_map *map2);
4151 isl_bool isl_union_map_is_subset(
4152 __isl_keep isl_union_map *umap1,
4153 __isl_keep isl_union_map *umap2);
4154 isl_bool isl_union_map_is_strict_subset(
4155 __isl_keep isl_union_map *umap1,
4156 __isl_keep isl_union_map *umap2);
4158 Check whether the first argument is a (strict) subset of the
4163 Every comparison function returns a negative value if the first
4164 argument is considered smaller than the second, a positive value
4165 if the first argument is considered greater and zero if the two
4166 constraints are considered the same by the comparison criterion.
4168 #include <isl/constraint.h>
4169 int isl_constraint_plain_cmp(
4170 __isl_keep isl_constraint *c1,
4171 __isl_keep isl_constraint *c2);
4173 This function is useful for sorting C<isl_constraint>s.
4174 The order depends on the internal representation of the inputs.
4175 The order is fixed over different calls to the function (assuming
4176 the internal representation of the inputs has not changed), but may
4177 change over different versions of C<isl>.
4179 #include <isl/constraint.h>
4180 int isl_constraint_cmp_last_non_zero(
4181 __isl_keep isl_constraint *c1,
4182 __isl_keep isl_constraint *c2);
4184 This function can be used to sort constraints that live in the same
4185 local space. Constraints that involve ``earlier'' dimensions or
4186 that have a smaller coefficient for the shared latest dimension
4187 are considered smaller than other constraints.
4188 This function only defines a B<partial> order.
4190 #include <isl/set.h>
4191 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4192 __isl_keep isl_set *set2);
4194 This function is useful for sorting C<isl_set>s.
4195 The order depends on the internal representation of the inputs.
4196 The order is fixed over different calls to the function (assuming
4197 the internal representation of the inputs has not changed), but may
4198 change over different versions of C<isl>.
4200 #include <isl/aff.h>
4201 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4202 __isl_keep isl_pw_aff *pa2);
4204 The function C<isl_pw_aff_plain_cmp> can be used to sort
4205 C<isl_pw_aff>s. The order is not strictly defined.
4206 The current order sorts expressions that only involve
4207 earlier dimensions before those that involve later dimensions.
4211 =head2 Unary Operations
4217 __isl_give isl_set *isl_set_complement(
4218 __isl_take isl_set *set);
4219 __isl_give isl_map *isl_map_complement(
4220 __isl_take isl_map *map);
4224 #include <isl/space.h>
4225 __isl_give isl_space *isl_space_reverse(
4226 __isl_take isl_space *space);
4228 #include <isl/map.h>
4229 __isl_give isl_basic_map *isl_basic_map_reverse(
4230 __isl_take isl_basic_map *bmap);
4231 __isl_give isl_map *isl_map_reverse(
4232 __isl_take isl_map *map);
4234 #include <isl/union_map.h>
4235 __isl_give isl_union_map *isl_union_map_reverse(
4236 __isl_take isl_union_map *umap);
4240 #include <isl/space.h>
4241 __isl_give isl_space *isl_space_domain(
4242 __isl_take isl_space *space);
4243 __isl_give isl_space *isl_space_range(
4244 __isl_take isl_space *space);
4245 __isl_give isl_space *isl_space_params(
4246 __isl_take isl_space *space);
4248 #include <isl/local_space.h>
4249 __isl_give isl_local_space *isl_local_space_domain(
4250 __isl_take isl_local_space *ls);
4251 __isl_give isl_local_space *isl_local_space_range(
4252 __isl_take isl_local_space *ls);
4254 #include <isl/set.h>
4255 __isl_give isl_basic_set *isl_basic_set_project_out(
4256 __isl_take isl_basic_set *bset,
4257 enum isl_dim_type type, unsigned first, unsigned n);
4258 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4259 enum isl_dim_type type, unsigned first, unsigned n);
4260 __isl_give isl_basic_set *isl_basic_set_params(
4261 __isl_take isl_basic_set *bset);
4262 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4264 #include <isl/map.h>
4265 __isl_give isl_basic_map *isl_basic_map_project_out(
4266 __isl_take isl_basic_map *bmap,
4267 enum isl_dim_type type, unsigned first, unsigned n);
4268 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4269 enum isl_dim_type type, unsigned first, unsigned n);
4270 __isl_give isl_basic_set *isl_basic_map_domain(
4271 __isl_take isl_basic_map *bmap);
4272 __isl_give isl_basic_set *isl_basic_map_range(
4273 __isl_take isl_basic_map *bmap);
4274 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4275 __isl_give isl_set *isl_map_domain(
4276 __isl_take isl_map *bmap);
4277 __isl_give isl_set *isl_map_range(
4278 __isl_take isl_map *map);
4280 #include <isl/union_set.h>
4281 __isl_give isl_union_set *isl_union_set_project_out(
4282 __isl_take isl_union_set *uset,
4283 enum isl_dim_type type,
4284 unsigned first, unsigned n);
4285 __isl_give isl_set *isl_union_set_params(
4286 __isl_take isl_union_set *uset);
4288 The function C<isl_union_set_project_out> can only project out
4291 #include <isl/union_map.h>
4292 __isl_give isl_union_map *isl_union_map_project_out(
4293 __isl_take isl_union_map *umap,
4294 enum isl_dim_type type, unsigned first, unsigned n);
4295 __isl_give isl_set *isl_union_map_params(
4296 __isl_take isl_union_map *umap);
4297 __isl_give isl_union_set *isl_union_map_domain(
4298 __isl_take isl_union_map *umap);
4299 __isl_give isl_union_set *isl_union_map_range(
4300 __isl_take isl_union_map *umap);
4302 The function C<isl_union_map_project_out> can only project out
4305 #include <isl/aff.h>
4306 __isl_give isl_aff *isl_aff_project_domain_on_params(
4307 __isl_take isl_aff *aff);
4308 __isl_give isl_pw_multi_aff *
4309 isl_pw_multi_aff_project_domain_on_params(
4310 __isl_take isl_pw_multi_aff *pma);
4311 __isl_give isl_set *isl_pw_aff_domain(
4312 __isl_take isl_pw_aff *pwaff);
4313 __isl_give isl_set *isl_pw_multi_aff_domain(
4314 __isl_take isl_pw_multi_aff *pma);
4315 __isl_give isl_set *isl_multi_pw_aff_domain(
4316 __isl_take isl_multi_pw_aff *mpa);
4317 __isl_give isl_union_set *isl_union_pw_aff_domain(
4318 __isl_take isl_union_pw_aff *upa);
4319 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4320 __isl_take isl_union_pw_multi_aff *upma);
4321 __isl_give isl_union_set *
4322 isl_multi_union_pw_aff_domain(
4323 __isl_take isl_multi_union_pw_aff *mupa);
4324 __isl_give isl_set *isl_pw_aff_params(
4325 __isl_take isl_pw_aff *pwa);
4327 The function C<isl_multi_union_pw_aff_domain> requires its
4328 input to have at least one set dimension.
4330 #include <isl/polynomial.h>
4331 __isl_give isl_qpolynomial *
4332 isl_qpolynomial_project_domain_on_params(
4333 __isl_take isl_qpolynomial *qp);
4334 __isl_give isl_pw_qpolynomial *
4335 isl_pw_qpolynomial_project_domain_on_params(
4336 __isl_take isl_pw_qpolynomial *pwqp);
4337 __isl_give isl_pw_qpolynomial_fold *
4338 isl_pw_qpolynomial_fold_project_domain_on_params(
4339 __isl_take isl_pw_qpolynomial_fold *pwf);
4340 __isl_give isl_set *isl_pw_qpolynomial_domain(
4341 __isl_take isl_pw_qpolynomial *pwqp);
4342 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4343 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4344 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4345 __isl_take isl_union_pw_qpolynomial *upwqp);
4347 #include <isl/space.h>
4348 __isl_give isl_space *isl_space_domain_map(
4349 __isl_take isl_space *space);
4350 __isl_give isl_space *isl_space_range_map(
4351 __isl_take isl_space *space);
4353 #include <isl/map.h>
4354 __isl_give isl_map *isl_set_wrapped_domain_map(
4355 __isl_take isl_set *set);
4356 __isl_give isl_basic_map *isl_basic_map_domain_map(
4357 __isl_take isl_basic_map *bmap);
4358 __isl_give isl_basic_map *isl_basic_map_range_map(
4359 __isl_take isl_basic_map *bmap);
4360 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4361 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4363 #include <isl/union_map.h>
4364 __isl_give isl_union_map *isl_union_map_domain_map(
4365 __isl_take isl_union_map *umap);
4366 __isl_give isl_union_pw_multi_aff *
4367 isl_union_map_domain_map_union_pw_multi_aff(
4368 __isl_take isl_union_map *umap);
4369 __isl_give isl_union_map *isl_union_map_range_map(
4370 __isl_take isl_union_map *umap);
4371 __isl_give isl_union_map *
4372 isl_union_set_wrapped_domain_map(
4373 __isl_take isl_union_set *uset);
4375 The functions above construct a (basic, regular or union) relation
4376 that maps (a wrapped version of) the input relation to its domain or range.
4377 C<isl_set_wrapped_domain_map> maps the input set to the domain
4378 of its wrapped relation.
4382 __isl_give isl_basic_set *isl_basic_set_eliminate(
4383 __isl_take isl_basic_set *bset,
4384 enum isl_dim_type type,
4385 unsigned first, unsigned n);
4386 __isl_give isl_set *isl_set_eliminate(
4387 __isl_take isl_set *set, enum isl_dim_type type,
4388 unsigned first, unsigned n);
4389 __isl_give isl_basic_map *isl_basic_map_eliminate(
4390 __isl_take isl_basic_map *bmap,
4391 enum isl_dim_type type,
4392 unsigned first, unsigned n);
4393 __isl_give isl_map *isl_map_eliminate(
4394 __isl_take isl_map *map, enum isl_dim_type type,
4395 unsigned first, unsigned n);
4397 Eliminate the coefficients for the given dimensions from the constraints,
4398 without removing the dimensions.
4400 =item * Constructing a set from a parameter domain
4402 A zero-dimensional space or (basic) set can be constructed
4403 on a given parameter domain using the following functions.
4405 #include <isl/space.h>
4406 __isl_give isl_space *isl_space_set_from_params(
4407 __isl_take isl_space *space);
4409 #include <isl/set.h>
4410 __isl_give isl_basic_set *isl_basic_set_from_params(
4411 __isl_take isl_basic_set *bset);
4412 __isl_give isl_set *isl_set_from_params(
4413 __isl_take isl_set *set);
4415 =item * Constructing a relation from one or two sets
4417 Create a relation with the given set(s) as domain and/or range.
4418 If only the domain or the range is specified, then
4419 the range or domain of the created relation is a zero-dimensional
4420 flat anonymous space.
4422 #include <isl/space.h>
4423 __isl_give isl_space *isl_space_from_domain(
4424 __isl_take isl_space *space);
4425 __isl_give isl_space *isl_space_from_range(
4426 __isl_take isl_space *space);
4427 __isl_give isl_space *isl_space_map_from_set(
4428 __isl_take isl_space *space);
4429 __isl_give isl_space *isl_space_map_from_domain_and_range(
4430 __isl_take isl_space *domain,
4431 __isl_take isl_space *range);
4433 #include <isl/local_space.h>
4434 __isl_give isl_local_space *isl_local_space_from_domain(
4435 __isl_take isl_local_space *ls);
4437 #include <isl/map.h>
4438 __isl_give isl_map *isl_map_from_domain(
4439 __isl_take isl_set *set);
4440 __isl_give isl_map *isl_map_from_range(
4441 __isl_take isl_set *set);
4443 #include <isl/union_map.h>
4444 __isl_give isl_union_map *
4445 isl_union_map_from_domain_and_range(
4446 __isl_take isl_union_set *domain,
4447 __isl_take isl_union_set *range);
4449 #include <isl/val.h>
4450 __isl_give isl_multi_val *isl_multi_val_from_range(
4451 __isl_take isl_multi_val *mv);
4453 #include <isl/aff.h>
4454 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4455 __isl_take isl_multi_aff *ma);
4456 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4457 __isl_take isl_pw_aff *pwa);
4458 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4459 __isl_take isl_multi_pw_aff *mpa);
4460 __isl_give isl_multi_union_pw_aff *
4461 isl_multi_union_pw_aff_from_range(
4462 __isl_take isl_multi_union_pw_aff *mupa);
4463 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4464 __isl_take isl_set *set);
4465 __isl_give isl_union_pw_multi_aff *
4466 isl_union_pw_multi_aff_from_domain(
4467 __isl_take isl_union_set *uset);
4471 #include <isl/set.h>
4472 __isl_give isl_basic_set *isl_basic_set_fix_si(
4473 __isl_take isl_basic_set *bset,
4474 enum isl_dim_type type, unsigned pos, int value);
4475 __isl_give isl_basic_set *isl_basic_set_fix_val(
4476 __isl_take isl_basic_set *bset,
4477 enum isl_dim_type type, unsigned pos,
4478 __isl_take isl_val *v);
4479 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4480 enum isl_dim_type type, unsigned pos, int value);
4481 __isl_give isl_set *isl_set_fix_val(
4482 __isl_take isl_set *set,
4483 enum isl_dim_type type, unsigned pos,
4484 __isl_take isl_val *v);
4486 #include <isl/map.h>
4487 __isl_give isl_basic_map *isl_basic_map_fix_si(
4488 __isl_take isl_basic_map *bmap,
4489 enum isl_dim_type type, unsigned pos, int value);
4490 __isl_give isl_basic_map *isl_basic_map_fix_val(
4491 __isl_take isl_basic_map *bmap,
4492 enum isl_dim_type type, unsigned pos,
4493 __isl_take isl_val *v);
4494 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4495 enum isl_dim_type type, unsigned pos, int value);
4496 __isl_give isl_map *isl_map_fix_val(
4497 __isl_take isl_map *map,
4498 enum isl_dim_type type, unsigned pos,
4499 __isl_take isl_val *v);
4501 #include <isl/aff.h>
4502 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4503 __isl_take isl_pw_multi_aff *pma,
4504 enum isl_dim_type type, unsigned pos, int value);
4506 #include <isl/polynomial.h>
4507 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4508 __isl_take isl_pw_qpolynomial *pwqp,
4509 enum isl_dim_type type, unsigned n,
4510 __isl_take isl_val *v);
4512 Intersect the set, relation or function domain
4513 with the hyperplane where the given
4514 dimension has the fixed given value.
4516 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4517 __isl_take isl_basic_map *bmap,
4518 enum isl_dim_type type, unsigned pos, int value);
4519 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4520 __isl_take isl_basic_map *bmap,
4521 enum isl_dim_type type, unsigned pos, int value);
4522 __isl_give isl_set *isl_set_lower_bound_si(
4523 __isl_take isl_set *set,
4524 enum isl_dim_type type, unsigned pos, int value);
4525 __isl_give isl_set *isl_set_lower_bound_val(
4526 __isl_take isl_set *set,
4527 enum isl_dim_type type, unsigned pos,
4528 __isl_take isl_val *value);
4529 __isl_give isl_map *isl_map_lower_bound_si(
4530 __isl_take isl_map *map,
4531 enum isl_dim_type type, unsigned pos, int value);
4532 __isl_give isl_set *isl_set_upper_bound_si(
4533 __isl_take isl_set *set,
4534 enum isl_dim_type type, unsigned pos, int value);
4535 __isl_give isl_set *isl_set_upper_bound_val(
4536 __isl_take isl_set *set,
4537 enum isl_dim_type type, unsigned pos,
4538 __isl_take isl_val *value);
4539 __isl_give isl_map *isl_map_upper_bound_si(
4540 __isl_take isl_map *map,
4541 enum isl_dim_type type, unsigned pos, int value);
4543 Intersect the set or relation with the half-space where the given
4544 dimension has a value bounded by the fixed given integer value.
4546 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4547 enum isl_dim_type type1, int pos1,
4548 enum isl_dim_type type2, int pos2);
4549 __isl_give isl_basic_map *isl_basic_map_equate(
4550 __isl_take isl_basic_map *bmap,
4551 enum isl_dim_type type1, int pos1,
4552 enum isl_dim_type type2, int pos2);
4553 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4554 enum isl_dim_type type1, int pos1,
4555 enum isl_dim_type type2, int pos2);
4557 Intersect the set or relation with the hyperplane where the given
4558 dimensions are equal to each other.
4560 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4561 enum isl_dim_type type1, int pos1,
4562 enum isl_dim_type type2, int pos2);
4564 Intersect the relation with the hyperplane where the given
4565 dimensions have opposite values.
4567 __isl_give isl_map *isl_map_order_le(
4568 __isl_take isl_map *map,
4569 enum isl_dim_type type1, int pos1,
4570 enum isl_dim_type type2, int pos2);
4571 __isl_give isl_basic_map *isl_basic_map_order_ge(
4572 __isl_take isl_basic_map *bmap,
4573 enum isl_dim_type type1, int pos1,
4574 enum isl_dim_type type2, int pos2);
4575 __isl_give isl_map *isl_map_order_ge(
4576 __isl_take isl_map *map,
4577 enum isl_dim_type type1, int pos1,
4578 enum isl_dim_type type2, int pos2);
4579 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4580 enum isl_dim_type type1, int pos1,
4581 enum isl_dim_type type2, int pos2);
4582 __isl_give isl_basic_map *isl_basic_map_order_gt(
4583 __isl_take isl_basic_map *bmap,
4584 enum isl_dim_type type1, int pos1,
4585 enum isl_dim_type type2, int pos2);
4586 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4587 enum isl_dim_type type1, int pos1,
4588 enum isl_dim_type type2, int pos2);
4590 Intersect the relation with the half-space where the given
4591 dimensions satisfy the given ordering.
4595 #include <isl/aff.h>
4596 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4597 __isl_take isl_aff *aff);
4598 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4599 __isl_take isl_aff *aff);
4600 __isl_give isl_set *isl_pw_aff_pos_set(
4601 __isl_take isl_pw_aff *pa);
4602 __isl_give isl_set *isl_pw_aff_nonneg_set(
4603 __isl_take isl_pw_aff *pwaff);
4604 __isl_give isl_set *isl_pw_aff_zero_set(
4605 __isl_take isl_pw_aff *pwaff);
4606 __isl_give isl_set *isl_pw_aff_non_zero_set(
4607 __isl_take isl_pw_aff *pwaff);
4608 __isl_give isl_union_set *
4609 isl_union_pw_aff_zero_union_set(
4610 __isl_take isl_union_pw_aff *upa);
4611 __isl_give isl_union_set *
4612 isl_multi_union_pw_aff_zero_union_set(
4613 __isl_take isl_multi_union_pw_aff *mupa);
4615 The function C<isl_aff_neg_basic_set> returns a basic set
4616 containing those elements in the domain space
4617 of C<aff> where C<aff> is negative.
4618 The function C<isl_pw_aff_nonneg_set> returns a set
4619 containing those elements in the domain
4620 of C<pwaff> where C<pwaff> is non-negative.
4621 The function C<isl_multi_union_pw_aff_zero_union_set>
4622 returns a union set containing those elements
4623 in the domains of its elements where they are all zero.
4627 __isl_give isl_map *isl_set_identity(
4628 __isl_take isl_set *set);
4629 __isl_give isl_union_map *isl_union_set_identity(
4630 __isl_take isl_union_set *uset);
4631 __isl_give isl_union_pw_multi_aff *
4632 isl_union_set_identity_union_pw_multi_aff(
4633 __isl_take isl_union_set *uset);
4635 Construct an identity relation on the given (union) set.
4637 =item * Function Extraction
4639 A piecewise quasi affine expression that is equal to 1 on a set
4640 and 0 outside the set can be created using the following function.
4642 #include <isl/aff.h>
4643 __isl_give isl_pw_aff *isl_set_indicator_function(
4644 __isl_take isl_set *set);
4646 A piecewise multiple quasi affine expression can be extracted
4647 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4648 and the C<isl_map> is single-valued.
4649 In case of a conversion from an C<isl_union_map>
4650 to an C<isl_union_pw_multi_aff>, these properties need to hold
4651 in each domain space.
4652 A conversion to a C<isl_multi_union_pw_aff> additionally
4653 requires that the input is non-empty and involves only a single
4656 #include <isl/aff.h>
4657 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4658 __isl_take isl_set *set);
4659 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4660 __isl_take isl_map *map);
4662 __isl_give isl_union_pw_multi_aff *
4663 isl_union_pw_multi_aff_from_union_set(
4664 __isl_take isl_union_set *uset);
4665 __isl_give isl_union_pw_multi_aff *
4666 isl_union_pw_multi_aff_from_union_map(
4667 __isl_take isl_union_map *umap);
4669 __isl_give isl_multi_union_pw_aff *
4670 isl_multi_union_pw_aff_from_union_map(
4671 __isl_take isl_union_map *umap);
4675 __isl_give isl_basic_set *isl_basic_map_deltas(
4676 __isl_take isl_basic_map *bmap);
4677 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4678 __isl_give isl_union_set *isl_union_map_deltas(
4679 __isl_take isl_union_map *umap);
4681 These functions return a (basic) set containing the differences
4682 between image elements and corresponding domain elements in the input.
4684 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4685 __isl_take isl_basic_map *bmap);
4686 __isl_give isl_map *isl_map_deltas_map(
4687 __isl_take isl_map *map);
4688 __isl_give isl_union_map *isl_union_map_deltas_map(
4689 __isl_take isl_union_map *umap);
4691 The functions above construct a (basic, regular or union) relation
4692 that maps (a wrapped version of) the input relation to its delta set.
4696 Simplify the representation of a set, relation or functions by trying
4697 to combine pairs of basic sets or relations into a single
4698 basic set or relation.
4700 #include <isl/set.h>
4701 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4703 #include <isl/map.h>
4704 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4706 #include <isl/union_set.h>
4707 __isl_give isl_union_set *isl_union_set_coalesce(
4708 __isl_take isl_union_set *uset);
4710 #include <isl/union_map.h>
4711 __isl_give isl_union_map *isl_union_map_coalesce(
4712 __isl_take isl_union_map *umap);
4714 #include <isl/aff.h>
4715 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4716 __isl_take isl_pw_aff *pwqp);
4717 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4718 __isl_take isl_pw_multi_aff *pma);
4719 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4720 __isl_take isl_multi_pw_aff *mpa);
4721 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4722 __isl_take isl_union_pw_aff *upa);
4723 __isl_give isl_union_pw_multi_aff *
4724 isl_union_pw_multi_aff_coalesce(
4725 __isl_take isl_union_pw_multi_aff *upma);
4726 __isl_give isl_multi_union_pw_aff *
4727 isl_multi_union_pw_aff_coalesce(
4728 __isl_take isl_multi_union_pw_aff *aff);
4730 #include <isl/polynomial.h>
4731 __isl_give isl_pw_qpolynomial_fold *
4732 isl_pw_qpolynomial_fold_coalesce(
4733 __isl_take isl_pw_qpolynomial_fold *pwf);
4734 __isl_give isl_union_pw_qpolynomial *
4735 isl_union_pw_qpolynomial_coalesce(
4736 __isl_take isl_union_pw_qpolynomial *upwqp);
4737 __isl_give isl_union_pw_qpolynomial_fold *
4738 isl_union_pw_qpolynomial_fold_coalesce(
4739 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4741 One of the methods for combining pairs of basic sets or relations
4742 can result in coefficients that are much larger than those that appear
4743 in the constraints of the input. By default, the coefficients are
4744 not allowed to grow larger, but this can be changed by unsetting
4745 the following option.
4747 isl_stat isl_options_set_coalesce_bounded_wrapping(
4748 isl_ctx *ctx, int val);
4749 int isl_options_get_coalesce_bounded_wrapping(
4752 =item * Detecting equalities
4754 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4755 __isl_take isl_basic_set *bset);
4756 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4757 __isl_take isl_basic_map *bmap);
4758 __isl_give isl_set *isl_set_detect_equalities(
4759 __isl_take isl_set *set);
4760 __isl_give isl_map *isl_map_detect_equalities(
4761 __isl_take isl_map *map);
4762 __isl_give isl_union_set *isl_union_set_detect_equalities(
4763 __isl_take isl_union_set *uset);
4764 __isl_give isl_union_map *isl_union_map_detect_equalities(
4765 __isl_take isl_union_map *umap);
4767 Simplify the representation of a set or relation by detecting implicit
4770 =item * Removing redundant constraints
4772 #include <isl/set.h>
4773 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4774 __isl_take isl_basic_set *bset);
4775 __isl_give isl_set *isl_set_remove_redundancies(
4776 __isl_take isl_set *set);
4778 #include <isl/union_set.h>
4779 __isl_give isl_union_set *
4780 isl_union_set_remove_redundancies(
4781 __isl_take isl_union_set *uset);
4783 #include <isl/map.h>
4784 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4785 __isl_take isl_basic_map *bmap);
4786 __isl_give isl_map *isl_map_remove_redundancies(
4787 __isl_take isl_map *map);
4789 #include <isl/union_map.h>
4790 __isl_give isl_union_map *
4791 isl_union_map_remove_redundancies(
4792 __isl_take isl_union_map *umap);
4796 __isl_give isl_basic_set *isl_set_convex_hull(
4797 __isl_take isl_set *set);
4798 __isl_give isl_basic_map *isl_map_convex_hull(
4799 __isl_take isl_map *map);
4801 If the input set or relation has any existentially quantified
4802 variables, then the result of these operations is currently undefined.
4806 #include <isl/set.h>
4807 __isl_give isl_basic_set *
4808 isl_set_unshifted_simple_hull(
4809 __isl_take isl_set *set);
4810 __isl_give isl_basic_set *isl_set_simple_hull(
4811 __isl_take isl_set *set);
4812 __isl_give isl_basic_set *
4813 isl_set_unshifted_simple_hull_from_set_list(
4814 __isl_take isl_set *set,
4815 __isl_take isl_set_list *list);
4817 #include <isl/map.h>
4818 __isl_give isl_basic_map *
4819 isl_map_unshifted_simple_hull(
4820 __isl_take isl_map *map);
4821 __isl_give isl_basic_map *isl_map_simple_hull(
4822 __isl_take isl_map *map);
4823 __isl_give isl_basic_map *
4824 isl_map_unshifted_simple_hull_from_map_list(
4825 __isl_take isl_map *map,
4826 __isl_take isl_map_list *list);
4828 #include <isl/union_map.h>
4829 __isl_give isl_union_map *isl_union_map_simple_hull(
4830 __isl_take isl_union_map *umap);
4832 These functions compute a single basic set or relation
4833 that contains the whole input set or relation.
4834 In particular, the output is described by translates
4835 of the constraints describing the basic sets or relations in the input.
4836 In case of C<isl_set_unshifted_simple_hull>, only the original
4837 constraints are used, without any translation.
4838 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4839 C<isl_map_unshifted_simple_hull_from_map_list>, the
4840 constraints are taken from the elements of the second argument.
4844 (See \autoref{s:simple hull}.)
4850 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4851 __isl_take isl_basic_set *bset);
4852 __isl_give isl_basic_set *isl_set_affine_hull(
4853 __isl_take isl_set *set);
4854 __isl_give isl_union_set *isl_union_set_affine_hull(
4855 __isl_take isl_union_set *uset);
4856 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4857 __isl_take isl_basic_map *bmap);
4858 __isl_give isl_basic_map *isl_map_affine_hull(
4859 __isl_take isl_map *map);
4860 __isl_give isl_union_map *isl_union_map_affine_hull(
4861 __isl_take isl_union_map *umap);
4863 In case of union sets and relations, the affine hull is computed
4866 =item * Polyhedral hull
4868 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4869 __isl_take isl_set *set);
4870 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4871 __isl_take isl_map *map);
4872 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4873 __isl_take isl_union_set *uset);
4874 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4875 __isl_take isl_union_map *umap);
4877 These functions compute a single basic set or relation
4878 not involving any existentially quantified variables
4879 that contains the whole input set or relation.
4880 In case of union sets and relations, the polyhedral hull is computed
4883 =item * Other approximations
4885 #include <isl/set.h>
4886 __isl_give isl_basic_set *
4887 isl_basic_set_drop_constraints_involving_dims(
4888 __isl_take isl_basic_set *bset,
4889 enum isl_dim_type type,
4890 unsigned first, unsigned n);
4891 __isl_give isl_basic_set *
4892 isl_basic_set_drop_constraints_not_involving_dims(
4893 __isl_take isl_basic_set *bset,
4894 enum isl_dim_type type,
4895 unsigned first, unsigned n);
4896 __isl_give isl_set *
4897 isl_set_drop_constraints_involving_dims(
4898 __isl_take isl_set *set,
4899 enum isl_dim_type type,
4900 unsigned first, unsigned n);
4902 #include <isl/map.h>
4903 __isl_give isl_basic_map *
4904 isl_basic_map_drop_constraints_involving_dims(
4905 __isl_take isl_basic_map *bmap,
4906 enum isl_dim_type type,
4907 unsigned first, unsigned n);
4908 __isl_give isl_basic_map *
4909 isl_basic_map_drop_constraints_not_involving_dims(
4910 __isl_take isl_basic_map *bmap,
4911 enum isl_dim_type type,
4912 unsigned first, unsigned n);
4913 __isl_give isl_map *
4914 isl_map_drop_constraints_involving_dims(
4915 __isl_take isl_map *map,
4916 enum isl_dim_type type,
4917 unsigned first, unsigned n);
4919 These functions drop any constraints (not) involving the specified dimensions.
4920 Note that the result depends on the representation of the input.
4922 #include <isl/polynomial.h>
4923 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4924 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4925 __isl_give isl_union_pw_qpolynomial *
4926 isl_union_pw_qpolynomial_to_polynomial(
4927 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4929 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4930 the polynomial will be an overapproximation. If C<sign> is negative,
4931 it will be an underapproximation. If C<sign> is zero, the approximation
4932 will lie somewhere in between.
4936 __isl_give isl_basic_set *isl_basic_set_sample(
4937 __isl_take isl_basic_set *bset);
4938 __isl_give isl_basic_set *isl_set_sample(
4939 __isl_take isl_set *set);
4940 __isl_give isl_basic_map *isl_basic_map_sample(
4941 __isl_take isl_basic_map *bmap);
4942 __isl_give isl_basic_map *isl_map_sample(
4943 __isl_take isl_map *map);
4945 If the input (basic) set or relation is non-empty, then return
4946 a singleton subset of the input. Otherwise, return an empty set.
4948 =item * Optimization
4950 #include <isl/ilp.h>
4951 __isl_give isl_val *isl_basic_set_max_val(
4952 __isl_keep isl_basic_set *bset,
4953 __isl_keep isl_aff *obj);
4954 __isl_give isl_val *isl_set_min_val(
4955 __isl_keep isl_set *set,
4956 __isl_keep isl_aff *obj);
4957 __isl_give isl_val *isl_set_max_val(
4958 __isl_keep isl_set *set,
4959 __isl_keep isl_aff *obj);
4961 Compute the minimum or maximum of the integer affine expression C<obj>
4962 over the points in C<set>, returning the result in C<opt>.
4963 The result is C<NULL> in case of an error, the optimal value in case
4964 there is one, negative infinity or infinity if the problem is unbounded and
4965 NaN if the problem is empty.
4967 =item * Parametric optimization
4969 __isl_give isl_pw_aff *isl_set_dim_min(
4970 __isl_take isl_set *set, int pos);
4971 __isl_give isl_pw_aff *isl_set_dim_max(
4972 __isl_take isl_set *set, int pos);
4973 __isl_give isl_pw_aff *isl_map_dim_max(
4974 __isl_take isl_map *map, int pos);
4976 Compute the minimum or maximum of the given set or output dimension
4977 as a function of the parameters (and input dimensions), but independently
4978 of the other set or output dimensions.
4979 For lexicographic optimization, see L<"Lexicographic Optimization">.
4983 The following functions compute either the set of (rational) coefficient
4984 values of valid constraints for the given set or the set of (rational)
4985 values satisfying the constraints with coefficients from the given set.
4986 Internally, these two sets of functions perform essentially the
4987 same operations, except that the set of coefficients is assumed to
4988 be a cone, while the set of values may be any polyhedron.
4989 The current implementation is based on the Farkas lemma and
4990 Fourier-Motzkin elimination, but this may change or be made optional
4991 in future. In particular, future implementations may use different
4992 dualization algorithms or skip the elimination step.
4994 __isl_give isl_basic_set *isl_basic_set_coefficients(
4995 __isl_take isl_basic_set *bset);
4996 __isl_give isl_basic_set *isl_set_coefficients(
4997 __isl_take isl_set *set);
4998 __isl_give isl_union_set *isl_union_set_coefficients(
4999 __isl_take isl_union_set *bset);
5000 __isl_give isl_basic_set *isl_basic_set_solutions(
5001 __isl_take isl_basic_set *bset);
5002 __isl_give isl_basic_set *isl_set_solutions(
5003 __isl_take isl_set *set);
5004 __isl_give isl_union_set *isl_union_set_solutions(
5005 __isl_take isl_union_set *bset);
5009 __isl_give isl_map *isl_map_fixed_power_val(
5010 __isl_take isl_map *map,
5011 __isl_take isl_val *exp);
5012 __isl_give isl_union_map *
5013 isl_union_map_fixed_power_val(
5014 __isl_take isl_union_map *umap,
5015 __isl_take isl_val *exp);
5017 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5018 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5019 of C<map> is computed.
5021 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5023 __isl_give isl_union_map *isl_union_map_power(
5024 __isl_take isl_union_map *umap, int *exact);
5026 Compute a parametric representation for all positive powers I<k> of C<map>.
5027 The result maps I<k> to a nested relation corresponding to the
5028 I<k>th power of C<map>.
5029 The result may be an overapproximation. If the result is known to be exact,
5030 then C<*exact> is set to C<1>.
5032 =item * Transitive closure
5034 __isl_give isl_map *isl_map_transitive_closure(
5035 __isl_take isl_map *map, int *exact);
5036 __isl_give isl_union_map *isl_union_map_transitive_closure(
5037 __isl_take isl_union_map *umap, int *exact);
5039 Compute the transitive closure of C<map>.
5040 The result may be an overapproximation. If the result is known to be exact,
5041 then C<*exact> is set to C<1>.
5043 =item * Reaching path lengths
5045 __isl_give isl_map *isl_map_reaching_path_lengths(
5046 __isl_take isl_map *map, int *exact);
5048 Compute a relation that maps each element in the range of C<map>
5049 to the lengths of all paths composed of edges in C<map> that
5050 end up in the given element.
5051 The result may be an overapproximation. If the result is known to be exact,
5052 then C<*exact> is set to C<1>.
5053 To compute the I<maximal> path length, the resulting relation
5054 should be postprocessed by C<isl_map_lexmax>.
5055 In particular, if the input relation is a dependence relation
5056 (mapping sources to sinks), then the maximal path length corresponds
5057 to the free schedule.
5058 Note, however, that C<isl_map_lexmax> expects the maximum to be
5059 finite, so if the path lengths are unbounded (possibly due to
5060 the overapproximation), then you will get an error message.
5064 #include <isl/space.h>
5065 __isl_give isl_space *isl_space_wrap(
5066 __isl_take isl_space *space);
5067 __isl_give isl_space *isl_space_unwrap(
5068 __isl_take isl_space *space);
5070 #include <isl/local_space.h>
5071 __isl_give isl_local_space *isl_local_space_wrap(
5072 __isl_take isl_local_space *ls);
5074 #include <isl/set.h>
5075 __isl_give isl_basic_map *isl_basic_set_unwrap(
5076 __isl_take isl_basic_set *bset);
5077 __isl_give isl_map *isl_set_unwrap(
5078 __isl_take isl_set *set);
5080 #include <isl/map.h>
5081 __isl_give isl_basic_set *isl_basic_map_wrap(
5082 __isl_take isl_basic_map *bmap);
5083 __isl_give isl_set *isl_map_wrap(
5084 __isl_take isl_map *map);
5086 #include <isl/union_set.h>
5087 __isl_give isl_union_map *isl_union_set_unwrap(
5088 __isl_take isl_union_set *uset);
5090 #include <isl/union_map.h>
5091 __isl_give isl_union_set *isl_union_map_wrap(
5092 __isl_take isl_union_map *umap);
5094 The input to C<isl_space_unwrap> should
5095 be the space of a set, while that of
5096 C<isl_space_wrap> should be the space of a relation.
5097 Conversely, the output of C<isl_space_unwrap> is the space
5098 of a relation, while that of C<isl_space_wrap> is the space of a set.
5102 Remove any internal structure of domain (and range) of the given
5103 set or relation. If there is any such internal structure in the input,
5104 then the name of the space is also removed.
5106 #include <isl/local_space.h>
5107 __isl_give isl_local_space *
5108 isl_local_space_flatten_domain(
5109 __isl_take isl_local_space *ls);
5110 __isl_give isl_local_space *
5111 isl_local_space_flatten_range(
5112 __isl_take isl_local_space *ls);
5114 #include <isl/set.h>
5115 __isl_give isl_basic_set *isl_basic_set_flatten(
5116 __isl_take isl_basic_set *bset);
5117 __isl_give isl_set *isl_set_flatten(
5118 __isl_take isl_set *set);
5120 #include <isl/map.h>
5121 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5122 __isl_take isl_basic_map *bmap);
5123 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5124 __isl_take isl_basic_map *bmap);
5125 __isl_give isl_map *isl_map_flatten_range(
5126 __isl_take isl_map *map);
5127 __isl_give isl_map *isl_map_flatten_domain(
5128 __isl_take isl_map *map);
5129 __isl_give isl_basic_map *isl_basic_map_flatten(
5130 __isl_take isl_basic_map *bmap);
5131 __isl_give isl_map *isl_map_flatten(
5132 __isl_take isl_map *map);
5134 #include <isl/val.h>
5135 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5136 __isl_take isl_multi_val *mv);
5138 #include <isl/aff.h>
5139 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5140 __isl_take isl_multi_aff *ma);
5141 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5142 __isl_take isl_multi_aff *ma);
5143 __isl_give isl_multi_pw_aff *
5144 isl_multi_pw_aff_flatten_range(
5145 __isl_take isl_multi_pw_aff *mpa);
5146 __isl_give isl_multi_union_pw_aff *
5147 isl_multi_union_pw_aff_flatten_range(
5148 __isl_take isl_multi_union_pw_aff *mupa);
5150 #include <isl/map.h>
5151 __isl_give isl_map *isl_set_flatten_map(
5152 __isl_take isl_set *set);
5154 The function above constructs a relation
5155 that maps the input set to a flattened version of the set.
5159 Lift the input set to a space with extra dimensions corresponding
5160 to the existentially quantified variables in the input.
5161 In particular, the result lives in a wrapped map where the domain
5162 is the original space and the range corresponds to the original
5163 existentially quantified variables.
5165 #include <isl/set.h>
5166 __isl_give isl_basic_set *isl_basic_set_lift(
5167 __isl_take isl_basic_set *bset);
5168 __isl_give isl_set *isl_set_lift(
5169 __isl_take isl_set *set);
5170 __isl_give isl_union_set *isl_union_set_lift(
5171 __isl_take isl_union_set *uset);
5173 Given a local space that contains the existentially quantified
5174 variables of a set, a basic relation that, when applied to
5175 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5176 can be constructed using the following function.
5178 #include <isl/local_space.h>
5179 __isl_give isl_basic_map *isl_local_space_lifting(
5180 __isl_take isl_local_space *ls);
5182 #include <isl/aff.h>
5183 __isl_give isl_multi_aff *isl_multi_aff_lift(
5184 __isl_take isl_multi_aff *maff,
5185 __isl_give isl_local_space **ls);
5187 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5188 then it is assigned the local space that lies at the basis of
5189 the lifting applied.
5191 =item * Internal Product
5193 #include <isl/space.h>
5194 __isl_give isl_space *isl_space_zip(
5195 __isl_take isl_space *space);
5197 #include <isl/map.h>
5198 __isl_give isl_basic_map *isl_basic_map_zip(
5199 __isl_take isl_basic_map *bmap);
5200 __isl_give isl_map *isl_map_zip(
5201 __isl_take isl_map *map);
5203 #include <isl/union_map.h>
5204 __isl_give isl_union_map *isl_union_map_zip(
5205 __isl_take isl_union_map *umap);
5207 Given a relation with nested relations for domain and range,
5208 interchange the range of the domain with the domain of the range.
5212 #include <isl/space.h>
5213 __isl_give isl_space *isl_space_curry(
5214 __isl_take isl_space *space);
5215 __isl_give isl_space *isl_space_uncurry(
5216 __isl_take isl_space *space);
5218 #include <isl/map.h>
5219 __isl_give isl_basic_map *isl_basic_map_curry(
5220 __isl_take isl_basic_map *bmap);
5221 __isl_give isl_basic_map *isl_basic_map_uncurry(
5222 __isl_take isl_basic_map *bmap);
5223 __isl_give isl_map *isl_map_curry(
5224 __isl_take isl_map *map);
5225 __isl_give isl_map *isl_map_uncurry(
5226 __isl_take isl_map *map);
5228 #include <isl/union_map.h>
5229 __isl_give isl_union_map *isl_union_map_curry(
5230 __isl_take isl_union_map *umap);
5231 __isl_give isl_union_map *isl_union_map_uncurry(
5232 __isl_take isl_union_map *umap);
5234 Given a relation with a nested relation for domain,
5235 the C<curry> functions
5236 move the range of the nested relation out of the domain
5237 and use it as the domain of a nested relation in the range,
5238 with the original range as range of this nested relation.
5239 The C<uncurry> functions perform the inverse operation.
5241 #include <isl/space.h>
5242 __isl_give isl_space *isl_space_range_curry(
5243 __isl_take isl_space *space);
5245 #include <isl/map.h>
5246 __isl_give isl_map *isl_map_range_curry(
5247 __isl_take isl_map *map);
5249 #include <isl/union_map.h>
5250 __isl_give isl_union_map *isl_union_map_range_curry(
5251 __isl_take isl_union_map *umap);
5253 These functions apply the currying to the relation that
5254 is nested inside the range of the input.
5256 =item * Aligning parameters
5258 Change the order of the parameters of the given set, relation
5260 such that the first parameters match those of C<model>.
5261 This may involve the introduction of extra parameters.
5262 All parameters need to be named.
5264 #include <isl/space.h>
5265 __isl_give isl_space *isl_space_align_params(
5266 __isl_take isl_space *space1,
5267 __isl_take isl_space *space2)
5269 #include <isl/set.h>
5270 __isl_give isl_basic_set *isl_basic_set_align_params(
5271 __isl_take isl_basic_set *bset,
5272 __isl_take isl_space *model);
5273 __isl_give isl_set *isl_set_align_params(
5274 __isl_take isl_set *set,
5275 __isl_take isl_space *model);
5277 #include <isl/map.h>
5278 __isl_give isl_basic_map *isl_basic_map_align_params(
5279 __isl_take isl_basic_map *bmap,
5280 __isl_take isl_space *model);
5281 __isl_give isl_map *isl_map_align_params(
5282 __isl_take isl_map *map,
5283 __isl_take isl_space *model);
5285 #include <isl/val.h>
5286 __isl_give isl_multi_val *isl_multi_val_align_params(
5287 __isl_take isl_multi_val *mv,
5288 __isl_take isl_space *model);
5290 #include <isl/aff.h>
5291 __isl_give isl_aff *isl_aff_align_params(
5292 __isl_take isl_aff *aff,
5293 __isl_take isl_space *model);
5294 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5295 __isl_take isl_multi_aff *multi,
5296 __isl_take isl_space *model);
5297 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5298 __isl_take isl_pw_aff *pwaff,
5299 __isl_take isl_space *model);
5300 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5301 __isl_take isl_pw_multi_aff *pma,
5302 __isl_take isl_space *model);
5303 __isl_give isl_union_pw_aff *
5304 isl_union_pw_aff_align_params(
5305 __isl_take isl_union_pw_aff *upa,
5306 __isl_take isl_space *model);
5307 __isl_give isl_union_pw_multi_aff *
5308 isl_union_pw_multi_aff_align_params(
5309 __isl_take isl_union_pw_multi_aff *upma,
5310 __isl_take isl_space *model);
5311 __isl_give isl_multi_union_pw_aff *
5312 isl_multi_union_pw_aff_align_params(
5313 __isl_take isl_multi_union_pw_aff *mupa,
5314 __isl_take isl_space *model);
5316 #include <isl/polynomial.h>
5317 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5318 __isl_take isl_qpolynomial *qp,
5319 __isl_take isl_space *model);
5321 =item * Unary Arithmetic Operations
5323 #include <isl/set.h>
5324 __isl_give isl_set *isl_set_neg(
5325 __isl_take isl_set *set);
5326 #include <isl/map.h>
5327 __isl_give isl_map *isl_map_neg(
5328 __isl_take isl_map *map);
5330 C<isl_set_neg> constructs a set containing the opposites of
5331 the elements in its argument.
5332 The domain of the result of C<isl_map_neg> is the same
5333 as the domain of its argument. The corresponding range
5334 elements are the opposites of the corresponding range
5335 elements in the argument.
5337 #include <isl/val.h>
5338 __isl_give isl_multi_val *isl_multi_val_neg(
5339 __isl_take isl_multi_val *mv);
5341 #include <isl/aff.h>
5342 __isl_give isl_aff *isl_aff_neg(
5343 __isl_take isl_aff *aff);
5344 __isl_give isl_multi_aff *isl_multi_aff_neg(
5345 __isl_take isl_multi_aff *ma);
5346 __isl_give isl_pw_aff *isl_pw_aff_neg(
5347 __isl_take isl_pw_aff *pwaff);
5348 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5349 __isl_take isl_pw_multi_aff *pma);
5350 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5351 __isl_take isl_multi_pw_aff *mpa);
5352 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5353 __isl_take isl_union_pw_aff *upa);
5354 __isl_give isl_union_pw_multi_aff *
5355 isl_union_pw_multi_aff_neg(
5356 __isl_take isl_union_pw_multi_aff *upma);
5357 __isl_give isl_multi_union_pw_aff *
5358 isl_multi_union_pw_aff_neg(
5359 __isl_take isl_multi_union_pw_aff *mupa);
5360 __isl_give isl_aff *isl_aff_ceil(
5361 __isl_take isl_aff *aff);
5362 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5363 __isl_take isl_pw_aff *pwaff);
5364 __isl_give isl_aff *isl_aff_floor(
5365 __isl_take isl_aff *aff);
5366 __isl_give isl_multi_aff *isl_multi_aff_floor(
5367 __isl_take isl_multi_aff *ma);
5368 __isl_give isl_pw_aff *isl_pw_aff_floor(
5369 __isl_take isl_pw_aff *pwaff);
5370 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5371 __isl_take isl_union_pw_aff *upa);
5372 __isl_give isl_multi_union_pw_aff *
5373 isl_multi_union_pw_aff_floor(
5374 __isl_take isl_multi_union_pw_aff *mupa);
5376 #include <isl/aff.h>
5377 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5378 __isl_take isl_pw_aff_list *list);
5379 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5380 __isl_take isl_pw_aff_list *list);
5382 #include <isl/polynomial.h>
5383 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5384 __isl_take isl_qpolynomial *qp);
5385 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5386 __isl_take isl_pw_qpolynomial *pwqp);
5387 __isl_give isl_union_pw_qpolynomial *
5388 isl_union_pw_qpolynomial_neg(
5389 __isl_take isl_union_pw_qpolynomial *upwqp);
5390 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5391 __isl_take isl_qpolynomial *qp,
5393 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5394 __isl_take isl_pw_qpolynomial *pwqp,
5399 The following functions evaluate a function in a point.
5401 #include <isl/polynomial.h>
5402 __isl_give isl_val *isl_pw_qpolynomial_eval(
5403 __isl_take isl_pw_qpolynomial *pwqp,
5404 __isl_take isl_point *pnt);
5405 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5406 __isl_take isl_pw_qpolynomial_fold *pwf,
5407 __isl_take isl_point *pnt);
5408 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5409 __isl_take isl_union_pw_qpolynomial *upwqp,
5410 __isl_take isl_point *pnt);
5411 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5412 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5413 __isl_take isl_point *pnt);
5415 =item * Dimension manipulation
5417 It is usually not advisable to directly change the (input or output)
5418 space of a set or a relation as this removes the name and the internal
5419 structure of the space. However, the functions below can be useful
5420 to add new parameters, assuming
5421 C<isl_set_align_params> and C<isl_map_align_params>
5424 #include <isl/space.h>
5425 __isl_give isl_space *isl_space_add_dims(
5426 __isl_take isl_space *space,
5427 enum isl_dim_type type, unsigned n);
5428 __isl_give isl_space *isl_space_insert_dims(
5429 __isl_take isl_space *space,
5430 enum isl_dim_type type, unsigned pos, unsigned n);
5431 __isl_give isl_space *isl_space_drop_dims(
5432 __isl_take isl_space *space,
5433 enum isl_dim_type type, unsigned first, unsigned n);
5434 __isl_give isl_space *isl_space_move_dims(
5435 __isl_take isl_space *space,
5436 enum isl_dim_type dst_type, unsigned dst_pos,
5437 enum isl_dim_type src_type, unsigned src_pos,
5440 #include <isl/local_space.h>
5441 __isl_give isl_local_space *isl_local_space_add_dims(
5442 __isl_take isl_local_space *ls,
5443 enum isl_dim_type type, unsigned n);
5444 __isl_give isl_local_space *isl_local_space_insert_dims(
5445 __isl_take isl_local_space *ls,
5446 enum isl_dim_type type, unsigned first, unsigned n);
5447 __isl_give isl_local_space *isl_local_space_drop_dims(
5448 __isl_take isl_local_space *ls,
5449 enum isl_dim_type type, unsigned first, unsigned n);
5451 #include <isl/set.h>
5452 __isl_give isl_basic_set *isl_basic_set_add_dims(
5453 __isl_take isl_basic_set *bset,
5454 enum isl_dim_type type, unsigned n);
5455 __isl_give isl_set *isl_set_add_dims(
5456 __isl_take isl_set *set,
5457 enum isl_dim_type type, unsigned n);
5458 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5459 __isl_take isl_basic_set *bset,
5460 enum isl_dim_type type, unsigned pos,
5462 __isl_give isl_set *isl_set_insert_dims(
5463 __isl_take isl_set *set,
5464 enum isl_dim_type type, unsigned pos, unsigned n);
5465 __isl_give isl_basic_set *isl_basic_set_move_dims(
5466 __isl_take isl_basic_set *bset,
5467 enum isl_dim_type dst_type, unsigned dst_pos,
5468 enum isl_dim_type src_type, unsigned src_pos,
5470 __isl_give isl_set *isl_set_move_dims(
5471 __isl_take isl_set *set,
5472 enum isl_dim_type dst_type, unsigned dst_pos,
5473 enum isl_dim_type src_type, unsigned src_pos,
5476 #include <isl/map.h>
5477 __isl_give isl_basic_map *isl_basic_map_add_dims(
5478 __isl_take isl_basic_map *bmap,
5479 enum isl_dim_type type, unsigned n);
5480 __isl_give isl_map *isl_map_add_dims(
5481 __isl_take isl_map *map,
5482 enum isl_dim_type type, unsigned n);
5483 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5484 __isl_take isl_basic_map *bmap,
5485 enum isl_dim_type type, unsigned pos,
5487 __isl_give isl_map *isl_map_insert_dims(
5488 __isl_take isl_map *map,
5489 enum isl_dim_type type, unsigned pos, unsigned n);
5490 __isl_give isl_basic_map *isl_basic_map_move_dims(
5491 __isl_take isl_basic_map *bmap,
5492 enum isl_dim_type dst_type, unsigned dst_pos,
5493 enum isl_dim_type src_type, unsigned src_pos,
5495 __isl_give isl_map *isl_map_move_dims(
5496 __isl_take isl_map *map,
5497 enum isl_dim_type dst_type, unsigned dst_pos,
5498 enum isl_dim_type src_type, unsigned src_pos,
5501 #include <isl/val.h>
5502 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5503 __isl_take isl_multi_val *mv,
5504 enum isl_dim_type type, unsigned first, unsigned n);
5505 __isl_give isl_multi_val *isl_multi_val_add_dims(
5506 __isl_take isl_multi_val *mv,
5507 enum isl_dim_type type, unsigned n);
5508 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5509 __isl_take isl_multi_val *mv,
5510 enum isl_dim_type type, unsigned first, unsigned n);
5512 #include <isl/aff.h>
5513 __isl_give isl_aff *isl_aff_insert_dims(
5514 __isl_take isl_aff *aff,
5515 enum isl_dim_type type, unsigned first, unsigned n);
5516 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5517 __isl_take isl_multi_aff *ma,
5518 enum isl_dim_type type, unsigned first, unsigned n);
5519 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5520 __isl_take isl_pw_aff *pwaff,
5521 enum isl_dim_type type, unsigned first, unsigned n);
5522 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5523 __isl_take isl_multi_pw_aff *mpa,
5524 enum isl_dim_type type, unsigned first, unsigned n);
5525 __isl_give isl_aff *isl_aff_add_dims(
5526 __isl_take isl_aff *aff,
5527 enum isl_dim_type type, unsigned n);
5528 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5529 __isl_take isl_multi_aff *ma,
5530 enum isl_dim_type type, unsigned n);
5531 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5532 __isl_take isl_pw_aff *pwaff,
5533 enum isl_dim_type type, unsigned n);
5534 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5535 __isl_take isl_multi_pw_aff *mpa,
5536 enum isl_dim_type type, unsigned n);
5537 __isl_give isl_aff *isl_aff_drop_dims(
5538 __isl_take isl_aff *aff,
5539 enum isl_dim_type type, unsigned first, unsigned n);
5540 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5541 __isl_take isl_multi_aff *maff,
5542 enum isl_dim_type type, unsigned first, unsigned n);
5543 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5544 __isl_take isl_pw_aff *pwaff,
5545 enum isl_dim_type type, unsigned first, unsigned n);
5546 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5547 __isl_take isl_pw_multi_aff *pma,
5548 enum isl_dim_type type, unsigned first, unsigned n);
5549 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5550 __isl_take isl_union_pw_aff *upa,
5551 enum isl_dim_type type, unsigned first, unsigned n);
5552 __isl_give isl_union_pw_multi_aff *
5553 isl_union_pw_multi_aff_drop_dims(
5554 __isl_take isl_union_pw_multi_aff *upma,
5555 enum isl_dim_type type,
5556 unsigned first, unsigned n);
5557 __isl_give isl_multi_union_pw_aff *
5558 isl_multi_union_pw_aff_drop_dims(
5559 __isl_take isl_multi_union_pw_aff *mupa,
5560 enum isl_dim_type type, unsigned first,
5562 __isl_give isl_aff *isl_aff_move_dims(
5563 __isl_take isl_aff *aff,
5564 enum isl_dim_type dst_type, unsigned dst_pos,
5565 enum isl_dim_type src_type, unsigned src_pos,
5567 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5568 __isl_take isl_multi_aff *ma,
5569 enum isl_dim_type dst_type, unsigned dst_pos,
5570 enum isl_dim_type src_type, unsigned src_pos,
5572 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5573 __isl_take isl_pw_aff *pa,
5574 enum isl_dim_type dst_type, unsigned dst_pos,
5575 enum isl_dim_type src_type, unsigned src_pos,
5577 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5578 __isl_take isl_multi_pw_aff *pma,
5579 enum isl_dim_type dst_type, unsigned dst_pos,
5580 enum isl_dim_type src_type, unsigned src_pos,
5583 #include <isl/polynomial.h>
5584 __isl_give isl_union_pw_qpolynomial *
5585 isl_union_pw_qpolynomial_drop_dims(
5586 __isl_take isl_union_pw_qpolynomial *upwqp,
5587 enum isl_dim_type type,
5588 unsigned first, unsigned n);
5589 __isl_give isl_union_pw_qpolynomial_fold *
5590 isl_union_pw_qpolynomial_fold_drop_dims(
5591 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5592 enum isl_dim_type type,
5593 unsigned first, unsigned n);
5595 The operations on union expressions can only manipulate parameters.
5599 =head2 Binary Operations
5601 The two arguments of a binary operation not only need to live
5602 in the same C<isl_ctx>, they currently also need to have
5603 the same (number of) parameters.
5605 =head3 Basic Operations
5609 =item * Intersection
5611 #include <isl/local_space.h>
5612 __isl_give isl_local_space *isl_local_space_intersect(
5613 __isl_take isl_local_space *ls1,
5614 __isl_take isl_local_space *ls2);
5616 #include <isl/set.h>
5617 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5618 __isl_take isl_basic_set *bset1,
5619 __isl_take isl_basic_set *bset2);
5620 __isl_give isl_basic_set *isl_basic_set_intersect(
5621 __isl_take isl_basic_set *bset1,
5622 __isl_take isl_basic_set *bset2);
5623 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5624 __isl_take struct isl_basic_set_list *list);
5625 __isl_give isl_set *isl_set_intersect_params(
5626 __isl_take isl_set *set,
5627 __isl_take isl_set *params);
5628 __isl_give isl_set *isl_set_intersect(
5629 __isl_take isl_set *set1,
5630 __isl_take isl_set *set2);
5632 #include <isl/map.h>
5633 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5634 __isl_take isl_basic_map *bmap,
5635 __isl_take isl_basic_set *bset);
5636 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5637 __isl_take isl_basic_map *bmap,
5638 __isl_take isl_basic_set *bset);
5639 __isl_give isl_basic_map *isl_basic_map_intersect(
5640 __isl_take isl_basic_map *bmap1,
5641 __isl_take isl_basic_map *bmap2);
5642 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5643 __isl_take isl_basic_map_list *list);
5644 __isl_give isl_map *isl_map_intersect_params(
5645 __isl_take isl_map *map,
5646 __isl_take isl_set *params);
5647 __isl_give isl_map *isl_map_intersect_domain(
5648 __isl_take isl_map *map,
5649 __isl_take isl_set *set);
5650 __isl_give isl_map *isl_map_intersect_range(
5651 __isl_take isl_map *map,
5652 __isl_take isl_set *set);
5653 __isl_give isl_map *isl_map_intersect(
5654 __isl_take isl_map *map1,
5655 __isl_take isl_map *map2);
5657 #include <isl/union_set.h>
5658 __isl_give isl_union_set *isl_union_set_intersect_params(
5659 __isl_take isl_union_set *uset,
5660 __isl_take isl_set *set);
5661 __isl_give isl_union_set *isl_union_set_intersect(
5662 __isl_take isl_union_set *uset1,
5663 __isl_take isl_union_set *uset2);
5665 #include <isl/union_map.h>
5666 __isl_give isl_union_map *isl_union_map_intersect_params(
5667 __isl_take isl_union_map *umap,
5668 __isl_take isl_set *set);
5669 __isl_give isl_union_map *isl_union_map_intersect_domain(
5670 __isl_take isl_union_map *umap,
5671 __isl_take isl_union_set *uset);
5672 __isl_give isl_union_map *isl_union_map_intersect_range(
5673 __isl_take isl_union_map *umap,
5674 __isl_take isl_union_set *uset);
5675 __isl_give isl_union_map *isl_union_map_intersect(
5676 __isl_take isl_union_map *umap1,
5677 __isl_take isl_union_map *umap2);
5679 #include <isl/aff.h>
5680 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5681 __isl_take isl_pw_aff *pa,
5682 __isl_take isl_set *set);
5683 __isl_give isl_multi_pw_aff *
5684 isl_multi_pw_aff_intersect_domain(
5685 __isl_take isl_multi_pw_aff *mpa,
5686 __isl_take isl_set *domain);
5687 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5688 __isl_take isl_pw_multi_aff *pma,
5689 __isl_take isl_set *set);
5690 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5691 __isl_take isl_union_pw_aff *upa,
5692 __isl_take isl_union_set *uset);
5693 __isl_give isl_union_pw_multi_aff *
5694 isl_union_pw_multi_aff_intersect_domain(
5695 __isl_take isl_union_pw_multi_aff *upma,
5696 __isl_take isl_union_set *uset);
5697 __isl_give isl_multi_union_pw_aff *
5698 isl_multi_union_pw_aff_intersect_domain(
5699 __isl_take isl_multi_union_pw_aff *mupa,
5700 __isl_take isl_union_set *uset);
5701 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5702 __isl_take isl_pw_aff *pa,
5703 __isl_take isl_set *set);
5704 __isl_give isl_multi_pw_aff *
5705 isl_multi_pw_aff_intersect_params(
5706 __isl_take isl_multi_pw_aff *mpa,
5707 __isl_take isl_set *set);
5708 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5709 __isl_take isl_pw_multi_aff *pma,
5710 __isl_take isl_set *set);
5711 __isl_give isl_union_pw_aff *
5712 isl_union_pw_aff_intersect_params(
5713 __isl_take isl_union_pw_aff *upa,
5714 __isl_give isl_union_pw_multi_aff *
5715 isl_union_pw_multi_aff_intersect_params(
5716 __isl_take isl_union_pw_multi_aff *upma,
5717 __isl_take isl_set *set);
5718 __isl_give isl_multi_union_pw_aff *
5719 isl_multi_union_pw_aff_intersect_params(
5720 __isl_take isl_multi_union_pw_aff *mupa,
5721 __isl_take isl_set *params);
5722 isl_multi_union_pw_aff_intersect_range(
5723 __isl_take isl_multi_union_pw_aff *mupa,
5724 __isl_take isl_set *set);
5726 #include <isl/polynomial.h>
5727 __isl_give isl_pw_qpolynomial *
5728 isl_pw_qpolynomial_intersect_domain(
5729 __isl_take isl_pw_qpolynomial *pwpq,
5730 __isl_take isl_set *set);
5731 __isl_give isl_union_pw_qpolynomial *
5732 isl_union_pw_qpolynomial_intersect_domain(
5733 __isl_take isl_union_pw_qpolynomial *upwpq,
5734 __isl_take isl_union_set *uset);
5735 __isl_give isl_union_pw_qpolynomial_fold *
5736 isl_union_pw_qpolynomial_fold_intersect_domain(
5737 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5738 __isl_take isl_union_set *uset);
5739 __isl_give isl_pw_qpolynomial *
5740 isl_pw_qpolynomial_intersect_params(
5741 __isl_take isl_pw_qpolynomial *pwpq,
5742 __isl_take isl_set *set);
5743 __isl_give isl_pw_qpolynomial_fold *
5744 isl_pw_qpolynomial_fold_intersect_params(
5745 __isl_take isl_pw_qpolynomial_fold *pwf,
5746 __isl_take isl_set *set);
5747 __isl_give isl_union_pw_qpolynomial *
5748 isl_union_pw_qpolynomial_intersect_params(
5749 __isl_take isl_union_pw_qpolynomial *upwpq,
5750 __isl_take isl_set *set);
5751 __isl_give isl_union_pw_qpolynomial_fold *
5752 isl_union_pw_qpolynomial_fold_intersect_params(
5753 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5754 __isl_take isl_set *set);
5756 The second argument to the C<_params> functions needs to be
5757 a parametric (basic) set. For the other functions, a parametric set
5758 for either argument is only allowed if the other argument is
5759 a parametric set as well.
5760 The list passed to C<isl_basic_set_list_intersect> needs to have
5761 at least one element and all elements need to live in the same space.
5762 The function C<isl_multi_union_pw_aff_intersect_range>
5763 restricts the input function to those shared domain elements
5764 that map to the specified range.
5768 #include <isl/set.h>
5769 __isl_give isl_set *isl_basic_set_union(
5770 __isl_take isl_basic_set *bset1,
5771 __isl_take isl_basic_set *bset2);
5772 __isl_give isl_set *isl_set_union(
5773 __isl_take isl_set *set1,
5774 __isl_take isl_set *set2);
5775 __isl_give isl_set *isl_set_list_union(
5776 __isl_take isl_set_list *list);
5778 #include <isl/map.h>
5779 __isl_give isl_map *isl_basic_map_union(
5780 __isl_take isl_basic_map *bmap1,
5781 __isl_take isl_basic_map *bmap2);
5782 __isl_give isl_map *isl_map_union(
5783 __isl_take isl_map *map1,
5784 __isl_take isl_map *map2);
5786 #include <isl/union_set.h>
5787 __isl_give isl_union_set *isl_union_set_union(
5788 __isl_take isl_union_set *uset1,
5789 __isl_take isl_union_set *uset2);
5790 __isl_give isl_union_set *isl_union_set_list_union(
5791 __isl_take isl_union_set_list *list);
5793 #include <isl/union_map.h>
5794 __isl_give isl_union_map *isl_union_map_union(
5795 __isl_take isl_union_map *umap1,
5796 __isl_take isl_union_map *umap2);
5798 The list passed to C<isl_set_list_union> needs to have
5799 at least one element and all elements need to live in the same space.
5801 =item * Set difference
5803 #include <isl/set.h>
5804 __isl_give isl_set *isl_set_subtract(
5805 __isl_take isl_set *set1,
5806 __isl_take isl_set *set2);
5808 #include <isl/map.h>
5809 __isl_give isl_map *isl_map_subtract(
5810 __isl_take isl_map *map1,
5811 __isl_take isl_map *map2);
5812 __isl_give isl_map *isl_map_subtract_domain(
5813 __isl_take isl_map *map,
5814 __isl_take isl_set *dom);
5815 __isl_give isl_map *isl_map_subtract_range(
5816 __isl_take isl_map *map,
5817 __isl_take isl_set *dom);
5819 #include <isl/union_set.h>
5820 __isl_give isl_union_set *isl_union_set_subtract(
5821 __isl_take isl_union_set *uset1,
5822 __isl_take isl_union_set *uset2);
5824 #include <isl/union_map.h>
5825 __isl_give isl_union_map *isl_union_map_subtract(
5826 __isl_take isl_union_map *umap1,
5827 __isl_take isl_union_map *umap2);
5828 __isl_give isl_union_map *isl_union_map_subtract_domain(
5829 __isl_take isl_union_map *umap,
5830 __isl_take isl_union_set *dom);
5831 __isl_give isl_union_map *isl_union_map_subtract_range(
5832 __isl_take isl_union_map *umap,
5833 __isl_take isl_union_set *dom);
5835 #include <isl/aff.h>
5836 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5837 __isl_take isl_pw_aff *pa,
5838 __isl_take isl_set *set);
5839 __isl_give isl_pw_multi_aff *
5840 isl_pw_multi_aff_subtract_domain(
5841 __isl_take isl_pw_multi_aff *pma,
5842 __isl_take isl_set *set);
5843 __isl_give isl_union_pw_aff *
5844 isl_union_pw_aff_subtract_domain(
5845 __isl_take isl_union_pw_aff *upa,
5846 __isl_take isl_union_set *uset);
5847 __isl_give isl_union_pw_multi_aff *
5848 isl_union_pw_multi_aff_subtract_domain(
5849 __isl_take isl_union_pw_multi_aff *upma,
5850 __isl_take isl_set *set);
5852 #include <isl/polynomial.h>
5853 __isl_give isl_pw_qpolynomial *
5854 isl_pw_qpolynomial_subtract_domain(
5855 __isl_take isl_pw_qpolynomial *pwpq,
5856 __isl_take isl_set *set);
5857 __isl_give isl_pw_qpolynomial_fold *
5858 isl_pw_qpolynomial_fold_subtract_domain(
5859 __isl_take isl_pw_qpolynomial_fold *pwf,
5860 __isl_take isl_set *set);
5861 __isl_give isl_union_pw_qpolynomial *
5862 isl_union_pw_qpolynomial_subtract_domain(
5863 __isl_take isl_union_pw_qpolynomial *upwpq,
5864 __isl_take isl_union_set *uset);
5865 __isl_give isl_union_pw_qpolynomial_fold *
5866 isl_union_pw_qpolynomial_fold_subtract_domain(
5867 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5868 __isl_take isl_union_set *uset);
5872 #include <isl/space.h>
5873 __isl_give isl_space *isl_space_join(
5874 __isl_take isl_space *left,
5875 __isl_take isl_space *right);
5877 #include <isl/map.h>
5878 __isl_give isl_basic_set *isl_basic_set_apply(
5879 __isl_take isl_basic_set *bset,
5880 __isl_take isl_basic_map *bmap);
5881 __isl_give isl_set *isl_set_apply(
5882 __isl_take isl_set *set,
5883 __isl_take isl_map *map);
5884 __isl_give isl_union_set *isl_union_set_apply(
5885 __isl_take isl_union_set *uset,
5886 __isl_take isl_union_map *umap);
5887 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5888 __isl_take isl_basic_map *bmap1,
5889 __isl_take isl_basic_map *bmap2);
5890 __isl_give isl_basic_map *isl_basic_map_apply_range(
5891 __isl_take isl_basic_map *bmap1,
5892 __isl_take isl_basic_map *bmap2);
5893 __isl_give isl_map *isl_map_apply_domain(
5894 __isl_take isl_map *map1,
5895 __isl_take isl_map *map2);
5896 __isl_give isl_map *isl_map_apply_range(
5897 __isl_take isl_map *map1,
5898 __isl_take isl_map *map2);
5900 #include <isl/union_map.h>
5901 __isl_give isl_union_map *isl_union_map_apply_domain(
5902 __isl_take isl_union_map *umap1,
5903 __isl_take isl_union_map *umap2);
5904 __isl_give isl_union_map *isl_union_map_apply_range(
5905 __isl_take isl_union_map *umap1,
5906 __isl_take isl_union_map *umap2);
5908 #include <isl/aff.h>
5909 __isl_give isl_union_pw_aff *
5910 isl_multi_union_pw_aff_apply_aff(
5911 __isl_take isl_multi_union_pw_aff *mupa,
5912 __isl_take isl_aff *aff);
5913 __isl_give isl_union_pw_aff *
5914 isl_multi_union_pw_aff_apply_pw_aff(
5915 __isl_take isl_multi_union_pw_aff *mupa,
5916 __isl_take isl_pw_aff *pa);
5917 __isl_give isl_multi_union_pw_aff *
5918 isl_multi_union_pw_aff_apply_multi_aff(
5919 __isl_take isl_multi_union_pw_aff *mupa,
5920 __isl_take isl_multi_aff *ma);
5921 __isl_give isl_multi_union_pw_aff *
5922 isl_multi_union_pw_aff_apply_pw_multi_aff(
5923 __isl_take isl_multi_union_pw_aff *mupa,
5924 __isl_take isl_pw_multi_aff *pma);
5926 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5927 over the shared domain of the elements of the input. The dimension is
5928 required to be greater than zero.
5929 The C<isl_multi_union_pw_aff> argument of
5930 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5931 but only if the range of the C<isl_multi_aff> argument
5932 is also zero-dimensional.
5933 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5935 #include <isl/polynomial.h>
5936 __isl_give isl_pw_qpolynomial_fold *
5937 isl_set_apply_pw_qpolynomial_fold(
5938 __isl_take isl_set *set,
5939 __isl_take isl_pw_qpolynomial_fold *pwf,
5941 __isl_give isl_pw_qpolynomial_fold *
5942 isl_map_apply_pw_qpolynomial_fold(
5943 __isl_take isl_map *map,
5944 __isl_take isl_pw_qpolynomial_fold *pwf,
5946 __isl_give isl_union_pw_qpolynomial_fold *
5947 isl_union_set_apply_union_pw_qpolynomial_fold(
5948 __isl_take isl_union_set *uset,
5949 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5951 __isl_give isl_union_pw_qpolynomial_fold *
5952 isl_union_map_apply_union_pw_qpolynomial_fold(
5953 __isl_take isl_union_map *umap,
5954 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5957 The functions taking a map
5958 compose the given map with the given piecewise quasipolynomial reduction.
5959 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5960 over all elements in the intersection of the range of the map
5961 and the domain of the piecewise quasipolynomial reduction
5962 as a function of an element in the domain of the map.
5963 The functions taking a set compute a bound over all elements in the
5964 intersection of the set and the domain of the
5965 piecewise quasipolynomial reduction.
5969 #include <isl/set.h>
5970 __isl_give isl_basic_set *
5971 isl_basic_set_preimage_multi_aff(
5972 __isl_take isl_basic_set *bset,
5973 __isl_take isl_multi_aff *ma);
5974 __isl_give isl_set *isl_set_preimage_multi_aff(
5975 __isl_take isl_set *set,
5976 __isl_take isl_multi_aff *ma);
5977 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5978 __isl_take isl_set *set,
5979 __isl_take isl_pw_multi_aff *pma);
5980 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5981 __isl_take isl_set *set,
5982 __isl_take isl_multi_pw_aff *mpa);
5984 #include <isl/union_set.h>
5985 __isl_give isl_union_set *
5986 isl_union_set_preimage_multi_aff(
5987 __isl_take isl_union_set *uset,
5988 __isl_take isl_multi_aff *ma);
5989 __isl_give isl_union_set *
5990 isl_union_set_preimage_pw_multi_aff(
5991 __isl_take isl_union_set *uset,
5992 __isl_take isl_pw_multi_aff *pma);
5993 __isl_give isl_union_set *
5994 isl_union_set_preimage_union_pw_multi_aff(
5995 __isl_take isl_union_set *uset,
5996 __isl_take isl_union_pw_multi_aff *upma);
5998 #include <isl/map.h>
5999 __isl_give isl_basic_map *
6000 isl_basic_map_preimage_domain_multi_aff(
6001 __isl_take isl_basic_map *bmap,
6002 __isl_take isl_multi_aff *ma);
6003 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6004 __isl_take isl_map *map,
6005 __isl_take isl_multi_aff *ma);
6006 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6007 __isl_take isl_map *map,
6008 __isl_take isl_multi_aff *ma);
6009 __isl_give isl_map *
6010 isl_map_preimage_domain_pw_multi_aff(
6011 __isl_take isl_map *map,
6012 __isl_take isl_pw_multi_aff *pma);
6013 __isl_give isl_map *
6014 isl_map_preimage_range_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_domain_multi_pw_aff(
6019 __isl_take isl_map *map,
6020 __isl_take isl_multi_pw_aff *mpa);
6021 __isl_give isl_basic_map *
6022 isl_basic_map_preimage_range_multi_aff(
6023 __isl_take isl_basic_map *bmap,
6024 __isl_take isl_multi_aff *ma);
6026 #include <isl/union_map.h>
6027 __isl_give isl_union_map *
6028 isl_union_map_preimage_domain_multi_aff(
6029 __isl_take isl_union_map *umap,
6030 __isl_take isl_multi_aff *ma);
6031 __isl_give isl_union_map *
6032 isl_union_map_preimage_range_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_domain_pw_multi_aff(
6037 __isl_take isl_union_map *umap,
6038 __isl_take isl_pw_multi_aff *pma);
6039 __isl_give isl_union_map *
6040 isl_union_map_preimage_range_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_domain_union_pw_multi_aff(
6045 __isl_take isl_union_map *umap,
6046 __isl_take isl_union_pw_multi_aff *upma);
6047 __isl_give isl_union_map *
6048 isl_union_map_preimage_range_union_pw_multi_aff(
6049 __isl_take isl_union_map *umap,
6050 __isl_take isl_union_pw_multi_aff *upma);
6052 These functions compute the preimage of the given set or map domain/range under
6053 the given function. In other words, the expression is plugged
6054 into the set description or into the domain/range of the map.
6058 #include <isl/aff.h>
6059 __isl_give isl_aff *isl_aff_pullback_aff(
6060 __isl_take isl_aff *aff1,
6061 __isl_take isl_aff *aff2);
6062 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6063 __isl_take isl_aff *aff,
6064 __isl_take isl_multi_aff *ma);
6065 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6066 __isl_take isl_pw_aff *pa,
6067 __isl_take isl_multi_aff *ma);
6068 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6069 __isl_take isl_pw_aff *pa,
6070 __isl_take isl_pw_multi_aff *pma);
6071 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6072 __isl_take isl_pw_aff *pa,
6073 __isl_take isl_multi_pw_aff *mpa);
6074 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6075 __isl_take isl_multi_aff *ma1,
6076 __isl_take isl_multi_aff *ma2);
6077 __isl_give isl_pw_multi_aff *
6078 isl_pw_multi_aff_pullback_multi_aff(
6079 __isl_take isl_pw_multi_aff *pma,
6080 __isl_take isl_multi_aff *ma);
6081 __isl_give isl_multi_pw_aff *
6082 isl_multi_pw_aff_pullback_multi_aff(
6083 __isl_take isl_multi_pw_aff *mpa,
6084 __isl_take isl_multi_aff *ma);
6085 __isl_give isl_pw_multi_aff *
6086 isl_pw_multi_aff_pullback_pw_multi_aff(
6087 __isl_take isl_pw_multi_aff *pma1,
6088 __isl_take isl_pw_multi_aff *pma2);
6089 __isl_give isl_multi_pw_aff *
6090 isl_multi_pw_aff_pullback_pw_multi_aff(
6091 __isl_take isl_multi_pw_aff *mpa,
6092 __isl_take isl_pw_multi_aff *pma);
6093 __isl_give isl_multi_pw_aff *
6094 isl_multi_pw_aff_pullback_multi_pw_aff(
6095 __isl_take isl_multi_pw_aff *mpa1,
6096 __isl_take isl_multi_pw_aff *mpa2);
6097 __isl_give isl_union_pw_aff *
6098 isl_union_pw_aff_pullback_union_pw_multi_aff(
6099 __isl_take isl_union_pw_aff *upa,
6100 __isl_take isl_union_pw_multi_aff *upma);
6101 __isl_give isl_union_pw_multi_aff *
6102 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6103 __isl_take isl_union_pw_multi_aff *upma1,
6104 __isl_take isl_union_pw_multi_aff *upma2);
6105 __isl_give isl_multi_union_pw_aff *
6106 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6107 __isl_take isl_multi_union_pw_aff *mupa,
6108 __isl_take isl_union_pw_multi_aff *upma);
6110 These functions precompose the first expression by the second function.
6111 In other words, the second function is plugged
6112 into the first expression.
6116 #include <isl/aff.h>
6117 __isl_give isl_basic_set *isl_aff_le_basic_set(
6118 __isl_take isl_aff *aff1,
6119 __isl_take isl_aff *aff2);
6120 __isl_give isl_set *isl_aff_le_set(
6121 __isl_take isl_aff *aff1,
6122 __isl_take isl_aff *aff2);
6123 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6124 __isl_take isl_aff *aff1,
6125 __isl_take isl_aff *aff2);
6126 __isl_give isl_set *isl_aff_ge_set(
6127 __isl_take isl_aff *aff1,
6128 __isl_take isl_aff *aff2);
6129 __isl_give isl_set *isl_pw_aff_eq_set(
6130 __isl_take isl_pw_aff *pwaff1,
6131 __isl_take isl_pw_aff *pwaff2);
6132 __isl_give isl_set *isl_pw_aff_ne_set(
6133 __isl_take isl_pw_aff *pwaff1,
6134 __isl_take isl_pw_aff *pwaff2);
6135 __isl_give isl_set *isl_pw_aff_le_set(
6136 __isl_take isl_pw_aff *pwaff1,
6137 __isl_take isl_pw_aff *pwaff2);
6138 __isl_give isl_set *isl_pw_aff_lt_set(
6139 __isl_take isl_pw_aff *pwaff1,
6140 __isl_take isl_pw_aff *pwaff2);
6141 __isl_give isl_set *isl_pw_aff_ge_set(
6142 __isl_take isl_pw_aff *pwaff1,
6143 __isl_take isl_pw_aff *pwaff2);
6144 __isl_give isl_set *isl_pw_aff_gt_set(
6145 __isl_take isl_pw_aff *pwaff1,
6146 __isl_take isl_pw_aff *pwaff2);
6148 __isl_give isl_set *isl_multi_aff_lex_le_set(
6149 __isl_take isl_multi_aff *ma1,
6150 __isl_take isl_multi_aff *ma2);
6151 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6152 __isl_take isl_multi_aff *ma1,
6153 __isl_take isl_multi_aff *ma2);
6154 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6155 __isl_take isl_multi_aff *ma1,
6156 __isl_take isl_multi_aff *ma2);
6157 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6158 __isl_take isl_multi_aff *ma1,
6159 __isl_take isl_multi_aff *ma2);
6161 __isl_give isl_set *isl_pw_aff_list_eq_set(
6162 __isl_take isl_pw_aff_list *list1,
6163 __isl_take isl_pw_aff_list *list2);
6164 __isl_give isl_set *isl_pw_aff_list_ne_set(
6165 __isl_take isl_pw_aff_list *list1,
6166 __isl_take isl_pw_aff_list *list2);
6167 __isl_give isl_set *isl_pw_aff_list_le_set(
6168 __isl_take isl_pw_aff_list *list1,
6169 __isl_take isl_pw_aff_list *list2);
6170 __isl_give isl_set *isl_pw_aff_list_lt_set(
6171 __isl_take isl_pw_aff_list *list1,
6172 __isl_take isl_pw_aff_list *list2);
6173 __isl_give isl_set *isl_pw_aff_list_ge_set(
6174 __isl_take isl_pw_aff_list *list1,
6175 __isl_take isl_pw_aff_list *list2);
6176 __isl_give isl_set *isl_pw_aff_list_gt_set(
6177 __isl_take isl_pw_aff_list *list1,
6178 __isl_take isl_pw_aff_list *list2);
6180 The function C<isl_aff_ge_basic_set> returns a basic set
6181 containing those elements in the shared space
6182 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6183 The function C<isl_pw_aff_ge_set> returns a set
6184 containing those elements in the shared domain
6185 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6186 greater than or equal to C<pwaff2>.
6187 The function C<isl_multi_aff_lex_le_set> returns a set
6188 containing those elements in the shared domain space
6189 where C<ma1> is lexicographically smaller than or
6191 The functions operating on C<isl_pw_aff_list> apply the corresponding
6192 C<isl_pw_aff> function to each pair of elements in the two lists.
6194 #include <isl/aff.h>
6195 __isl_give isl_map *isl_pw_aff_eq_map(
6196 __isl_take isl_pw_aff *pa1,
6197 __isl_take isl_pw_aff *pa2);
6198 __isl_give isl_map *isl_pw_aff_lt_map(
6199 __isl_take isl_pw_aff *pa1,
6200 __isl_take isl_pw_aff *pa2);
6201 __isl_give isl_map *isl_pw_aff_gt_map(
6202 __isl_take isl_pw_aff *pa1,
6203 __isl_take isl_pw_aff *pa2);
6205 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6206 __isl_take isl_multi_pw_aff *mpa1,
6207 __isl_take isl_multi_pw_aff *mpa2);
6208 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6209 __isl_take isl_multi_pw_aff *mpa1,
6210 __isl_take isl_multi_pw_aff *mpa2);
6211 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6212 __isl_take isl_multi_pw_aff *mpa1,
6213 __isl_take isl_multi_pw_aff *mpa2);
6215 These functions return a map between domain elements of the arguments
6216 where the function values satisfy the given relation.
6218 #include <isl/union_map.h>
6219 __isl_give isl_union_map *
6220 isl_union_map_eq_at_multi_union_pw_aff(
6221 __isl_take isl_union_map *umap,
6222 __isl_take isl_multi_union_pw_aff *mupa);
6223 __isl_give isl_union_map *
6224 isl_union_map_lex_lt_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_gt_at_multi_union_pw_aff(
6229 __isl_take isl_union_map *umap,
6230 __isl_take isl_multi_union_pw_aff *mupa);
6232 These functions select the subset of elements in the union map
6233 that have an equal or lexicographically smaller function value.
6235 =item * Cartesian Product
6237 #include <isl/space.h>
6238 __isl_give isl_space *isl_space_product(
6239 __isl_take isl_space *space1,
6240 __isl_take isl_space *space2);
6241 __isl_give isl_space *isl_space_domain_product(
6242 __isl_take isl_space *space1,
6243 __isl_take isl_space *space2);
6244 __isl_give isl_space *isl_space_range_product(
6245 __isl_take isl_space *space1,
6246 __isl_take isl_space *space2);
6249 C<isl_space_product>, C<isl_space_domain_product>
6250 and C<isl_space_range_product> take pairs or relation spaces and
6251 produce a single relations space, where either the domain, the range
6252 or both domain and range are wrapped spaces of relations between
6253 the domains and/or ranges of the input spaces.
6254 If the product is only constructed over the domain or the range
6255 then the ranges or the domains of the inputs should be the same.
6256 The function C<isl_space_product> also accepts a pair of set spaces,
6257 in which case it returns a wrapped space of a relation between the
6260 #include <isl/set.h>
6261 __isl_give isl_set *isl_set_product(
6262 __isl_take isl_set *set1,
6263 __isl_take isl_set *set2);
6265 #include <isl/map.h>
6266 __isl_give isl_basic_map *isl_basic_map_domain_product(
6267 __isl_take isl_basic_map *bmap1,
6268 __isl_take isl_basic_map *bmap2);
6269 __isl_give isl_basic_map *isl_basic_map_range_product(
6270 __isl_take isl_basic_map *bmap1,
6271 __isl_take isl_basic_map *bmap2);
6272 __isl_give isl_basic_map *isl_basic_map_product(
6273 __isl_take isl_basic_map *bmap1,
6274 __isl_take isl_basic_map *bmap2);
6275 __isl_give isl_map *isl_map_domain_product(
6276 __isl_take isl_map *map1,
6277 __isl_take isl_map *map2);
6278 __isl_give isl_map *isl_map_range_product(
6279 __isl_take isl_map *map1,
6280 __isl_take isl_map *map2);
6281 __isl_give isl_map *isl_map_product(
6282 __isl_take isl_map *map1,
6283 __isl_take isl_map *map2);
6285 #include <isl/union_set.h>
6286 __isl_give isl_union_set *isl_union_set_product(
6287 __isl_take isl_union_set *uset1,
6288 __isl_take isl_union_set *uset2);
6290 #include <isl/union_map.h>
6291 __isl_give isl_union_map *isl_union_map_domain_product(
6292 __isl_take isl_union_map *umap1,
6293 __isl_take isl_union_map *umap2);
6294 __isl_give isl_union_map *isl_union_map_range_product(
6295 __isl_take isl_union_map *umap1,
6296 __isl_take isl_union_map *umap2);
6297 __isl_give isl_union_map *isl_union_map_product(
6298 __isl_take isl_union_map *umap1,
6299 __isl_take isl_union_map *umap2);
6301 #include <isl/val.h>
6302 __isl_give isl_multi_val *isl_multi_val_range_product(
6303 __isl_take isl_multi_val *mv1,
6304 __isl_take isl_multi_val *mv2);
6305 __isl_give isl_multi_val *isl_multi_val_product(
6306 __isl_take isl_multi_val *mv1,
6307 __isl_take isl_multi_val *mv2);
6309 #include <isl/aff.h>
6310 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6311 __isl_take isl_multi_aff *ma1,
6312 __isl_take isl_multi_aff *ma2);
6313 __isl_give isl_multi_aff *isl_multi_aff_product(
6314 __isl_take isl_multi_aff *ma1,
6315 __isl_take isl_multi_aff *ma2);
6316 __isl_give isl_multi_pw_aff *
6317 isl_multi_pw_aff_range_product(
6318 __isl_take isl_multi_pw_aff *mpa1,
6319 __isl_take isl_multi_pw_aff *mpa2);
6320 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6321 __isl_take isl_multi_pw_aff *mpa1,
6322 __isl_take isl_multi_pw_aff *mpa2);
6323 __isl_give isl_pw_multi_aff *
6324 isl_pw_multi_aff_range_product(
6325 __isl_take isl_pw_multi_aff *pma1,
6326 __isl_take isl_pw_multi_aff *pma2);
6327 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6328 __isl_take isl_pw_multi_aff *pma1,
6329 __isl_take isl_pw_multi_aff *pma2);
6330 __isl_give isl_multi_union_pw_aff *
6331 isl_multi_union_pw_aff_range_product(
6332 __isl_take isl_multi_union_pw_aff *mupa1,
6333 __isl_take isl_multi_union_pw_aff *mupa2);
6335 The above functions compute the cross product of the given
6336 sets, relations or functions. The domains and ranges of the results
6337 are wrapped maps between domains and ranges of the inputs.
6338 To obtain a ``flat'' product, use the following functions
6341 #include <isl/set.h>
6342 __isl_give isl_basic_set *isl_basic_set_flat_product(
6343 __isl_take isl_basic_set *bset1,
6344 __isl_take isl_basic_set *bset2);
6345 __isl_give isl_set *isl_set_flat_product(
6346 __isl_take isl_set *set1,
6347 __isl_take isl_set *set2);
6349 #include <isl/map.h>
6350 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6351 __isl_take isl_basic_map *bmap1,
6352 __isl_take isl_basic_map *bmap2);
6353 __isl_give isl_map *isl_map_flat_domain_product(
6354 __isl_take isl_map *map1,
6355 __isl_take isl_map *map2);
6356 __isl_give isl_map *isl_map_flat_range_product(
6357 __isl_take isl_map *map1,
6358 __isl_take isl_map *map2);
6359 __isl_give isl_basic_map *isl_basic_map_flat_product(
6360 __isl_take isl_basic_map *bmap1,
6361 __isl_take isl_basic_map *bmap2);
6362 __isl_give isl_map *isl_map_flat_product(
6363 __isl_take isl_map *map1,
6364 __isl_take isl_map *map2);
6366 #include <isl/union_map.h>
6367 __isl_give isl_union_map *
6368 isl_union_map_flat_domain_product(
6369 __isl_take isl_union_map *umap1,
6370 __isl_take isl_union_map *umap2);
6371 __isl_give isl_union_map *
6372 isl_union_map_flat_range_product(
6373 __isl_take isl_union_map *umap1,
6374 __isl_take isl_union_map *umap2);
6376 #include <isl/val.h>
6377 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6378 __isl_take isl_multi_val *mv1,
6379 __isl_take isl_multi_aff *mv2);
6381 #include <isl/aff.h>
6382 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6383 __isl_take isl_multi_aff *ma1,
6384 __isl_take isl_multi_aff *ma2);
6385 __isl_give isl_pw_multi_aff *
6386 isl_pw_multi_aff_flat_range_product(
6387 __isl_take isl_pw_multi_aff *pma1,
6388 __isl_take isl_pw_multi_aff *pma2);
6389 __isl_give isl_multi_pw_aff *
6390 isl_multi_pw_aff_flat_range_product(
6391 __isl_take isl_multi_pw_aff *mpa1,
6392 __isl_take isl_multi_pw_aff *mpa2);
6393 __isl_give isl_union_pw_multi_aff *
6394 isl_union_pw_multi_aff_flat_range_product(
6395 __isl_take isl_union_pw_multi_aff *upma1,
6396 __isl_take isl_union_pw_multi_aff *upma2);
6397 __isl_give isl_multi_union_pw_aff *
6398 isl_multi_union_pw_aff_flat_range_product(
6399 __isl_take isl_multi_union_pw_aff *mupa1,
6400 __isl_take isl_multi_union_pw_aff *mupa2);
6402 #include <isl/space.h>
6403 __isl_give isl_space *isl_space_factor_domain(
6404 __isl_take isl_space *space);
6405 __isl_give isl_space *isl_space_factor_range(
6406 __isl_take isl_space *space);
6407 __isl_give isl_space *isl_space_domain_factor_domain(
6408 __isl_take isl_space *space);
6409 __isl_give isl_space *isl_space_domain_factor_range(
6410 __isl_take isl_space *space);
6411 __isl_give isl_space *isl_space_range_factor_domain(
6412 __isl_take isl_space *space);
6413 __isl_give isl_space *isl_space_range_factor_range(
6414 __isl_take isl_space *space);
6416 The functions C<isl_space_range_factor_domain> and
6417 C<isl_space_range_factor_range> extract the two arguments from
6418 the result of a call to C<isl_space_range_product>.
6420 The arguments of a call to a product can be extracted
6421 from the result using the following functions.
6423 #include <isl/map.h>
6424 __isl_give isl_map *isl_map_factor_domain(
6425 __isl_take isl_map *map);
6426 __isl_give isl_map *isl_map_factor_range(
6427 __isl_take isl_map *map);
6428 __isl_give isl_map *isl_map_domain_factor_domain(
6429 __isl_take isl_map *map);
6430 __isl_give isl_map *isl_map_domain_factor_range(
6431 __isl_take isl_map *map);
6432 __isl_give isl_map *isl_map_range_factor_domain(
6433 __isl_take isl_map *map);
6434 __isl_give isl_map *isl_map_range_factor_range(
6435 __isl_take isl_map *map);
6437 #include <isl/union_map.h>
6438 __isl_give isl_union_map *isl_union_map_factor_domain(
6439 __isl_take isl_union_map *umap);
6440 __isl_give isl_union_map *isl_union_map_factor_range(
6441 __isl_take isl_union_map *umap);
6442 __isl_give isl_union_map *
6443 isl_union_map_domain_factor_domain(
6444 __isl_take isl_union_map *umap);
6445 __isl_give isl_union_map *
6446 isl_union_map_domain_factor_range(
6447 __isl_take isl_union_map *umap);
6448 __isl_give isl_union_map *
6449 isl_union_map_range_factor_domain(
6450 __isl_take isl_union_map *umap);
6451 __isl_give isl_union_map *
6452 isl_union_map_range_factor_range(
6453 __isl_take isl_union_map *umap);
6455 #include <isl/val.h>
6456 __isl_give isl_multi_val *isl_multi_val_factor_range(
6457 __isl_take isl_multi_val *mv);
6458 __isl_give isl_multi_val *
6459 isl_multi_val_range_factor_domain(
6460 __isl_take isl_multi_val *mv);
6461 __isl_give isl_multi_val *
6462 isl_multi_val_range_factor_range(
6463 __isl_take isl_multi_val *mv);
6465 #include <isl/aff.h>
6466 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6467 __isl_take isl_multi_aff *ma);
6468 __isl_give isl_multi_aff *
6469 isl_multi_aff_range_factor_domain(
6470 __isl_take isl_multi_aff *ma);
6471 __isl_give isl_multi_aff *
6472 isl_multi_aff_range_factor_range(
6473 __isl_take isl_multi_aff *ma);
6474 __isl_give isl_multi_pw_aff *
6475 isl_multi_pw_aff_factor_range(
6476 __isl_take isl_multi_pw_aff *mpa);
6477 __isl_give isl_multi_pw_aff *
6478 isl_multi_pw_aff_range_factor_domain(
6479 __isl_take isl_multi_pw_aff *mpa);
6480 __isl_give isl_multi_pw_aff *
6481 isl_multi_pw_aff_range_factor_range(
6482 __isl_take isl_multi_pw_aff *mpa);
6483 __isl_give isl_multi_union_pw_aff *
6484 isl_multi_union_pw_aff_factor_range(
6485 __isl_take isl_multi_union_pw_aff *mupa);
6486 __isl_give isl_multi_union_pw_aff *
6487 isl_multi_union_pw_aff_range_factor_domain(
6488 __isl_take isl_multi_union_pw_aff *mupa);
6489 __isl_give isl_multi_union_pw_aff *
6490 isl_multi_union_pw_aff_range_factor_range(
6491 __isl_take isl_multi_union_pw_aff *mupa);
6493 The splice functions are a generalization of the flat product functions,
6494 where the second argument may be inserted at any position inside
6495 the first argument rather than being placed at the end.
6496 The functions C<isl_multi_val_factor_range>,
6497 C<isl_multi_aff_factor_range>,
6498 C<isl_multi_pw_aff_factor_range> and
6499 C<isl_multi_union_pw_aff_factor_range>
6500 take functions that live in a set space.
6502 #include <isl/val.h>
6503 __isl_give isl_multi_val *isl_multi_val_range_splice(
6504 __isl_take isl_multi_val *mv1, unsigned pos,
6505 __isl_take isl_multi_val *mv2);
6507 #include <isl/aff.h>
6508 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6509 __isl_take isl_multi_aff *ma1, unsigned pos,
6510 __isl_take isl_multi_aff *ma2);
6511 __isl_give isl_multi_aff *isl_multi_aff_splice(
6512 __isl_take isl_multi_aff *ma1,
6513 unsigned in_pos, unsigned out_pos,
6514 __isl_take isl_multi_aff *ma2);
6515 __isl_give isl_multi_pw_aff *
6516 isl_multi_pw_aff_range_splice(
6517 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6518 __isl_take isl_multi_pw_aff *mpa2);
6519 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6520 __isl_take isl_multi_pw_aff *mpa1,
6521 unsigned in_pos, unsigned out_pos,
6522 __isl_take isl_multi_pw_aff *mpa2);
6523 __isl_give isl_multi_union_pw_aff *
6524 isl_multi_union_pw_aff_range_splice(
6525 __isl_take isl_multi_union_pw_aff *mupa1,
6527 __isl_take isl_multi_union_pw_aff *mupa2);
6529 =item * Simplification
6531 When applied to a set or relation,
6532 the gist operation returns a set or relation that has the
6533 same intersection with the context as the input set or relation.
6534 Any implicit equality in the intersection is made explicit in the result,
6535 while all inequalities that are redundant with respect to the intersection
6537 In case of union sets and relations, the gist operation is performed
6540 When applied to a function,
6541 the gist operation applies the set gist operation to each of
6542 the cells in the domain of the input piecewise expression.
6543 The context is also exploited
6544 to simplify the expression associated to each cell.
6546 #include <isl/set.h>
6547 __isl_give isl_basic_set *isl_basic_set_gist(
6548 __isl_take isl_basic_set *bset,
6549 __isl_take isl_basic_set *context);
6550 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6551 __isl_take isl_set *context);
6552 __isl_give isl_set *isl_set_gist_params(
6553 __isl_take isl_set *set,
6554 __isl_take isl_set *context);
6556 #include <isl/map.h>
6557 __isl_give isl_basic_map *isl_basic_map_gist(
6558 __isl_take isl_basic_map *bmap,
6559 __isl_take isl_basic_map *context);
6560 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6561 __isl_take isl_basic_map *bmap,
6562 __isl_take isl_basic_set *context);
6563 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6564 __isl_take isl_map *context);
6565 __isl_give isl_map *isl_map_gist_params(
6566 __isl_take isl_map *map,
6567 __isl_take isl_set *context);
6568 __isl_give isl_map *isl_map_gist_domain(
6569 __isl_take isl_map *map,
6570 __isl_take isl_set *context);
6571 __isl_give isl_map *isl_map_gist_range(
6572 __isl_take isl_map *map,
6573 __isl_take isl_set *context);
6575 #include <isl/union_set.h>
6576 __isl_give isl_union_set *isl_union_set_gist(
6577 __isl_take isl_union_set *uset,
6578 __isl_take isl_union_set *context);
6579 __isl_give isl_union_set *isl_union_set_gist_params(
6580 __isl_take isl_union_set *uset,
6581 __isl_take isl_set *set);
6583 #include <isl/union_map.h>
6584 __isl_give isl_union_map *isl_union_map_gist(
6585 __isl_take isl_union_map *umap,
6586 __isl_take isl_union_map *context);
6587 __isl_give isl_union_map *isl_union_map_gist_params(
6588 __isl_take isl_union_map *umap,
6589 __isl_take isl_set *set);
6590 __isl_give isl_union_map *isl_union_map_gist_domain(
6591 __isl_take isl_union_map *umap,
6592 __isl_take isl_union_set *uset);
6593 __isl_give isl_union_map *isl_union_map_gist_range(
6594 __isl_take isl_union_map *umap,
6595 __isl_take isl_union_set *uset);
6597 #include <isl/aff.h>
6598 __isl_give isl_aff *isl_aff_gist_params(
6599 __isl_take isl_aff *aff,
6600 __isl_take isl_set *context);
6601 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6602 __isl_take isl_set *context);
6603 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6604 __isl_take isl_multi_aff *maff,
6605 __isl_take isl_set *context);
6606 __isl_give isl_multi_aff *isl_multi_aff_gist(
6607 __isl_take isl_multi_aff *maff,
6608 __isl_take isl_set *context);
6609 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6610 __isl_take isl_pw_aff *pwaff,
6611 __isl_take isl_set *context);
6612 __isl_give isl_pw_aff *isl_pw_aff_gist(
6613 __isl_take isl_pw_aff *pwaff,
6614 __isl_take isl_set *context);
6615 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6616 __isl_take isl_pw_multi_aff *pma,
6617 __isl_take isl_set *set);
6618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6619 __isl_take isl_pw_multi_aff *pma,
6620 __isl_take isl_set *set);
6621 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6622 __isl_take isl_multi_pw_aff *mpa,
6623 __isl_take isl_set *set);
6624 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6625 __isl_take isl_multi_pw_aff *mpa,
6626 __isl_take isl_set *set);
6627 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6628 __isl_take isl_union_pw_aff *upa,
6629 __isl_take isl_union_set *context);
6630 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6631 __isl_take isl_union_pw_aff *upa,
6632 __isl_take isl_set *context);
6633 __isl_give isl_union_pw_multi_aff *
6634 isl_union_pw_multi_aff_gist_params(
6635 __isl_take isl_union_pw_multi_aff *upma,
6636 __isl_take isl_set *context);
6637 __isl_give isl_union_pw_multi_aff *
6638 isl_union_pw_multi_aff_gist(
6639 __isl_take isl_union_pw_multi_aff *upma,
6640 __isl_take isl_union_set *context);
6641 __isl_give isl_multi_union_pw_aff *
6642 isl_multi_union_pw_aff_gist_params(
6643 __isl_take isl_multi_union_pw_aff *aff,
6644 __isl_take isl_set *context);
6645 __isl_give isl_multi_union_pw_aff *
6646 isl_multi_union_pw_aff_gist(
6647 __isl_take isl_multi_union_pw_aff *aff,
6648 __isl_take isl_union_set *context);
6650 #include <isl/polynomial.h>
6651 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6652 __isl_take isl_qpolynomial *qp,
6653 __isl_take isl_set *context);
6654 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6655 __isl_take isl_qpolynomial *qp,
6656 __isl_take isl_set *context);
6657 __isl_give isl_qpolynomial_fold *
6658 isl_qpolynomial_fold_gist_params(
6659 __isl_take isl_qpolynomial_fold *fold,
6660 __isl_take isl_set *context);
6661 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6662 __isl_take isl_qpolynomial_fold *fold,
6663 __isl_take isl_set *context);
6664 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6665 __isl_take isl_pw_qpolynomial *pwqp,
6666 __isl_take isl_set *context);
6667 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6668 __isl_take isl_pw_qpolynomial *pwqp,
6669 __isl_take isl_set *context);
6670 __isl_give isl_pw_qpolynomial_fold *
6671 isl_pw_qpolynomial_fold_gist(
6672 __isl_take isl_pw_qpolynomial_fold *pwf,
6673 __isl_take isl_set *context);
6674 __isl_give isl_pw_qpolynomial_fold *
6675 isl_pw_qpolynomial_fold_gist_params(
6676 __isl_take isl_pw_qpolynomial_fold *pwf,
6677 __isl_take isl_set *context);
6678 __isl_give isl_union_pw_qpolynomial *
6679 isl_union_pw_qpolynomial_gist_params(
6680 __isl_take isl_union_pw_qpolynomial *upwqp,
6681 __isl_take isl_set *context);
6682 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6683 __isl_take isl_union_pw_qpolynomial *upwqp,
6684 __isl_take isl_union_set *context);
6685 __isl_give isl_union_pw_qpolynomial_fold *
6686 isl_union_pw_qpolynomial_fold_gist(
6687 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6688 __isl_take isl_union_set *context);
6689 __isl_give isl_union_pw_qpolynomial_fold *
6690 isl_union_pw_qpolynomial_fold_gist_params(
6691 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6692 __isl_take isl_set *context);
6694 =item * Binary Arithmetic Operations
6696 #include <isl/set.h>
6697 __isl_give isl_set *isl_set_sum(
6698 __isl_take isl_set *set1,
6699 __isl_take isl_set *set2);
6700 #include <isl/map.h>
6701 __isl_give isl_map *isl_map_sum(
6702 __isl_take isl_map *map1,
6703 __isl_take isl_map *map2);
6705 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6706 i.e., the set containing the sums of pairs of elements from
6707 C<set1> and C<set2>.
6708 The domain of the result of C<isl_map_sum> is the intersection
6709 of the domains of its two arguments. The corresponding range
6710 elements are the sums of the corresponding range elements
6711 in the two arguments.
6713 #include <isl/val.h>
6714 __isl_give isl_multi_val *isl_multi_val_add(
6715 __isl_take isl_multi_val *mv1,
6716 __isl_take isl_multi_val *mv2);
6717 __isl_give isl_multi_val *isl_multi_val_sub(
6718 __isl_take isl_multi_val *mv1,
6719 __isl_take isl_multi_val *mv2);
6721 #include <isl/aff.h>
6722 __isl_give isl_aff *isl_aff_add(
6723 __isl_take isl_aff *aff1,
6724 __isl_take isl_aff *aff2);
6725 __isl_give isl_multi_aff *isl_multi_aff_add(
6726 __isl_take isl_multi_aff *maff1,
6727 __isl_take isl_multi_aff *maff2);
6728 __isl_give isl_pw_aff *isl_pw_aff_add(
6729 __isl_take isl_pw_aff *pwaff1,
6730 __isl_take isl_pw_aff *pwaff2);
6731 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6732 __isl_take isl_multi_pw_aff *mpa1,
6733 __isl_take isl_multi_pw_aff *mpa2);
6734 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6735 __isl_take isl_pw_multi_aff *pma1,
6736 __isl_take isl_pw_multi_aff *pma2);
6737 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6738 __isl_take isl_union_pw_aff *upa1,
6739 __isl_take isl_union_pw_aff *upa2);
6740 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6741 __isl_take isl_union_pw_multi_aff *upma1,
6742 __isl_take isl_union_pw_multi_aff *upma2);
6743 __isl_give isl_multi_union_pw_aff *
6744 isl_multi_union_pw_aff_add(
6745 __isl_take isl_multi_union_pw_aff *mupa1,
6746 __isl_take isl_multi_union_pw_aff *mupa2);
6747 __isl_give isl_pw_aff *isl_pw_aff_min(
6748 __isl_take isl_pw_aff *pwaff1,
6749 __isl_take isl_pw_aff *pwaff2);
6750 __isl_give isl_pw_aff *isl_pw_aff_max(
6751 __isl_take isl_pw_aff *pwaff1,
6752 __isl_take isl_pw_aff *pwaff2);
6753 __isl_give isl_aff *isl_aff_sub(
6754 __isl_take isl_aff *aff1,
6755 __isl_take isl_aff *aff2);
6756 __isl_give isl_multi_aff *isl_multi_aff_sub(
6757 __isl_take isl_multi_aff *ma1,
6758 __isl_take isl_multi_aff *ma2);
6759 __isl_give isl_pw_aff *isl_pw_aff_sub(
6760 __isl_take isl_pw_aff *pwaff1,
6761 __isl_take isl_pw_aff *pwaff2);
6762 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6763 __isl_take isl_multi_pw_aff *mpa1,
6764 __isl_take isl_multi_pw_aff *mpa2);
6765 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6766 __isl_take isl_pw_multi_aff *pma1,
6767 __isl_take isl_pw_multi_aff *pma2);
6768 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6769 __isl_take isl_union_pw_aff *upa1,
6770 __isl_take isl_union_pw_aff *upa2);
6771 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6772 __isl_take isl_union_pw_multi_aff *upma1,
6773 __isl_take isl_union_pw_multi_aff *upma2);
6774 __isl_give isl_multi_union_pw_aff *
6775 isl_multi_union_pw_aff_sub(
6776 __isl_take isl_multi_union_pw_aff *mupa1,
6777 __isl_take isl_multi_union_pw_aff *mupa2);
6779 C<isl_aff_sub> subtracts the second argument from the first.
6781 #include <isl/polynomial.h>
6782 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6783 __isl_take isl_qpolynomial *qp1,
6784 __isl_take isl_qpolynomial *qp2);
6785 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6786 __isl_take isl_pw_qpolynomial *pwqp1,
6787 __isl_take isl_pw_qpolynomial *pwqp2);
6788 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6789 __isl_take isl_pw_qpolynomial *pwqp1,
6790 __isl_take isl_pw_qpolynomial *pwqp2);
6791 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6792 __isl_take isl_pw_qpolynomial_fold *pwf1,
6793 __isl_take isl_pw_qpolynomial_fold *pwf2);
6794 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6795 __isl_take isl_union_pw_qpolynomial *upwqp1,
6796 __isl_take isl_union_pw_qpolynomial *upwqp2);
6797 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6798 __isl_take isl_qpolynomial *qp1,
6799 __isl_take isl_qpolynomial *qp2);
6800 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6801 __isl_take isl_pw_qpolynomial *pwqp1,
6802 __isl_take isl_pw_qpolynomial *pwqp2);
6803 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6804 __isl_take isl_union_pw_qpolynomial *upwqp1,
6805 __isl_take isl_union_pw_qpolynomial *upwqp2);
6806 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6807 __isl_take isl_pw_qpolynomial_fold *pwf1,
6808 __isl_take isl_pw_qpolynomial_fold *pwf2);
6809 __isl_give isl_union_pw_qpolynomial_fold *
6810 isl_union_pw_qpolynomial_fold_fold(
6811 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6812 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6814 #include <isl/aff.h>
6815 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6816 __isl_take isl_pw_aff *pwaff1,
6817 __isl_take isl_pw_aff *pwaff2);
6818 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6819 __isl_take isl_pw_multi_aff *pma1,
6820 __isl_take isl_pw_multi_aff *pma2);
6821 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6822 __isl_take isl_union_pw_aff *upa1,
6823 __isl_take isl_union_pw_aff *upa2);
6824 __isl_give isl_union_pw_multi_aff *
6825 isl_union_pw_multi_aff_union_add(
6826 __isl_take isl_union_pw_multi_aff *upma1,
6827 __isl_take isl_union_pw_multi_aff *upma2);
6828 __isl_give isl_multi_union_pw_aff *
6829 isl_multi_union_pw_aff_union_add(
6830 __isl_take isl_multi_union_pw_aff *mupa1,
6831 __isl_take isl_multi_union_pw_aff *mupa2);
6832 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6833 __isl_take isl_pw_aff *pwaff1,
6834 __isl_take isl_pw_aff *pwaff2);
6835 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6836 __isl_take isl_pw_aff *pwaff1,
6837 __isl_take isl_pw_aff *pwaff2);
6839 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6840 expression with a domain that is the union of those of C<pwaff1> and
6841 C<pwaff2> and such that on each cell, the quasi-affine expression is
6842 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6843 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6844 associated expression is the defined one.
6845 This in contrast to the C<isl_pw_aff_max> function, which is
6846 only defined on the shared definition domain of the arguments.
6848 #include <isl/val.h>
6849 __isl_give isl_multi_val *isl_multi_val_add_val(
6850 __isl_take isl_multi_val *mv,
6851 __isl_take isl_val *v);
6852 __isl_give isl_multi_val *isl_multi_val_mod_val(
6853 __isl_take isl_multi_val *mv,
6854 __isl_take isl_val *v);
6855 __isl_give isl_multi_val *isl_multi_val_scale_val(
6856 __isl_take isl_multi_val *mv,
6857 __isl_take isl_val *v);
6858 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6859 __isl_take isl_multi_val *mv,
6860 __isl_take isl_val *v);
6862 #include <isl/aff.h>
6863 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6864 __isl_take isl_val *mod);
6865 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6866 __isl_take isl_pw_aff *pa,
6867 __isl_take isl_val *mod);
6868 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6869 __isl_take isl_union_pw_aff *upa,
6870 __isl_take isl_val *f);
6871 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6872 __isl_take isl_val *v);
6873 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6874 __isl_take isl_multi_aff *ma,
6875 __isl_take isl_val *v);
6876 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6877 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6878 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6879 __isl_take isl_multi_pw_aff *mpa,
6880 __isl_take isl_val *v);
6881 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6882 __isl_take isl_pw_multi_aff *pma,
6883 __isl_take isl_val *v);
6884 __isl_give isl_union_pw_multi_aff *
6885 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6886 __isl_take isl_union_pw_aff *upa,
6887 __isl_take isl_val *f);
6888 isl_union_pw_multi_aff_scale_val(
6889 __isl_take isl_union_pw_multi_aff *upma,
6890 __isl_take isl_val *val);
6891 __isl_give isl_multi_union_pw_aff *
6892 isl_multi_union_pw_aff_scale_val(
6893 __isl_take isl_multi_union_pw_aff *mupa,
6894 __isl_take isl_val *v);
6895 __isl_give isl_aff *isl_aff_scale_down_ui(
6896 __isl_take isl_aff *aff, unsigned f);
6897 __isl_give isl_aff *isl_aff_scale_down_val(
6898 __isl_take isl_aff *aff, __isl_take isl_val *v);
6899 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6900 __isl_take isl_multi_aff *ma,
6901 __isl_take isl_val *v);
6902 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6903 __isl_take isl_pw_aff *pa,
6904 __isl_take isl_val *f);
6905 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6906 __isl_take isl_multi_pw_aff *mpa,
6907 __isl_take isl_val *v);
6908 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6909 __isl_take isl_pw_multi_aff *pma,
6910 __isl_take isl_val *v);
6911 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6912 __isl_take isl_union_pw_aff *upa,
6913 __isl_take isl_val *v);
6914 __isl_give isl_union_pw_multi_aff *
6915 isl_union_pw_multi_aff_scale_down_val(
6916 __isl_take isl_union_pw_multi_aff *upma,
6917 __isl_take isl_val *val);
6918 __isl_give isl_multi_union_pw_aff *
6919 isl_multi_union_pw_aff_scale_down_val(
6920 __isl_take isl_multi_union_pw_aff *mupa,
6921 __isl_take isl_val *v);
6923 #include <isl/polynomial.h>
6924 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6925 __isl_take isl_qpolynomial *qp,
6926 __isl_take isl_val *v);
6927 __isl_give isl_qpolynomial_fold *
6928 isl_qpolynomial_fold_scale_val(
6929 __isl_take isl_qpolynomial_fold *fold,
6930 __isl_take isl_val *v);
6931 __isl_give isl_pw_qpolynomial *
6932 isl_pw_qpolynomial_scale_val(
6933 __isl_take isl_pw_qpolynomial *pwqp,
6934 __isl_take isl_val *v);
6935 __isl_give isl_pw_qpolynomial_fold *
6936 isl_pw_qpolynomial_fold_scale_val(
6937 __isl_take isl_pw_qpolynomial_fold *pwf,
6938 __isl_take isl_val *v);
6939 __isl_give isl_union_pw_qpolynomial *
6940 isl_union_pw_qpolynomial_scale_val(
6941 __isl_take isl_union_pw_qpolynomial *upwqp,
6942 __isl_take isl_val *v);
6943 __isl_give isl_union_pw_qpolynomial_fold *
6944 isl_union_pw_qpolynomial_fold_scale_val(
6945 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6946 __isl_take isl_val *v);
6947 __isl_give isl_qpolynomial *
6948 isl_qpolynomial_scale_down_val(
6949 __isl_take isl_qpolynomial *qp,
6950 __isl_take isl_val *v);
6951 __isl_give isl_qpolynomial_fold *
6952 isl_qpolynomial_fold_scale_down_val(
6953 __isl_take isl_qpolynomial_fold *fold,
6954 __isl_take isl_val *v);
6955 __isl_give isl_pw_qpolynomial *
6956 isl_pw_qpolynomial_scale_down_val(
6957 __isl_take isl_pw_qpolynomial *pwqp,
6958 __isl_take isl_val *v);
6959 __isl_give isl_pw_qpolynomial_fold *
6960 isl_pw_qpolynomial_fold_scale_down_val(
6961 __isl_take isl_pw_qpolynomial_fold *pwf,
6962 __isl_take isl_val *v);
6963 __isl_give isl_union_pw_qpolynomial *
6964 isl_union_pw_qpolynomial_scale_down_val(
6965 __isl_take isl_union_pw_qpolynomial *upwqp,
6966 __isl_take isl_val *v);
6967 __isl_give isl_union_pw_qpolynomial_fold *
6968 isl_union_pw_qpolynomial_fold_scale_down_val(
6969 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6970 __isl_take isl_val *v);
6972 #include <isl/val.h>
6973 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6974 __isl_take isl_multi_val *mv1,
6975 __isl_take isl_multi_val *mv2);
6976 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6977 __isl_take isl_multi_val *mv1,
6978 __isl_take isl_multi_val *mv2);
6979 __isl_give isl_multi_val *
6980 isl_multi_val_scale_down_multi_val(
6981 __isl_take isl_multi_val *mv1,
6982 __isl_take isl_multi_val *mv2);
6984 #include <isl/aff.h>
6985 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6986 __isl_take isl_multi_aff *ma,
6987 __isl_take isl_multi_val *mv);
6988 __isl_give isl_multi_union_pw_aff *
6989 isl_multi_union_pw_aff_mod_multi_val(
6990 __isl_take isl_multi_union_pw_aff *upma,
6991 __isl_take isl_multi_val *mv);
6992 __isl_give isl_multi_pw_aff *
6993 isl_multi_pw_aff_mod_multi_val(
6994 __isl_take isl_multi_pw_aff *mpa,
6995 __isl_take isl_multi_val *mv);
6996 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6997 __isl_take isl_multi_aff *ma,
6998 __isl_take isl_multi_val *mv);
6999 __isl_give isl_pw_multi_aff *
7000 isl_pw_multi_aff_scale_multi_val(
7001 __isl_take isl_pw_multi_aff *pma,
7002 __isl_take isl_multi_val *mv);
7003 __isl_give isl_multi_pw_aff *
7004 isl_multi_pw_aff_scale_multi_val(
7005 __isl_take isl_multi_pw_aff *mpa,
7006 __isl_take isl_multi_val *mv);
7007 __isl_give isl_multi_union_pw_aff *
7008 isl_multi_union_pw_aff_scale_multi_val(
7009 __isl_take isl_multi_union_pw_aff *mupa,
7010 __isl_take isl_multi_val *mv);
7011 __isl_give isl_union_pw_multi_aff *
7012 isl_union_pw_multi_aff_scale_multi_val(
7013 __isl_take isl_union_pw_multi_aff *upma,
7014 __isl_take isl_multi_val *mv);
7015 __isl_give isl_multi_aff *
7016 isl_multi_aff_scale_down_multi_val(
7017 __isl_take isl_multi_aff *ma,
7018 __isl_take isl_multi_val *mv);
7019 __isl_give isl_multi_pw_aff *
7020 isl_multi_pw_aff_scale_down_multi_val(
7021 __isl_take isl_multi_pw_aff *mpa,
7022 __isl_take isl_multi_val *mv);
7023 __isl_give isl_multi_union_pw_aff *
7024 isl_multi_union_pw_aff_scale_down_multi_val(
7025 __isl_take isl_multi_union_pw_aff *mupa,
7026 __isl_take isl_multi_val *mv);
7028 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7029 by the corresponding elements of C<mv>.
7031 #include <isl/aff.h>
7032 __isl_give isl_aff *isl_aff_mul(
7033 __isl_take isl_aff *aff1,
7034 __isl_take isl_aff *aff2);
7035 __isl_give isl_aff *isl_aff_div(
7036 __isl_take isl_aff *aff1,
7037 __isl_take isl_aff *aff2);
7038 __isl_give isl_pw_aff *isl_pw_aff_mul(
7039 __isl_take isl_pw_aff *pwaff1,
7040 __isl_take isl_pw_aff *pwaff2);
7041 __isl_give isl_pw_aff *isl_pw_aff_div(
7042 __isl_take isl_pw_aff *pa1,
7043 __isl_take isl_pw_aff *pa2);
7044 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7045 __isl_take isl_pw_aff *pa1,
7046 __isl_take isl_pw_aff *pa2);
7047 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7048 __isl_take isl_pw_aff *pa1,
7049 __isl_take isl_pw_aff *pa2);
7051 When multiplying two affine expressions, at least one of the two needs
7052 to be a constant. Similarly, when dividing an affine expression by another,
7053 the second expression needs to be a constant.
7054 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7055 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7058 #include <isl/polynomial.h>
7059 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7060 __isl_take isl_qpolynomial *qp1,
7061 __isl_take isl_qpolynomial *qp2);
7062 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7063 __isl_take isl_pw_qpolynomial *pwqp1,
7064 __isl_take isl_pw_qpolynomial *pwqp2);
7065 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7066 __isl_take isl_union_pw_qpolynomial *upwqp1,
7067 __isl_take isl_union_pw_qpolynomial *upwqp2);
7071 =head3 Lexicographic Optimization
7073 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7074 the following functions
7075 compute a set that contains the lexicographic minimum or maximum
7076 of the elements in C<set> (or C<bset>) for those values of the parameters
7077 that satisfy C<dom>.
7078 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7079 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7081 In other words, the union of the parameter values
7082 for which the result is non-empty and of C<*empty>
7085 #include <isl/set.h>
7086 __isl_give isl_set *isl_basic_set_partial_lexmin(
7087 __isl_take isl_basic_set *bset,
7088 __isl_take isl_basic_set *dom,
7089 __isl_give isl_set **empty);
7090 __isl_give isl_set *isl_basic_set_partial_lexmax(
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_set_partial_lexmin(
7095 __isl_take isl_set *set, __isl_take isl_set *dom,
7096 __isl_give isl_set **empty);
7097 __isl_give isl_set *isl_set_partial_lexmax(
7098 __isl_take isl_set *set, __isl_take isl_set *dom,
7099 __isl_give isl_set **empty);
7101 Given a (basic) set C<set> (or C<bset>), the following functions simply
7102 return a set containing the lexicographic minimum or maximum
7103 of the elements in C<set> (or C<bset>).
7104 In case of union sets, the optimum is computed per space.
7106 #include <isl/set.h>
7107 __isl_give isl_set *isl_basic_set_lexmin(
7108 __isl_take isl_basic_set *bset);
7109 __isl_give isl_set *isl_basic_set_lexmax(
7110 __isl_take isl_basic_set *bset);
7111 __isl_give isl_set *isl_set_lexmin(
7112 __isl_take isl_set *set);
7113 __isl_give isl_set *isl_set_lexmax(
7114 __isl_take isl_set *set);
7115 __isl_give isl_union_set *isl_union_set_lexmin(
7116 __isl_take isl_union_set *uset);
7117 __isl_give isl_union_set *isl_union_set_lexmax(
7118 __isl_take isl_union_set *uset);
7120 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7121 the following functions
7122 compute a relation that maps each element of C<dom>
7123 to the single lexicographic minimum or maximum
7124 of the elements that are associated to that same
7125 element in C<map> (or C<bmap>).
7126 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7127 that contains the elements in C<dom> that do not map
7128 to any elements in C<map> (or C<bmap>).
7129 In other words, the union of the domain of the result and of C<*empty>
7132 #include <isl/map.h>
7133 __isl_give isl_map *isl_basic_map_partial_lexmax(
7134 __isl_take isl_basic_map *bmap,
7135 __isl_take isl_basic_set *dom,
7136 __isl_give isl_set **empty);
7137 __isl_give isl_map *isl_basic_map_partial_lexmin(
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_map_partial_lexmax(
7142 __isl_take isl_map *map, __isl_take isl_set *dom,
7143 __isl_give isl_set **empty);
7144 __isl_give isl_map *isl_map_partial_lexmin(
7145 __isl_take isl_map *map, __isl_take isl_set *dom,
7146 __isl_give isl_set **empty);
7148 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7149 return a map mapping each element in the domain of
7150 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7151 of all elements associated to that element.
7152 In case of union relations, the optimum is computed per space.
7154 #include <isl/map.h>
7155 __isl_give isl_map *isl_basic_map_lexmin(
7156 __isl_take isl_basic_map *bmap);
7157 __isl_give isl_map *isl_basic_map_lexmax(
7158 __isl_take isl_basic_map *bmap);
7159 __isl_give isl_map *isl_map_lexmin(
7160 __isl_take isl_map *map);
7161 __isl_give isl_map *isl_map_lexmax(
7162 __isl_take isl_map *map);
7163 __isl_give isl_union_map *isl_union_map_lexmin(
7164 __isl_take isl_union_map *umap);
7165 __isl_give isl_union_map *isl_union_map_lexmax(
7166 __isl_take isl_union_map *umap);
7168 The following functions return their result in the form of
7169 a piecewise multi-affine expression,
7170 but are otherwise equivalent to the corresponding functions
7171 returning a basic set or relation.
7173 #include <isl/set.h>
7174 __isl_give isl_pw_multi_aff *
7175 isl_basic_set_partial_lexmin_pw_multi_aff(
7176 __isl_take isl_basic_set *bset,
7177 __isl_take isl_basic_set *dom,
7178 __isl_give isl_set **empty);
7179 __isl_give isl_pw_multi_aff *
7180 isl_basic_set_partial_lexmax_pw_multi_aff(
7181 __isl_take isl_basic_set *bset,
7182 __isl_take isl_basic_set *dom,
7183 __isl_give isl_set **empty);
7184 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7185 __isl_take isl_set *set);
7186 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7187 __isl_take isl_set *set);
7189 #include <isl/map.h>
7190 __isl_give isl_pw_multi_aff *
7191 isl_basic_map_lexmin_pw_multi_aff(
7192 __isl_take isl_basic_map *bmap);
7193 __isl_give isl_pw_multi_aff *
7194 isl_basic_map_partial_lexmin_pw_multi_aff(
7195 __isl_take isl_basic_map *bmap,
7196 __isl_take isl_basic_set *dom,
7197 __isl_give isl_set **empty);
7198 __isl_give isl_pw_multi_aff *
7199 isl_basic_map_partial_lexmax_pw_multi_aff(
7200 __isl_take isl_basic_map *bmap,
7201 __isl_take isl_basic_set *dom,
7202 __isl_give isl_set **empty);
7203 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7204 __isl_take isl_map *map);
7205 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7206 __isl_take isl_map *map);
7208 The following functions return the lexicographic minimum or maximum
7209 on the shared domain of the inputs and the single defined function
7210 on those parts of the domain where only a single function is defined.
7212 #include <isl/aff.h>
7213 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7214 __isl_take isl_pw_multi_aff *pma1,
7215 __isl_take isl_pw_multi_aff *pma2);
7216 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7217 __isl_take isl_pw_multi_aff *pma1,
7218 __isl_take isl_pw_multi_aff *pma2);
7220 =head2 Ternary Operations
7222 #include <isl/aff.h>
7223 __isl_give isl_pw_aff *isl_pw_aff_cond(
7224 __isl_take isl_pw_aff *cond,
7225 __isl_take isl_pw_aff *pwaff_true,
7226 __isl_take isl_pw_aff *pwaff_false);
7228 The function C<isl_pw_aff_cond> performs a conditional operator
7229 and returns an expression that is equal to C<pwaff_true>
7230 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7231 where C<cond> is zero.
7235 Lists are defined over several element types, including
7236 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7237 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7238 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7239 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7240 Here we take lists of C<isl_set>s as an example.
7241 Lists can be created, copied, modified and freed using the following functions.
7243 #include <isl/set.h>
7244 __isl_give isl_set_list *isl_set_list_from_set(
7245 __isl_take isl_set *el);
7246 __isl_give isl_set_list *isl_set_list_alloc(
7247 isl_ctx *ctx, int n);
7248 __isl_give isl_set_list *isl_set_list_copy(
7249 __isl_keep isl_set_list *list);
7250 __isl_give isl_set_list *isl_set_list_insert(
7251 __isl_take isl_set_list *list, unsigned pos,
7252 __isl_take isl_set *el);
7253 __isl_give isl_set_list *isl_set_list_add(
7254 __isl_take isl_set_list *list,
7255 __isl_take isl_set *el);
7256 __isl_give isl_set_list *isl_set_list_drop(
7257 __isl_take isl_set_list *list,
7258 unsigned first, unsigned n);
7259 __isl_give isl_set_list *isl_set_list_set_set(
7260 __isl_take isl_set_list *list, int index,
7261 __isl_take isl_set *set);
7262 __isl_give isl_set_list *isl_set_list_concat(
7263 __isl_take isl_set_list *list1,
7264 __isl_take isl_set_list *list2);
7265 __isl_give isl_set_list *isl_set_list_sort(
7266 __isl_take isl_set_list *list,
7267 int (*cmp)(__isl_keep isl_set *a,
7268 __isl_keep isl_set *b, void *user),
7270 __isl_null isl_set_list *isl_set_list_free(
7271 __isl_take isl_set_list *list);
7273 C<isl_set_list_alloc> creates an empty list with an initial capacity
7274 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7275 add elements to a list, increasing its capacity as needed.
7276 C<isl_set_list_from_set> creates a list with a single element.
7278 Lists can be inspected using the following functions.
7280 #include <isl/set.h>
7281 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7282 __isl_give isl_set *isl_set_list_get_set(
7283 __isl_keep isl_set_list *list, int index);
7284 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7285 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7287 isl_stat isl_set_list_foreach_scc(
7288 __isl_keep isl_set_list *list,
7289 isl_bool (*follows)(__isl_keep isl_set *a,
7290 __isl_keep isl_set *b, void *user),
7292 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7295 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7296 strongly connected components of the graph with as vertices the elements
7297 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7298 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
7299 should return C<-1> on error.
7301 Lists can be printed using
7303 #include <isl/set.h>
7304 __isl_give isl_printer *isl_printer_print_set_list(
7305 __isl_take isl_printer *p,
7306 __isl_keep isl_set_list *list);
7308 =head2 Associative arrays
7310 Associative arrays map isl objects of a specific type to isl objects
7311 of some (other) specific type. They are defined for several pairs
7312 of types, including (C<isl_map>, C<isl_basic_set>),
7313 (C<isl_id>, C<isl_ast_expr>),
7314 (C<isl_id>, C<isl_id>) and
7315 (C<isl_id>, C<isl_pw_aff>).
7316 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7319 Associative arrays can be created, copied and freed using
7320 the following functions.
7322 #include <isl/id_to_ast_expr.h>
7323 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7324 isl_ctx *ctx, int min_size);
7325 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7326 __isl_keep isl_id_to_ast_expr *id2expr);
7327 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7328 __isl_take isl_id_to_ast_expr *id2expr);
7330 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7331 to specify the expected size of the associative array.
7332 The associative array will be grown automatically as needed.
7334 Associative arrays can be inspected using the following functions.
7336 #include <isl/id_to_ast_expr.h>
7337 __isl_give isl_maybe_isl_ast_expr
7338 isl_id_to_ast_expr_try_get(
7339 __isl_keep isl_id_to_ast_expr *id2expr,
7340 __isl_keep isl_id *key);
7341 isl_bool isl_id_to_ast_expr_has(
7342 __isl_keep isl_id_to_ast_expr *id2expr,
7343 __isl_keep isl_id *key);
7344 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7345 __isl_keep isl_id_to_ast_expr *id2expr,
7346 __isl_take isl_id *key);
7347 isl_stat isl_id_to_ast_expr_foreach(
7348 __isl_keep isl_id_to_ast_expr *id2expr,
7349 isl_stat (*fn)(__isl_take isl_id *key,
7350 __isl_take isl_ast_expr *val, void *user),
7353 The function C<isl_id_to_ast_expr_try_get> returns a structure
7354 containing two elements, C<valid> and C<value>.
7355 If there is a value associated to the key, then C<valid>
7356 is set to C<isl_bool_true> and C<value> contains a copy of
7357 the associated value. Otherwise C<value> is C<NULL> and
7358 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7359 on whether some error has occurred or there simply is no associated value.
7360 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7361 in the structure and
7362 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7364 Associative arrays can be modified using the following functions.
7366 #include <isl/id_to_ast_expr.h>
7367 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7368 __isl_take isl_id_to_ast_expr *id2expr,
7369 __isl_take isl_id *key,
7370 __isl_take isl_ast_expr *val);
7371 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7372 __isl_take isl_id_to_ast_expr *id2expr,
7373 __isl_take isl_id *key);
7375 Associative arrays can be printed using the following function.
7377 #include <isl/id_to_ast_expr.h>
7378 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7379 __isl_take isl_printer *p,
7380 __isl_keep isl_id_to_ast_expr *id2expr);
7384 Vectors can be created, copied and freed using the following functions.
7386 #include <isl/vec.h>
7387 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7389 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7390 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7392 Note that the elements of a newly created vector may have arbitrary values.
7393 The elements can be changed and inspected using the following functions.
7395 int isl_vec_size(__isl_keep isl_vec *vec);
7396 __isl_give isl_val *isl_vec_get_element_val(
7397 __isl_keep isl_vec *vec, int pos);
7398 __isl_give isl_vec *isl_vec_set_element_si(
7399 __isl_take isl_vec *vec, int pos, int v);
7400 __isl_give isl_vec *isl_vec_set_element_val(
7401 __isl_take isl_vec *vec, int pos,
7402 __isl_take isl_val *v);
7403 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7405 __isl_give isl_vec *isl_vec_set_val(
7406 __isl_take isl_vec *vec, __isl_take isl_val *v);
7407 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7408 __isl_keep isl_vec *vec2, int pos);
7410 C<isl_vec_get_element> will return a negative value if anything went wrong.
7411 In that case, the value of C<*v> is undefined.
7413 The following function can be used to concatenate two vectors.
7415 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7416 __isl_take isl_vec *vec2);
7420 Matrices can be created, copied and freed using the following functions.
7422 #include <isl/mat.h>
7423 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7424 unsigned n_row, unsigned n_col);
7425 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7426 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7428 Note that the elements of a newly created matrix may have arbitrary values.
7429 The elements can be changed and inspected using the following functions.
7431 int isl_mat_rows(__isl_keep isl_mat *mat);
7432 int isl_mat_cols(__isl_keep isl_mat *mat);
7433 __isl_give isl_val *isl_mat_get_element_val(
7434 __isl_keep isl_mat *mat, int row, int col);
7435 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7436 int row, int col, int v);
7437 __isl_give isl_mat *isl_mat_set_element_val(
7438 __isl_take isl_mat *mat, int row, int col,
7439 __isl_take isl_val *v);
7441 C<isl_mat_get_element> will return a negative value if anything went wrong.
7442 In that case, the value of C<*v> is undefined.
7444 The following function can be used to compute the (right) inverse
7445 of a matrix, i.e., a matrix such that the product of the original
7446 and the inverse (in that order) is a multiple of the identity matrix.
7447 The input matrix is assumed to be of full row-rank.
7449 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7451 The following function can be used to compute the (right) kernel
7452 (or null space) of a matrix, i.e., a matrix such that the product of
7453 the original and the kernel (in that order) is the zero matrix.
7455 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7457 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7459 The following functions determine
7460 an upper or lower bound on a quasipolynomial over its domain.
7462 __isl_give isl_pw_qpolynomial_fold *
7463 isl_pw_qpolynomial_bound(
7464 __isl_take isl_pw_qpolynomial *pwqp,
7465 enum isl_fold type, int *tight);
7467 __isl_give isl_union_pw_qpolynomial_fold *
7468 isl_union_pw_qpolynomial_bound(
7469 __isl_take isl_union_pw_qpolynomial *upwqp,
7470 enum isl_fold type, int *tight);
7472 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7473 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7474 is the returned bound is known be tight, i.e., for each value
7475 of the parameters there is at least
7476 one element in the domain that reaches the bound.
7477 If the domain of C<pwqp> is not wrapping, then the bound is computed
7478 over all elements in that domain and the result has a purely parametric
7479 domain. If the domain of C<pwqp> is wrapping, then the bound is
7480 computed over the range of the wrapped relation. The domain of the
7481 wrapped relation becomes the domain of the result.
7483 =head2 Parametric Vertex Enumeration
7485 The parametric vertex enumeration described in this section
7486 is mainly intended to be used internally and by the C<barvinok>
7489 #include <isl/vertices.h>
7490 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7491 __isl_keep isl_basic_set *bset);
7493 The function C<isl_basic_set_compute_vertices> performs the
7494 actual computation of the parametric vertices and the chamber
7495 decomposition and store the result in an C<isl_vertices> object.
7496 This information can be queried by either iterating over all
7497 the vertices or iterating over all the chambers or cells
7498 and then iterating over all vertices that are active on the chamber.
7500 isl_stat isl_vertices_foreach_vertex(
7501 __isl_keep isl_vertices *vertices,
7502 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7503 void *user), void *user);
7505 isl_stat isl_vertices_foreach_cell(
7506 __isl_keep isl_vertices *vertices,
7507 isl_stat (*fn)(__isl_take isl_cell *cell,
7508 void *user), void *user);
7509 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7510 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7511 void *user), void *user);
7513 Other operations that can be performed on an C<isl_vertices> object are
7516 int isl_vertices_get_n_vertices(
7517 __isl_keep isl_vertices *vertices);
7518 void isl_vertices_free(__isl_take isl_vertices *vertices);
7520 Vertices can be inspected and destroyed using the following functions.
7522 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7523 __isl_give isl_basic_set *isl_vertex_get_domain(
7524 __isl_keep isl_vertex *vertex);
7525 __isl_give isl_multi_aff *isl_vertex_get_expr(
7526 __isl_keep isl_vertex *vertex);
7527 void isl_vertex_free(__isl_take isl_vertex *vertex);
7529 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7530 describing the vertex in terms of the parameters,
7531 while C<isl_vertex_get_domain> returns the activity domain
7534 Chambers can be inspected and destroyed using the following functions.
7536 __isl_give isl_basic_set *isl_cell_get_domain(
7537 __isl_keep isl_cell *cell);
7538 void isl_cell_free(__isl_take isl_cell *cell);
7540 =head1 Polyhedral Compilation Library
7542 This section collects functionality in C<isl> that has been specifically
7543 designed for use during polyhedral compilation.
7545 =head2 Schedule Trees
7547 A schedule tree is a structured representation of a schedule,
7548 assigning a relative order to a set of domain elements.
7549 The relative order expressed by the schedule tree is
7550 defined recursively. In particular, the order between
7551 two domain elements is determined by the node that is closest
7552 to the root that refers to both elements and that orders them apart.
7553 Each node in the tree is of one of several types.
7554 The root node is always of type C<isl_schedule_node_domain>
7555 (or C<isl_schedule_node_extension>)
7556 and it describes the (extra) domain elements to which the schedule applies.
7557 The other types of nodes are as follows.
7561 =item C<isl_schedule_node_band>
7563 A band of schedule dimensions. Each schedule dimension is represented
7564 by a union piecewise quasi-affine expression. If this expression
7565 assigns a different value to two domain elements, while all previous
7566 schedule dimensions in the same band assign them the same value,
7567 then the two domain elements are ordered according to these two
7569 Each expression is required to be total in the domain elements
7570 that reach the band node.
7572 =item C<isl_schedule_node_expansion>
7574 An expansion node maps each of the domain elements that reach the node
7575 to one or more domain elements. The image of this mapping forms
7576 the set of domain elements that reach the child of the expansion node.
7577 The function that maps each of the expanded domain elements
7578 to the original domain element from which it was expanded
7579 is called the contraction.
7581 =item C<isl_schedule_node_filter>
7583 A filter node does not impose any ordering, but rather intersects
7584 the set of domain elements that the current subtree refers to
7585 with a given union set. The subtree of the filter node only
7586 refers to domain elements in the intersection.
7587 A filter node is typically only used a child of a sequence or
7590 =item C<isl_schedule_node_leaf>
7592 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7594 =item C<isl_schedule_node_mark>
7596 A mark node can be used to attach any kind of information to a subtree
7597 of the schedule tree.
7599 =item C<isl_schedule_node_sequence>
7601 A sequence node has one or more children, each of which is a filter node.
7602 The filters on these filter nodes form a partition of
7603 the domain elements that the current subtree refers to.
7604 If two domain elements appear in distinct filters then the sequence
7605 node orders them according to the child positions of the corresponding
7608 =item C<isl_schedule_node_set>
7610 A set node is similar to a sequence node, except that
7611 it expresses that domain elements appearing in distinct filters
7612 may have any order. The order of the children of a set node
7613 is therefore also immaterial.
7617 The following node types are only supported by the AST generator.
7621 =item C<isl_schedule_node_context>
7623 The context describes constraints on the parameters and
7624 the schedule dimensions of outer
7625 bands that the AST generator may assume to hold. It is also the only
7626 kind of node that may introduce additional parameters.
7627 The space of the context is that of the flat product of the outer
7628 band nodes. In particular, if there are no outer band nodes, then
7629 this space is the unnamed zero-dimensional space.
7630 Since a context node references the outer band nodes, any tree
7631 containing a context node is considered to be anchored.
7633 =item C<isl_schedule_node_extension>
7635 An extension node instructs the AST generator to add additional
7636 domain elements that need to be scheduled.
7637 The additional domain elements are described by the range of
7638 the extension map in terms of the outer schedule dimensions,
7639 i.e., the flat product of the outer band nodes.
7640 Note that domain elements are added whenever the AST generator
7641 reaches the extension node, meaning that there are still some
7642 active domain elements for which an AST needs to be generated.
7643 The conditions under which some domain elements are still active
7644 may however not be completely described by the outer AST nodes
7645 generated at that point.
7647 An extension node may also appear as the root of a schedule tree,
7648 when it is intended to be inserted into another tree
7649 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7650 In this case, the domain of the extension node should
7651 correspond to the flat product of the outer band nodes
7652 in this other schedule tree at the point where the extension tree
7655 =item C<isl_schedule_node_guard>
7657 The guard describes constraints on the parameters and
7658 the schedule dimensions of outer
7659 bands that need to be enforced by the outer nodes
7660 in the generated AST.
7661 The space of the guard is that of the flat product of the outer
7662 band nodes. In particular, if there are no outer band nodes, then
7663 this space is the unnamed zero-dimensional space.
7664 Since a guard node references the outer band nodes, any tree
7665 containing a guard node is considered to be anchored.
7669 Except for the C<isl_schedule_node_context> nodes,
7670 none of the nodes may introduce any parameters that were not
7671 already present in the root domain node.
7673 A schedule tree is encapsulated in an C<isl_schedule> object.
7674 The simplest such objects, those with a tree consisting of single domain node,
7675 can be created using the following functions with either an empty
7676 domain or a given domain.
7678 #include <isl/schedule.h>
7679 __isl_give isl_schedule *isl_schedule_empty(
7680 __isl_take isl_space *space);
7681 __isl_give isl_schedule *isl_schedule_from_domain(
7682 __isl_take isl_union_set *domain);
7684 The function C<isl_schedule_constraints_compute_schedule> described
7685 in L</"Scheduling"> can also be used to construct schedules.
7687 C<isl_schedule> objects may be copied and freed using the following functions.
7689 #include <isl/schedule.h>
7690 __isl_give isl_schedule *isl_schedule_copy(
7691 __isl_keep isl_schedule *sched);
7692 __isl_null isl_schedule *isl_schedule_free(
7693 __isl_take isl_schedule *sched);
7695 The following functions checks whether two C<isl_schedule> objects
7696 are obviously the same.
7698 #include <isl/schedule.h>
7699 isl_bool isl_schedule_plain_is_equal(
7700 __isl_keep isl_schedule *schedule1,
7701 __isl_keep isl_schedule *schedule2);
7703 The domain of the schedule, i.e., the domain described by the root node,
7704 can be obtained using the following function.
7706 #include <isl/schedule.h>
7707 __isl_give isl_union_set *isl_schedule_get_domain(
7708 __isl_keep isl_schedule *schedule);
7710 An extra top-level band node (right underneath the domain node) can
7711 be introduced into the schedule using the following function.
7712 The schedule tree is assumed not to have any anchored nodes.
7714 #include <isl/schedule.h>
7715 __isl_give isl_schedule *
7716 isl_schedule_insert_partial_schedule(
7717 __isl_take isl_schedule *schedule,
7718 __isl_take isl_multi_union_pw_aff *partial);
7720 A top-level context node (right underneath the domain node) can
7721 be introduced into the schedule using the following function.
7723 #include <isl/schedule.h>
7724 __isl_give isl_schedule *isl_schedule_insert_context(
7725 __isl_take isl_schedule *schedule,
7726 __isl_take isl_set *context)
7728 A top-level guard node (right underneath the domain node) can
7729 be introduced into the schedule using the following function.
7731 #include <isl/schedule.h>
7732 __isl_give isl_schedule *isl_schedule_insert_guard(
7733 __isl_take isl_schedule *schedule,
7734 __isl_take isl_set *guard)
7736 A schedule that combines two schedules either in the given
7737 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7738 or an C<isl_schedule_node_set> node,
7739 can be created using the following functions.
7741 #include <isl/schedule.h>
7742 __isl_give isl_schedule *isl_schedule_sequence(
7743 __isl_take isl_schedule *schedule1,
7744 __isl_take isl_schedule *schedule2);
7745 __isl_give isl_schedule *isl_schedule_set(
7746 __isl_take isl_schedule *schedule1,
7747 __isl_take isl_schedule *schedule2);
7749 The domains of the two input schedules need to be disjoint.
7751 The following function can be used to restrict the domain
7752 of a schedule with a domain node as root to be a subset of the given union set.
7753 This operation may remove nodes in the tree that have become
7756 #include <isl/schedule.h>
7757 __isl_give isl_schedule *isl_schedule_intersect_domain(
7758 __isl_take isl_schedule *schedule,
7759 __isl_take isl_union_set *domain);
7761 The following function can be used to simplify the domain
7762 of a schedule with a domain node as root with respect to the given
7765 #include <isl/schedule.h>
7766 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7767 __isl_take isl_schedule *schedule,
7768 __isl_take isl_set *context);
7770 The following function resets the user pointers on all parameter
7771 and tuple identifiers referenced by the nodes of the given schedule.
7773 #include <isl/schedule.h>
7774 __isl_give isl_schedule *isl_schedule_reset_user(
7775 __isl_take isl_schedule *schedule);
7777 The following function aligns the parameters of all nodes
7778 in the given schedule to the given space.
7780 #include <isl/schedule.h>
7781 __isl_give isl_schedule *isl_schedule_align_params(
7782 __isl_take isl_schedule *schedule,
7783 __isl_take isl_space *space);
7785 The following function allows the user to plug in a given function
7786 in the iteration domains. The input schedule is not allowed to contain
7787 any expansion nodes.
7789 #include <isl/schedule.h>
7790 __isl_give isl_schedule *
7791 isl_schedule_pullback_union_pw_multi_aff(
7792 __isl_take isl_schedule *schedule,
7793 __isl_take isl_union_pw_multi_aff *upma);
7795 An C<isl_union_map> representation of the schedule can be obtained
7796 from an C<isl_schedule> using the following function.
7798 #include <isl/schedule.h>
7799 __isl_give isl_union_map *isl_schedule_get_map(
7800 __isl_keep isl_schedule *sched);
7802 The resulting relation encodes the same relative ordering as
7803 the schedule by mapping the domain elements to a common schedule space.
7804 If the schedule_separate_components option is set, then the order
7805 of the children of a set node is explicitly encoded in the result.
7806 If the tree contains any expansion nodes, then the relation
7807 is formulated in terms of the expanded domain elements.
7809 Schedules can be read from input using the following functions.
7811 #include <isl/schedule.h>
7812 __isl_give isl_schedule *isl_schedule_read_from_file(
7813 isl_ctx *ctx, FILE *input);
7814 __isl_give isl_schedule *isl_schedule_read_from_str(
7815 isl_ctx *ctx, const char *str);
7817 A representation of the schedule can be printed using
7819 #include <isl/schedule.h>
7820 __isl_give isl_printer *isl_printer_print_schedule(
7821 __isl_take isl_printer *p,
7822 __isl_keep isl_schedule *schedule);
7823 __isl_give char *isl_schedule_to_str(
7824 __isl_keep isl_schedule *schedule);
7826 C<isl_schedule_to_str> prints the schedule in flow format.
7828 The schedule tree can be traversed through the use of
7829 C<isl_schedule_node> objects that point to a particular
7830 position in the schedule tree. Whenever a C<isl_schedule_node>
7831 is use to modify a node in the schedule tree, the original schedule
7832 tree is left untouched and the modifications are performed to a copy
7833 of the tree. The returned C<isl_schedule_node> then points to
7834 this modified copy of the tree.
7836 The root of the schedule tree can be obtained using the following function.
7838 #include <isl/schedule.h>
7839 __isl_give isl_schedule_node *isl_schedule_get_root(
7840 __isl_keep isl_schedule *schedule);
7842 A pointer to a newly created schedule tree with a single domain
7843 node can be created using the following functions.
7845 #include <isl/schedule_node.h>
7846 __isl_give isl_schedule_node *
7847 isl_schedule_node_from_domain(
7848 __isl_take isl_union_set *domain);
7849 __isl_give isl_schedule_node *
7850 isl_schedule_node_from_extension(
7851 __isl_take isl_union_map *extension);
7853 C<isl_schedule_node_from_extension> creates a tree with an extension
7856 Schedule nodes can be copied and freed using the following functions.
7858 #include <isl/schedule_node.h>
7859 __isl_give isl_schedule_node *isl_schedule_node_copy(
7860 __isl_keep isl_schedule_node *node);
7861 __isl_null isl_schedule_node *isl_schedule_node_free(
7862 __isl_take isl_schedule_node *node);
7864 The following functions can be used to check if two schedule
7865 nodes point to the same position in the same schedule.
7867 #include <isl/schedule_node.h>
7868 isl_bool isl_schedule_node_is_equal(
7869 __isl_keep isl_schedule_node *node1,
7870 __isl_keep isl_schedule_node *node2);
7872 The following properties can be obtained from a schedule node.
7874 #include <isl/schedule_node.h>
7875 enum isl_schedule_node_type isl_schedule_node_get_type(
7876 __isl_keep isl_schedule_node *node);
7877 enum isl_schedule_node_type
7878 isl_schedule_node_get_parent_type(
7879 __isl_keep isl_schedule_node *node);
7880 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7881 __isl_keep isl_schedule_node *node);
7883 The function C<isl_schedule_node_get_type> returns the type of
7884 the node, while C<isl_schedule_node_get_parent_type> returns
7885 type of the parent of the node, which is required to exist.
7886 The function C<isl_schedule_node_get_schedule> returns a copy
7887 to the schedule to which the node belongs.
7889 The following functions can be used to move the schedule node
7890 to a different position in the tree or to check if such a position
7893 #include <isl/schedule_node.h>
7894 isl_bool isl_schedule_node_has_parent(
7895 __isl_keep isl_schedule_node *node);
7896 __isl_give isl_schedule_node *isl_schedule_node_parent(
7897 __isl_take isl_schedule_node *node);
7898 __isl_give isl_schedule_node *isl_schedule_node_root(
7899 __isl_take isl_schedule_node *node);
7900 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
7901 __isl_take isl_schedule_node *node,
7903 int isl_schedule_node_n_children(
7904 __isl_keep isl_schedule_node *node);
7905 __isl_give isl_schedule_node *isl_schedule_node_child(
7906 __isl_take isl_schedule_node *node, int pos);
7907 isl_bool isl_schedule_node_has_children(
7908 __isl_keep isl_schedule_node *node);
7909 __isl_give isl_schedule_node *isl_schedule_node_first_child(
7910 __isl_take isl_schedule_node *node);
7911 isl_bool isl_schedule_node_has_previous_sibling(
7912 __isl_keep isl_schedule_node *node);
7913 __isl_give isl_schedule_node *
7914 isl_schedule_node_previous_sibling(
7915 __isl_take isl_schedule_node *node);
7916 isl_bool isl_schedule_node_has_next_sibling(
7917 __isl_keep isl_schedule_node *node);
7918 __isl_give isl_schedule_node *
7919 isl_schedule_node_next_sibling(
7920 __isl_take isl_schedule_node *node);
7922 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
7923 is the node itself, the ancestor of generation 1 is its parent and so on.
7925 It is also possible to query the number of ancestors of a node,
7926 the position of the current node
7927 within the children of its parent, the position of the subtree
7928 containing a node within the children of an ancestor
7929 or to obtain a copy of a given
7930 child without destroying the current node.
7931 Given two nodes that point to the same schedule, their closest
7932 shared ancestor can be obtained using
7933 C<isl_schedule_node_get_shared_ancestor>.
7935 #include <isl/schedule_node.h>
7936 int isl_schedule_node_get_tree_depth(
7937 __isl_keep isl_schedule_node *node);
7938 int isl_schedule_node_get_child_position(
7939 __isl_keep isl_schedule_node *node);
7940 int isl_schedule_node_get_ancestor_child_position(
7941 __isl_keep isl_schedule_node *node,
7942 __isl_keep isl_schedule_node *ancestor);
7943 __isl_give isl_schedule_node *isl_schedule_node_get_child(
7944 __isl_keep isl_schedule_node *node, int pos);
7945 __isl_give isl_schedule_node *
7946 isl_schedule_node_get_shared_ancestor(
7947 __isl_keep isl_schedule_node *node1,
7948 __isl_keep isl_schedule_node *node2);
7950 All nodes in a schedule tree or
7951 all descendants of a specific node (including the node) can be visited
7952 in depth-first pre-order using the following functions.
7954 #include <isl/schedule.h>
7955 isl_stat isl_schedule_foreach_schedule_node_top_down(
7956 __isl_keep isl_schedule *sched,
7957 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7958 void *user), void *user);
7960 #include <isl/schedule_node.h>
7961 isl_stat isl_schedule_node_foreach_descendant_top_down(
7962 __isl_keep isl_schedule_node *node,
7963 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7964 void *user), void *user);
7966 The callback function is slightly different from the usual
7967 callbacks in that it not only indicates success (non-negative result)
7968 or failure (negative result), but also indicates whether the children
7969 of the given node should be visited. In particular, if the callback
7970 returns a positive value, then the children are visited, but if
7971 the callback returns zero, then the children are not visited.
7973 The ancestors of a node in a schedule tree can be visited from
7974 the root down to and including the parent of the node using
7975 the following function.
7977 #include <isl/schedule_node.h>
7978 isl_stat isl_schedule_node_foreach_ancestor_top_down(
7979 __isl_keep isl_schedule_node *node,
7980 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
7981 void *user), void *user);
7983 The following functions allows for a depth-first post-order
7984 traversal of the nodes in a schedule tree or
7985 of the descendants of a specific node (including the node
7986 itself), where the user callback is allowed to modify the
7989 #include <isl/schedule.h>
7990 __isl_give isl_schedule *
7991 isl_schedule_map_schedule_node_bottom_up(
7992 __isl_take isl_schedule *schedule,
7993 __isl_give isl_schedule_node *(*fn)(
7994 __isl_take isl_schedule_node *node,
7995 void *user), void *user);
7997 #include <isl/schedule_node.h>
7998 __isl_give isl_schedule_node *
7999 isl_schedule_node_map_descendant_bottom_up(
8000 __isl_take isl_schedule_node *node,
8001 __isl_give isl_schedule_node *(*fn)(
8002 __isl_take isl_schedule_node *node,
8003 void *user), void *user);
8005 The traversal continues from the node returned by the callback function.
8006 It is the responsibility of the user to ensure that this does not
8007 lead to an infinite loop. It is safest to always return a pointer
8008 to the same position (same ancestors and child positions) as the input node.
8010 The following function removes a node (along with its descendants)
8011 from a schedule tree and returns a pointer to the leaf at the
8012 same position in the updated tree.
8013 It is not allowed to remove the root of a schedule tree or
8014 a child of a set or sequence node.
8016 #include <isl/schedule_node.h>
8017 __isl_give isl_schedule_node *isl_schedule_node_cut(
8018 __isl_take isl_schedule_node *node);
8020 The following function removes a single node
8021 from a schedule tree and returns a pointer to the child
8022 of the node, now located at the position of the original node
8023 or to a leaf node at that position if there was no child.
8024 It is not allowed to remove the root of a schedule tree,
8025 a set or sequence node, a child of a set or sequence node or
8026 a band node with an anchored subtree.
8028 #include <isl/schedule_node.h>
8029 __isl_give isl_schedule_node *isl_schedule_node_delete(
8030 __isl_take isl_schedule_node *node);
8032 Most nodes in a schedule tree only contain local information.
8033 In some cases, however, a node may also refer to outer band nodes.
8034 This means that the position of the node within the tree should
8035 not be changed, or at least that no changes are performed to the
8036 outer band nodes. The following function can be used to test
8037 whether the subtree rooted at a given node contains any such nodes.
8039 #include <isl/schedule_node.h>
8040 isl_bool isl_schedule_node_is_subtree_anchored(
8041 __isl_keep isl_schedule_node *node);
8043 The following function resets the user pointers on all parameter
8044 and tuple identifiers referenced by the given schedule node.
8046 #include <isl/schedule_node.h>
8047 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8048 __isl_take isl_schedule_node *node);
8050 The following function aligns the parameters of the given schedule
8051 node to the given space.
8053 #include <isl/schedule_node.h>
8054 __isl_give isl_schedule_node *
8055 isl_schedule_node_align_params(
8056 __isl_take isl_schedule_node *node,
8057 __isl_take isl_space *space);
8059 Several node types have their own functions for querying
8060 (and in some cases setting) some node type specific properties.
8062 #include <isl/schedule_node.h>
8063 __isl_give isl_space *isl_schedule_node_band_get_space(
8064 __isl_keep isl_schedule_node *node);
8065 __isl_give isl_multi_union_pw_aff *
8066 isl_schedule_node_band_get_partial_schedule(
8067 __isl_keep isl_schedule_node *node);
8068 __isl_give isl_union_map *
8069 isl_schedule_node_band_get_partial_schedule_union_map(
8070 __isl_keep isl_schedule_node *node);
8071 unsigned isl_schedule_node_band_n_member(
8072 __isl_keep isl_schedule_node *node);
8073 isl_bool isl_schedule_node_band_member_get_coincident(
8074 __isl_keep isl_schedule_node *node, int pos);
8075 __isl_give isl_schedule_node *
8076 isl_schedule_node_band_member_set_coincident(
8077 __isl_take isl_schedule_node *node, int pos,
8079 isl_bool isl_schedule_node_band_get_permutable(
8080 __isl_keep isl_schedule_node *node);
8081 __isl_give isl_schedule_node *
8082 isl_schedule_node_band_set_permutable(
8083 __isl_take isl_schedule_node *node, int permutable);
8084 enum isl_ast_loop_type
8085 isl_schedule_node_band_member_get_ast_loop_type(
8086 __isl_keep isl_schedule_node *node, int pos);
8087 __isl_give isl_schedule_node *
8088 isl_schedule_node_band_member_set_ast_loop_type(
8089 __isl_take isl_schedule_node *node, int pos,
8090 enum isl_ast_loop_type type);
8091 __isl_give isl_union_set *
8092 enum isl_ast_loop_type
8093 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8094 __isl_keep isl_schedule_node *node, int pos);
8095 __isl_give isl_schedule_node *
8096 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8097 __isl_take isl_schedule_node *node, int pos,
8098 enum isl_ast_loop_type type);
8099 isl_schedule_node_band_get_ast_build_options(
8100 __isl_keep isl_schedule_node *node);
8101 __isl_give isl_schedule_node *
8102 isl_schedule_node_band_set_ast_build_options(
8103 __isl_take isl_schedule_node *node,
8104 __isl_take isl_union_set *options);
8106 The function C<isl_schedule_node_band_get_space> returns the space
8107 of the partial schedule of the band.
8108 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8109 returns a representation of the partial schedule of the band node
8110 in the form of an C<isl_union_map>.
8111 The coincident and permutable properties are set by
8112 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8114 A scheduling dimension is considered to be ``coincident''
8115 if it satisfies the coincidence constraints within its band.
8116 That is, if the dependence distances of the coincidence
8117 constraints are all zero in that direction (for fixed
8118 iterations of outer bands).
8119 A band is marked permutable if it was produced using the Pluto-like scheduler.
8120 Note that the scheduler may have to resort to a Feautrier style scheduling
8121 step even if the default scheduler is used.
8122 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8123 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8124 For the meaning of these loop AST generation types and the difference
8125 between the regular loop AST generation type and the isolate
8126 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8127 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8128 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8129 may return C<isl_ast_loop_error> if an error occurs.
8130 The AST build options govern how an AST is generated for
8131 the individual schedule dimensions during AST generation.
8132 See L</"AST Generation Options (Schedule Tree)">.
8134 #include <isl/schedule_node.h>
8135 __isl_give isl_set *
8136 isl_schedule_node_context_get_context(
8137 __isl_keep isl_schedule_node *node);
8139 #include <isl/schedule_node.h>
8140 __isl_give isl_union_set *
8141 isl_schedule_node_domain_get_domain(
8142 __isl_keep isl_schedule_node *node);
8144 #include <isl/schedule_node.h>
8145 __isl_give isl_union_map *
8146 isl_schedule_node_expansion_get_expansion(
8147 __isl_keep isl_schedule_node *node);
8148 __isl_give isl_union_pw_multi_aff *
8149 isl_schedule_node_expansion_get_contraction(
8150 __isl_keep isl_schedule_node *node);
8152 #include <isl/schedule_node.h>
8153 __isl_give isl_union_map *
8154 isl_schedule_node_extension_get_extension(
8155 __isl_keep isl_schedule_node *node);
8157 #include <isl/schedule_node.h>
8158 __isl_give isl_union_set *
8159 isl_schedule_node_filter_get_filter(
8160 __isl_keep isl_schedule_node *node);
8162 #include <isl/schedule_node.h>
8163 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8164 __isl_keep isl_schedule_node *node);
8166 #include <isl/schedule_node.h>
8167 __isl_give isl_id *isl_schedule_node_mark_get_id(
8168 __isl_keep isl_schedule_node *node);
8170 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8171 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8172 partial schedules related to the node.
8174 #include <isl/schedule_node.h>
8175 __isl_give isl_multi_union_pw_aff *
8176 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8177 __isl_keep isl_schedule_node *node);
8178 __isl_give isl_union_pw_multi_aff *
8179 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8180 __isl_keep isl_schedule_node *node);
8181 __isl_give isl_union_map *
8182 isl_schedule_node_get_prefix_schedule_union_map(
8183 __isl_keep isl_schedule_node *node);
8184 __isl_give isl_union_map *
8185 isl_schedule_node_get_prefix_schedule_relation(
8186 __isl_keep isl_schedule_node *node);
8187 __isl_give isl_union_map *
8188 isl_schedule_node_get_subtree_schedule_union_map(
8189 __isl_keep isl_schedule_node *node);
8191 In particular, the functions
8192 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8193 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8194 and C<isl_schedule_node_get_prefix_schedule_union_map>
8195 return a relative ordering on the domain elements that reach the given
8196 node determined by its ancestors.
8197 The function C<isl_schedule_node_get_prefix_schedule_relation>
8198 additionally includes the domain constraints in the result.
8199 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8200 returns a representation of the partial schedule defined by the
8201 subtree rooted at the given node.
8202 If the tree contains any expansion nodes, then the subtree schedule
8203 is formulated in terms of the expanded domain elements.
8204 The tree passed to functions returning a prefix schedule
8205 may only contain extension nodes if these would not affect
8206 the result of these functions. That is, if one of the ancestors
8207 is an extension node, then all of the domain elements that were
8208 added by the extension node need to have been filtered out
8209 by filter nodes between the extension node and the input node.
8210 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8211 may not contain in extension nodes in the selected subtree.
8213 The expansion/contraction defined by an entire subtree, combining
8214 the expansions/contractions
8215 on the expansion nodes in the subtree, can be obtained using
8216 the following functions.
8218 #include <isl/schedule_node.h>
8219 __isl_give isl_union_map *
8220 isl_schedule_node_get_subtree_expansion(
8221 __isl_keep isl_schedule_node *node);
8222 __isl_give isl_union_pw_multi_aff *
8223 isl_schedule_node_get_subtree_contraction(
8224 __isl_keep isl_schedule_node *node);
8226 The total number of outer band members of given node, i.e.,
8227 the shared output dimension of the maps in the result
8228 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8229 using the following function.
8231 #include <isl/schedule_node.h>
8232 int isl_schedule_node_get_schedule_depth(
8233 __isl_keep isl_schedule_node *node);
8235 The following functions return the elements that reach the given node
8236 or the union of universes in the spaces that contain these elements.
8238 #include <isl/schedule_node.h>
8239 __isl_give isl_union_set *
8240 isl_schedule_node_get_domain(
8241 __isl_keep isl_schedule_node *node);
8242 __isl_give isl_union_set *
8243 isl_schedule_node_get_universe_domain(
8244 __isl_keep isl_schedule_node *node);
8246 The input tree of C<isl_schedule_node_get_domain>
8247 may only contain extension nodes if these would not affect
8248 the result of this function. That is, if one of the ancestors
8249 is an extension node, then all of the domain elements that were
8250 added by the extension node need to have been filtered out
8251 by filter nodes between the extension node and the input node.
8253 The following functions can be used to introduce additional nodes
8254 in the schedule tree. The new node is introduced at the point
8255 in the tree where the C<isl_schedule_node> points to and
8256 the results points to the new node.
8258 #include <isl/schedule_node.h>
8259 __isl_give isl_schedule_node *
8260 isl_schedule_node_insert_partial_schedule(
8261 __isl_take isl_schedule_node *node,
8262 __isl_take isl_multi_union_pw_aff *schedule);
8264 This function inserts a new band node with (the greatest integer
8265 part of) the given partial schedule.
8266 The subtree rooted at the given node is assumed not to have
8269 #include <isl/schedule_node.h>
8270 __isl_give isl_schedule_node *
8271 isl_schedule_node_insert_context(
8272 __isl_take isl_schedule_node *node,
8273 __isl_take isl_set *context);
8275 This function inserts a new context node with the given context constraints.
8277 #include <isl/schedule_node.h>
8278 __isl_give isl_schedule_node *
8279 isl_schedule_node_insert_filter(
8280 __isl_take isl_schedule_node *node,
8281 __isl_take isl_union_set *filter);
8283 This function inserts a new filter node with the given filter.
8284 If the original node already pointed to a filter node, then the
8285 two filter nodes are merged into one.
8287 #include <isl/schedule_node.h>
8288 __isl_give isl_schedule_node *
8289 isl_schedule_node_insert_guard(
8290 __isl_take isl_schedule_node *node,
8291 __isl_take isl_set *guard);
8293 This function inserts a new guard node with the given guard constraints.
8295 #include <isl/schedule_node.h>
8296 __isl_give isl_schedule_node *
8297 isl_schedule_node_insert_mark(
8298 __isl_take isl_schedule_node *node,
8299 __isl_take isl_id *mark);
8301 This function inserts a new mark node with the give mark identifier.
8303 #include <isl/schedule_node.h>
8304 __isl_give isl_schedule_node *
8305 isl_schedule_node_insert_sequence(
8306 __isl_take isl_schedule_node *node,
8307 __isl_take isl_union_set_list *filters);
8308 __isl_give isl_schedule_node *
8309 isl_schedule_node_insert_set(
8310 __isl_take isl_schedule_node *node,
8311 __isl_take isl_union_set_list *filters);
8313 These functions insert a new sequence or set node with the given
8314 filters as children.
8316 #include <isl/schedule_node.h>
8317 __isl_give isl_schedule_node *isl_schedule_node_group(
8318 __isl_take isl_schedule_node *node,
8319 __isl_take isl_id *group_id);
8321 This function introduces an expansion node in between the current
8322 node and its parent that expands instances of a space with tuple
8323 identifier C<group_id> to the original domain elements that reach
8324 the node. The group instances are identified by the prefix schedule
8325 of those domain elements. The ancestors of the node are adjusted
8326 to refer to the group instances instead of the original domain
8327 elements. The return value points to the same node in the updated
8328 schedule tree as the input node, i.e., to the child of the newly
8329 introduced expansion node. Grouping instances of different statements
8330 ensures that they will be treated as a single statement by the
8331 AST generator up to the point of the expansion node.
8333 The following function can be used to flatten a nested
8336 #include <isl/schedule_node.h>
8337 __isl_give isl_schedule_node *
8338 isl_schedule_node_sequence_splice_child(
8339 __isl_take isl_schedule_node *node, int pos);
8341 That is, given a sequence node C<node> that has another sequence node
8342 in its child at position C<pos> (in particular, the child of that filter
8343 node is a sequence node), attach the children of that other sequence
8344 node as children of C<node>, replacing the original child at position
8347 The partial schedule of a band node can be scaled (down) or reduced using
8348 the following functions.
8350 #include <isl/schedule_node.h>
8351 __isl_give isl_schedule_node *
8352 isl_schedule_node_band_scale(
8353 __isl_take isl_schedule_node *node,
8354 __isl_take isl_multi_val *mv);
8355 __isl_give isl_schedule_node *
8356 isl_schedule_node_band_scale_down(
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_mod(
8361 __isl_take isl_schedule_node *node,
8362 __isl_take isl_multi_val *mv);
8364 The spaces of the two arguments need to match.
8365 After scaling, the partial schedule is replaced by its greatest
8366 integer part to ensure that the schedule remains integral.
8368 The partial schedule of a band node can be shifted by an
8369 C<isl_multi_union_pw_aff> with a domain that is a superset
8370 of the domain of the partial schedule using
8371 the following function.
8373 #include <isl/schedule_node.h>
8374 __isl_give isl_schedule_node *
8375 isl_schedule_node_band_shift(
8376 __isl_take isl_schedule_node *node,
8377 __isl_take isl_multi_union_pw_aff *shift);
8379 A band node can be tiled using the following function.
8381 #include <isl/schedule_node.h>
8382 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8383 __isl_take isl_schedule_node *node,
8384 __isl_take isl_multi_val *sizes);
8386 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8388 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8389 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8391 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8393 The C<isl_schedule_node_band_tile> function tiles
8394 the band using the given tile sizes inside its schedule.
8395 A new child band node is created to represent the point loops and it is
8396 inserted between the modified band and its children.
8397 The subtree rooted at the given node is assumed not to have
8399 The C<tile_scale_tile_loops> option specifies whether the tile
8400 loops iterators should be scaled by the tile sizes.
8401 If the C<tile_shift_point_loops> option is set, then the point loops
8402 are shifted to start at zero.
8404 A band node can be split into two nested band nodes
8405 using the following function.
8407 #include <isl/schedule_node.h>
8408 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8409 __isl_take isl_schedule_node *node, int pos);
8411 The resulting outer band node contains the first C<pos> dimensions of
8412 the schedule of C<node> while the inner band contains the remaining dimensions.
8413 The schedules of the two band nodes live in anonymous spaces.
8415 A band node can be moved down to the leaves of the subtree rooted
8416 at the band node using the following function.
8418 #include <isl/schedule_node.h>
8419 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8420 __isl_take isl_schedule_node *node);
8422 The subtree rooted at the given node is assumed not to have
8424 The result points to the node in the resulting tree that is in the same
8425 position as the node pointed to by C<node> in the original tree.
8427 #include <isl/schedule_node.h>
8428 __isl_give isl_schedule_node *
8429 isl_schedule_node_order_before(
8430 __isl_take isl_schedule_node *node,
8431 __isl_take isl_union_set *filter);
8432 __isl_give isl_schedule_node *
8433 isl_schedule_node_order_after(
8434 __isl_take isl_schedule_node *node,
8435 __isl_take isl_union_set *filter);
8437 These functions split the domain elements that reach C<node>
8438 into those that satisfy C<filter> and those that do not and
8439 arranges for the elements that do satisfy the filter to be
8440 executed before (in case of C<isl_schedule_node_order_before>)
8441 or after (in case of C<isl_schedule_node_order_after>)
8442 those that do not. The order is imposed by
8443 a sequence node, possibly reusing the grandparent of C<node>
8444 on two copies of the subtree attached to the original C<node>.
8445 Both copies are simplified with respect to their filter.
8447 Return a pointer to the copy of the subtree that does not
8448 satisfy C<filter>. If there is no such copy (because all
8449 reaching domain elements satisfy the filter), then return
8450 the original pointer.
8452 #include <isl/schedule_node.h>
8453 __isl_give isl_schedule_node *
8454 isl_schedule_node_graft_before(
8455 __isl_take isl_schedule_node *node,
8456 __isl_take isl_schedule_node *graft);
8457 __isl_give isl_schedule_node *
8458 isl_schedule_node_graft_after(
8459 __isl_take isl_schedule_node *node,
8460 __isl_take isl_schedule_node *graft);
8462 This function inserts the C<graft> tree into the tree containing C<node>
8463 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8464 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8465 The root node of C<graft>
8466 should be an extension node where the domain of the extension
8467 is the flat product of all outer band nodes of C<node>.
8468 The root node may also be a domain node.
8469 The elements of the domain or the range of the extension may not
8470 intersect with the domain elements that reach "node".
8471 The schedule tree of C<graft> may not be anchored.
8473 The schedule tree of C<node> is modified to include an extension node
8474 corresponding to the root node of C<graft> as a child of the original
8475 parent of C<node>. The original node that C<node> points to and the
8476 child of the root node of C<graft> are attached to this extension node
8477 through a sequence, with appropriate filters and with the child
8478 of C<graft> appearing before or after the original C<node>.
8480 If C<node> already appears inside a sequence that is the child of
8481 an extension node and if the spaces of the new domain elements
8482 do not overlap with those of the original domain elements,
8483 then that extension node is extended with the new extension
8484 rather than introducing a new segment of extension and sequence nodes.
8486 Return a pointer to the same node in the modified tree that
8487 C<node> pointed to in the original tree.
8489 A representation of the schedule node can be printed using
8491 #include <isl/schedule_node.h>
8492 __isl_give isl_printer *isl_printer_print_schedule_node(
8493 __isl_take isl_printer *p,
8494 __isl_keep isl_schedule_node *node);
8495 __isl_give char *isl_schedule_node_to_str(
8496 __isl_keep isl_schedule_node *node);
8498 C<isl_schedule_node_to_str> prints the schedule node in block format.
8500 =head2 Dependence Analysis
8502 C<isl> contains specialized functionality for performing
8503 array dataflow analysis. That is, given a I<sink> access relation
8504 and a collection of possible I<source> access relations,
8505 C<isl> can compute relations that describe
8506 for each iteration of the sink access, which iteration
8507 of which of the source access relations was the last
8508 to access the same data element before the given iteration
8510 The resulting dependence relations map source iterations
8511 to either the corresponding sink iterations or
8512 pairs of corresponding sink iterations and accessed data elements.
8513 To compute standard flow dependences, the sink should be
8514 a read, while the sources should be writes.
8515 If any of the source accesses are marked as being I<may>
8516 accesses, then there will be a dependence from the last
8517 I<must> access B<and> from any I<may> access that follows
8518 this last I<must> access.
8519 In particular, if I<all> sources are I<may> accesses,
8520 then memory based dependence analysis is performed.
8521 If, on the other hand, all sources are I<must> accesses,
8522 then value based dependence analysis is performed.
8524 =head3 High-level Interface
8526 A high-level interface to dependence analysis is provided
8527 by the following function.
8529 #include <isl/flow.h>
8530 __isl_give isl_union_flow *
8531 isl_union_access_info_compute_flow(
8532 __isl_take isl_union_access_info *access);
8534 The input C<isl_union_access_info> object describes the sink
8535 access relations, the source access relations and a schedule,
8536 while the output C<isl_union_flow> object describes
8537 the resulting dependence relations and the subsets of the
8538 sink relations for which no source was found.
8540 An C<isl_union_access_info> is created, modified, copied and freed using
8541 the following functions.
8543 #include <isl/flow.h>
8544 __isl_give isl_union_access_info *
8545 isl_union_access_info_from_sink(
8546 __isl_take isl_union_map *sink);
8547 __isl_give isl_union_access_info *
8548 isl_union_access_info_set_must_source(
8549 __isl_take isl_union_access_info *access,
8550 __isl_take isl_union_map *must_source);
8551 __isl_give isl_union_access_info *
8552 isl_union_access_info_set_may_source(
8553 __isl_take isl_union_access_info *access,
8554 __isl_take isl_union_map *may_source);
8555 __isl_give isl_union_access_info *
8556 isl_union_access_info_set_schedule(
8557 __isl_take isl_union_access_info *access,
8558 __isl_take isl_schedule *schedule);
8559 __isl_give isl_union_access_info *
8560 isl_union_access_info_set_schedule_map(
8561 __isl_take isl_union_access_info *access,
8562 __isl_take isl_union_map *schedule_map);
8563 __isl_give isl_union_access_info *
8564 isl_union_access_info_copy(
8565 __isl_keep isl_union_access_info *access);
8566 __isl_null isl_union_access_info *
8567 isl_union_access_info_free(
8568 __isl_take isl_union_access_info *access);
8570 The may sources set by C<isl_union_access_info_set_may_source>
8571 do not need to include the must sources set by
8572 C<isl_union_access_info_set_must_source> as a subset.
8573 The user is free not to call one (or both) of these functions,
8574 in which case the corresponding set is kept to its empty default.
8575 Similarly, the default schedule initialized by
8576 C<isl_union_access_info_from_sink> is empty.
8577 The current schedule is determined by the last call to either
8578 C<isl_union_access_info_set_schedule> or
8579 C<isl_union_access_info_set_schedule_map>.
8580 The domain of the schedule corresponds to the domains of
8581 the access relations. In particular, the domains of the access
8582 relations are effectively intersected with the domain of the schedule
8583 and only the resulting accesses are considered by the dependence analysis.
8585 A representation of the information contained in an object
8586 of type C<isl_union_access_info> can be obtained using
8588 #include <isl/flow.h>
8589 __isl_give isl_printer *
8590 isl_printer_print_union_access_info(
8591 __isl_take isl_printer *p,
8592 __isl_keep isl_union_access_info *access);
8593 __isl_give char *isl_union_access_info_to_str(
8594 __isl_keep isl_union_access_info *access);
8596 C<isl_union_access_info_to_str> prints the information in flow format.
8598 The output of C<isl_union_access_info_compute_flow> can be examined
8599 and freed using the following functions.
8601 #include <isl/flow.h>
8602 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8603 __isl_keep isl_union_flow *flow);
8604 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8605 __isl_keep isl_union_flow *flow);
8606 __isl_give isl_union_map *
8607 isl_union_flow_get_full_must_dependence(
8608 __isl_keep isl_union_flow *flow);
8609 __isl_give isl_union_map *
8610 isl_union_flow_get_full_may_dependence(
8611 __isl_keep isl_union_flow *flow);
8612 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8613 __isl_keep isl_union_flow *flow);
8614 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8615 __isl_keep isl_union_flow *flow);
8616 __isl_null isl_union_flow *isl_union_flow_free(
8617 __isl_take isl_union_flow *flow);
8619 The relation returned by C<isl_union_flow_get_must_dependence>
8620 relates domain elements of must sources to domain elements of the sink.
8621 The relation returned by C<isl_union_flow_get_may_dependence>
8622 relates domain elements of must or may sources to domain elements of the sink
8623 and includes the previous relation as a subset.
8624 The relation returned by C<isl_union_flow_get_full_must_dependence>
8625 relates domain elements of must sources to pairs of domain elements of the sink
8626 and accessed data elements.
8627 The relation returned by C<isl_union_flow_get_full_may_dependence>
8628 relates domain elements of must or may sources to pairs of
8629 domain elements of the sink and accessed data elements.
8630 This relation includes the previous relation as a subset.
8631 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8632 of the sink relation for which no dependences have been found.
8633 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8634 of the sink relation for which no definite dependences have been found.
8635 That is, it contains those sink access that do not contribute to any
8636 of the elements in the relation returned
8637 by C<isl_union_flow_get_must_dependence>.
8639 A representation of the information contained in an object
8640 of type C<isl_union_flow> can be obtained using
8642 #include <isl/flow.h>
8643 __isl_give isl_printer *isl_printer_print_union_flow(
8644 __isl_take isl_printer *p,
8645 __isl_keep isl_union_flow *flow);
8646 __isl_give char *isl_union_flow_to_str(
8647 __isl_keep isl_union_flow *flow);
8649 C<isl_union_flow_to_str> prints the information in flow format.
8651 =head3 Low-level Interface
8653 A lower-level interface is provided by the following functions.
8655 #include <isl/flow.h>
8657 typedef int (*isl_access_level_before)(void *first, void *second);
8659 __isl_give isl_access_info *isl_access_info_alloc(
8660 __isl_take isl_map *sink,
8661 void *sink_user, isl_access_level_before fn,
8663 __isl_give isl_access_info *isl_access_info_add_source(
8664 __isl_take isl_access_info *acc,
8665 __isl_take isl_map *source, int must,
8667 __isl_null isl_access_info *isl_access_info_free(
8668 __isl_take isl_access_info *acc);
8670 __isl_give isl_flow *isl_access_info_compute_flow(
8671 __isl_take isl_access_info *acc);
8673 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8674 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8675 void *dep_user, void *user),
8677 __isl_give isl_map *isl_flow_get_no_source(
8678 __isl_keep isl_flow *deps, int must);
8679 void isl_flow_free(__isl_take isl_flow *deps);
8681 The function C<isl_access_info_compute_flow> performs the actual
8682 dependence analysis. The other functions are used to construct
8683 the input for this function or to read off the output.
8685 The input is collected in an C<isl_access_info>, which can
8686 be created through a call to C<isl_access_info_alloc>.
8687 The arguments to this functions are the sink access relation
8688 C<sink>, a token C<sink_user> used to identify the sink
8689 access to the user, a callback function for specifying the
8690 relative order of source and sink accesses, and the number
8691 of source access relations that will be added.
8692 The callback function has type C<int (*)(void *first, void *second)>.
8693 The function is called with two user supplied tokens identifying
8694 either a source or the sink and it should return the shared nesting
8695 level and the relative order of the two accesses.
8696 In particular, let I<n> be the number of loops shared by
8697 the two accesses. If C<first> precedes C<second> textually,
8698 then the function should return I<2 * n + 1>; otherwise,
8699 it should return I<2 * n>.
8700 The sources can be added to the C<isl_access_info> by performing
8701 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8702 C<must> indicates whether the source is a I<must> access
8703 or a I<may> access. Note that a multi-valued access relation
8704 should only be marked I<must> if every iteration in the domain
8705 of the relation accesses I<all> elements in its image.
8706 The C<source_user> token is again used to identify
8707 the source access. The range of the source access relation
8708 C<source> should have the same dimension as the range
8709 of the sink access relation.
8710 The C<isl_access_info_free> function should usually not be
8711 called explicitly, because it is called implicitly by
8712 C<isl_access_info_compute_flow>.
8714 The result of the dependence analysis is collected in an
8715 C<isl_flow>. There may be elements of
8716 the sink access for which no preceding source access could be
8717 found or for which all preceding sources are I<may> accesses.
8718 The relations containing these elements can be obtained through
8719 calls to C<isl_flow_get_no_source>, the first with C<must> set
8720 and the second with C<must> unset.
8721 In the case of standard flow dependence analysis,
8722 with the sink a read and the sources I<must> writes,
8723 the first relation corresponds to the reads from uninitialized
8724 array elements and the second relation is empty.
8725 The actual flow dependences can be extracted using
8726 C<isl_flow_foreach>. This function will call the user-specified
8727 callback function C<fn> for each B<non-empty> dependence between
8728 a source and the sink. The callback function is called
8729 with four arguments, the actual flow dependence relation
8730 mapping source iterations to sink iterations, a boolean that
8731 indicates whether it is a I<must> or I<may> dependence, a token
8732 identifying the source and an additional C<void *> with value
8733 equal to the third argument of the C<isl_flow_foreach> call.
8734 A dependence is marked I<must> if it originates from a I<must>
8735 source and if it is not followed by any I<may> sources.
8737 After finishing with an C<isl_flow>, the user should call
8738 C<isl_flow_free> to free all associated memory.
8740 =head3 Interaction with the Low-level Interface
8742 During the dependence analysis, we frequently need to perform
8743 the following operation. Given a relation between sink iterations
8744 and potential source iterations from a particular source domain,
8745 what is the last potential source iteration corresponding to each
8746 sink iteration. It can sometimes be convenient to adjust
8747 the set of potential source iterations before or after each such operation.
8748 The prototypical example is fuzzy array dataflow analysis,
8749 where we need to analyze if, based on data-dependent constraints,
8750 the sink iteration can ever be executed without one or more of
8751 the corresponding potential source iterations being executed.
8752 If so, we can introduce extra parameters and select an unknown
8753 but fixed source iteration from the potential source iterations.
8754 To be able to perform such manipulations, C<isl> provides the following
8757 #include <isl/flow.h>
8759 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8760 __isl_keep isl_map *source_map,
8761 __isl_keep isl_set *sink, void *source_user,
8763 __isl_give isl_access_info *isl_access_info_set_restrict(
8764 __isl_take isl_access_info *acc,
8765 isl_access_restrict fn, void *user);
8767 The function C<isl_access_info_set_restrict> should be called
8768 before calling C<isl_access_info_compute_flow> and registers a callback function
8769 that will be called any time C<isl> is about to compute the last
8770 potential source. The first argument is the (reverse) proto-dependence,
8771 mapping sink iterations to potential source iterations.
8772 The second argument represents the sink iterations for which
8773 we want to compute the last source iteration.
8774 The third argument is the token corresponding to the source
8775 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8776 The callback is expected to return a restriction on either the input or
8777 the output of the operation computing the last potential source.
8778 If the input needs to be restricted then restrictions are needed
8779 for both the source and the sink iterations. The sink iterations
8780 and the potential source iterations will be intersected with these sets.
8781 If the output needs to be restricted then only a restriction on the source
8782 iterations is required.
8783 If any error occurs, the callback should return C<NULL>.
8784 An C<isl_restriction> object can be created, freed and inspected
8785 using the following functions.
8787 #include <isl/flow.h>
8789 __isl_give isl_restriction *isl_restriction_input(
8790 __isl_take isl_set *source_restr,
8791 __isl_take isl_set *sink_restr);
8792 __isl_give isl_restriction *isl_restriction_output(
8793 __isl_take isl_set *source_restr);
8794 __isl_give isl_restriction *isl_restriction_none(
8795 __isl_take isl_map *source_map);
8796 __isl_give isl_restriction *isl_restriction_empty(
8797 __isl_take isl_map *source_map);
8798 __isl_null isl_restriction *isl_restriction_free(
8799 __isl_take isl_restriction *restr);
8801 C<isl_restriction_none> and C<isl_restriction_empty> are special
8802 cases of C<isl_restriction_input>. C<isl_restriction_none>
8803 is essentially equivalent to
8805 isl_restriction_input(isl_set_universe(
8806 isl_space_range(isl_map_get_space(source_map))),
8808 isl_space_domain(isl_map_get_space(source_map))));
8810 whereas C<isl_restriction_empty> is essentially equivalent to
8812 isl_restriction_input(isl_set_empty(
8813 isl_space_range(isl_map_get_space(source_map))),
8815 isl_space_domain(isl_map_get_space(source_map))));
8819 B<The functionality described in this section is fairly new
8820 and may be subject to change.>
8822 #include <isl/schedule.h>
8823 __isl_give isl_schedule *
8824 isl_schedule_constraints_compute_schedule(
8825 __isl_take isl_schedule_constraints *sc);
8827 The function C<isl_schedule_constraints_compute_schedule> can be
8828 used to compute a schedule that satisfies the given schedule constraints.
8829 These schedule constraints include the iteration domain for which
8830 a schedule should be computed and dependences between pairs of
8831 iterations. In particular, these dependences include
8832 I<validity> dependences and I<proximity> dependences.
8833 By default, the algorithm used to construct the schedule is similar
8834 to that of C<Pluto>.
8835 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8837 The generated schedule respects all validity dependences.
8838 That is, all dependence distances over these dependences in the
8839 scheduled space are lexicographically positive.
8841 The default algorithm tries to ensure that the dependence distances
8842 over coincidence constraints are zero and to minimize the
8843 dependence distances over proximity dependences.
8844 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8845 for groups of domains where the dependence distances over validity
8846 dependences have only non-negative values.
8847 Note that when minimizing the maximal dependence distance
8848 over proximity dependences, a single affine expression in the parameters
8849 is constructed that bounds all dependence distances. If no such expression
8850 exists, then the algorithm will fail and resort to an alternative
8851 scheduling algorithm. In particular, this means that adding proximity
8852 dependences may eliminate valid solutions. A typical example where this
8853 phenomenon may occur is when some subset of the proximity dependences
8854 has no restriction on some parameter, forcing the coefficient of that
8855 parameter to be zero, while some other subset forces the dependence
8856 distance to depend on that parameter, requiring the same coefficient
8858 When using Feautrier's algorithm, the coincidence and proximity constraints
8859 are only taken into account during the extension to a
8860 full-dimensional schedule.
8862 An C<isl_schedule_constraints> object can be constructed
8863 and manipulated using the following functions.
8865 #include <isl/schedule.h>
8866 __isl_give isl_schedule_constraints *
8867 isl_schedule_constraints_copy(
8868 __isl_keep isl_schedule_constraints *sc);
8869 __isl_give isl_schedule_constraints *
8870 isl_schedule_constraints_on_domain(
8871 __isl_take isl_union_set *domain);
8872 __isl_give isl_schedule_constraints *
8873 isl_schedule_constraints_set_context(
8874 __isl_take isl_schedule_constraints *sc,
8875 __isl_take isl_set *context);
8876 __isl_give isl_schedule_constraints *
8877 isl_schedule_constraints_set_validity(
8878 __isl_take isl_schedule_constraints *sc,
8879 __isl_take isl_union_map *validity);
8880 __isl_give isl_schedule_constraints *
8881 isl_schedule_constraints_set_coincidence(
8882 __isl_take isl_schedule_constraints *sc,
8883 __isl_take isl_union_map *coincidence);
8884 __isl_give isl_schedule_constraints *
8885 isl_schedule_constraints_set_proximity(
8886 __isl_take isl_schedule_constraints *sc,
8887 __isl_take isl_union_map *proximity);
8888 __isl_give isl_schedule_constraints *
8889 isl_schedule_constraints_set_conditional_validity(
8890 __isl_take isl_schedule_constraints *sc,
8891 __isl_take isl_union_map *condition,
8892 __isl_take isl_union_map *validity);
8893 __isl_null isl_schedule_constraints *
8894 isl_schedule_constraints_free(
8895 __isl_take isl_schedule_constraints *sc);
8897 The initial C<isl_schedule_constraints> object created by
8898 C<isl_schedule_constraints_on_domain> does not impose any constraints.
8899 That is, it has an empty set of dependences.
8900 The function C<isl_schedule_constraints_set_context> allows the user
8901 to specify additional constraints on the parameters that may
8902 be assumed to hold during the construction of the schedule.
8903 The function C<isl_schedule_constraints_set_validity> replaces the
8904 validity dependences, mapping domain elements I<i> to domain
8905 elements that should be scheduled after I<i>.
8906 The function C<isl_schedule_constraints_set_coincidence> replaces the
8907 coincidence dependences, mapping domain elements I<i> to domain
8908 elements that should be scheduled together with I<I>, if possible.
8909 The function C<isl_schedule_constraints_set_proximity> replaces the
8910 proximity dependences, mapping domain elements I<i> to domain
8911 elements that should be scheduled either before I<I>
8912 or as early as possible after I<i>.
8914 The function C<isl_schedule_constraints_set_conditional_validity>
8915 replaces the conditional validity constraints.
8916 A conditional validity constraint is only imposed when any of the corresponding
8917 conditions is satisfied, i.e., when any of them is non-zero.
8918 That is, the scheduler ensures that within each band if the dependence
8919 distances over the condition constraints are not all zero
8920 then all corresponding conditional validity constraints are respected.
8921 A conditional validity constraint corresponds to a condition
8922 if the two are adjacent, i.e., if the domain of one relation intersect
8923 the range of the other relation.
8924 The typical use case of conditional validity constraints is
8925 to allow order constraints between live ranges to be violated
8926 as long as the live ranges themselves are local to the band.
8927 To allow more fine-grained control over which conditions correspond
8928 to which conditional validity constraints, the domains and ranges
8929 of these relations may include I<tags>. That is, the domains and
8930 ranges of those relation may themselves be wrapped relations
8931 where the iteration domain appears in the domain of those wrapped relations
8932 and the range of the wrapped relations can be arbitrarily chosen
8933 by the user. Conditions and conditional validity constraints are only
8934 considered adjacent to each other if the entire wrapped relation matches.
8935 In particular, a relation with a tag will never be considered adjacent
8936 to a relation without a tag.
8938 An C<isl_schedule_constraints> object can be inspected
8939 using the following functions.
8941 #include <isl/schedule.h>
8942 __isl_give isl_union_set *
8943 isl_schedule_constraints_get_domain(
8944 __isl_keep isl_schedule_constraints *sc);
8945 __isl_give isl_union_map *
8946 isl_schedule_constraints_get_validity(
8947 __isl_keep isl_schedule_constraints *sc);
8948 __isl_give isl_union_map *
8949 isl_schedule_constraints_get_coincidence(
8950 __isl_keep isl_schedule_constraints *sc);
8951 __isl_give isl_union_map *
8952 isl_schedule_constraints_get_conditional_validity(
8953 __isl_keep isl_schedule_constraints *sc);
8954 __isl_give isl_union_map *
8955 isl_schedule_constraints_get_conditional_validity_condition(
8956 __isl_keep isl_schedule_constraints *sc);
8958 The following function computes a schedule directly from
8959 an iteration domain and validity and proximity dependences
8960 and is implemented in terms of the functions described above.
8961 The use of C<isl_union_set_compute_schedule> is discouraged.
8963 #include <isl/schedule.h>
8964 __isl_give isl_schedule *isl_union_set_compute_schedule(
8965 __isl_take isl_union_set *domain,
8966 __isl_take isl_union_map *validity,
8967 __isl_take isl_union_map *proximity);
8969 The generated schedule represents a schedule tree.
8970 For more information on schedule trees, see
8971 L</"Schedule Trees">.
8975 #include <isl/schedule.h>
8976 isl_stat isl_options_set_schedule_max_coefficient(
8977 isl_ctx *ctx, int val);
8978 int isl_options_get_schedule_max_coefficient(
8980 isl_stat isl_options_set_schedule_max_constant_term(
8981 isl_ctx *ctx, int val);
8982 int isl_options_get_schedule_max_constant_term(
8984 isl_stat isl_options_set_schedule_serialize_sccs(
8985 isl_ctx *ctx, int val);
8986 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
8987 isl_stat isl_options_set_schedule_whole_component(
8988 isl_ctx *ctx, int val);
8989 int isl_options_get_schedule_whole_component(
8991 isl_stat isl_options_set_schedule_maximize_band_depth(
8992 isl_ctx *ctx, int val);
8993 int isl_options_get_schedule_maximize_band_depth(
8995 isl_stat isl_options_set_schedule_outer_coincidence(
8996 isl_ctx *ctx, int val);
8997 int isl_options_get_schedule_outer_coincidence(
8999 isl_stat isl_options_set_schedule_split_scaled(
9000 isl_ctx *ctx, int val);
9001 int isl_options_get_schedule_split_scaled(
9003 isl_stat isl_options_set_schedule_algorithm(
9004 isl_ctx *ctx, int val);
9005 int isl_options_get_schedule_algorithm(
9007 isl_stat isl_options_set_schedule_separate_components(
9008 isl_ctx *ctx, int val);
9009 int isl_options_get_schedule_separate_components(
9014 =item * schedule_max_coefficient
9016 This option enforces that the coefficients for variable and parameter
9017 dimensions in the calculated schedule are not larger than the specified value.
9018 This option can significantly increase the speed of the scheduling calculation
9019 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9020 this option does not introduce bounds on the variable or parameter
9023 =item * schedule_max_constant_term
9025 This option enforces that the constant coefficients in the calculated schedule
9026 are not larger than the maximal constant term. This option can significantly
9027 increase the speed of the scheduling calculation and may also prevent fusing of
9028 unrelated dimensions. A value of -1 means that this option does not introduce
9029 bounds on the constant coefficients.
9031 =item * schedule_serialize_sccs
9033 If this option is set, then all strongly connected components
9034 in the dependence graph are serialized as soon as they are detected.
9035 This means in particular that instances of statements will only
9036 appear in the same band node if these statements belong
9037 to the same strongly connected component at the point where
9038 the band node is constructed.
9040 =item * schedule_whole_component
9042 If this option is set, then entire (weakly) connected
9043 components in the dependence graph are scheduled together
9045 Otherwise, each strongly connected component within
9046 such a weakly connected component is first scheduled separately
9047 and then combined with other strongly connected components.
9048 This option has no effect if C<schedule_serialize_sccs> is set.
9050 =item * schedule_maximize_band_depth
9052 If this option is set, then the scheduler tries to maximize
9053 the width of the bands. Wider bands give more possibilities for tiling.
9054 In particular, if the C<schedule_whole_component> option is set,
9055 then bands are split if this might result in wider bands.
9056 Otherwise, the effect of this option is to only allow
9057 strongly connected components to be combined if this does
9058 not reduce the width of the bands.
9059 Note that if the C<schedule_serialize_sccs> options is set, then
9060 the C<schedule_maximize_band_depth> option therefore has no effect.
9062 =item * schedule_maximize_coincidence
9064 This option is only effective if the C<schedule_whole_component>
9065 option is turned off.
9066 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9067 strongly connected components are only combined with each other
9068 if this does not reduce the number of coincident band members.
9070 =item * schedule_outer_coincidence
9072 If this option is set, then we try to construct schedules
9073 where the outermost scheduling dimension in each band
9074 satisfies the coincidence constraints.
9076 =item * schedule_split_scaled
9078 If this option is set, then we try to construct schedules in which the
9079 constant term is split off from the linear part if the linear parts of
9080 the scheduling rows for all nodes in the graphs have a common non-trivial
9082 The constant term is then placed in a separate band and the linear
9085 =item * schedule_algorithm
9087 Selects the scheduling algorithm to be used.
9088 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9089 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9091 =item * schedule_separate_components
9093 If this option is set then the function C<isl_schedule_get_map>
9094 will treat set nodes in the same way as sequence nodes.
9098 =head2 AST Generation
9100 This section describes the C<isl> functionality for generating
9101 ASTs that visit all the elements
9102 in a domain in an order specified by a schedule tree or
9104 In case the schedule given as a C<isl_union_map>, an AST is generated
9105 that visits all the elements in the domain of the C<isl_union_map>
9106 according to the lexicographic order of the corresponding image
9107 element(s). If the range of the C<isl_union_map> consists of
9108 elements in more than one space, then each of these spaces is handled
9109 separately in an arbitrary order.
9110 It should be noted that the schedule tree or the image elements
9111 in a schedule map only specify the I<order>
9112 in which the corresponding domain elements should be visited.
9113 No direct relation between the partial schedule values
9114 or the image elements on the one hand and the loop iterators
9115 in the generated AST on the other hand should be assumed.
9117 Each AST is generated within a build. The initial build
9118 simply specifies the constraints on the parameters (if any)
9119 and can be created, inspected, copied and freed using the following functions.
9121 #include <isl/ast_build.h>
9122 __isl_give isl_ast_build *isl_ast_build_alloc(
9124 __isl_give isl_ast_build *isl_ast_build_from_context(
9125 __isl_take isl_set *set);
9126 __isl_give isl_ast_build *isl_ast_build_copy(
9127 __isl_keep isl_ast_build *build);
9128 __isl_null isl_ast_build *isl_ast_build_free(
9129 __isl_take isl_ast_build *build);
9131 The C<set> argument is usually a parameter set with zero or more parameters.
9132 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9133 this set is required to be a parameter set.
9134 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9135 specify any parameter constraints.
9136 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9137 and L</"Fine-grained Control over AST Generation">.
9138 Finally, the AST itself can be constructed using one of the following
9141 #include <isl/ast_build.h>
9142 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9143 __isl_keep isl_ast_build *build,
9144 __isl_take isl_schedule *schedule);
9145 __isl_give isl_ast_node *
9146 isl_ast_build_node_from_schedule_map(
9147 __isl_keep isl_ast_build *build,
9148 __isl_take isl_union_map *schedule);
9150 =head3 Inspecting the AST
9152 The basic properties of an AST node can be obtained as follows.
9154 #include <isl/ast.h>
9155 enum isl_ast_node_type isl_ast_node_get_type(
9156 __isl_keep isl_ast_node *node);
9158 The type of an AST node is one of
9159 C<isl_ast_node_for>,
9161 C<isl_ast_node_block>,
9162 C<isl_ast_node_mark> or
9163 C<isl_ast_node_user>.
9164 An C<isl_ast_node_for> represents a for node.
9165 An C<isl_ast_node_if> represents an if node.
9166 An C<isl_ast_node_block> represents a compound node.
9167 An C<isl_ast_node_mark> introduces a mark in the AST.
9168 An C<isl_ast_node_user> represents an expression statement.
9169 An expression statement typically corresponds to a domain element, i.e.,
9170 one of the elements that is visited by the AST.
9172 Each type of node has its own additional properties.
9174 #include <isl/ast.h>
9175 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9176 __isl_keep isl_ast_node *node);
9177 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9178 __isl_keep isl_ast_node *node);
9179 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9180 __isl_keep isl_ast_node *node);
9181 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9182 __isl_keep isl_ast_node *node);
9183 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9184 __isl_keep isl_ast_node *node);
9185 isl_bool isl_ast_node_for_is_degenerate(
9186 __isl_keep isl_ast_node *node);
9188 An C<isl_ast_for> is considered degenerate if it is known to execute
9191 #include <isl/ast.h>
9192 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9193 __isl_keep isl_ast_node *node);
9194 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9195 __isl_keep isl_ast_node *node);
9196 isl_bool isl_ast_node_if_has_else(
9197 __isl_keep isl_ast_node *node);
9198 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9199 __isl_keep isl_ast_node *node);
9201 __isl_give isl_ast_node_list *
9202 isl_ast_node_block_get_children(
9203 __isl_keep isl_ast_node *node);
9205 __isl_give isl_id *isl_ast_node_mark_get_id(
9206 __isl_keep isl_ast_node *node);
9207 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9208 __isl_keep isl_ast_node *node);
9210 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9211 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9213 #include <isl/ast.h>
9214 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9215 __isl_keep isl_ast_node *node);
9217 All descendants of a specific node in the AST (including the node itself)
9219 in depth-first pre-order using the following function.
9221 #include <isl/ast.h>
9222 isl_stat isl_ast_node_foreach_descendant_top_down(
9223 __isl_keep isl_ast_node *node,
9224 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9225 void *user), void *user);
9227 The callback function should return C<isl_bool_true> if the children
9228 of the given node should be visited and C<isl_bool_false> if they should not.
9229 It should return C<isl_bool_error> in case of failure, in which case
9230 the entire traversal is aborted.
9232 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9233 the following functions.
9235 #include <isl/ast.h>
9236 enum isl_ast_expr_type isl_ast_expr_get_type(
9237 __isl_keep isl_ast_expr *expr);
9239 The type of an AST expression is one of
9241 C<isl_ast_expr_id> or
9242 C<isl_ast_expr_int>.
9243 An C<isl_ast_expr_op> represents the result of an operation.
9244 An C<isl_ast_expr_id> represents an identifier.
9245 An C<isl_ast_expr_int> represents an integer value.
9247 Each type of expression has its own additional properties.
9249 #include <isl/ast.h>
9250 enum isl_ast_op_type isl_ast_expr_get_op_type(
9251 __isl_keep isl_ast_expr *expr);
9252 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9253 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9254 __isl_keep isl_ast_expr *expr, int pos);
9255 isl_stat isl_ast_expr_foreach_ast_op_type(
9256 __isl_keep isl_ast_expr *expr,
9257 isl_stat (*fn)(enum isl_ast_op_type type,
9258 void *user), void *user);
9259 isl_stat isl_ast_node_foreach_ast_op_type(
9260 __isl_keep isl_ast_node *node,
9261 isl_stat (*fn)(enum isl_ast_op_type type,
9262 void *user), void *user);
9264 C<isl_ast_expr_get_op_type> returns the type of the operation
9265 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9266 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9268 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9269 C<isl_ast_op_type> that appears in C<expr>.
9270 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9271 C<isl_ast_op_type> that appears in C<node>.
9272 The operation type is one of the following.
9276 =item C<isl_ast_op_and>
9278 Logical I<and> of two arguments.
9279 Both arguments can be evaluated.
9281 =item C<isl_ast_op_and_then>
9283 Logical I<and> of two arguments.
9284 The second argument can only be evaluated if the first evaluates to true.
9286 =item C<isl_ast_op_or>
9288 Logical I<or> of two arguments.
9289 Both arguments can be evaluated.
9291 =item C<isl_ast_op_or_else>
9293 Logical I<or> of two arguments.
9294 The second argument can only be evaluated if the first evaluates to false.
9296 =item C<isl_ast_op_max>
9298 Maximum of two or more arguments.
9300 =item C<isl_ast_op_min>
9302 Minimum of two or more arguments.
9304 =item C<isl_ast_op_minus>
9308 =item C<isl_ast_op_add>
9310 Sum of two arguments.
9312 =item C<isl_ast_op_sub>
9314 Difference of two arguments.
9316 =item C<isl_ast_op_mul>
9318 Product of two arguments.
9320 =item C<isl_ast_op_div>
9322 Exact division. That is, the result is known to be an integer.
9324 =item C<isl_ast_op_fdiv_q>
9326 Result of integer division, rounded towards negative
9329 =item C<isl_ast_op_pdiv_q>
9331 Result of integer division, where dividend is known to be non-negative.
9333 =item C<isl_ast_op_pdiv_r>
9335 Remainder of integer division, where dividend is known to be non-negative.
9337 =item C<isl_ast_op_zdiv_r>
9339 Equal to zero iff the remainder on integer division is zero.
9341 =item C<isl_ast_op_cond>
9343 Conditional operator defined on three arguments.
9344 If the first argument evaluates to true, then the result
9345 is equal to the second argument. Otherwise, the result
9346 is equal to the third argument.
9347 The second and third argument may only be evaluated if
9348 the first argument evaluates to true and false, respectively.
9349 Corresponds to C<a ? b : c> in C.
9351 =item C<isl_ast_op_select>
9353 Conditional operator defined on three arguments.
9354 If the first argument evaluates to true, then the result
9355 is equal to the second argument. Otherwise, the result
9356 is equal to the third argument.
9357 The second and third argument may be evaluated independently
9358 of the value of the first argument.
9359 Corresponds to C<a * b + (1 - a) * c> in C.
9361 =item C<isl_ast_op_eq>
9365 =item C<isl_ast_op_le>
9367 Less than or equal relation.
9369 =item C<isl_ast_op_lt>
9373 =item C<isl_ast_op_ge>
9375 Greater than or equal relation.
9377 =item C<isl_ast_op_gt>
9379 Greater than relation.
9381 =item C<isl_ast_op_call>
9384 The number of arguments of the C<isl_ast_expr> is one more than
9385 the number of arguments in the function call, the first argument
9386 representing the function being called.
9388 =item C<isl_ast_op_access>
9391 The number of arguments of the C<isl_ast_expr> is one more than
9392 the number of index expressions in the array access, the first argument
9393 representing the array being accessed.
9395 =item C<isl_ast_op_member>
9398 This operation has two arguments, a structure and the name of
9399 the member of the structure being accessed.
9403 #include <isl/ast.h>
9404 __isl_give isl_id *isl_ast_expr_get_id(
9405 __isl_keep isl_ast_expr *expr);
9407 Return the identifier represented by the AST expression.
9409 #include <isl/ast.h>
9410 __isl_give isl_val *isl_ast_expr_get_val(
9411 __isl_keep isl_ast_expr *expr);
9413 Return the integer represented by the AST expression.
9415 =head3 Properties of ASTs
9417 #include <isl/ast.h>
9418 isl_bool isl_ast_expr_is_equal(
9419 __isl_keep isl_ast_expr *expr1,
9420 __isl_keep isl_ast_expr *expr2);
9422 Check if two C<isl_ast_expr>s are equal to each other.
9424 =head3 Manipulating and printing the AST
9426 AST nodes can be copied and freed using the following functions.
9428 #include <isl/ast.h>
9429 __isl_give isl_ast_node *isl_ast_node_copy(
9430 __isl_keep isl_ast_node *node);
9431 __isl_null isl_ast_node *isl_ast_node_free(
9432 __isl_take isl_ast_node *node);
9434 AST expressions can be copied and freed using the following functions.
9436 #include <isl/ast.h>
9437 __isl_give isl_ast_expr *isl_ast_expr_copy(
9438 __isl_keep isl_ast_expr *expr);
9439 __isl_null isl_ast_expr *isl_ast_expr_free(
9440 __isl_take isl_ast_expr *expr);
9442 New AST expressions can be created either directly or within
9443 the context of an C<isl_ast_build>.
9445 #include <isl/ast.h>
9446 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9447 __isl_take isl_val *v);
9448 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9449 __isl_take isl_id *id);
9450 __isl_give isl_ast_expr *isl_ast_expr_neg(
9451 __isl_take isl_ast_expr *expr);
9452 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9453 __isl_take isl_ast_expr *expr);
9454 __isl_give isl_ast_expr *isl_ast_expr_add(
9455 __isl_take isl_ast_expr *expr1,
9456 __isl_take isl_ast_expr *expr2);
9457 __isl_give isl_ast_expr *isl_ast_expr_sub(
9458 __isl_take isl_ast_expr *expr1,
9459 __isl_take isl_ast_expr *expr2);
9460 __isl_give isl_ast_expr *isl_ast_expr_mul(
9461 __isl_take isl_ast_expr *expr1,
9462 __isl_take isl_ast_expr *expr2);
9463 __isl_give isl_ast_expr *isl_ast_expr_div(
9464 __isl_take isl_ast_expr *expr1,
9465 __isl_take isl_ast_expr *expr2);
9466 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9467 __isl_take isl_ast_expr *expr1,
9468 __isl_take isl_ast_expr *expr2);
9469 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9470 __isl_take isl_ast_expr *expr1,
9471 __isl_take isl_ast_expr *expr2);
9472 __isl_give isl_ast_expr *isl_ast_expr_and(
9473 __isl_take isl_ast_expr *expr1,
9474 __isl_take isl_ast_expr *expr2)
9475 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9476 __isl_take isl_ast_expr *expr1,
9477 __isl_take isl_ast_expr *expr2)
9478 __isl_give isl_ast_expr *isl_ast_expr_or(
9479 __isl_take isl_ast_expr *expr1,
9480 __isl_take isl_ast_expr *expr2)
9481 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9482 __isl_take isl_ast_expr *expr1,
9483 __isl_take isl_ast_expr *expr2)
9484 __isl_give isl_ast_expr *isl_ast_expr_eq(
9485 __isl_take isl_ast_expr *expr1,
9486 __isl_take isl_ast_expr *expr2);
9487 __isl_give isl_ast_expr *isl_ast_expr_le(
9488 __isl_take isl_ast_expr *expr1,
9489 __isl_take isl_ast_expr *expr2);
9490 __isl_give isl_ast_expr *isl_ast_expr_lt(
9491 __isl_take isl_ast_expr *expr1,
9492 __isl_take isl_ast_expr *expr2);
9493 __isl_give isl_ast_expr *isl_ast_expr_ge(
9494 __isl_take isl_ast_expr *expr1,
9495 __isl_take isl_ast_expr *expr2);
9496 __isl_give isl_ast_expr *isl_ast_expr_gt(
9497 __isl_take isl_ast_expr *expr1,
9498 __isl_take isl_ast_expr *expr2);
9499 __isl_give isl_ast_expr *isl_ast_expr_access(
9500 __isl_take isl_ast_expr *array,
9501 __isl_take isl_ast_expr_list *indices);
9502 __isl_give isl_ast_expr *isl_ast_expr_call(
9503 __isl_take isl_ast_expr *function,
9504 __isl_take isl_ast_expr_list *arguments);
9506 The function C<isl_ast_expr_address_of> can be applied to an
9507 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9508 to represent the address of the C<isl_ast_expr_access>. The function
9509 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9510 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9512 #include <isl/ast_build.h>
9513 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9514 __isl_keep isl_ast_build *build,
9515 __isl_take isl_set *set);
9516 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9517 __isl_keep isl_ast_build *build,
9518 __isl_take isl_pw_aff *pa);
9519 __isl_give isl_ast_expr *
9520 isl_ast_build_access_from_pw_multi_aff(
9521 __isl_keep isl_ast_build *build,
9522 __isl_take isl_pw_multi_aff *pma);
9523 __isl_give isl_ast_expr *
9524 isl_ast_build_access_from_multi_pw_aff(
9525 __isl_keep isl_ast_build *build,
9526 __isl_take isl_multi_pw_aff *mpa);
9527 __isl_give isl_ast_expr *
9528 isl_ast_build_call_from_pw_multi_aff(
9529 __isl_keep isl_ast_build *build,
9530 __isl_take isl_pw_multi_aff *pma);
9531 __isl_give isl_ast_expr *
9532 isl_ast_build_call_from_multi_pw_aff(
9533 __isl_keep isl_ast_build *build,
9534 __isl_take isl_multi_pw_aff *mpa);
9537 the domains of C<pa>, C<mpa> and C<pma> should correspond
9538 to the schedule space of C<build>.
9539 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9540 the function being called.
9541 If the accessed space is a nested relation, then it is taken
9542 to represent an access of the member specified by the range
9543 of this nested relation of the structure specified by the domain
9544 of the nested relation.
9546 The following functions can be used to modify an C<isl_ast_expr>.
9548 #include <isl/ast.h>
9549 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9550 __isl_take isl_ast_expr *expr, int pos,
9551 __isl_take isl_ast_expr *arg);
9553 Replace the argument of C<expr> at position C<pos> by C<arg>.
9555 #include <isl/ast.h>
9556 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9557 __isl_take isl_ast_expr *expr,
9558 __isl_take isl_id_to_ast_expr *id2expr);
9560 The function C<isl_ast_expr_substitute_ids> replaces the
9561 subexpressions of C<expr> of type C<isl_ast_expr_id>
9562 by the corresponding expression in C<id2expr>, if there is any.
9565 User specified data can be attached to an C<isl_ast_node> and obtained
9566 from the same C<isl_ast_node> using the following functions.
9568 #include <isl/ast.h>
9569 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9570 __isl_take isl_ast_node *node,
9571 __isl_take isl_id *annotation);
9572 __isl_give isl_id *isl_ast_node_get_annotation(
9573 __isl_keep isl_ast_node *node);
9575 Basic printing can be performed using the following functions.
9577 #include <isl/ast.h>
9578 __isl_give isl_printer *isl_printer_print_ast_expr(
9579 __isl_take isl_printer *p,
9580 __isl_keep isl_ast_expr *expr);
9581 __isl_give isl_printer *isl_printer_print_ast_node(
9582 __isl_take isl_printer *p,
9583 __isl_keep isl_ast_node *node);
9584 __isl_give char *isl_ast_expr_to_str(
9585 __isl_keep isl_ast_expr *expr);
9587 More advanced printing can be performed using the following functions.
9589 #include <isl/ast.h>
9590 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9591 __isl_take isl_printer *p,
9592 enum isl_ast_op_type type,
9593 __isl_keep const char *name);
9594 isl_stat isl_options_set_ast_print_macro_once(
9595 isl_ctx *ctx, int val);
9596 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9597 __isl_give isl_printer *isl_ast_op_type_print_macro(
9598 enum isl_ast_op_type type,
9599 __isl_take isl_printer *p);
9600 __isl_give isl_printer *isl_ast_expr_print_macros(
9601 __isl_keep isl_ast_expr *expr,
9602 __isl_take isl_printer *p);
9603 __isl_give isl_printer *isl_ast_node_print_macros(
9604 __isl_keep isl_ast_node *node,
9605 __isl_take isl_printer *p);
9606 __isl_give isl_printer *isl_ast_node_print(
9607 __isl_keep isl_ast_node *node,
9608 __isl_take isl_printer *p,
9609 __isl_take isl_ast_print_options *options);
9610 __isl_give isl_printer *isl_ast_node_for_print(
9611 __isl_keep isl_ast_node *node,
9612 __isl_take isl_printer *p,
9613 __isl_take isl_ast_print_options *options);
9614 __isl_give isl_printer *isl_ast_node_if_print(
9615 __isl_keep isl_ast_node *node,
9616 __isl_take isl_printer *p,
9617 __isl_take isl_ast_print_options *options);
9619 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9620 C<isl> may print out an AST that makes use of macros such
9621 as C<floord>, C<min> and C<max>.
9622 The names of these macros may be modified by a call
9623 to C<isl_ast_op_type_set_print_name>. The user-specified
9624 names are associated to the printer object.
9625 C<isl_ast_op_type_print_macro> prints out the macro
9626 corresponding to a specific C<isl_ast_op_type>.
9627 If the print-macro-once option is set, then a given macro definition
9628 is only printed once to any given printer object.
9629 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9630 for subexpressions where these macros would be used and prints
9631 out the required macro definitions.
9632 Essentially, C<isl_ast_expr_print_macros> calls
9633 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9634 as function argument.
9635 C<isl_ast_node_print_macros> does the same
9636 for expressions in its C<isl_ast_node> argument.
9637 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9638 C<isl_ast_node_if_print> print an C<isl_ast_node>
9639 in C<ISL_FORMAT_C>, but allow for some extra control
9640 through an C<isl_ast_print_options> object.
9641 This object can be created using the following functions.
9643 #include <isl/ast.h>
9644 __isl_give isl_ast_print_options *
9645 isl_ast_print_options_alloc(isl_ctx *ctx);
9646 __isl_give isl_ast_print_options *
9647 isl_ast_print_options_copy(
9648 __isl_keep isl_ast_print_options *options);
9649 __isl_null isl_ast_print_options *
9650 isl_ast_print_options_free(
9651 __isl_take isl_ast_print_options *options);
9653 __isl_give isl_ast_print_options *
9654 isl_ast_print_options_set_print_user(
9655 __isl_take isl_ast_print_options *options,
9656 __isl_give isl_printer *(*print_user)(
9657 __isl_take isl_printer *p,
9658 __isl_take isl_ast_print_options *options,
9659 __isl_keep isl_ast_node *node, void *user),
9661 __isl_give isl_ast_print_options *
9662 isl_ast_print_options_set_print_for(
9663 __isl_take isl_ast_print_options *options,
9664 __isl_give isl_printer *(*print_for)(
9665 __isl_take isl_printer *p,
9666 __isl_take isl_ast_print_options *options,
9667 __isl_keep isl_ast_node *node, void *user),
9670 The callback set by C<isl_ast_print_options_set_print_user>
9671 is called whenever a node of type C<isl_ast_node_user> needs to
9673 The callback set by C<isl_ast_print_options_set_print_for>
9674 is called whenever a node of type C<isl_ast_node_for> needs to
9676 Note that C<isl_ast_node_for_print> will I<not> call the
9677 callback set by C<isl_ast_print_options_set_print_for> on the node
9678 on which C<isl_ast_node_for_print> is called, but only on nested
9679 nodes of type C<isl_ast_node_for>. It is therefore safe to
9680 call C<isl_ast_node_for_print> from within the callback set by
9681 C<isl_ast_print_options_set_print_for>.
9683 The following option determines the type to be used for iterators
9684 while printing the AST.
9686 isl_stat isl_options_set_ast_iterator_type(
9687 isl_ctx *ctx, const char *val);
9688 const char *isl_options_get_ast_iterator_type(
9691 The AST printer only prints body nodes as blocks if these
9692 blocks cannot be safely omitted.
9693 For example, a C<for> node with one body node will not be
9694 surrounded with braces in C<ISL_FORMAT_C>.
9695 A block will always be printed by setting the following option.
9697 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9699 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9703 #include <isl/ast_build.h>
9704 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9705 isl_ctx *ctx, int val);
9706 int isl_options_get_ast_build_atomic_upper_bound(
9708 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9710 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9711 isl_stat isl_options_set_ast_build_detect_min_max(
9712 isl_ctx *ctx, int val);
9713 int isl_options_get_ast_build_detect_min_max(
9715 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9716 isl_ctx *ctx, int val);
9717 int isl_options_get_ast_build_exploit_nested_bounds(
9719 isl_stat isl_options_set_ast_build_group_coscheduled(
9720 isl_ctx *ctx, int val);
9721 int isl_options_get_ast_build_group_coscheduled(
9723 isl_stat isl_options_set_ast_build_scale_strides(
9724 isl_ctx *ctx, int val);
9725 int isl_options_get_ast_build_scale_strides(
9727 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9729 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9730 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9732 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9736 =item * ast_build_atomic_upper_bound
9738 Generate loop upper bounds that consist of the current loop iterator,
9739 an operator and an expression not involving the iterator.
9740 If this option is not set, then the current loop iterator may appear
9741 several times in the upper bound.
9742 For example, when this option is turned off, AST generation
9745 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9749 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9752 When the option is turned on, the following AST is generated
9754 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9757 =item * ast_build_prefer_pdiv
9759 If this option is turned off, then the AST generation will
9760 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9761 operators, but no C<isl_ast_op_pdiv_q> or
9762 C<isl_ast_op_pdiv_r> operators.
9763 If this option is turned on, then C<isl> will try to convert
9764 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9765 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9767 =item * ast_build_detect_min_max
9769 If this option is turned on, then C<isl> will try and detect
9770 min or max-expressions when building AST expressions from
9771 piecewise affine expressions.
9773 =item * ast_build_exploit_nested_bounds
9775 Simplify conditions based on bounds of nested for loops.
9776 In particular, remove conditions that are implied by the fact
9777 that one or more nested loops have at least one iteration,
9778 meaning that the upper bound is at least as large as the lower bound.
9779 For example, when this option is turned off, AST generation
9782 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
9788 for (int c0 = 0; c0 <= N; c0 += 1)
9789 for (int c1 = 0; c1 <= M; c1 += 1)
9792 When the option is turned on, the following AST is generated
9794 for (int c0 = 0; c0 <= N; c0 += 1)
9795 for (int c1 = 0; c1 <= M; c1 += 1)
9798 =item * ast_build_group_coscheduled
9800 If two domain elements are assigned the same schedule point, then
9801 they may be executed in any order and they may even appear in different
9802 loops. If this options is set, then the AST generator will make
9803 sure that coscheduled domain elements do not appear in separate parts
9804 of the AST. This is useful in case of nested AST generation
9805 if the outer AST generation is given only part of a schedule
9806 and the inner AST generation should handle the domains that are
9807 coscheduled by this initial part of the schedule together.
9808 For example if an AST is generated for a schedule
9810 { A[i] -> [0]; B[i] -> [0] }
9812 then the C<isl_ast_build_set_create_leaf> callback described
9813 below may get called twice, once for each domain.
9814 Setting this option ensures that the callback is only called once
9815 on both domains together.
9817 =item * ast_build_separation_bounds
9819 This option specifies which bounds to use during separation.
9820 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
9821 then all (possibly implicit) bounds on the current dimension will
9822 be used during separation.
9823 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
9824 then only those bounds that are explicitly available will
9825 be used during separation.
9827 =item * ast_build_scale_strides
9829 This option specifies whether the AST generator is allowed
9830 to scale down iterators of strided loops.
9832 =item * ast_build_allow_else
9834 This option specifies whether the AST generator is allowed
9835 to construct if statements with else branches.
9837 =item * ast_build_allow_or
9839 This option specifies whether the AST generator is allowed
9840 to construct if conditions with disjunctions.
9844 =head3 AST Generation Options (Schedule Tree)
9846 In case of AST construction from a schedule tree, the options
9847 that control how an AST is created from the individual schedule
9848 dimensions are stored in the band nodes of the tree
9849 (see L</"Schedule Trees">).
9851 In particular, a schedule dimension can be handled in four
9852 different ways, atomic, separate, unroll or the default.
9853 This loop AST generation type can be set using
9854 C<isl_schedule_node_band_member_set_ast_loop_type>.
9856 the first three can be selected by including a one-dimensional
9857 element with as value the position of the schedule dimension
9858 within the band and as name one of C<atomic>, C<separate>
9859 or C<unroll> in the options
9860 set by C<isl_schedule_node_band_set_ast_build_options>.
9861 Only one of these three may be specified for
9862 any given schedule dimension within a band node.
9863 If none of these is specified, then the default
9864 is used. The meaning of the options is as follows.
9870 When this option is specified, the AST generator will make
9871 sure that a given domains space only appears in a single
9872 loop at the specified level.
9874 For example, for the schedule tree
9876 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9878 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9879 options: "{ atomic[x] }"
9881 the following AST will be generated
9883 for (int c0 = 0; c0 <= 10; c0 += 1) {
9890 On the other hand, for the schedule tree
9892 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9894 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9895 options: "{ separate[x] }"
9897 the following AST will be generated
9901 for (int c0 = 1; c0 <= 9; c0 += 1) {
9908 If neither C<atomic> nor C<separate> is specified, then the AST generator
9909 may produce either of these two results or some intermediate form.
9913 When this option is specified, the AST generator will
9914 split the domain of the specified schedule dimension
9915 into pieces with a fixed set of statements for which
9916 instances need to be executed by the iterations in
9917 the schedule domain part. This option tends to avoid
9918 the generation of guards inside the corresponding loops.
9919 See also the C<atomic> option.
9923 When this option is specified, the AST generator will
9924 I<completely> unroll the corresponding schedule dimension.
9925 It is the responsibility of the user to ensure that such
9926 unrolling is possible.
9927 To obtain a partial unrolling, the user should apply an additional
9928 strip-mining to the schedule and fully unroll the inner schedule
9933 The C<isolate> option is a bit more involved. It allows the user
9934 to isolate a range of schedule dimension values from smaller and
9935 greater values. Additionally, the user may specify a different
9936 atomic/separate/unroll choice for the isolated part and the remaining
9937 parts. The typical use case of the C<isolate> option is to isolate
9938 full tiles from partial tiles.
9939 The part that needs to be isolated may depend on outer schedule dimensions.
9940 The option therefore needs to be able to reference those outer schedule
9941 dimensions. In particular, the space of the C<isolate> option is that
9942 of a wrapped map with as domain the flat product of all outer band nodes
9943 and as range the space of the current band node.
9944 The atomic/separate/unroll choice for the isolated part is determined
9945 by an option that lives in an unnamed wrapped space with as domain
9946 a zero-dimensional C<isolate> space and as range the regular
9947 C<atomic>, C<separate> or C<unroll> space.
9948 This option may also be set directly using
9949 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
9950 The atomic/separate/unroll choice for the remaining part is determined
9951 by the regular C<atomic>, C<separate> or C<unroll> option.
9952 The use of the C<isolate> option causes any tree containing the node
9953 to be considered anchored.
9955 As an example, consider the isolation of full tiles from partial tiles
9956 in a tiling of a triangular domain. The original schedule is as follows.
9958 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9960 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9961 { A[i,j] -> [floor(j/10)] }, \
9962 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9966 for (int c0 = 0; c0 <= 10; c0 += 1)
9967 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9968 for (int c2 = 10 * c0;
9969 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9970 for (int c3 = 10 * c1;
9971 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9974 Isolating the full tiles, we have the following input
9976 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9978 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9979 { A[i,j] -> [floor(j/10)] }, \
9980 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9981 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9982 10a+9+10b+9 <= 100 }"
9987 for (int c0 = 0; c0 <= 8; c0 += 1) {
9988 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9989 for (int c2 = 10 * c0;
9990 c2 <= 10 * c0 + 9; c2 += 1)
9991 for (int c3 = 10 * c1;
9992 c3 <= 10 * c1 + 9; c3 += 1)
9994 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9995 for (int c2 = 10 * c0;
9996 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9997 for (int c3 = 10 * c1;
9998 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10001 for (int c0 = 9; c0 <= 10; c0 += 1)
10002 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10003 for (int c2 = 10 * c0;
10004 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10005 for (int c3 = 10 * c1;
10006 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10010 We may then additionally unroll the innermost loop of the isolated part
10012 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10014 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10015 { A[i,j] -> [floor(j/10)] }, \
10016 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10017 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10018 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10023 for (int c0 = 0; c0 <= 8; c0 += 1) {
10024 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10025 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10027 A(c2, 10 * c1 + 1);
10028 A(c2, 10 * c1 + 2);
10029 A(c2, 10 * c1 + 3);
10030 A(c2, 10 * c1 + 4);
10031 A(c2, 10 * c1 + 5);
10032 A(c2, 10 * c1 + 6);
10033 A(c2, 10 * c1 + 7);
10034 A(c2, 10 * c1 + 8);
10035 A(c2, 10 * c1 + 9);
10037 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10038 for (int c2 = 10 * c0;
10039 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10040 for (int c3 = 10 * c1;
10041 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10044 for (int c0 = 9; c0 <= 10; c0 += 1)
10045 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10046 for (int c2 = 10 * c0;
10047 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10048 for (int c3 = 10 * c1;
10049 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10054 =head3 AST Generation Options (Schedule Map)
10056 In case of AST construction using
10057 C<isl_ast_build_node_from_schedule_map>, the options
10058 that control how an AST is created from the individual schedule
10059 dimensions are stored in the C<isl_ast_build>.
10060 They can be set using the following function.
10062 #include <isl/ast_build.h>
10063 __isl_give isl_ast_build *
10064 isl_ast_build_set_options(
10065 __isl_take isl_ast_build *control,
10066 __isl_take isl_union_map *options);
10068 The options are encoded in an C<isl_union_map>.
10069 The domain of this union relation refers to the schedule domain,
10070 i.e., the range of the schedule passed
10071 to C<isl_ast_build_node_from_schedule_map>.
10072 In the case of nested AST generation (see L</"Nested AST Generation">),
10073 the domain of C<options> should refer to the extra piece of the schedule.
10074 That is, it should be equal to the range of the wrapped relation in the
10075 range of the schedule.
10076 The range of the options can consist of elements in one or more spaces,
10077 the names of which determine the effect of the option.
10078 The values of the range typically also refer to the schedule dimension
10079 to which the option applies. In case of nested AST generation
10080 (see L</"Nested AST Generation">), these values refer to the position
10081 of the schedule dimension within the innermost AST generation.
10082 The constraints on the domain elements of
10083 the option should only refer to this dimension and earlier dimensions.
10084 We consider the following spaces.
10088 =item C<separation_class>
10090 B<This option has been deprecated. Use the isolate option on
10091 schedule trees instead.>
10093 This space is a wrapped relation between two one dimensional spaces.
10094 The input space represents the schedule dimension to which the option
10095 applies and the output space represents the separation class.
10096 While constructing a loop corresponding to the specified schedule
10097 dimension(s), the AST generator will try to generate separate loops
10098 for domain elements that are assigned different classes.
10099 If only some of the elements are assigned a class, then those elements
10100 that are not assigned any class will be treated as belonging to a class
10101 that is separate from the explicitly assigned classes.
10102 The typical use case for this option is to separate full tiles from
10104 The other options, described below, are applied after the separation
10107 As an example, consider the separation into full and partial tiles
10108 of a tiling of a triangular domain.
10109 Take, for example, the domain
10111 { A[i,j] : 0 <= i,j and i + j <= 100 }
10113 and a tiling into tiles of 10 by 10. The input to the AST generator
10114 is then the schedule
10116 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10119 Without any options, the following AST is generated
10121 for (int c0 = 0; c0 <= 10; c0 += 1)
10122 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10123 for (int c2 = 10 * c0;
10124 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10126 for (int c3 = 10 * c1;
10127 c3 <= min(10 * c1 + 9, -c2 + 100);
10131 Separation into full and partial tiles can be obtained by assigning
10132 a class, say C<0>, to the full tiles. The full tiles are represented by those
10133 values of the first and second schedule dimensions for which there are
10134 values of the third and fourth dimensions to cover an entire tile.
10135 That is, we need to specify the following option
10137 { [a,b,c,d] -> separation_class[[0]->[0]] :
10138 exists b': 0 <= 10a,10b' and
10139 10a+9+10b'+9 <= 100;
10140 [a,b,c,d] -> separation_class[[1]->[0]] :
10141 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10143 which simplifies to
10145 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10146 a >= 0 and b >= 0 and b <= 8 - a;
10147 [a, b, c, d] -> separation_class[[0] -> [0]] :
10148 a >= 0 and a <= 8 }
10150 With this option, the generated AST is as follows
10153 for (int c0 = 0; c0 <= 8; c0 += 1) {
10154 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10155 for (int c2 = 10 * c0;
10156 c2 <= 10 * c0 + 9; c2 += 1)
10157 for (int c3 = 10 * c1;
10158 c3 <= 10 * c1 + 9; c3 += 1)
10160 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10161 for (int c2 = 10 * c0;
10162 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10164 for (int c3 = 10 * c1;
10165 c3 <= min(-c2 + 100, 10 * c1 + 9);
10169 for (int c0 = 9; c0 <= 10; c0 += 1)
10170 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10171 for (int c2 = 10 * c0;
10172 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10174 for (int c3 = 10 * c1;
10175 c3 <= min(10 * c1 + 9, -c2 + 100);
10182 This is a single-dimensional space representing the schedule dimension(s)
10183 to which ``separation'' should be applied. Separation tries to split
10184 a loop into several pieces if this can avoid the generation of guards
10186 See also the C<atomic> option.
10190 This is a single-dimensional space representing the schedule dimension(s)
10191 for which the domains should be considered ``atomic''. That is, the
10192 AST generator will make sure that any given domain space will only appear
10193 in a single loop at the specified level.
10195 Consider the following schedule
10197 { a[i] -> [i] : 0 <= i < 10;
10198 b[i] -> [i+1] : 0 <= i < 10 }
10200 If the following option is specified
10202 { [i] -> separate[x] }
10204 then the following AST will be generated
10208 for (int c0 = 1; c0 <= 9; c0 += 1) {
10215 If, on the other hand, the following option is specified
10217 { [i] -> atomic[x] }
10219 then the following AST will be generated
10221 for (int c0 = 0; c0 <= 10; c0 += 1) {
10228 If neither C<atomic> nor C<separate> is specified, then the AST generator
10229 may produce either of these two results or some intermediate form.
10233 This is a single-dimensional space representing the schedule dimension(s)
10234 that should be I<completely> unrolled.
10235 To obtain a partial unrolling, the user should apply an additional
10236 strip-mining to the schedule and fully unroll the inner loop.
10240 =head3 Fine-grained Control over AST Generation
10242 Besides specifying the constraints on the parameters,
10243 an C<isl_ast_build> object can be used to control
10244 various aspects of the AST generation process.
10245 In case of AST construction using
10246 C<isl_ast_build_node_from_schedule_map>,
10247 the most prominent way of control is through ``options'',
10248 as explained above.
10250 Additional control is available through the following functions.
10252 #include <isl/ast_build.h>
10253 __isl_give isl_ast_build *
10254 isl_ast_build_set_iterators(
10255 __isl_take isl_ast_build *control,
10256 __isl_take isl_id_list *iterators);
10258 The function C<isl_ast_build_set_iterators> allows the user to
10259 specify a list of iterator C<isl_id>s to be used as iterators.
10260 If the input schedule is injective, then
10261 the number of elements in this list should be as large as the dimension
10262 of the schedule space, but no direct correspondence should be assumed
10263 between dimensions and elements.
10264 If the input schedule is not injective, then an additional number
10265 of C<isl_id>s equal to the largest dimension of the input domains
10267 If the number of provided C<isl_id>s is insufficient, then additional
10268 names are automatically generated.
10270 #include <isl/ast_build.h>
10271 __isl_give isl_ast_build *
10272 isl_ast_build_set_create_leaf(
10273 __isl_take isl_ast_build *control,
10274 __isl_give isl_ast_node *(*fn)(
10275 __isl_take isl_ast_build *build,
10276 void *user), void *user);
10279 C<isl_ast_build_set_create_leaf> function allows for the
10280 specification of a callback that should be called whenever the AST
10281 generator arrives at an element of the schedule domain.
10282 The callback should return an AST node that should be inserted
10283 at the corresponding position of the AST. The default action (when
10284 the callback is not set) is to continue generating parts of the AST to scan
10285 all the domain elements associated to the schedule domain element
10286 and to insert user nodes, ``calling'' the domain element, for each of them.
10287 The C<build> argument contains the current state of the C<isl_ast_build>.
10288 To ease nested AST generation (see L</"Nested AST Generation">),
10289 all control information that is
10290 specific to the current AST generation such as the options and
10291 the callbacks has been removed from this C<isl_ast_build>.
10292 The callback would typically return the result of a nested
10293 AST generation or a
10294 user defined node created using the following function.
10296 #include <isl/ast.h>
10297 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10298 __isl_take isl_ast_expr *expr);
10300 #include <isl/ast_build.h>
10301 __isl_give isl_ast_build *
10302 isl_ast_build_set_at_each_domain(
10303 __isl_take isl_ast_build *build,
10304 __isl_give isl_ast_node *(*fn)(
10305 __isl_take isl_ast_node *node,
10306 __isl_keep isl_ast_build *build,
10307 void *user), void *user);
10308 __isl_give isl_ast_build *
10309 isl_ast_build_set_before_each_for(
10310 __isl_take isl_ast_build *build,
10311 __isl_give isl_id *(*fn)(
10312 __isl_keep isl_ast_build *build,
10313 void *user), void *user);
10314 __isl_give isl_ast_build *
10315 isl_ast_build_set_after_each_for(
10316 __isl_take isl_ast_build *build,
10317 __isl_give isl_ast_node *(*fn)(
10318 __isl_take isl_ast_node *node,
10319 __isl_keep isl_ast_build *build,
10320 void *user), void *user);
10321 __isl_give isl_ast_build *
10322 isl_ast_build_set_before_each_mark(
10323 __isl_take isl_ast_build *build,
10324 isl_stat (*fn)(__isl_keep isl_id *mark,
10325 __isl_keep isl_ast_build *build,
10326 void *user), void *user);
10327 __isl_give isl_ast_build *
10328 isl_ast_build_set_after_each_mark(
10329 __isl_take isl_ast_build *build,
10330 __isl_give isl_ast_node *(*fn)(
10331 __isl_take isl_ast_node *node,
10332 __isl_keep isl_ast_build *build,
10333 void *user), void *user);
10335 The callback set by C<isl_ast_build_set_at_each_domain> will
10336 be called for each domain AST node.
10337 The callbacks set by C<isl_ast_build_set_before_each_for>
10338 and C<isl_ast_build_set_after_each_for> will be called
10339 for each for AST node. The first will be called in depth-first
10340 pre-order, while the second will be called in depth-first post-order.
10341 Since C<isl_ast_build_set_before_each_for> is called before the for
10342 node is actually constructed, it is only passed an C<isl_ast_build>.
10343 The returned C<isl_id> will be added as an annotation (using
10344 C<isl_ast_node_set_annotation>) to the constructed for node.
10345 In particular, if the user has also specified an C<after_each_for>
10346 callback, then the annotation can be retrieved from the node passed to
10347 that callback using C<isl_ast_node_get_annotation>.
10348 The callbacks set by C<isl_ast_build_set_before_each_mark>
10349 and C<isl_ast_build_set_after_each_mark> will be called for each
10350 mark AST node that is created, i.e., for each mark schedule node
10351 in the input schedule tree. The first will be called in depth-first
10352 pre-order, while the second will be called in depth-first post-order.
10353 Since the callback set by C<isl_ast_build_set_before_each_mark>
10354 is called before the mark AST node is actually constructed, it is passed
10355 the identifier of the mark node.
10356 All callbacks should C<NULL> (or -1) on failure.
10357 The given C<isl_ast_build> can be used to create new
10358 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10359 or C<isl_ast_build_call_from_pw_multi_aff>.
10361 =head3 Nested AST Generation
10363 C<isl> allows the user to create an AST within the context
10364 of another AST. These nested ASTs are created using the
10365 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10366 the outer AST. The C<build> argument should be an C<isl_ast_build>
10367 passed to a callback set by
10368 C<isl_ast_build_set_create_leaf>.
10369 The space of the range of the C<schedule> argument should refer
10370 to this build. In particular, the space should be a wrapped
10371 relation and the domain of this wrapped relation should be the
10372 same as that of the range of the schedule returned by
10373 C<isl_ast_build_get_schedule> below.
10374 In practice, the new schedule is typically
10375 created by calling C<isl_union_map_range_product> on the old schedule
10376 and some extra piece of the schedule.
10377 The space of the schedule domain is also available from
10378 the C<isl_ast_build>.
10380 #include <isl/ast_build.h>
10381 __isl_give isl_union_map *isl_ast_build_get_schedule(
10382 __isl_keep isl_ast_build *build);
10383 __isl_give isl_space *isl_ast_build_get_schedule_space(
10384 __isl_keep isl_ast_build *build);
10385 __isl_give isl_ast_build *isl_ast_build_restrict(
10386 __isl_take isl_ast_build *build,
10387 __isl_take isl_set *set);
10389 The C<isl_ast_build_get_schedule> function returns a (partial)
10390 schedule for the domains elements for which part of the AST still needs to
10391 be generated in the current build.
10392 In particular, the domain elements are mapped to those iterations of the loops
10393 enclosing the current point of the AST generation inside which
10394 the domain elements are executed.
10395 No direct correspondence between
10396 the input schedule and this schedule should be assumed.
10397 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10398 to create a set for C<isl_ast_build_restrict> to intersect
10399 with the current build. In particular, the set passed to
10400 C<isl_ast_build_restrict> can have additional parameters.
10401 The ids of the set dimensions in the space returned by
10402 C<isl_ast_build_get_schedule_space> correspond to the
10403 iterators of the already generated loops.
10404 The user should not rely on the ids of the output dimensions
10405 of the relations in the union relation returned by
10406 C<isl_ast_build_get_schedule> having any particular value.
10408 =head1 Applications
10410 Although C<isl> is mainly meant to be used as a library,
10411 it also contains some basic applications that use some
10412 of the functionality of C<isl>.
10413 The input may be specified in either the L<isl format>
10414 or the L<PolyLib format>.
10416 =head2 C<isl_polyhedron_sample>
10418 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10419 an integer element of the polyhedron, if there is any.
10420 The first column in the output is the denominator and is always
10421 equal to 1. If the polyhedron contains no integer points,
10422 then a vector of length zero is printed.
10426 C<isl_pip> takes the same input as the C<example> program
10427 from the C<piplib> distribution, i.e., a set of constraints
10428 on the parameters, a line containing only -1 and finally a set
10429 of constraints on a parametric polyhedron.
10430 The coefficients of the parameters appear in the last columns
10431 (but before the final constant column).
10432 The output is the lexicographic minimum of the parametric polyhedron.
10433 As C<isl> currently does not have its own output format, the output
10434 is just a dump of the internal state.
10436 =head2 C<isl_polyhedron_minimize>
10438 C<isl_polyhedron_minimize> computes the minimum of some linear
10439 or affine objective function over the integer points in a polyhedron.
10440 If an affine objective function
10441 is given, then the constant should appear in the last column.
10443 =head2 C<isl_polytope_scan>
10445 Given a polytope, C<isl_polytope_scan> prints
10446 all integer points in the polytope.
10448 =head2 C<isl_codegen>
10450 Given a schedule, a context set and an options relation,
10451 C<isl_codegen> prints out an AST that scans the domain elements
10452 of the schedule in the order of their image(s) taking into account
10453 the constraints in the context set.