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 __isl_give isl_val *
3778 isl_basic_map_plain_get_val_if_fixed(
3779 __isl_keep isl_basic_map *bmap,
3780 enum isl_dim_type type, unsigned pos);
3781 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3782 __isl_keep isl_set *set,
3783 enum isl_dim_type type, unsigned pos);
3784 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3785 __isl_keep isl_map *map,
3786 enum isl_dim_type type, unsigned pos);
3788 If the set or relation obviously lies on a hyperplane where the given dimension
3789 has a fixed value, then return that value.
3790 Otherwise return NaN.
3794 isl_stat isl_set_dim_residue_class_val(
3795 __isl_keep isl_set *set,
3796 int pos, __isl_give isl_val **modulo,
3797 __isl_give isl_val **residue);
3799 Check if the values of the given set dimension are equal to a fixed
3800 value modulo some integer value. If so, assign the modulo to C<*modulo>
3801 and the fixed value to C<*residue>. If the given dimension attains only
3802 a single value, then assign C<0> to C<*modulo> and the fixed value to
3804 If the dimension does not attain only a single value and if no modulo
3805 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3809 To check whether the description of a set, relation or function depends
3810 on one or more given dimensions,
3811 the following functions can be used.
3813 #include <isl/constraint.h>
3814 isl_bool isl_constraint_involves_dims(
3815 __isl_keep isl_constraint *constraint,
3816 enum isl_dim_type type, unsigned first, unsigned n);
3818 #include <isl/set.h>
3819 isl_bool isl_basic_set_involves_dims(
3820 __isl_keep isl_basic_set *bset,
3821 enum isl_dim_type type, unsigned first, unsigned n);
3822 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3823 enum isl_dim_type type, unsigned first, unsigned n);
3825 #include <isl/map.h>
3826 isl_bool isl_basic_map_involves_dims(
3827 __isl_keep isl_basic_map *bmap,
3828 enum isl_dim_type type, unsigned first, unsigned n);
3829 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3830 enum isl_dim_type type, unsigned first, unsigned n);
3832 #include <isl/union_map.h>
3833 isl_bool isl_union_map_involves_dims(
3834 __isl_keep isl_union_map *umap,
3835 enum isl_dim_type type, unsigned first, unsigned n);
3837 #include <isl/aff.h>
3838 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3839 enum isl_dim_type type, unsigned first, unsigned n);
3840 isl_bool isl_pw_aff_involves_dims(
3841 __isl_keep isl_pw_aff *pwaff,
3842 enum isl_dim_type type, unsigned first, unsigned n);
3843 isl_bool isl_multi_aff_involves_dims(
3844 __isl_keep isl_multi_aff *ma,
3845 enum isl_dim_type type, unsigned first, unsigned n);
3846 isl_bool isl_multi_pw_aff_involves_dims(
3847 __isl_keep isl_multi_pw_aff *mpa,
3848 enum isl_dim_type type, unsigned first, unsigned n);
3850 #include <isl/polynomial.h>
3851 isl_bool isl_qpolynomial_involves_dims(
3852 __isl_keep isl_qpolynomial *qp,
3853 enum isl_dim_type type, unsigned first, unsigned n);
3855 Similarly, the following functions can be used to check whether
3856 a given dimension is involved in any lower or upper bound.
3858 #include <isl/set.h>
3859 isl_bool isl_set_dim_has_any_lower_bound(
3860 __isl_keep isl_set *set,
3861 enum isl_dim_type type, unsigned pos);
3862 isl_bool isl_set_dim_has_any_upper_bound(
3863 __isl_keep isl_set *set,
3864 enum isl_dim_type type, unsigned pos);
3866 Note that these functions return true even if there is a bound on
3867 the dimension on only some of the basic sets of C<set>.
3868 To check if they have a bound for all of the basic sets in C<set>,
3869 use the following functions instead.
3871 #include <isl/set.h>
3872 isl_bool isl_set_dim_has_lower_bound(
3873 __isl_keep isl_set *set,
3874 enum isl_dim_type type, unsigned pos);
3875 isl_bool isl_set_dim_has_upper_bound(
3876 __isl_keep isl_set *set,
3877 enum isl_dim_type type, unsigned pos);
3881 To check whether a set is a parameter domain, use this function:
3883 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3884 isl_bool isl_union_set_is_params(
3885 __isl_keep isl_union_set *uset);
3889 The following functions check whether the space of the given
3890 (basic) set or relation range is a wrapped relation.
3892 #include <isl/space.h>
3893 isl_bool isl_space_is_wrapping(
3894 __isl_keep isl_space *space);
3895 isl_bool isl_space_domain_is_wrapping(
3896 __isl_keep isl_space *space);
3897 isl_bool isl_space_range_is_wrapping(
3898 __isl_keep isl_space *space);
3900 #include <isl/set.h>
3901 isl_bool isl_basic_set_is_wrapping(
3902 __isl_keep isl_basic_set *bset);
3903 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3905 #include <isl/map.h>
3906 isl_bool isl_map_domain_is_wrapping(
3907 __isl_keep isl_map *map);
3908 isl_bool isl_map_range_is_wrapping(
3909 __isl_keep isl_map *map);
3911 #include <isl/val.h>
3912 isl_bool isl_multi_val_range_is_wrapping(
3913 __isl_keep isl_multi_val *mv);
3915 #include <isl/aff.h>
3916 isl_bool isl_multi_aff_range_is_wrapping(
3917 __isl_keep isl_multi_aff *ma);
3918 isl_bool isl_multi_pw_aff_range_is_wrapping(
3919 __isl_keep isl_multi_pw_aff *mpa);
3920 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3921 __isl_keep isl_multi_union_pw_aff *mupa);
3923 The input to C<isl_space_is_wrapping> should
3924 be the space of a set, while that of
3925 C<isl_space_domain_is_wrapping> and
3926 C<isl_space_range_is_wrapping> should be the space of a relation.
3928 =item * Internal Product
3930 isl_bool isl_basic_map_can_zip(
3931 __isl_keep isl_basic_map *bmap);
3932 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
3934 Check whether the product of domain and range of the given relation
3936 i.e., whether both domain and range are nested relations.
3940 #include <isl/space.h>
3941 isl_bool isl_space_can_curry(
3942 __isl_keep isl_space *space);
3944 #include <isl/map.h>
3945 isl_bool isl_basic_map_can_curry(
3946 __isl_keep isl_basic_map *bmap);
3947 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
3949 Check whether the domain of the (basic) relation is a wrapped relation.
3951 #include <isl/space.h>
3952 __isl_give isl_space *isl_space_uncurry(
3953 __isl_take isl_space *space);
3955 #include <isl/map.h>
3956 isl_bool isl_basic_map_can_uncurry(
3957 __isl_keep isl_basic_map *bmap);
3958 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
3960 Check whether the range of the (basic) relation is a wrapped relation.
3962 #include <isl/space.h>
3963 isl_bool isl_space_can_range_curry(
3964 __isl_keep isl_space *space);
3966 #include <isl/map.h>
3967 isl_bool isl_map_can_range_curry(
3968 __isl_keep isl_map *map);
3970 Check whether the domain of the relation wrapped in the range of
3971 the input is itself a wrapped relation.
3973 =item * Special Values
3975 #include <isl/aff.h>
3976 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
3977 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3978 isl_bool isl_multi_pw_aff_is_cst(
3979 __isl_keep isl_multi_pw_aff *mpa);
3981 Check whether the given expression is a constant.
3983 #include <isl/aff.h>
3984 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
3985 isl_bool isl_pw_aff_involves_nan(
3986 __isl_keep isl_pw_aff *pa);
3988 #include <isl/polynomial.h>
3989 isl_bool isl_qpolynomial_fold_is_nan(
3990 __isl_keep isl_qpolynomial_fold *fold);
3992 Check whether the given expression is equal to or involves NaN.
3994 #include <isl/aff.h>
3995 isl_bool isl_aff_plain_is_zero(
3996 __isl_keep isl_aff *aff);
3998 Check whether the affine expression is obviously zero.
4002 =head3 Binary Properties
4008 The following functions check whether two objects
4009 represent the same set, relation or function.
4010 The C<plain> variants only return true if the objects
4011 are obviously the same. That is, they may return false
4012 even if the objects are the same, but they will never
4013 return true if the objects are not the same.
4015 #include <isl/set.h>
4016 isl_bool isl_basic_set_plain_is_equal(
4017 __isl_keep isl_basic_set *bset1,
4018 __isl_keep isl_basic_set *bset2);
4019 isl_bool isl_basic_set_is_equal(
4020 __isl_keep isl_basic_set *bset1,
4021 __isl_keep isl_basic_set *bset2);
4022 isl_bool isl_set_plain_is_equal(
4023 __isl_keep isl_set *set1,
4024 __isl_keep isl_set *set2);
4025 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4026 __isl_keep isl_set *set2);
4028 #include <isl/map.h>
4029 isl_bool isl_basic_map_is_equal(
4030 __isl_keep isl_basic_map *bmap1,
4031 __isl_keep isl_basic_map *bmap2);
4032 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4033 __isl_keep isl_map *map2);
4034 isl_bool isl_map_plain_is_equal(
4035 __isl_keep isl_map *map1,
4036 __isl_keep isl_map *map2);
4038 #include <isl/union_set.h>
4039 isl_bool isl_union_set_is_equal(
4040 __isl_keep isl_union_set *uset1,
4041 __isl_keep isl_union_set *uset2);
4043 #include <isl/union_map.h>
4044 isl_bool isl_union_map_is_equal(
4045 __isl_keep isl_union_map *umap1,
4046 __isl_keep isl_union_map *umap2);
4048 #include <isl/aff.h>
4049 isl_bool isl_aff_plain_is_equal(
4050 __isl_keep isl_aff *aff1,
4051 __isl_keep isl_aff *aff2);
4052 isl_bool isl_multi_aff_plain_is_equal(
4053 __isl_keep isl_multi_aff *maff1,
4054 __isl_keep isl_multi_aff *maff2);
4055 isl_bool isl_pw_aff_plain_is_equal(
4056 __isl_keep isl_pw_aff *pwaff1,
4057 __isl_keep isl_pw_aff *pwaff2);
4058 isl_bool isl_pw_multi_aff_plain_is_equal(
4059 __isl_keep isl_pw_multi_aff *pma1,
4060 __isl_keep isl_pw_multi_aff *pma2);
4061 isl_bool isl_multi_pw_aff_plain_is_equal(
4062 __isl_keep isl_multi_pw_aff *mpa1,
4063 __isl_keep isl_multi_pw_aff *mpa2);
4064 isl_bool isl_multi_pw_aff_is_equal(
4065 __isl_keep isl_multi_pw_aff *mpa1,
4066 __isl_keep isl_multi_pw_aff *mpa2);
4067 isl_bool isl_union_pw_aff_plain_is_equal(
4068 __isl_keep isl_union_pw_aff *upa1,
4069 __isl_keep isl_union_pw_aff *upa2);
4070 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4071 __isl_keep isl_union_pw_multi_aff *upma1,
4072 __isl_keep isl_union_pw_multi_aff *upma2);
4073 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4074 __isl_keep isl_multi_union_pw_aff *mupa1,
4075 __isl_keep isl_multi_union_pw_aff *mupa2);
4077 #include <isl/polynomial.h>
4078 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4079 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4080 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4081 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4082 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4083 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4085 =item * Disjointness
4087 #include <isl/set.h>
4088 isl_bool isl_basic_set_is_disjoint(
4089 __isl_keep isl_basic_set *bset1,
4090 __isl_keep isl_basic_set *bset2);
4091 isl_bool isl_set_plain_is_disjoint(
4092 __isl_keep isl_set *set1,
4093 __isl_keep isl_set *set2);
4094 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4095 __isl_keep isl_set *set2);
4097 #include <isl/map.h>
4098 isl_bool isl_basic_map_is_disjoint(
4099 __isl_keep isl_basic_map *bmap1,
4100 __isl_keep isl_basic_map *bmap2);
4101 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4102 __isl_keep isl_map *map2);
4104 #include <isl/union_set.h>
4105 isl_bool isl_union_set_is_disjoint(
4106 __isl_keep isl_union_set *uset1,
4107 __isl_keep isl_union_set *uset2);
4109 #include <isl/union_map.h>
4110 isl_bool isl_union_map_is_disjoint(
4111 __isl_keep isl_union_map *umap1,
4112 __isl_keep isl_union_map *umap2);
4116 isl_bool isl_basic_set_is_subset(
4117 __isl_keep isl_basic_set *bset1,
4118 __isl_keep isl_basic_set *bset2);
4119 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4120 __isl_keep isl_set *set2);
4121 isl_bool isl_set_is_strict_subset(
4122 __isl_keep isl_set *set1,
4123 __isl_keep isl_set *set2);
4124 isl_bool isl_union_set_is_subset(
4125 __isl_keep isl_union_set *uset1,
4126 __isl_keep isl_union_set *uset2);
4127 isl_bool isl_union_set_is_strict_subset(
4128 __isl_keep isl_union_set *uset1,
4129 __isl_keep isl_union_set *uset2);
4130 isl_bool isl_basic_map_is_subset(
4131 __isl_keep isl_basic_map *bmap1,
4132 __isl_keep isl_basic_map *bmap2);
4133 isl_bool isl_basic_map_is_strict_subset(
4134 __isl_keep isl_basic_map *bmap1,
4135 __isl_keep isl_basic_map *bmap2);
4136 isl_bool isl_map_is_subset(
4137 __isl_keep isl_map *map1,
4138 __isl_keep isl_map *map2);
4139 isl_bool isl_map_is_strict_subset(
4140 __isl_keep isl_map *map1,
4141 __isl_keep isl_map *map2);
4142 isl_bool isl_union_map_is_subset(
4143 __isl_keep isl_union_map *umap1,
4144 __isl_keep isl_union_map *umap2);
4145 isl_bool isl_union_map_is_strict_subset(
4146 __isl_keep isl_union_map *umap1,
4147 __isl_keep isl_union_map *umap2);
4149 Check whether the first argument is a (strict) subset of the
4154 Every comparison function returns a negative value if the first
4155 argument is considered smaller than the second, a positive value
4156 if the first argument is considered greater and zero if the two
4157 constraints are considered the same by the comparison criterion.
4159 #include <isl/constraint.h>
4160 int isl_constraint_plain_cmp(
4161 __isl_keep isl_constraint *c1,
4162 __isl_keep isl_constraint *c2);
4164 This function is useful for sorting C<isl_constraint>s.
4165 The order depends on the internal representation of the inputs.
4166 The order is fixed over different calls to the function (assuming
4167 the internal representation of the inputs has not changed), but may
4168 change over different versions of C<isl>.
4170 #include <isl/constraint.h>
4171 int isl_constraint_cmp_last_non_zero(
4172 __isl_keep isl_constraint *c1,
4173 __isl_keep isl_constraint *c2);
4175 This function can be used to sort constraints that live in the same
4176 local space. Constraints that involve ``earlier'' dimensions or
4177 that have a smaller coefficient for the shared latest dimension
4178 are considered smaller than other constraints.
4179 This function only defines a B<partial> order.
4181 #include <isl/set.h>
4182 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4183 __isl_keep isl_set *set2);
4185 This function is useful for sorting C<isl_set>s.
4186 The order depends on the internal representation of the inputs.
4187 The order is fixed over different calls to the function (assuming
4188 the internal representation of the inputs has not changed), but may
4189 change over different versions of C<isl>.
4191 #include <isl/aff.h>
4192 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4193 __isl_keep isl_pw_aff *pa2);
4195 The function C<isl_pw_aff_plain_cmp> can be used to sort
4196 C<isl_pw_aff>s. The order is not strictly defined.
4197 The current order sorts expressions that only involve
4198 earlier dimensions before those that involve later dimensions.
4202 =head2 Unary Operations
4208 __isl_give isl_set *isl_set_complement(
4209 __isl_take isl_set *set);
4210 __isl_give isl_map *isl_map_complement(
4211 __isl_take isl_map *map);
4215 #include <isl/space.h>
4216 __isl_give isl_space *isl_space_reverse(
4217 __isl_take isl_space *space);
4219 #include <isl/map.h>
4220 __isl_give isl_basic_map *isl_basic_map_reverse(
4221 __isl_take isl_basic_map *bmap);
4222 __isl_give isl_map *isl_map_reverse(
4223 __isl_take isl_map *map);
4225 #include <isl/union_map.h>
4226 __isl_give isl_union_map *isl_union_map_reverse(
4227 __isl_take isl_union_map *umap);
4231 #include <isl/space.h>
4232 __isl_give isl_space *isl_space_domain(
4233 __isl_take isl_space *space);
4234 __isl_give isl_space *isl_space_range(
4235 __isl_take isl_space *space);
4236 __isl_give isl_space *isl_space_params(
4237 __isl_take isl_space *space);
4239 #include <isl/local_space.h>
4240 __isl_give isl_local_space *isl_local_space_domain(
4241 __isl_take isl_local_space *ls);
4242 __isl_give isl_local_space *isl_local_space_range(
4243 __isl_take isl_local_space *ls);
4245 #include <isl/set.h>
4246 __isl_give isl_basic_set *isl_basic_set_project_out(
4247 __isl_take isl_basic_set *bset,
4248 enum isl_dim_type type, unsigned first, unsigned n);
4249 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4250 enum isl_dim_type type, unsigned first, unsigned n);
4251 __isl_give isl_basic_set *isl_basic_set_params(
4252 __isl_take isl_basic_set *bset);
4253 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4255 #include <isl/map.h>
4256 __isl_give isl_basic_map *isl_basic_map_project_out(
4257 __isl_take isl_basic_map *bmap,
4258 enum isl_dim_type type, unsigned first, unsigned n);
4259 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4260 enum isl_dim_type type, unsigned first, unsigned n);
4261 __isl_give isl_basic_set *isl_basic_map_domain(
4262 __isl_take isl_basic_map *bmap);
4263 __isl_give isl_basic_set *isl_basic_map_range(
4264 __isl_take isl_basic_map *bmap);
4265 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4266 __isl_give isl_set *isl_map_domain(
4267 __isl_take isl_map *bmap);
4268 __isl_give isl_set *isl_map_range(
4269 __isl_take isl_map *map);
4271 #include <isl/union_set.h>
4272 __isl_give isl_union_set *isl_union_set_project_out(
4273 __isl_take isl_union_set *uset,
4274 enum isl_dim_type type,
4275 unsigned first, unsigned n);
4276 __isl_give isl_set *isl_union_set_params(
4277 __isl_take isl_union_set *uset);
4279 The function C<isl_union_set_project_out> can only project out
4282 #include <isl/union_map.h>
4283 __isl_give isl_union_map *isl_union_map_project_out(
4284 __isl_take isl_union_map *umap,
4285 enum isl_dim_type type, unsigned first, unsigned n);
4286 __isl_give isl_set *isl_union_map_params(
4287 __isl_take isl_union_map *umap);
4288 __isl_give isl_union_set *isl_union_map_domain(
4289 __isl_take isl_union_map *umap);
4290 __isl_give isl_union_set *isl_union_map_range(
4291 __isl_take isl_union_map *umap);
4293 The function C<isl_union_map_project_out> can only project out
4296 #include <isl/aff.h>
4297 __isl_give isl_aff *isl_aff_project_domain_on_params(
4298 __isl_take isl_aff *aff);
4299 __isl_give isl_pw_multi_aff *
4300 isl_pw_multi_aff_project_domain_on_params(
4301 __isl_take isl_pw_multi_aff *pma);
4302 __isl_give isl_set *isl_pw_aff_domain(
4303 __isl_take isl_pw_aff *pwaff);
4304 __isl_give isl_set *isl_pw_multi_aff_domain(
4305 __isl_take isl_pw_multi_aff *pma);
4306 __isl_give isl_set *isl_multi_pw_aff_domain(
4307 __isl_take isl_multi_pw_aff *mpa);
4308 __isl_give isl_union_set *isl_union_pw_aff_domain(
4309 __isl_take isl_union_pw_aff *upa);
4310 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4311 __isl_take isl_union_pw_multi_aff *upma);
4312 __isl_give isl_union_set *
4313 isl_multi_union_pw_aff_domain(
4314 __isl_take isl_multi_union_pw_aff *mupa);
4315 __isl_give isl_set *isl_pw_aff_params(
4316 __isl_take isl_pw_aff *pwa);
4318 The function C<isl_multi_union_pw_aff_domain> requires its
4319 input to have at least one set dimension.
4321 #include <isl/polynomial.h>
4322 __isl_give isl_qpolynomial *
4323 isl_qpolynomial_project_domain_on_params(
4324 __isl_take isl_qpolynomial *qp);
4325 __isl_give isl_pw_qpolynomial *
4326 isl_pw_qpolynomial_project_domain_on_params(
4327 __isl_take isl_pw_qpolynomial *pwqp);
4328 __isl_give isl_pw_qpolynomial_fold *
4329 isl_pw_qpolynomial_fold_project_domain_on_params(
4330 __isl_take isl_pw_qpolynomial_fold *pwf);
4331 __isl_give isl_set *isl_pw_qpolynomial_domain(
4332 __isl_take isl_pw_qpolynomial *pwqp);
4333 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4334 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4335 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4336 __isl_take isl_union_pw_qpolynomial *upwqp);
4338 #include <isl/space.h>
4339 __isl_give isl_space *isl_space_domain_map(
4340 __isl_take isl_space *space);
4341 __isl_give isl_space *isl_space_range_map(
4342 __isl_take isl_space *space);
4344 #include <isl/map.h>
4345 __isl_give isl_map *isl_set_wrapped_domain_map(
4346 __isl_take isl_set *set);
4347 __isl_give isl_basic_map *isl_basic_map_domain_map(
4348 __isl_take isl_basic_map *bmap);
4349 __isl_give isl_basic_map *isl_basic_map_range_map(
4350 __isl_take isl_basic_map *bmap);
4351 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4352 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4354 #include <isl/union_map.h>
4355 __isl_give isl_union_map *isl_union_map_domain_map(
4356 __isl_take isl_union_map *umap);
4357 __isl_give isl_union_pw_multi_aff *
4358 isl_union_map_domain_map_union_pw_multi_aff(
4359 __isl_take isl_union_map *umap);
4360 __isl_give isl_union_map *isl_union_map_range_map(
4361 __isl_take isl_union_map *umap);
4362 __isl_give isl_union_map *
4363 isl_union_set_wrapped_domain_map(
4364 __isl_take isl_union_set *uset);
4366 The functions above construct a (basic, regular or union) relation
4367 that maps (a wrapped version of) the input relation to its domain or range.
4368 C<isl_set_wrapped_domain_map> maps the input set to the domain
4369 of its wrapped relation.
4373 __isl_give isl_basic_set *isl_basic_set_eliminate(
4374 __isl_take isl_basic_set *bset,
4375 enum isl_dim_type type,
4376 unsigned first, unsigned n);
4377 __isl_give isl_set *isl_set_eliminate(
4378 __isl_take isl_set *set, enum isl_dim_type type,
4379 unsigned first, unsigned n);
4380 __isl_give isl_basic_map *isl_basic_map_eliminate(
4381 __isl_take isl_basic_map *bmap,
4382 enum isl_dim_type type,
4383 unsigned first, unsigned n);
4384 __isl_give isl_map *isl_map_eliminate(
4385 __isl_take isl_map *map, enum isl_dim_type type,
4386 unsigned first, unsigned n);
4388 Eliminate the coefficients for the given dimensions from the constraints,
4389 without removing the dimensions.
4391 =item * Constructing a set from a parameter domain
4393 A zero-dimensional space or (basic) set can be constructed
4394 on a given parameter domain using the following functions.
4396 #include <isl/space.h>
4397 __isl_give isl_space *isl_space_set_from_params(
4398 __isl_take isl_space *space);
4400 #include <isl/set.h>
4401 __isl_give isl_basic_set *isl_basic_set_from_params(
4402 __isl_take isl_basic_set *bset);
4403 __isl_give isl_set *isl_set_from_params(
4404 __isl_take isl_set *set);
4406 =item * Constructing a relation from one or two sets
4408 Create a relation with the given set(s) as domain and/or range.
4409 If only the domain or the range is specified, then
4410 the range or domain of the created relation is a zero-dimensional
4411 flat anonymous space.
4413 #include <isl/space.h>
4414 __isl_give isl_space *isl_space_from_domain(
4415 __isl_take isl_space *space);
4416 __isl_give isl_space *isl_space_from_range(
4417 __isl_take isl_space *space);
4418 __isl_give isl_space *isl_space_map_from_set(
4419 __isl_take isl_space *space);
4420 __isl_give isl_space *isl_space_map_from_domain_and_range(
4421 __isl_take isl_space *domain,
4422 __isl_take isl_space *range);
4424 #include <isl/local_space.h>
4425 __isl_give isl_local_space *isl_local_space_from_domain(
4426 __isl_take isl_local_space *ls);
4428 #include <isl/map.h>
4429 __isl_give isl_map *isl_map_from_domain(
4430 __isl_take isl_set *set);
4431 __isl_give isl_map *isl_map_from_range(
4432 __isl_take isl_set *set);
4434 #include <isl/union_map.h>
4435 __isl_give isl_union_map *
4436 isl_union_map_from_domain_and_range(
4437 __isl_take isl_union_set *domain,
4438 __isl_take isl_union_set *range);
4440 #include <isl/val.h>
4441 __isl_give isl_multi_val *isl_multi_val_from_range(
4442 __isl_take isl_multi_val *mv);
4444 #include <isl/aff.h>
4445 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4446 __isl_take isl_multi_aff *ma);
4447 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4448 __isl_take isl_pw_aff *pwa);
4449 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4450 __isl_take isl_multi_pw_aff *mpa);
4451 __isl_give isl_multi_union_pw_aff *
4452 isl_multi_union_pw_aff_from_range(
4453 __isl_take isl_multi_union_pw_aff *mupa);
4454 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4455 __isl_take isl_set *set);
4456 __isl_give isl_union_pw_multi_aff *
4457 isl_union_pw_multi_aff_from_domain(
4458 __isl_take isl_union_set *uset);
4462 #include <isl/set.h>
4463 __isl_give isl_basic_set *isl_basic_set_fix_si(
4464 __isl_take isl_basic_set *bset,
4465 enum isl_dim_type type, unsigned pos, int value);
4466 __isl_give isl_basic_set *isl_basic_set_fix_val(
4467 __isl_take isl_basic_set *bset,
4468 enum isl_dim_type type, unsigned pos,
4469 __isl_take isl_val *v);
4470 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4471 enum isl_dim_type type, unsigned pos, int value);
4472 __isl_give isl_set *isl_set_fix_val(
4473 __isl_take isl_set *set,
4474 enum isl_dim_type type, unsigned pos,
4475 __isl_take isl_val *v);
4477 #include <isl/map.h>
4478 __isl_give isl_basic_map *isl_basic_map_fix_si(
4479 __isl_take isl_basic_map *bmap,
4480 enum isl_dim_type type, unsigned pos, int value);
4481 __isl_give isl_basic_map *isl_basic_map_fix_val(
4482 __isl_take isl_basic_map *bmap,
4483 enum isl_dim_type type, unsigned pos,
4484 __isl_take isl_val *v);
4485 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4486 enum isl_dim_type type, unsigned pos, int value);
4487 __isl_give isl_map *isl_map_fix_val(
4488 __isl_take isl_map *map,
4489 enum isl_dim_type type, unsigned pos,
4490 __isl_take isl_val *v);
4492 #include <isl/aff.h>
4493 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4494 __isl_take isl_pw_multi_aff *pma,
4495 enum isl_dim_type type, unsigned pos, int value);
4497 #include <isl/polynomial.h>
4498 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4499 __isl_take isl_pw_qpolynomial *pwqp,
4500 enum isl_dim_type type, unsigned n,
4501 __isl_take isl_val *v);
4503 Intersect the set, relation or function domain
4504 with the hyperplane where the given
4505 dimension has the fixed given value.
4507 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4508 __isl_take isl_basic_map *bmap,
4509 enum isl_dim_type type, unsigned pos, int value);
4510 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4511 __isl_take isl_basic_map *bmap,
4512 enum isl_dim_type type, unsigned pos, int value);
4513 __isl_give isl_set *isl_set_lower_bound_si(
4514 __isl_take isl_set *set,
4515 enum isl_dim_type type, unsigned pos, int value);
4516 __isl_give isl_set *isl_set_lower_bound_val(
4517 __isl_take isl_set *set,
4518 enum isl_dim_type type, unsigned pos,
4519 __isl_take isl_val *value);
4520 __isl_give isl_map *isl_map_lower_bound_si(
4521 __isl_take isl_map *map,
4522 enum isl_dim_type type, unsigned pos, int value);
4523 __isl_give isl_set *isl_set_upper_bound_si(
4524 __isl_take isl_set *set,
4525 enum isl_dim_type type, unsigned pos, int value);
4526 __isl_give isl_set *isl_set_upper_bound_val(
4527 __isl_take isl_set *set,
4528 enum isl_dim_type type, unsigned pos,
4529 __isl_take isl_val *value);
4530 __isl_give isl_map *isl_map_upper_bound_si(
4531 __isl_take isl_map *map,
4532 enum isl_dim_type type, unsigned pos, int value);
4534 Intersect the set or relation with the half-space where the given
4535 dimension has a value bounded by the fixed given integer value.
4537 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4538 enum isl_dim_type type1, int pos1,
4539 enum isl_dim_type type2, int pos2);
4540 __isl_give isl_basic_map *isl_basic_map_equate(
4541 __isl_take isl_basic_map *bmap,
4542 enum isl_dim_type type1, int pos1,
4543 enum isl_dim_type type2, int pos2);
4544 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4545 enum isl_dim_type type1, int pos1,
4546 enum isl_dim_type type2, int pos2);
4548 Intersect the set or relation with the hyperplane where the given
4549 dimensions are equal to each other.
4551 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4552 enum isl_dim_type type1, int pos1,
4553 enum isl_dim_type type2, int pos2);
4555 Intersect the relation with the hyperplane where the given
4556 dimensions have opposite values.
4558 __isl_give isl_map *isl_map_order_le(
4559 __isl_take isl_map *map,
4560 enum isl_dim_type type1, int pos1,
4561 enum isl_dim_type type2, int pos2);
4562 __isl_give isl_basic_map *isl_basic_map_order_ge(
4563 __isl_take isl_basic_map *bmap,
4564 enum isl_dim_type type1, int pos1,
4565 enum isl_dim_type type2, int pos2);
4566 __isl_give isl_map *isl_map_order_ge(
4567 __isl_take isl_map *map,
4568 enum isl_dim_type type1, int pos1,
4569 enum isl_dim_type type2, int pos2);
4570 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4571 enum isl_dim_type type1, int pos1,
4572 enum isl_dim_type type2, int pos2);
4573 __isl_give isl_basic_map *isl_basic_map_order_gt(
4574 __isl_take isl_basic_map *bmap,
4575 enum isl_dim_type type1, int pos1,
4576 enum isl_dim_type type2, int pos2);
4577 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4578 enum isl_dim_type type1, int pos1,
4579 enum isl_dim_type type2, int pos2);
4581 Intersect the relation with the half-space where the given
4582 dimensions satisfy the given ordering.
4586 #include <isl/aff.h>
4587 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4588 __isl_take isl_aff *aff);
4589 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4590 __isl_take isl_aff *aff);
4591 __isl_give isl_set *isl_pw_aff_pos_set(
4592 __isl_take isl_pw_aff *pa);
4593 __isl_give isl_set *isl_pw_aff_nonneg_set(
4594 __isl_take isl_pw_aff *pwaff);
4595 __isl_give isl_set *isl_pw_aff_zero_set(
4596 __isl_take isl_pw_aff *pwaff);
4597 __isl_give isl_set *isl_pw_aff_non_zero_set(
4598 __isl_take isl_pw_aff *pwaff);
4599 __isl_give isl_union_set *
4600 isl_union_pw_aff_zero_union_set(
4601 __isl_take isl_union_pw_aff *upa);
4602 __isl_give isl_union_set *
4603 isl_multi_union_pw_aff_zero_union_set(
4604 __isl_take isl_multi_union_pw_aff *mupa);
4606 The function C<isl_aff_neg_basic_set> returns a basic set
4607 containing those elements in the domain space
4608 of C<aff> where C<aff> is negative.
4609 The function C<isl_pw_aff_nonneg_set> returns a set
4610 containing those elements in the domain
4611 of C<pwaff> where C<pwaff> is non-negative.
4612 The function C<isl_multi_union_pw_aff_zero_union_set>
4613 returns a union set containing those elements
4614 in the domains of its elements where they are all zero.
4618 __isl_give isl_map *isl_set_identity(
4619 __isl_take isl_set *set);
4620 __isl_give isl_union_map *isl_union_set_identity(
4621 __isl_take isl_union_set *uset);
4622 __isl_give isl_union_pw_multi_aff *
4623 isl_union_set_identity_union_pw_multi_aff(
4624 __isl_take isl_union_set *uset);
4626 Construct an identity relation on the given (union) set.
4628 =item * Function Extraction
4630 A piecewise quasi affine expression that is equal to 1 on a set
4631 and 0 outside the set can be created using the following function.
4633 #include <isl/aff.h>
4634 __isl_give isl_pw_aff *isl_set_indicator_function(
4635 __isl_take isl_set *set);
4637 A piecewise multiple quasi affine expression can be extracted
4638 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4639 and the C<isl_map> is single-valued.
4640 In case of a conversion from an C<isl_union_map>
4641 to an C<isl_union_pw_multi_aff>, these properties need to hold
4642 in each domain space.
4643 A conversion to a C<isl_multi_union_pw_aff> additionally
4644 requires that the input is non-empty and involves only a single
4647 #include <isl/aff.h>
4648 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4649 __isl_take isl_set *set);
4650 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4651 __isl_take isl_map *map);
4653 __isl_give isl_union_pw_multi_aff *
4654 isl_union_pw_multi_aff_from_union_set(
4655 __isl_take isl_union_set *uset);
4656 __isl_give isl_union_pw_multi_aff *
4657 isl_union_pw_multi_aff_from_union_map(
4658 __isl_take isl_union_map *umap);
4660 __isl_give isl_multi_union_pw_aff *
4661 isl_multi_union_pw_aff_from_union_map(
4662 __isl_take isl_union_map *umap);
4666 __isl_give isl_basic_set *isl_basic_map_deltas(
4667 __isl_take isl_basic_map *bmap);
4668 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4669 __isl_give isl_union_set *isl_union_map_deltas(
4670 __isl_take isl_union_map *umap);
4672 These functions return a (basic) set containing the differences
4673 between image elements and corresponding domain elements in the input.
4675 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4676 __isl_take isl_basic_map *bmap);
4677 __isl_give isl_map *isl_map_deltas_map(
4678 __isl_take isl_map *map);
4679 __isl_give isl_union_map *isl_union_map_deltas_map(
4680 __isl_take isl_union_map *umap);
4682 The functions above construct a (basic, regular or union) relation
4683 that maps (a wrapped version of) the input relation to its delta set.
4687 Simplify the representation of a set, relation or functions by trying
4688 to combine pairs of basic sets or relations into a single
4689 basic set or relation.
4691 #include <isl/set.h>
4692 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4694 #include <isl/map.h>
4695 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4697 #include <isl/union_set.h>
4698 __isl_give isl_union_set *isl_union_set_coalesce(
4699 __isl_take isl_union_set *uset);
4701 #include <isl/union_map.h>
4702 __isl_give isl_union_map *isl_union_map_coalesce(
4703 __isl_take isl_union_map *umap);
4705 #include <isl/aff.h>
4706 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4707 __isl_take isl_pw_aff *pwqp);
4708 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4709 __isl_take isl_pw_multi_aff *pma);
4710 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4711 __isl_take isl_multi_pw_aff *mpa);
4712 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4713 __isl_take isl_union_pw_aff *upa);
4714 __isl_give isl_union_pw_multi_aff *
4715 isl_union_pw_multi_aff_coalesce(
4716 __isl_take isl_union_pw_multi_aff *upma);
4717 __isl_give isl_multi_union_pw_aff *
4718 isl_multi_union_pw_aff_coalesce(
4719 __isl_take isl_multi_union_pw_aff *aff);
4721 #include <isl/polynomial.h>
4722 __isl_give isl_pw_qpolynomial_fold *
4723 isl_pw_qpolynomial_fold_coalesce(
4724 __isl_take isl_pw_qpolynomial_fold *pwf);
4725 __isl_give isl_union_pw_qpolynomial *
4726 isl_union_pw_qpolynomial_coalesce(
4727 __isl_take isl_union_pw_qpolynomial *upwqp);
4728 __isl_give isl_union_pw_qpolynomial_fold *
4729 isl_union_pw_qpolynomial_fold_coalesce(
4730 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4732 One of the methods for combining pairs of basic sets or relations
4733 can result in coefficients that are much larger than those that appear
4734 in the constraints of the input. By default, the coefficients are
4735 not allowed to grow larger, but this can be changed by unsetting
4736 the following option.
4738 isl_stat isl_options_set_coalesce_bounded_wrapping(
4739 isl_ctx *ctx, int val);
4740 int isl_options_get_coalesce_bounded_wrapping(
4743 =item * Detecting equalities
4745 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4746 __isl_take isl_basic_set *bset);
4747 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4748 __isl_take isl_basic_map *bmap);
4749 __isl_give isl_set *isl_set_detect_equalities(
4750 __isl_take isl_set *set);
4751 __isl_give isl_map *isl_map_detect_equalities(
4752 __isl_take isl_map *map);
4753 __isl_give isl_union_set *isl_union_set_detect_equalities(
4754 __isl_take isl_union_set *uset);
4755 __isl_give isl_union_map *isl_union_map_detect_equalities(
4756 __isl_take isl_union_map *umap);
4758 Simplify the representation of a set or relation by detecting implicit
4761 =item * Removing redundant constraints
4763 #include <isl/set.h>
4764 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4765 __isl_take isl_basic_set *bset);
4766 __isl_give isl_set *isl_set_remove_redundancies(
4767 __isl_take isl_set *set);
4769 #include <isl/union_set.h>
4770 __isl_give isl_union_set *
4771 isl_union_set_remove_redundancies(
4772 __isl_take isl_union_set *uset);
4774 #include <isl/map.h>
4775 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4776 __isl_take isl_basic_map *bmap);
4777 __isl_give isl_map *isl_map_remove_redundancies(
4778 __isl_take isl_map *map);
4780 #include <isl/union_map.h>
4781 __isl_give isl_union_map *
4782 isl_union_map_remove_redundancies(
4783 __isl_take isl_union_map *umap);
4787 __isl_give isl_basic_set *isl_set_convex_hull(
4788 __isl_take isl_set *set);
4789 __isl_give isl_basic_map *isl_map_convex_hull(
4790 __isl_take isl_map *map);
4792 If the input set or relation has any existentially quantified
4793 variables, then the result of these operations is currently undefined.
4797 #include <isl/set.h>
4798 __isl_give isl_basic_set *
4799 isl_set_unshifted_simple_hull(
4800 __isl_take isl_set *set);
4801 __isl_give isl_basic_set *isl_set_simple_hull(
4802 __isl_take isl_set *set);
4803 __isl_give isl_basic_set *
4804 isl_set_unshifted_simple_hull_from_set_list(
4805 __isl_take isl_set *set,
4806 __isl_take isl_set_list *list);
4808 #include <isl/map.h>
4809 __isl_give isl_basic_map *
4810 isl_map_unshifted_simple_hull(
4811 __isl_take isl_map *map);
4812 __isl_give isl_basic_map *isl_map_simple_hull(
4813 __isl_take isl_map *map);
4814 __isl_give isl_basic_map *
4815 isl_map_unshifted_simple_hull_from_map_list(
4816 __isl_take isl_map *map,
4817 __isl_take isl_map_list *list);
4819 #include <isl/union_map.h>
4820 __isl_give isl_union_map *isl_union_map_simple_hull(
4821 __isl_take isl_union_map *umap);
4823 These functions compute a single basic set or relation
4824 that contains the whole input set or relation.
4825 In particular, the output is described by translates
4826 of the constraints describing the basic sets or relations in the input.
4827 In case of C<isl_set_unshifted_simple_hull>, only the original
4828 constraints are used, without any translation.
4829 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4830 C<isl_map_unshifted_simple_hull_from_map_list>, the
4831 constraints are taken from the elements of the second argument.
4835 (See \autoref{s:simple hull}.)
4841 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4842 __isl_take isl_basic_set *bset);
4843 __isl_give isl_basic_set *isl_set_affine_hull(
4844 __isl_take isl_set *set);
4845 __isl_give isl_union_set *isl_union_set_affine_hull(
4846 __isl_take isl_union_set *uset);
4847 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4848 __isl_take isl_basic_map *bmap);
4849 __isl_give isl_basic_map *isl_map_affine_hull(
4850 __isl_take isl_map *map);
4851 __isl_give isl_union_map *isl_union_map_affine_hull(
4852 __isl_take isl_union_map *umap);
4854 In case of union sets and relations, the affine hull is computed
4857 =item * Polyhedral hull
4859 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4860 __isl_take isl_set *set);
4861 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4862 __isl_take isl_map *map);
4863 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4864 __isl_take isl_union_set *uset);
4865 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4866 __isl_take isl_union_map *umap);
4868 These functions compute a single basic set or relation
4869 not involving any existentially quantified variables
4870 that contains the whole input set or relation.
4871 In case of union sets and relations, the polyhedral hull is computed
4874 =item * Other approximations
4876 #include <isl/set.h>
4877 __isl_give isl_basic_set *
4878 isl_basic_set_drop_constraints_involving_dims(
4879 __isl_take isl_basic_set *bset,
4880 enum isl_dim_type type,
4881 unsigned first, unsigned n);
4882 __isl_give isl_basic_set *
4883 isl_basic_set_drop_constraints_not_involving_dims(
4884 __isl_take isl_basic_set *bset,
4885 enum isl_dim_type type,
4886 unsigned first, unsigned n);
4887 __isl_give isl_set *
4888 isl_set_drop_constraints_involving_dims(
4889 __isl_take isl_set *set,
4890 enum isl_dim_type type,
4891 unsigned first, unsigned n);
4893 #include <isl/map.h>
4894 __isl_give isl_basic_map *
4895 isl_basic_map_drop_constraints_involving_dims(
4896 __isl_take isl_basic_map *bmap,
4897 enum isl_dim_type type,
4898 unsigned first, unsigned n);
4899 __isl_give isl_basic_map *
4900 isl_basic_map_drop_constraints_not_involving_dims(
4901 __isl_take isl_basic_map *bmap,
4902 enum isl_dim_type type,
4903 unsigned first, unsigned n);
4904 __isl_give isl_map *
4905 isl_map_drop_constraints_involving_dims(
4906 __isl_take isl_map *map,
4907 enum isl_dim_type type,
4908 unsigned first, unsigned n);
4910 These functions drop any constraints (not) involving the specified dimensions.
4911 Note that the result depends on the representation of the input.
4913 #include <isl/polynomial.h>
4914 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4915 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4916 __isl_give isl_union_pw_qpolynomial *
4917 isl_union_pw_qpolynomial_to_polynomial(
4918 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4920 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4921 the polynomial will be an overapproximation. If C<sign> is negative,
4922 it will be an underapproximation. If C<sign> is zero, the approximation
4923 will lie somewhere in between.
4927 __isl_give isl_basic_set *isl_basic_set_sample(
4928 __isl_take isl_basic_set *bset);
4929 __isl_give isl_basic_set *isl_set_sample(
4930 __isl_take isl_set *set);
4931 __isl_give isl_basic_map *isl_basic_map_sample(
4932 __isl_take isl_basic_map *bmap);
4933 __isl_give isl_basic_map *isl_map_sample(
4934 __isl_take isl_map *map);
4936 If the input (basic) set or relation is non-empty, then return
4937 a singleton subset of the input. Otherwise, return an empty set.
4939 =item * Optimization
4941 #include <isl/ilp.h>
4942 __isl_give isl_val *isl_basic_set_max_val(
4943 __isl_keep isl_basic_set *bset,
4944 __isl_keep isl_aff *obj);
4945 __isl_give isl_val *isl_set_min_val(
4946 __isl_keep isl_set *set,
4947 __isl_keep isl_aff *obj);
4948 __isl_give isl_val *isl_set_max_val(
4949 __isl_keep isl_set *set,
4950 __isl_keep isl_aff *obj);
4952 Compute the minimum or maximum of the integer affine expression C<obj>
4953 over the points in C<set>, returning the result in C<opt>.
4954 The result is C<NULL> in case of an error, the optimal value in case
4955 there is one, negative infinity or infinity if the problem is unbounded and
4956 NaN if the problem is empty.
4958 =item * Parametric optimization
4960 __isl_give isl_pw_aff *isl_set_dim_min(
4961 __isl_take isl_set *set, int pos);
4962 __isl_give isl_pw_aff *isl_set_dim_max(
4963 __isl_take isl_set *set, int pos);
4964 __isl_give isl_pw_aff *isl_map_dim_max(
4965 __isl_take isl_map *map, int pos);
4967 Compute the minimum or maximum of the given set or output dimension
4968 as a function of the parameters (and input dimensions), but independently
4969 of the other set or output dimensions.
4970 For lexicographic optimization, see L<"Lexicographic Optimization">.
4974 The following functions compute either the set of (rational) coefficient
4975 values of valid constraints for the given set or the set of (rational)
4976 values satisfying the constraints with coefficients from the given set.
4977 Internally, these two sets of functions perform essentially the
4978 same operations, except that the set of coefficients is assumed to
4979 be a cone, while the set of values may be any polyhedron.
4980 The current implementation is based on the Farkas lemma and
4981 Fourier-Motzkin elimination, but this may change or be made optional
4982 in future. In particular, future implementations may use different
4983 dualization algorithms or skip the elimination step.
4985 __isl_give isl_basic_set *isl_basic_set_coefficients(
4986 __isl_take isl_basic_set *bset);
4987 __isl_give isl_basic_set *isl_set_coefficients(
4988 __isl_take isl_set *set);
4989 __isl_give isl_union_set *isl_union_set_coefficients(
4990 __isl_take isl_union_set *bset);
4991 __isl_give isl_basic_set *isl_basic_set_solutions(
4992 __isl_take isl_basic_set *bset);
4993 __isl_give isl_basic_set *isl_set_solutions(
4994 __isl_take isl_set *set);
4995 __isl_give isl_union_set *isl_union_set_solutions(
4996 __isl_take isl_union_set *bset);
5000 __isl_give isl_map *isl_map_fixed_power_val(
5001 __isl_take isl_map *map,
5002 __isl_take isl_val *exp);
5003 __isl_give isl_union_map *
5004 isl_union_map_fixed_power_val(
5005 __isl_take isl_union_map *umap,
5006 __isl_take isl_val *exp);
5008 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5009 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5010 of C<map> is computed.
5012 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5014 __isl_give isl_union_map *isl_union_map_power(
5015 __isl_take isl_union_map *umap, int *exact);
5017 Compute a parametric representation for all positive powers I<k> of C<map>.
5018 The result maps I<k> to a nested relation corresponding to the
5019 I<k>th power of C<map>.
5020 The result may be an overapproximation. If the result is known to be exact,
5021 then C<*exact> is set to C<1>.
5023 =item * Transitive closure
5025 __isl_give isl_map *isl_map_transitive_closure(
5026 __isl_take isl_map *map, int *exact);
5027 __isl_give isl_union_map *isl_union_map_transitive_closure(
5028 __isl_take isl_union_map *umap, int *exact);
5030 Compute the transitive closure of C<map>.
5031 The result may be an overapproximation. If the result is known to be exact,
5032 then C<*exact> is set to C<1>.
5034 =item * Reaching path lengths
5036 __isl_give isl_map *isl_map_reaching_path_lengths(
5037 __isl_take isl_map *map, int *exact);
5039 Compute a relation that maps each element in the range of C<map>
5040 to the lengths of all paths composed of edges in C<map> that
5041 end up in the given element.
5042 The result may be an overapproximation. If the result is known to be exact,
5043 then C<*exact> is set to C<1>.
5044 To compute the I<maximal> path length, the resulting relation
5045 should be postprocessed by C<isl_map_lexmax>.
5046 In particular, if the input relation is a dependence relation
5047 (mapping sources to sinks), then the maximal path length corresponds
5048 to the free schedule.
5049 Note, however, that C<isl_map_lexmax> expects the maximum to be
5050 finite, so if the path lengths are unbounded (possibly due to
5051 the overapproximation), then you will get an error message.
5055 #include <isl/space.h>
5056 __isl_give isl_space *isl_space_wrap(
5057 __isl_take isl_space *space);
5058 __isl_give isl_space *isl_space_unwrap(
5059 __isl_take isl_space *space);
5061 #include <isl/local_space.h>
5062 __isl_give isl_local_space *isl_local_space_wrap(
5063 __isl_take isl_local_space *ls);
5065 #include <isl/set.h>
5066 __isl_give isl_basic_map *isl_basic_set_unwrap(
5067 __isl_take isl_basic_set *bset);
5068 __isl_give isl_map *isl_set_unwrap(
5069 __isl_take isl_set *set);
5071 #include <isl/map.h>
5072 __isl_give isl_basic_set *isl_basic_map_wrap(
5073 __isl_take isl_basic_map *bmap);
5074 __isl_give isl_set *isl_map_wrap(
5075 __isl_take isl_map *map);
5077 #include <isl/union_set.h>
5078 __isl_give isl_union_map *isl_union_set_unwrap(
5079 __isl_take isl_union_set *uset);
5081 #include <isl/union_map.h>
5082 __isl_give isl_union_set *isl_union_map_wrap(
5083 __isl_take isl_union_map *umap);
5085 The input to C<isl_space_unwrap> should
5086 be the space of a set, while that of
5087 C<isl_space_wrap> should be the space of a relation.
5088 Conversely, the output of C<isl_space_unwrap> is the space
5089 of a relation, while that of C<isl_space_wrap> is the space of a set.
5093 Remove any internal structure of domain (and range) of the given
5094 set or relation. If there is any such internal structure in the input,
5095 then the name of the space is also removed.
5097 #include <isl/local_space.h>
5098 __isl_give isl_local_space *
5099 isl_local_space_flatten_domain(
5100 __isl_take isl_local_space *ls);
5101 __isl_give isl_local_space *
5102 isl_local_space_flatten_range(
5103 __isl_take isl_local_space *ls);
5105 #include <isl/set.h>
5106 __isl_give isl_basic_set *isl_basic_set_flatten(
5107 __isl_take isl_basic_set *bset);
5108 __isl_give isl_set *isl_set_flatten(
5109 __isl_take isl_set *set);
5111 #include <isl/map.h>
5112 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5113 __isl_take isl_basic_map *bmap);
5114 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5115 __isl_take isl_basic_map *bmap);
5116 __isl_give isl_map *isl_map_flatten_range(
5117 __isl_take isl_map *map);
5118 __isl_give isl_map *isl_map_flatten_domain(
5119 __isl_take isl_map *map);
5120 __isl_give isl_basic_map *isl_basic_map_flatten(
5121 __isl_take isl_basic_map *bmap);
5122 __isl_give isl_map *isl_map_flatten(
5123 __isl_take isl_map *map);
5125 #include <isl/val.h>
5126 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5127 __isl_take isl_multi_val *mv);
5129 #include <isl/aff.h>
5130 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5131 __isl_take isl_multi_aff *ma);
5132 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5133 __isl_take isl_multi_aff *ma);
5134 __isl_give isl_multi_pw_aff *
5135 isl_multi_pw_aff_flatten_range(
5136 __isl_take isl_multi_pw_aff *mpa);
5137 __isl_give isl_multi_union_pw_aff *
5138 isl_multi_union_pw_aff_flatten_range(
5139 __isl_take isl_multi_union_pw_aff *mupa);
5141 #include <isl/map.h>
5142 __isl_give isl_map *isl_set_flatten_map(
5143 __isl_take isl_set *set);
5145 The function above constructs a relation
5146 that maps the input set to a flattened version of the set.
5150 Lift the input set to a space with extra dimensions corresponding
5151 to the existentially quantified variables in the input.
5152 In particular, the result lives in a wrapped map where the domain
5153 is the original space and the range corresponds to the original
5154 existentially quantified variables.
5156 #include <isl/set.h>
5157 __isl_give isl_basic_set *isl_basic_set_lift(
5158 __isl_take isl_basic_set *bset);
5159 __isl_give isl_set *isl_set_lift(
5160 __isl_take isl_set *set);
5161 __isl_give isl_union_set *isl_union_set_lift(
5162 __isl_take isl_union_set *uset);
5164 Given a local space that contains the existentially quantified
5165 variables of a set, a basic relation that, when applied to
5166 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5167 can be constructed using the following function.
5169 #include <isl/local_space.h>
5170 __isl_give isl_basic_map *isl_local_space_lifting(
5171 __isl_take isl_local_space *ls);
5173 #include <isl/aff.h>
5174 __isl_give isl_multi_aff *isl_multi_aff_lift(
5175 __isl_take isl_multi_aff *maff,
5176 __isl_give isl_local_space **ls);
5178 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5179 then it is assigned the local space that lies at the basis of
5180 the lifting applied.
5182 =item * Internal Product
5184 #include <isl/space.h>
5185 __isl_give isl_space *isl_space_zip(
5186 __isl_take isl_space *space);
5188 #include <isl/map.h>
5189 __isl_give isl_basic_map *isl_basic_map_zip(
5190 __isl_take isl_basic_map *bmap);
5191 __isl_give isl_map *isl_map_zip(
5192 __isl_take isl_map *map);
5194 #include <isl/union_map.h>
5195 __isl_give isl_union_map *isl_union_map_zip(
5196 __isl_take isl_union_map *umap);
5198 Given a relation with nested relations for domain and range,
5199 interchange the range of the domain with the domain of the range.
5203 #include <isl/space.h>
5204 __isl_give isl_space *isl_space_curry(
5205 __isl_take isl_space *space);
5206 __isl_give isl_space *isl_space_uncurry(
5207 __isl_take isl_space *space);
5209 #include <isl/map.h>
5210 __isl_give isl_basic_map *isl_basic_map_curry(
5211 __isl_take isl_basic_map *bmap);
5212 __isl_give isl_basic_map *isl_basic_map_uncurry(
5213 __isl_take isl_basic_map *bmap);
5214 __isl_give isl_map *isl_map_curry(
5215 __isl_take isl_map *map);
5216 __isl_give isl_map *isl_map_uncurry(
5217 __isl_take isl_map *map);
5219 #include <isl/union_map.h>
5220 __isl_give isl_union_map *isl_union_map_curry(
5221 __isl_take isl_union_map *umap);
5222 __isl_give isl_union_map *isl_union_map_uncurry(
5223 __isl_take isl_union_map *umap);
5225 Given a relation with a nested relation for domain,
5226 the C<curry> functions
5227 move the range of the nested relation out of the domain
5228 and use it as the domain of a nested relation in the range,
5229 with the original range as range of this nested relation.
5230 The C<uncurry> functions perform the inverse operation.
5232 #include <isl/space.h>
5233 __isl_give isl_space *isl_space_range_curry(
5234 __isl_take isl_space *space);
5236 #include <isl/map.h>
5237 __isl_give isl_map *isl_map_range_curry(
5238 __isl_take isl_map *map);
5240 #include <isl/union_map.h>
5241 __isl_give isl_union_map *isl_union_map_range_curry(
5242 __isl_take isl_union_map *umap);
5244 These functions apply the currying to the relation that
5245 is nested inside the range of the input.
5247 =item * Aligning parameters
5249 Change the order of the parameters of the given set, relation
5251 such that the first parameters match those of C<model>.
5252 This may involve the introduction of extra parameters.
5253 All parameters need to be named.
5255 #include <isl/space.h>
5256 __isl_give isl_space *isl_space_align_params(
5257 __isl_take isl_space *space1,
5258 __isl_take isl_space *space2)
5260 #include <isl/set.h>
5261 __isl_give isl_basic_set *isl_basic_set_align_params(
5262 __isl_take isl_basic_set *bset,
5263 __isl_take isl_space *model);
5264 __isl_give isl_set *isl_set_align_params(
5265 __isl_take isl_set *set,
5266 __isl_take isl_space *model);
5268 #include <isl/map.h>
5269 __isl_give isl_basic_map *isl_basic_map_align_params(
5270 __isl_take isl_basic_map *bmap,
5271 __isl_take isl_space *model);
5272 __isl_give isl_map *isl_map_align_params(
5273 __isl_take isl_map *map,
5274 __isl_take isl_space *model);
5276 #include <isl/val.h>
5277 __isl_give isl_multi_val *isl_multi_val_align_params(
5278 __isl_take isl_multi_val *mv,
5279 __isl_take isl_space *model);
5281 #include <isl/aff.h>
5282 __isl_give isl_aff *isl_aff_align_params(
5283 __isl_take isl_aff *aff,
5284 __isl_take isl_space *model);
5285 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5286 __isl_take isl_multi_aff *multi,
5287 __isl_take isl_space *model);
5288 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5289 __isl_take isl_pw_aff *pwaff,
5290 __isl_take isl_space *model);
5291 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5292 __isl_take isl_pw_multi_aff *pma,
5293 __isl_take isl_space *model);
5294 __isl_give isl_union_pw_aff *
5295 isl_union_pw_aff_align_params(
5296 __isl_take isl_union_pw_aff *upa,
5297 __isl_take isl_space *model);
5298 __isl_give isl_union_pw_multi_aff *
5299 isl_union_pw_multi_aff_align_params(
5300 __isl_take isl_union_pw_multi_aff *upma,
5301 __isl_take isl_space *model);
5302 __isl_give isl_multi_union_pw_aff *
5303 isl_multi_union_pw_aff_align_params(
5304 __isl_take isl_multi_union_pw_aff *mupa,
5305 __isl_take isl_space *model);
5307 #include <isl/polynomial.h>
5308 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5309 __isl_take isl_qpolynomial *qp,
5310 __isl_take isl_space *model);
5312 =item * Unary Arithmetic Operations
5314 #include <isl/set.h>
5315 __isl_give isl_set *isl_set_neg(
5316 __isl_take isl_set *set);
5317 #include <isl/map.h>
5318 __isl_give isl_map *isl_map_neg(
5319 __isl_take isl_map *map);
5321 C<isl_set_neg> constructs a set containing the opposites of
5322 the elements in its argument.
5323 The domain of the result of C<isl_map_neg> is the same
5324 as the domain of its argument. The corresponding range
5325 elements are the opposites of the corresponding range
5326 elements in the argument.
5328 #include <isl/val.h>
5329 __isl_give isl_multi_val *isl_multi_val_neg(
5330 __isl_take isl_multi_val *mv);
5332 #include <isl/aff.h>
5333 __isl_give isl_aff *isl_aff_neg(
5334 __isl_take isl_aff *aff);
5335 __isl_give isl_multi_aff *isl_multi_aff_neg(
5336 __isl_take isl_multi_aff *ma);
5337 __isl_give isl_pw_aff *isl_pw_aff_neg(
5338 __isl_take isl_pw_aff *pwaff);
5339 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5340 __isl_take isl_pw_multi_aff *pma);
5341 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5342 __isl_take isl_multi_pw_aff *mpa);
5343 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5344 __isl_take isl_union_pw_aff *upa);
5345 __isl_give isl_union_pw_multi_aff *
5346 isl_union_pw_multi_aff_neg(
5347 __isl_take isl_union_pw_multi_aff *upma);
5348 __isl_give isl_multi_union_pw_aff *
5349 isl_multi_union_pw_aff_neg(
5350 __isl_take isl_multi_union_pw_aff *mupa);
5351 __isl_give isl_aff *isl_aff_ceil(
5352 __isl_take isl_aff *aff);
5353 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5354 __isl_take isl_pw_aff *pwaff);
5355 __isl_give isl_aff *isl_aff_floor(
5356 __isl_take isl_aff *aff);
5357 __isl_give isl_multi_aff *isl_multi_aff_floor(
5358 __isl_take isl_multi_aff *ma);
5359 __isl_give isl_pw_aff *isl_pw_aff_floor(
5360 __isl_take isl_pw_aff *pwaff);
5361 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5362 __isl_take isl_union_pw_aff *upa);
5363 __isl_give isl_multi_union_pw_aff *
5364 isl_multi_union_pw_aff_floor(
5365 __isl_take isl_multi_union_pw_aff *mupa);
5367 #include <isl/aff.h>
5368 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5369 __isl_take isl_pw_aff_list *list);
5370 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5371 __isl_take isl_pw_aff_list *list);
5373 #include <isl/polynomial.h>
5374 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5375 __isl_take isl_qpolynomial *qp);
5376 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5377 __isl_take isl_pw_qpolynomial *pwqp);
5378 __isl_give isl_union_pw_qpolynomial *
5379 isl_union_pw_qpolynomial_neg(
5380 __isl_take isl_union_pw_qpolynomial *upwqp);
5381 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5382 __isl_take isl_qpolynomial *qp,
5384 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5385 __isl_take isl_pw_qpolynomial *pwqp,
5390 The following functions evaluate a function in a point.
5392 #include <isl/polynomial.h>
5393 __isl_give isl_val *isl_pw_qpolynomial_eval(
5394 __isl_take isl_pw_qpolynomial *pwqp,
5395 __isl_take isl_point *pnt);
5396 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5397 __isl_take isl_pw_qpolynomial_fold *pwf,
5398 __isl_take isl_point *pnt);
5399 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5400 __isl_take isl_union_pw_qpolynomial *upwqp,
5401 __isl_take isl_point *pnt);
5402 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5403 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5404 __isl_take isl_point *pnt);
5406 =item * Dimension manipulation
5408 It is usually not advisable to directly change the (input or output)
5409 space of a set or a relation as this removes the name and the internal
5410 structure of the space. However, the functions below can be useful
5411 to add new parameters, assuming
5412 C<isl_set_align_params> and C<isl_map_align_params>
5415 #include <isl/space.h>
5416 __isl_give isl_space *isl_space_add_dims(
5417 __isl_take isl_space *space,
5418 enum isl_dim_type type, unsigned n);
5419 __isl_give isl_space *isl_space_insert_dims(
5420 __isl_take isl_space *space,
5421 enum isl_dim_type type, unsigned pos, unsigned n);
5422 __isl_give isl_space *isl_space_drop_dims(
5423 __isl_take isl_space *space,
5424 enum isl_dim_type type, unsigned first, unsigned n);
5425 __isl_give isl_space *isl_space_move_dims(
5426 __isl_take isl_space *space,
5427 enum isl_dim_type dst_type, unsigned dst_pos,
5428 enum isl_dim_type src_type, unsigned src_pos,
5431 #include <isl/local_space.h>
5432 __isl_give isl_local_space *isl_local_space_add_dims(
5433 __isl_take isl_local_space *ls,
5434 enum isl_dim_type type, unsigned n);
5435 __isl_give isl_local_space *isl_local_space_insert_dims(
5436 __isl_take isl_local_space *ls,
5437 enum isl_dim_type type, unsigned first, unsigned n);
5438 __isl_give isl_local_space *isl_local_space_drop_dims(
5439 __isl_take isl_local_space *ls,
5440 enum isl_dim_type type, unsigned first, unsigned n);
5442 #include <isl/set.h>
5443 __isl_give isl_basic_set *isl_basic_set_add_dims(
5444 __isl_take isl_basic_set *bset,
5445 enum isl_dim_type type, unsigned n);
5446 __isl_give isl_set *isl_set_add_dims(
5447 __isl_take isl_set *set,
5448 enum isl_dim_type type, unsigned n);
5449 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5450 __isl_take isl_basic_set *bset,
5451 enum isl_dim_type type, unsigned pos,
5453 __isl_give isl_set *isl_set_insert_dims(
5454 __isl_take isl_set *set,
5455 enum isl_dim_type type, unsigned pos, unsigned n);
5456 __isl_give isl_basic_set *isl_basic_set_move_dims(
5457 __isl_take isl_basic_set *bset,
5458 enum isl_dim_type dst_type, unsigned dst_pos,
5459 enum isl_dim_type src_type, unsigned src_pos,
5461 __isl_give isl_set *isl_set_move_dims(
5462 __isl_take isl_set *set,
5463 enum isl_dim_type dst_type, unsigned dst_pos,
5464 enum isl_dim_type src_type, unsigned src_pos,
5467 #include <isl/map.h>
5468 __isl_give isl_basic_map *isl_basic_map_add_dims(
5469 __isl_take isl_basic_map *bmap,
5470 enum isl_dim_type type, unsigned n);
5471 __isl_give isl_map *isl_map_add_dims(
5472 __isl_take isl_map *map,
5473 enum isl_dim_type type, unsigned n);
5474 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5475 __isl_take isl_basic_map *bmap,
5476 enum isl_dim_type type, unsigned pos,
5478 __isl_give isl_map *isl_map_insert_dims(
5479 __isl_take isl_map *map,
5480 enum isl_dim_type type, unsigned pos, unsigned n);
5481 __isl_give isl_basic_map *isl_basic_map_move_dims(
5482 __isl_take isl_basic_map *bmap,
5483 enum isl_dim_type dst_type, unsigned dst_pos,
5484 enum isl_dim_type src_type, unsigned src_pos,
5486 __isl_give isl_map *isl_map_move_dims(
5487 __isl_take isl_map *map,
5488 enum isl_dim_type dst_type, unsigned dst_pos,
5489 enum isl_dim_type src_type, unsigned src_pos,
5492 #include <isl/val.h>
5493 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5494 __isl_take isl_multi_val *mv,
5495 enum isl_dim_type type, unsigned first, unsigned n);
5496 __isl_give isl_multi_val *isl_multi_val_add_dims(
5497 __isl_take isl_multi_val *mv,
5498 enum isl_dim_type type, unsigned n);
5499 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5500 __isl_take isl_multi_val *mv,
5501 enum isl_dim_type type, unsigned first, unsigned n);
5503 #include <isl/aff.h>
5504 __isl_give isl_aff *isl_aff_insert_dims(
5505 __isl_take isl_aff *aff,
5506 enum isl_dim_type type, unsigned first, unsigned n);
5507 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5508 __isl_take isl_multi_aff *ma,
5509 enum isl_dim_type type, unsigned first, unsigned n);
5510 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5511 __isl_take isl_pw_aff *pwaff,
5512 enum isl_dim_type type, unsigned first, unsigned n);
5513 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5514 __isl_take isl_multi_pw_aff *mpa,
5515 enum isl_dim_type type, unsigned first, unsigned n);
5516 __isl_give isl_aff *isl_aff_add_dims(
5517 __isl_take isl_aff *aff,
5518 enum isl_dim_type type, unsigned n);
5519 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5520 __isl_take isl_multi_aff *ma,
5521 enum isl_dim_type type, unsigned n);
5522 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5523 __isl_take isl_pw_aff *pwaff,
5524 enum isl_dim_type type, unsigned n);
5525 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5526 __isl_take isl_multi_pw_aff *mpa,
5527 enum isl_dim_type type, unsigned n);
5528 __isl_give isl_aff *isl_aff_drop_dims(
5529 __isl_take isl_aff *aff,
5530 enum isl_dim_type type, unsigned first, unsigned n);
5531 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5532 __isl_take isl_multi_aff *maff,
5533 enum isl_dim_type type, unsigned first, unsigned n);
5534 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5535 __isl_take isl_pw_aff *pwaff,
5536 enum isl_dim_type type, unsigned first, unsigned n);
5537 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5538 __isl_take isl_pw_multi_aff *pma,
5539 enum isl_dim_type type, unsigned first, unsigned n);
5540 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5541 __isl_take isl_union_pw_aff *upa,
5542 enum isl_dim_type type, unsigned first, unsigned n);
5543 __isl_give isl_union_pw_multi_aff *
5544 isl_union_pw_multi_aff_drop_dims(
5545 __isl_take isl_union_pw_multi_aff *upma,
5546 enum isl_dim_type type,
5547 unsigned first, unsigned n);
5548 __isl_give isl_multi_union_pw_aff *
5549 isl_multi_union_pw_aff_drop_dims(
5550 __isl_take isl_multi_union_pw_aff *mupa,
5551 enum isl_dim_type type, unsigned first,
5553 __isl_give isl_aff *isl_aff_move_dims(
5554 __isl_take isl_aff *aff,
5555 enum isl_dim_type dst_type, unsigned dst_pos,
5556 enum isl_dim_type src_type, unsigned src_pos,
5558 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5559 __isl_take isl_multi_aff *ma,
5560 enum isl_dim_type dst_type, unsigned dst_pos,
5561 enum isl_dim_type src_type, unsigned src_pos,
5563 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5564 __isl_take isl_pw_aff *pa,
5565 enum isl_dim_type dst_type, unsigned dst_pos,
5566 enum isl_dim_type src_type, unsigned src_pos,
5568 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5569 __isl_take isl_multi_pw_aff *pma,
5570 enum isl_dim_type dst_type, unsigned dst_pos,
5571 enum isl_dim_type src_type, unsigned src_pos,
5574 #include <isl/polynomial.h>
5575 __isl_give isl_union_pw_qpolynomial *
5576 isl_union_pw_qpolynomial_drop_dims(
5577 __isl_take isl_union_pw_qpolynomial *upwqp,
5578 enum isl_dim_type type,
5579 unsigned first, unsigned n);
5580 __isl_give isl_union_pw_qpolynomial_fold *
5581 isl_union_pw_qpolynomial_fold_drop_dims(
5582 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5583 enum isl_dim_type type,
5584 unsigned first, unsigned n);
5586 The operations on union expressions can only manipulate parameters.
5590 =head2 Binary Operations
5592 The two arguments of a binary operation not only need to live
5593 in the same C<isl_ctx>, they currently also need to have
5594 the same (number of) parameters.
5596 =head3 Basic Operations
5600 =item * Intersection
5602 #include <isl/local_space.h>
5603 __isl_give isl_local_space *isl_local_space_intersect(
5604 __isl_take isl_local_space *ls1,
5605 __isl_take isl_local_space *ls2);
5607 #include <isl/set.h>
5608 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5609 __isl_take isl_basic_set *bset1,
5610 __isl_take isl_basic_set *bset2);
5611 __isl_give isl_basic_set *isl_basic_set_intersect(
5612 __isl_take isl_basic_set *bset1,
5613 __isl_take isl_basic_set *bset2);
5614 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5615 __isl_take struct isl_basic_set_list *list);
5616 __isl_give isl_set *isl_set_intersect_params(
5617 __isl_take isl_set *set,
5618 __isl_take isl_set *params);
5619 __isl_give isl_set *isl_set_intersect(
5620 __isl_take isl_set *set1,
5621 __isl_take isl_set *set2);
5623 #include <isl/map.h>
5624 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5625 __isl_take isl_basic_map *bmap,
5626 __isl_take isl_basic_set *bset);
5627 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5628 __isl_take isl_basic_map *bmap,
5629 __isl_take isl_basic_set *bset);
5630 __isl_give isl_basic_map *isl_basic_map_intersect(
5631 __isl_take isl_basic_map *bmap1,
5632 __isl_take isl_basic_map *bmap2);
5633 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5634 __isl_take isl_basic_map_list *list);
5635 __isl_give isl_map *isl_map_intersect_params(
5636 __isl_take isl_map *map,
5637 __isl_take isl_set *params);
5638 __isl_give isl_map *isl_map_intersect_domain(
5639 __isl_take isl_map *map,
5640 __isl_take isl_set *set);
5641 __isl_give isl_map *isl_map_intersect_range(
5642 __isl_take isl_map *map,
5643 __isl_take isl_set *set);
5644 __isl_give isl_map *isl_map_intersect(
5645 __isl_take isl_map *map1,
5646 __isl_take isl_map *map2);
5648 #include <isl/union_set.h>
5649 __isl_give isl_union_set *isl_union_set_intersect_params(
5650 __isl_take isl_union_set *uset,
5651 __isl_take isl_set *set);
5652 __isl_give isl_union_set *isl_union_set_intersect(
5653 __isl_take isl_union_set *uset1,
5654 __isl_take isl_union_set *uset2);
5656 #include <isl/union_map.h>
5657 __isl_give isl_union_map *isl_union_map_intersect_params(
5658 __isl_take isl_union_map *umap,
5659 __isl_take isl_set *set);
5660 __isl_give isl_union_map *isl_union_map_intersect_domain(
5661 __isl_take isl_union_map *umap,
5662 __isl_take isl_union_set *uset);
5663 __isl_give isl_union_map *isl_union_map_intersect_range(
5664 __isl_take isl_union_map *umap,
5665 __isl_take isl_union_set *uset);
5666 __isl_give isl_union_map *isl_union_map_intersect(
5667 __isl_take isl_union_map *umap1,
5668 __isl_take isl_union_map *umap2);
5670 #include <isl/aff.h>
5671 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5672 __isl_take isl_pw_aff *pa,
5673 __isl_take isl_set *set);
5674 __isl_give isl_multi_pw_aff *
5675 isl_multi_pw_aff_intersect_domain(
5676 __isl_take isl_multi_pw_aff *mpa,
5677 __isl_take isl_set *domain);
5678 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5679 __isl_take isl_pw_multi_aff *pma,
5680 __isl_take isl_set *set);
5681 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5682 __isl_take isl_union_pw_aff *upa,
5683 __isl_take isl_union_set *uset);
5684 __isl_give isl_union_pw_multi_aff *
5685 isl_union_pw_multi_aff_intersect_domain(
5686 __isl_take isl_union_pw_multi_aff *upma,
5687 __isl_take isl_union_set *uset);
5688 __isl_give isl_multi_union_pw_aff *
5689 isl_multi_union_pw_aff_intersect_domain(
5690 __isl_take isl_multi_union_pw_aff *mupa,
5691 __isl_take isl_union_set *uset);
5692 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5693 __isl_take isl_pw_aff *pa,
5694 __isl_take isl_set *set);
5695 __isl_give isl_multi_pw_aff *
5696 isl_multi_pw_aff_intersect_params(
5697 __isl_take isl_multi_pw_aff *mpa,
5698 __isl_take isl_set *set);
5699 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5700 __isl_take isl_pw_multi_aff *pma,
5701 __isl_take isl_set *set);
5702 __isl_give isl_union_pw_aff *
5703 isl_union_pw_aff_intersect_params(
5704 __isl_take isl_union_pw_aff *upa,
5705 __isl_give isl_union_pw_multi_aff *
5706 isl_union_pw_multi_aff_intersect_params(
5707 __isl_take isl_union_pw_multi_aff *upma,
5708 __isl_take isl_set *set);
5709 __isl_give isl_multi_union_pw_aff *
5710 isl_multi_union_pw_aff_intersect_params(
5711 __isl_take isl_multi_union_pw_aff *mupa,
5712 __isl_take isl_set *params);
5713 isl_multi_union_pw_aff_intersect_range(
5714 __isl_take isl_multi_union_pw_aff *mupa,
5715 __isl_take isl_set *set);
5717 #include <isl/polynomial.h>
5718 __isl_give isl_pw_qpolynomial *
5719 isl_pw_qpolynomial_intersect_domain(
5720 __isl_take isl_pw_qpolynomial *pwpq,
5721 __isl_take isl_set *set);
5722 __isl_give isl_union_pw_qpolynomial *
5723 isl_union_pw_qpolynomial_intersect_domain(
5724 __isl_take isl_union_pw_qpolynomial *upwpq,
5725 __isl_take isl_union_set *uset);
5726 __isl_give isl_union_pw_qpolynomial_fold *
5727 isl_union_pw_qpolynomial_fold_intersect_domain(
5728 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5729 __isl_take isl_union_set *uset);
5730 __isl_give isl_pw_qpolynomial *
5731 isl_pw_qpolynomial_intersect_params(
5732 __isl_take isl_pw_qpolynomial *pwpq,
5733 __isl_take isl_set *set);
5734 __isl_give isl_pw_qpolynomial_fold *
5735 isl_pw_qpolynomial_fold_intersect_params(
5736 __isl_take isl_pw_qpolynomial_fold *pwf,
5737 __isl_take isl_set *set);
5738 __isl_give isl_union_pw_qpolynomial *
5739 isl_union_pw_qpolynomial_intersect_params(
5740 __isl_take isl_union_pw_qpolynomial *upwpq,
5741 __isl_take isl_set *set);
5742 __isl_give isl_union_pw_qpolynomial_fold *
5743 isl_union_pw_qpolynomial_fold_intersect_params(
5744 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5745 __isl_take isl_set *set);
5747 The second argument to the C<_params> functions needs to be
5748 a parametric (basic) set. For the other functions, a parametric set
5749 for either argument is only allowed if the other argument is
5750 a parametric set as well.
5751 The list passed to C<isl_basic_set_list_intersect> needs to have
5752 at least one element and all elements need to live in the same space.
5753 The function C<isl_multi_union_pw_aff_intersect_range>
5754 restricts the input function to those shared domain elements
5755 that map to the specified range.
5759 #include <isl/set.h>
5760 __isl_give isl_set *isl_basic_set_union(
5761 __isl_take isl_basic_set *bset1,
5762 __isl_take isl_basic_set *bset2);
5763 __isl_give isl_set *isl_set_union(
5764 __isl_take isl_set *set1,
5765 __isl_take isl_set *set2);
5766 __isl_give isl_set *isl_set_list_union(
5767 __isl_take isl_set_list *list);
5769 #include <isl/map.h>
5770 __isl_give isl_map *isl_basic_map_union(
5771 __isl_take isl_basic_map *bmap1,
5772 __isl_take isl_basic_map *bmap2);
5773 __isl_give isl_map *isl_map_union(
5774 __isl_take isl_map *map1,
5775 __isl_take isl_map *map2);
5777 #include <isl/union_set.h>
5778 __isl_give isl_union_set *isl_union_set_union(
5779 __isl_take isl_union_set *uset1,
5780 __isl_take isl_union_set *uset2);
5781 __isl_give isl_union_set *isl_union_set_list_union(
5782 __isl_take isl_union_set_list *list);
5784 #include <isl/union_map.h>
5785 __isl_give isl_union_map *isl_union_map_union(
5786 __isl_take isl_union_map *umap1,
5787 __isl_take isl_union_map *umap2);
5789 The list passed to C<isl_set_list_union> needs to have
5790 at least one element and all elements need to live in the same space.
5792 =item * Set difference
5794 #include <isl/set.h>
5795 __isl_give isl_set *isl_set_subtract(
5796 __isl_take isl_set *set1,
5797 __isl_take isl_set *set2);
5799 #include <isl/map.h>
5800 __isl_give isl_map *isl_map_subtract(
5801 __isl_take isl_map *map1,
5802 __isl_take isl_map *map2);
5803 __isl_give isl_map *isl_map_subtract_domain(
5804 __isl_take isl_map *map,
5805 __isl_take isl_set *dom);
5806 __isl_give isl_map *isl_map_subtract_range(
5807 __isl_take isl_map *map,
5808 __isl_take isl_set *dom);
5810 #include <isl/union_set.h>
5811 __isl_give isl_union_set *isl_union_set_subtract(
5812 __isl_take isl_union_set *uset1,
5813 __isl_take isl_union_set *uset2);
5815 #include <isl/union_map.h>
5816 __isl_give isl_union_map *isl_union_map_subtract(
5817 __isl_take isl_union_map *umap1,
5818 __isl_take isl_union_map *umap2);
5819 __isl_give isl_union_map *isl_union_map_subtract_domain(
5820 __isl_take isl_union_map *umap,
5821 __isl_take isl_union_set *dom);
5822 __isl_give isl_union_map *isl_union_map_subtract_range(
5823 __isl_take isl_union_map *umap,
5824 __isl_take isl_union_set *dom);
5826 #include <isl/aff.h>
5827 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5828 __isl_take isl_pw_aff *pa,
5829 __isl_take isl_set *set);
5830 __isl_give isl_pw_multi_aff *
5831 isl_pw_multi_aff_subtract_domain(
5832 __isl_take isl_pw_multi_aff *pma,
5833 __isl_take isl_set *set);
5834 __isl_give isl_union_pw_aff *
5835 isl_union_pw_aff_subtract_domain(
5836 __isl_take isl_union_pw_aff *upa,
5837 __isl_take isl_union_set *uset);
5838 __isl_give isl_union_pw_multi_aff *
5839 isl_union_pw_multi_aff_subtract_domain(
5840 __isl_take isl_union_pw_multi_aff *upma,
5841 __isl_take isl_set *set);
5843 #include <isl/polynomial.h>
5844 __isl_give isl_pw_qpolynomial *
5845 isl_pw_qpolynomial_subtract_domain(
5846 __isl_take isl_pw_qpolynomial *pwpq,
5847 __isl_take isl_set *set);
5848 __isl_give isl_pw_qpolynomial_fold *
5849 isl_pw_qpolynomial_fold_subtract_domain(
5850 __isl_take isl_pw_qpolynomial_fold *pwf,
5851 __isl_take isl_set *set);
5852 __isl_give isl_union_pw_qpolynomial *
5853 isl_union_pw_qpolynomial_subtract_domain(
5854 __isl_take isl_union_pw_qpolynomial *upwpq,
5855 __isl_take isl_union_set *uset);
5856 __isl_give isl_union_pw_qpolynomial_fold *
5857 isl_union_pw_qpolynomial_fold_subtract_domain(
5858 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5859 __isl_take isl_union_set *uset);
5863 #include <isl/space.h>
5864 __isl_give isl_space *isl_space_join(
5865 __isl_take isl_space *left,
5866 __isl_take isl_space *right);
5868 #include <isl/map.h>
5869 __isl_give isl_basic_set *isl_basic_set_apply(
5870 __isl_take isl_basic_set *bset,
5871 __isl_take isl_basic_map *bmap);
5872 __isl_give isl_set *isl_set_apply(
5873 __isl_take isl_set *set,
5874 __isl_take isl_map *map);
5875 __isl_give isl_union_set *isl_union_set_apply(
5876 __isl_take isl_union_set *uset,
5877 __isl_take isl_union_map *umap);
5878 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5879 __isl_take isl_basic_map *bmap1,
5880 __isl_take isl_basic_map *bmap2);
5881 __isl_give isl_basic_map *isl_basic_map_apply_range(
5882 __isl_take isl_basic_map *bmap1,
5883 __isl_take isl_basic_map *bmap2);
5884 __isl_give isl_map *isl_map_apply_domain(
5885 __isl_take isl_map *map1,
5886 __isl_take isl_map *map2);
5887 __isl_give isl_map *isl_map_apply_range(
5888 __isl_take isl_map *map1,
5889 __isl_take isl_map *map2);
5891 #include <isl/union_map.h>
5892 __isl_give isl_union_map *isl_union_map_apply_domain(
5893 __isl_take isl_union_map *umap1,
5894 __isl_take isl_union_map *umap2);
5895 __isl_give isl_union_map *isl_union_map_apply_range(
5896 __isl_take isl_union_map *umap1,
5897 __isl_take isl_union_map *umap2);
5899 #include <isl/aff.h>
5900 __isl_give isl_union_pw_aff *
5901 isl_multi_union_pw_aff_apply_aff(
5902 __isl_take isl_multi_union_pw_aff *mupa,
5903 __isl_take isl_aff *aff);
5904 __isl_give isl_union_pw_aff *
5905 isl_multi_union_pw_aff_apply_pw_aff(
5906 __isl_take isl_multi_union_pw_aff *mupa,
5907 __isl_take isl_pw_aff *pa);
5908 __isl_give isl_multi_union_pw_aff *
5909 isl_multi_union_pw_aff_apply_multi_aff(
5910 __isl_take isl_multi_union_pw_aff *mupa,
5911 __isl_take isl_multi_aff *ma);
5912 __isl_give isl_multi_union_pw_aff *
5913 isl_multi_union_pw_aff_apply_pw_multi_aff(
5914 __isl_take isl_multi_union_pw_aff *mupa,
5915 __isl_take isl_pw_multi_aff *pma);
5917 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5918 over the shared domain of the elements of the input. The dimension is
5919 required to be greater than zero.
5920 The C<isl_multi_union_pw_aff> argument of
5921 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5922 but only if the range of the C<isl_multi_aff> argument
5923 is also zero-dimensional.
5924 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5926 #include <isl/polynomial.h>
5927 __isl_give isl_pw_qpolynomial_fold *
5928 isl_set_apply_pw_qpolynomial_fold(
5929 __isl_take isl_set *set,
5930 __isl_take isl_pw_qpolynomial_fold *pwf,
5932 __isl_give isl_pw_qpolynomial_fold *
5933 isl_map_apply_pw_qpolynomial_fold(
5934 __isl_take isl_map *map,
5935 __isl_take isl_pw_qpolynomial_fold *pwf,
5937 __isl_give isl_union_pw_qpolynomial_fold *
5938 isl_union_set_apply_union_pw_qpolynomial_fold(
5939 __isl_take isl_union_set *uset,
5940 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5942 __isl_give isl_union_pw_qpolynomial_fold *
5943 isl_union_map_apply_union_pw_qpolynomial_fold(
5944 __isl_take isl_union_map *umap,
5945 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5948 The functions taking a map
5949 compose the given map with the given piecewise quasipolynomial reduction.
5950 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5951 over all elements in the intersection of the range of the map
5952 and the domain of the piecewise quasipolynomial reduction
5953 as a function of an element in the domain of the map.
5954 The functions taking a set compute a bound over all elements in the
5955 intersection of the set and the domain of the
5956 piecewise quasipolynomial reduction.
5960 #include <isl/set.h>
5961 __isl_give isl_basic_set *
5962 isl_basic_set_preimage_multi_aff(
5963 __isl_take isl_basic_set *bset,
5964 __isl_take isl_multi_aff *ma);
5965 __isl_give isl_set *isl_set_preimage_multi_aff(
5966 __isl_take isl_set *set,
5967 __isl_take isl_multi_aff *ma);
5968 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5969 __isl_take isl_set *set,
5970 __isl_take isl_pw_multi_aff *pma);
5971 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5972 __isl_take isl_set *set,
5973 __isl_take isl_multi_pw_aff *mpa);
5975 #include <isl/union_set.h>
5976 __isl_give isl_union_set *
5977 isl_union_set_preimage_multi_aff(
5978 __isl_take isl_union_set *uset,
5979 __isl_take isl_multi_aff *ma);
5980 __isl_give isl_union_set *
5981 isl_union_set_preimage_pw_multi_aff(
5982 __isl_take isl_union_set *uset,
5983 __isl_take isl_pw_multi_aff *pma);
5984 __isl_give isl_union_set *
5985 isl_union_set_preimage_union_pw_multi_aff(
5986 __isl_take isl_union_set *uset,
5987 __isl_take isl_union_pw_multi_aff *upma);
5989 #include <isl/map.h>
5990 __isl_give isl_basic_map *
5991 isl_basic_map_preimage_domain_multi_aff(
5992 __isl_take isl_basic_map *bmap,
5993 __isl_take isl_multi_aff *ma);
5994 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5995 __isl_take isl_map *map,
5996 __isl_take isl_multi_aff *ma);
5997 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5998 __isl_take isl_map *map,
5999 __isl_take isl_multi_aff *ma);
6000 __isl_give isl_map *
6001 isl_map_preimage_domain_pw_multi_aff(
6002 __isl_take isl_map *map,
6003 __isl_take isl_pw_multi_aff *pma);
6004 __isl_give isl_map *
6005 isl_map_preimage_range_pw_multi_aff(
6006 __isl_take isl_map *map,
6007 __isl_take isl_pw_multi_aff *pma);
6008 __isl_give isl_map *
6009 isl_map_preimage_domain_multi_pw_aff(
6010 __isl_take isl_map *map,
6011 __isl_take isl_multi_pw_aff *mpa);
6012 __isl_give isl_basic_map *
6013 isl_basic_map_preimage_range_multi_aff(
6014 __isl_take isl_basic_map *bmap,
6015 __isl_take isl_multi_aff *ma);
6017 #include <isl/union_map.h>
6018 __isl_give isl_union_map *
6019 isl_union_map_preimage_domain_multi_aff(
6020 __isl_take isl_union_map *umap,
6021 __isl_take isl_multi_aff *ma);
6022 __isl_give isl_union_map *
6023 isl_union_map_preimage_range_multi_aff(
6024 __isl_take isl_union_map *umap,
6025 __isl_take isl_multi_aff *ma);
6026 __isl_give isl_union_map *
6027 isl_union_map_preimage_domain_pw_multi_aff(
6028 __isl_take isl_union_map *umap,
6029 __isl_take isl_pw_multi_aff *pma);
6030 __isl_give isl_union_map *
6031 isl_union_map_preimage_range_pw_multi_aff(
6032 __isl_take isl_union_map *umap,
6033 __isl_take isl_pw_multi_aff *pma);
6034 __isl_give isl_union_map *
6035 isl_union_map_preimage_domain_union_pw_multi_aff(
6036 __isl_take isl_union_map *umap,
6037 __isl_take isl_union_pw_multi_aff *upma);
6038 __isl_give isl_union_map *
6039 isl_union_map_preimage_range_union_pw_multi_aff(
6040 __isl_take isl_union_map *umap,
6041 __isl_take isl_union_pw_multi_aff *upma);
6043 These functions compute the preimage of the given set or map domain/range under
6044 the given function. In other words, the expression is plugged
6045 into the set description or into the domain/range of the map.
6049 #include <isl/aff.h>
6050 __isl_give isl_aff *isl_aff_pullback_aff(
6051 __isl_take isl_aff *aff1,
6052 __isl_take isl_aff *aff2);
6053 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6054 __isl_take isl_aff *aff,
6055 __isl_take isl_multi_aff *ma);
6056 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6057 __isl_take isl_pw_aff *pa,
6058 __isl_take isl_multi_aff *ma);
6059 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6060 __isl_take isl_pw_aff *pa,
6061 __isl_take isl_pw_multi_aff *pma);
6062 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6063 __isl_take isl_pw_aff *pa,
6064 __isl_take isl_multi_pw_aff *mpa);
6065 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6066 __isl_take isl_multi_aff *ma1,
6067 __isl_take isl_multi_aff *ma2);
6068 __isl_give isl_pw_multi_aff *
6069 isl_pw_multi_aff_pullback_multi_aff(
6070 __isl_take isl_pw_multi_aff *pma,
6071 __isl_take isl_multi_aff *ma);
6072 __isl_give isl_multi_pw_aff *
6073 isl_multi_pw_aff_pullback_multi_aff(
6074 __isl_take isl_multi_pw_aff *mpa,
6075 __isl_take isl_multi_aff *ma);
6076 __isl_give isl_pw_multi_aff *
6077 isl_pw_multi_aff_pullback_pw_multi_aff(
6078 __isl_take isl_pw_multi_aff *pma1,
6079 __isl_take isl_pw_multi_aff *pma2);
6080 __isl_give isl_multi_pw_aff *
6081 isl_multi_pw_aff_pullback_pw_multi_aff(
6082 __isl_take isl_multi_pw_aff *mpa,
6083 __isl_take isl_pw_multi_aff *pma);
6084 __isl_give isl_multi_pw_aff *
6085 isl_multi_pw_aff_pullback_multi_pw_aff(
6086 __isl_take isl_multi_pw_aff *mpa1,
6087 __isl_take isl_multi_pw_aff *mpa2);
6088 __isl_give isl_union_pw_aff *
6089 isl_union_pw_aff_pullback_union_pw_multi_aff(
6090 __isl_take isl_union_pw_aff *upa,
6091 __isl_take isl_union_pw_multi_aff *upma);
6092 __isl_give isl_union_pw_multi_aff *
6093 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6094 __isl_take isl_union_pw_multi_aff *upma1,
6095 __isl_take isl_union_pw_multi_aff *upma2);
6096 __isl_give isl_multi_union_pw_aff *
6097 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6098 __isl_take isl_multi_union_pw_aff *mupa,
6099 __isl_take isl_union_pw_multi_aff *upma);
6101 These functions precompose the first expression by the second function.
6102 In other words, the second function is plugged
6103 into the first expression.
6107 #include <isl/aff.h>
6108 __isl_give isl_basic_set *isl_aff_le_basic_set(
6109 __isl_take isl_aff *aff1,
6110 __isl_take isl_aff *aff2);
6111 __isl_give isl_set *isl_aff_le_set(
6112 __isl_take isl_aff *aff1,
6113 __isl_take isl_aff *aff2);
6114 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6115 __isl_take isl_aff *aff1,
6116 __isl_take isl_aff *aff2);
6117 __isl_give isl_set *isl_aff_ge_set(
6118 __isl_take isl_aff *aff1,
6119 __isl_take isl_aff *aff2);
6120 __isl_give isl_set *isl_pw_aff_eq_set(
6121 __isl_take isl_pw_aff *pwaff1,
6122 __isl_take isl_pw_aff *pwaff2);
6123 __isl_give isl_set *isl_pw_aff_ne_set(
6124 __isl_take isl_pw_aff *pwaff1,
6125 __isl_take isl_pw_aff *pwaff2);
6126 __isl_give isl_set *isl_pw_aff_le_set(
6127 __isl_take isl_pw_aff *pwaff1,
6128 __isl_take isl_pw_aff *pwaff2);
6129 __isl_give isl_set *isl_pw_aff_lt_set(
6130 __isl_take isl_pw_aff *pwaff1,
6131 __isl_take isl_pw_aff *pwaff2);
6132 __isl_give isl_set *isl_pw_aff_ge_set(
6133 __isl_take isl_pw_aff *pwaff1,
6134 __isl_take isl_pw_aff *pwaff2);
6135 __isl_give isl_set *isl_pw_aff_gt_set(
6136 __isl_take isl_pw_aff *pwaff1,
6137 __isl_take isl_pw_aff *pwaff2);
6139 __isl_give isl_set *isl_multi_aff_lex_le_set(
6140 __isl_take isl_multi_aff *ma1,
6141 __isl_take isl_multi_aff *ma2);
6142 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6143 __isl_take isl_multi_aff *ma1,
6144 __isl_take isl_multi_aff *ma2);
6145 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6146 __isl_take isl_multi_aff *ma1,
6147 __isl_take isl_multi_aff *ma2);
6148 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6149 __isl_take isl_multi_aff *ma1,
6150 __isl_take isl_multi_aff *ma2);
6152 __isl_give isl_set *isl_pw_aff_list_eq_set(
6153 __isl_take isl_pw_aff_list *list1,
6154 __isl_take isl_pw_aff_list *list2);
6155 __isl_give isl_set *isl_pw_aff_list_ne_set(
6156 __isl_take isl_pw_aff_list *list1,
6157 __isl_take isl_pw_aff_list *list2);
6158 __isl_give isl_set *isl_pw_aff_list_le_set(
6159 __isl_take isl_pw_aff_list *list1,
6160 __isl_take isl_pw_aff_list *list2);
6161 __isl_give isl_set *isl_pw_aff_list_lt_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_ge_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_gt_set(
6168 __isl_take isl_pw_aff_list *list1,
6169 __isl_take isl_pw_aff_list *list2);
6171 The function C<isl_aff_ge_basic_set> returns a basic set
6172 containing those elements in the shared space
6173 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6174 The function C<isl_pw_aff_ge_set> returns a set
6175 containing those elements in the shared domain
6176 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6177 greater than or equal to C<pwaff2>.
6178 The function C<isl_multi_aff_lex_le_set> returns a set
6179 containing those elements in the shared domain space
6180 where C<ma1> is lexicographically smaller than or
6182 The functions operating on C<isl_pw_aff_list> apply the corresponding
6183 C<isl_pw_aff> function to each pair of elements in the two lists.
6185 #include <isl/aff.h>
6186 __isl_give isl_map *isl_pw_aff_eq_map(
6187 __isl_take isl_pw_aff *pa1,
6188 __isl_take isl_pw_aff *pa2);
6189 __isl_give isl_map *isl_pw_aff_lt_map(
6190 __isl_take isl_pw_aff *pa1,
6191 __isl_take isl_pw_aff *pa2);
6192 __isl_give isl_map *isl_pw_aff_gt_map(
6193 __isl_take isl_pw_aff *pa1,
6194 __isl_take isl_pw_aff *pa2);
6196 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6197 __isl_take isl_multi_pw_aff *mpa1,
6198 __isl_take isl_multi_pw_aff *mpa2);
6199 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6200 __isl_take isl_multi_pw_aff *mpa1,
6201 __isl_take isl_multi_pw_aff *mpa2);
6202 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6203 __isl_take isl_multi_pw_aff *mpa1,
6204 __isl_take isl_multi_pw_aff *mpa2);
6206 These functions return a map between domain elements of the arguments
6207 where the function values satisfy the given relation.
6209 #include <isl/union_map.h>
6210 __isl_give isl_union_map *
6211 isl_union_map_eq_at_multi_union_pw_aff(
6212 __isl_take isl_union_map *umap,
6213 __isl_take isl_multi_union_pw_aff *mupa);
6214 __isl_give isl_union_map *
6215 isl_union_map_lex_lt_at_multi_union_pw_aff(
6216 __isl_take isl_union_map *umap,
6217 __isl_take isl_multi_union_pw_aff *mupa);
6218 __isl_give isl_union_map *
6219 isl_union_map_lex_gt_at_multi_union_pw_aff(
6220 __isl_take isl_union_map *umap,
6221 __isl_take isl_multi_union_pw_aff *mupa);
6223 These functions select the subset of elements in the union map
6224 that have an equal or lexicographically smaller function value.
6226 =item * Cartesian Product
6228 #include <isl/space.h>
6229 __isl_give isl_space *isl_space_product(
6230 __isl_take isl_space *space1,
6231 __isl_take isl_space *space2);
6232 __isl_give isl_space *isl_space_domain_product(
6233 __isl_take isl_space *space1,
6234 __isl_take isl_space *space2);
6235 __isl_give isl_space *isl_space_range_product(
6236 __isl_take isl_space *space1,
6237 __isl_take isl_space *space2);
6240 C<isl_space_product>, C<isl_space_domain_product>
6241 and C<isl_space_range_product> take pairs or relation spaces and
6242 produce a single relations space, where either the domain, the range
6243 or both domain and range are wrapped spaces of relations between
6244 the domains and/or ranges of the input spaces.
6245 If the product is only constructed over the domain or the range
6246 then the ranges or the domains of the inputs should be the same.
6247 The function C<isl_space_product> also accepts a pair of set spaces,
6248 in which case it returns a wrapped space of a relation between the
6251 #include <isl/set.h>
6252 __isl_give isl_set *isl_set_product(
6253 __isl_take isl_set *set1,
6254 __isl_take isl_set *set2);
6256 #include <isl/map.h>
6257 __isl_give isl_basic_map *isl_basic_map_domain_product(
6258 __isl_take isl_basic_map *bmap1,
6259 __isl_take isl_basic_map *bmap2);
6260 __isl_give isl_basic_map *isl_basic_map_range_product(
6261 __isl_take isl_basic_map *bmap1,
6262 __isl_take isl_basic_map *bmap2);
6263 __isl_give isl_basic_map *isl_basic_map_product(
6264 __isl_take isl_basic_map *bmap1,
6265 __isl_take isl_basic_map *bmap2);
6266 __isl_give isl_map *isl_map_domain_product(
6267 __isl_take isl_map *map1,
6268 __isl_take isl_map *map2);
6269 __isl_give isl_map *isl_map_range_product(
6270 __isl_take isl_map *map1,
6271 __isl_take isl_map *map2);
6272 __isl_give isl_map *isl_map_product(
6273 __isl_take isl_map *map1,
6274 __isl_take isl_map *map2);
6276 #include <isl/union_set.h>
6277 __isl_give isl_union_set *isl_union_set_product(
6278 __isl_take isl_union_set *uset1,
6279 __isl_take isl_union_set *uset2);
6281 #include <isl/union_map.h>
6282 __isl_give isl_union_map *isl_union_map_domain_product(
6283 __isl_take isl_union_map *umap1,
6284 __isl_take isl_union_map *umap2);
6285 __isl_give isl_union_map *isl_union_map_range_product(
6286 __isl_take isl_union_map *umap1,
6287 __isl_take isl_union_map *umap2);
6288 __isl_give isl_union_map *isl_union_map_product(
6289 __isl_take isl_union_map *umap1,
6290 __isl_take isl_union_map *umap2);
6292 #include <isl/val.h>
6293 __isl_give isl_multi_val *isl_multi_val_range_product(
6294 __isl_take isl_multi_val *mv1,
6295 __isl_take isl_multi_val *mv2);
6296 __isl_give isl_multi_val *isl_multi_val_product(
6297 __isl_take isl_multi_val *mv1,
6298 __isl_take isl_multi_val *mv2);
6300 #include <isl/aff.h>
6301 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6302 __isl_take isl_multi_aff *ma1,
6303 __isl_take isl_multi_aff *ma2);
6304 __isl_give isl_multi_aff *isl_multi_aff_product(
6305 __isl_take isl_multi_aff *ma1,
6306 __isl_take isl_multi_aff *ma2);
6307 __isl_give isl_multi_pw_aff *
6308 isl_multi_pw_aff_range_product(
6309 __isl_take isl_multi_pw_aff *mpa1,
6310 __isl_take isl_multi_pw_aff *mpa2);
6311 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6312 __isl_take isl_multi_pw_aff *mpa1,
6313 __isl_take isl_multi_pw_aff *mpa2);
6314 __isl_give isl_pw_multi_aff *
6315 isl_pw_multi_aff_range_product(
6316 __isl_take isl_pw_multi_aff *pma1,
6317 __isl_take isl_pw_multi_aff *pma2);
6318 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6319 __isl_take isl_pw_multi_aff *pma1,
6320 __isl_take isl_pw_multi_aff *pma2);
6321 __isl_give isl_multi_union_pw_aff *
6322 isl_multi_union_pw_aff_range_product(
6323 __isl_take isl_multi_union_pw_aff *mupa1,
6324 __isl_take isl_multi_union_pw_aff *mupa2);
6326 The above functions compute the cross product of the given
6327 sets, relations or functions. The domains and ranges of the results
6328 are wrapped maps between domains and ranges of the inputs.
6329 To obtain a ``flat'' product, use the following functions
6332 #include <isl/set.h>
6333 __isl_give isl_basic_set *isl_basic_set_flat_product(
6334 __isl_take isl_basic_set *bset1,
6335 __isl_take isl_basic_set *bset2);
6336 __isl_give isl_set *isl_set_flat_product(
6337 __isl_take isl_set *set1,
6338 __isl_take isl_set *set2);
6340 #include <isl/map.h>
6341 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6342 __isl_take isl_basic_map *bmap1,
6343 __isl_take isl_basic_map *bmap2);
6344 __isl_give isl_map *isl_map_flat_domain_product(
6345 __isl_take isl_map *map1,
6346 __isl_take isl_map *map2);
6347 __isl_give isl_map *isl_map_flat_range_product(
6348 __isl_take isl_map *map1,
6349 __isl_take isl_map *map2);
6350 __isl_give isl_basic_map *isl_basic_map_flat_product(
6351 __isl_take isl_basic_map *bmap1,
6352 __isl_take isl_basic_map *bmap2);
6353 __isl_give isl_map *isl_map_flat_product(
6354 __isl_take isl_map *map1,
6355 __isl_take isl_map *map2);
6357 #include <isl/union_map.h>
6358 __isl_give isl_union_map *
6359 isl_union_map_flat_domain_product(
6360 __isl_take isl_union_map *umap1,
6361 __isl_take isl_union_map *umap2);
6362 __isl_give isl_union_map *
6363 isl_union_map_flat_range_product(
6364 __isl_take isl_union_map *umap1,
6365 __isl_take isl_union_map *umap2);
6367 #include <isl/val.h>
6368 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6369 __isl_take isl_multi_val *mv1,
6370 __isl_take isl_multi_aff *mv2);
6372 #include <isl/aff.h>
6373 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6374 __isl_take isl_multi_aff *ma1,
6375 __isl_take isl_multi_aff *ma2);
6376 __isl_give isl_pw_multi_aff *
6377 isl_pw_multi_aff_flat_range_product(
6378 __isl_take isl_pw_multi_aff *pma1,
6379 __isl_take isl_pw_multi_aff *pma2);
6380 __isl_give isl_multi_pw_aff *
6381 isl_multi_pw_aff_flat_range_product(
6382 __isl_take isl_multi_pw_aff *mpa1,
6383 __isl_take isl_multi_pw_aff *mpa2);
6384 __isl_give isl_union_pw_multi_aff *
6385 isl_union_pw_multi_aff_flat_range_product(
6386 __isl_take isl_union_pw_multi_aff *upma1,
6387 __isl_take isl_union_pw_multi_aff *upma2);
6388 __isl_give isl_multi_union_pw_aff *
6389 isl_multi_union_pw_aff_flat_range_product(
6390 __isl_take isl_multi_union_pw_aff *mupa1,
6391 __isl_take isl_multi_union_pw_aff *mupa2);
6393 #include <isl/space.h>
6394 __isl_give isl_space *isl_space_factor_domain(
6395 __isl_take isl_space *space);
6396 __isl_give isl_space *isl_space_factor_range(
6397 __isl_take isl_space *space);
6398 __isl_give isl_space *isl_space_domain_factor_domain(
6399 __isl_take isl_space *space);
6400 __isl_give isl_space *isl_space_domain_factor_range(
6401 __isl_take isl_space *space);
6402 __isl_give isl_space *isl_space_range_factor_domain(
6403 __isl_take isl_space *space);
6404 __isl_give isl_space *isl_space_range_factor_range(
6405 __isl_take isl_space *space);
6407 The functions C<isl_space_range_factor_domain> and
6408 C<isl_space_range_factor_range> extract the two arguments from
6409 the result of a call to C<isl_space_range_product>.
6411 The arguments of a call to a product can be extracted
6412 from the result using the following functions.
6414 #include <isl/map.h>
6415 __isl_give isl_map *isl_map_factor_domain(
6416 __isl_take isl_map *map);
6417 __isl_give isl_map *isl_map_factor_range(
6418 __isl_take isl_map *map);
6419 __isl_give isl_map *isl_map_domain_factor_domain(
6420 __isl_take isl_map *map);
6421 __isl_give isl_map *isl_map_domain_factor_range(
6422 __isl_take isl_map *map);
6423 __isl_give isl_map *isl_map_range_factor_domain(
6424 __isl_take isl_map *map);
6425 __isl_give isl_map *isl_map_range_factor_range(
6426 __isl_take isl_map *map);
6428 #include <isl/union_map.h>
6429 __isl_give isl_union_map *isl_union_map_factor_domain(
6430 __isl_take isl_union_map *umap);
6431 __isl_give isl_union_map *isl_union_map_factor_range(
6432 __isl_take isl_union_map *umap);
6433 __isl_give isl_union_map *
6434 isl_union_map_domain_factor_domain(
6435 __isl_take isl_union_map *umap);
6436 __isl_give isl_union_map *
6437 isl_union_map_domain_factor_range(
6438 __isl_take isl_union_map *umap);
6439 __isl_give isl_union_map *
6440 isl_union_map_range_factor_domain(
6441 __isl_take isl_union_map *umap);
6442 __isl_give isl_union_map *
6443 isl_union_map_range_factor_range(
6444 __isl_take isl_union_map *umap);
6446 #include <isl/val.h>
6447 __isl_give isl_multi_val *isl_multi_val_factor_range(
6448 __isl_take isl_multi_val *mv);
6449 __isl_give isl_multi_val *
6450 isl_multi_val_range_factor_domain(
6451 __isl_take isl_multi_val *mv);
6452 __isl_give isl_multi_val *
6453 isl_multi_val_range_factor_range(
6454 __isl_take isl_multi_val *mv);
6456 #include <isl/aff.h>
6457 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6458 __isl_take isl_multi_aff *ma);
6459 __isl_give isl_multi_aff *
6460 isl_multi_aff_range_factor_domain(
6461 __isl_take isl_multi_aff *ma);
6462 __isl_give isl_multi_aff *
6463 isl_multi_aff_range_factor_range(
6464 __isl_take isl_multi_aff *ma);
6465 __isl_give isl_multi_pw_aff *
6466 isl_multi_pw_aff_factor_range(
6467 __isl_take isl_multi_pw_aff *mpa);
6468 __isl_give isl_multi_pw_aff *
6469 isl_multi_pw_aff_range_factor_domain(
6470 __isl_take isl_multi_pw_aff *mpa);
6471 __isl_give isl_multi_pw_aff *
6472 isl_multi_pw_aff_range_factor_range(
6473 __isl_take isl_multi_pw_aff *mpa);
6474 __isl_give isl_multi_union_pw_aff *
6475 isl_multi_union_pw_aff_factor_range(
6476 __isl_take isl_multi_union_pw_aff *mupa);
6477 __isl_give isl_multi_union_pw_aff *
6478 isl_multi_union_pw_aff_range_factor_domain(
6479 __isl_take isl_multi_union_pw_aff *mupa);
6480 __isl_give isl_multi_union_pw_aff *
6481 isl_multi_union_pw_aff_range_factor_range(
6482 __isl_take isl_multi_union_pw_aff *mupa);
6484 The splice functions are a generalization of the flat product functions,
6485 where the second argument may be inserted at any position inside
6486 the first argument rather than being placed at the end.
6487 The functions C<isl_multi_val_factor_range>,
6488 C<isl_multi_aff_factor_range>,
6489 C<isl_multi_pw_aff_factor_range> and
6490 C<isl_multi_union_pw_aff_factor_range>
6491 take functions that live in a set space.
6493 #include <isl/val.h>
6494 __isl_give isl_multi_val *isl_multi_val_range_splice(
6495 __isl_take isl_multi_val *mv1, unsigned pos,
6496 __isl_take isl_multi_val *mv2);
6498 #include <isl/aff.h>
6499 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6500 __isl_take isl_multi_aff *ma1, unsigned pos,
6501 __isl_take isl_multi_aff *ma2);
6502 __isl_give isl_multi_aff *isl_multi_aff_splice(
6503 __isl_take isl_multi_aff *ma1,
6504 unsigned in_pos, unsigned out_pos,
6505 __isl_take isl_multi_aff *ma2);
6506 __isl_give isl_multi_pw_aff *
6507 isl_multi_pw_aff_range_splice(
6508 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6509 __isl_take isl_multi_pw_aff *mpa2);
6510 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6511 __isl_take isl_multi_pw_aff *mpa1,
6512 unsigned in_pos, unsigned out_pos,
6513 __isl_take isl_multi_pw_aff *mpa2);
6514 __isl_give isl_multi_union_pw_aff *
6515 isl_multi_union_pw_aff_range_splice(
6516 __isl_take isl_multi_union_pw_aff *mupa1,
6518 __isl_take isl_multi_union_pw_aff *mupa2);
6520 =item * Simplification
6522 When applied to a set or relation,
6523 the gist operation returns a set or relation that has the
6524 same intersection with the context as the input set or relation.
6525 Any implicit equality in the intersection is made explicit in the result,
6526 while all inequalities that are redundant with respect to the intersection
6528 In case of union sets and relations, the gist operation is performed
6531 When applied to a function,
6532 the gist operation applies the set gist operation to each of
6533 the cells in the domain of the input piecewise expression.
6534 The context is also exploited
6535 to simplify the expression associated to each cell.
6537 #include <isl/set.h>
6538 __isl_give isl_basic_set *isl_basic_set_gist(
6539 __isl_take isl_basic_set *bset,
6540 __isl_take isl_basic_set *context);
6541 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6542 __isl_take isl_set *context);
6543 __isl_give isl_set *isl_set_gist_params(
6544 __isl_take isl_set *set,
6545 __isl_take isl_set *context);
6547 #include <isl/map.h>
6548 __isl_give isl_basic_map *isl_basic_map_gist(
6549 __isl_take isl_basic_map *bmap,
6550 __isl_take isl_basic_map *context);
6551 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6552 __isl_take isl_basic_map *bmap,
6553 __isl_take isl_basic_set *context);
6554 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6555 __isl_take isl_map *context);
6556 __isl_give isl_map *isl_map_gist_params(
6557 __isl_take isl_map *map,
6558 __isl_take isl_set *context);
6559 __isl_give isl_map *isl_map_gist_domain(
6560 __isl_take isl_map *map,
6561 __isl_take isl_set *context);
6562 __isl_give isl_map *isl_map_gist_range(
6563 __isl_take isl_map *map,
6564 __isl_take isl_set *context);
6566 #include <isl/union_set.h>
6567 __isl_give isl_union_set *isl_union_set_gist(
6568 __isl_take isl_union_set *uset,
6569 __isl_take isl_union_set *context);
6570 __isl_give isl_union_set *isl_union_set_gist_params(
6571 __isl_take isl_union_set *uset,
6572 __isl_take isl_set *set);
6574 #include <isl/union_map.h>
6575 __isl_give isl_union_map *isl_union_map_gist(
6576 __isl_take isl_union_map *umap,
6577 __isl_take isl_union_map *context);
6578 __isl_give isl_union_map *isl_union_map_gist_params(
6579 __isl_take isl_union_map *umap,
6580 __isl_take isl_set *set);
6581 __isl_give isl_union_map *isl_union_map_gist_domain(
6582 __isl_take isl_union_map *umap,
6583 __isl_take isl_union_set *uset);
6584 __isl_give isl_union_map *isl_union_map_gist_range(
6585 __isl_take isl_union_map *umap,
6586 __isl_take isl_union_set *uset);
6588 #include <isl/aff.h>
6589 __isl_give isl_aff *isl_aff_gist_params(
6590 __isl_take isl_aff *aff,
6591 __isl_take isl_set *context);
6592 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6593 __isl_take isl_set *context);
6594 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6595 __isl_take isl_multi_aff *maff,
6596 __isl_take isl_set *context);
6597 __isl_give isl_multi_aff *isl_multi_aff_gist(
6598 __isl_take isl_multi_aff *maff,
6599 __isl_take isl_set *context);
6600 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6601 __isl_take isl_pw_aff *pwaff,
6602 __isl_take isl_set *context);
6603 __isl_give isl_pw_aff *isl_pw_aff_gist(
6604 __isl_take isl_pw_aff *pwaff,
6605 __isl_take isl_set *context);
6606 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6607 __isl_take isl_pw_multi_aff *pma,
6608 __isl_take isl_set *set);
6609 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6610 __isl_take isl_pw_multi_aff *pma,
6611 __isl_take isl_set *set);
6612 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6613 __isl_take isl_multi_pw_aff *mpa,
6614 __isl_take isl_set *set);
6615 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6616 __isl_take isl_multi_pw_aff *mpa,
6617 __isl_take isl_set *set);
6618 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6619 __isl_take isl_union_pw_aff *upa,
6620 __isl_take isl_union_set *context);
6621 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6622 __isl_take isl_union_pw_aff *upa,
6623 __isl_take isl_set *context);
6624 __isl_give isl_union_pw_multi_aff *
6625 isl_union_pw_multi_aff_gist_params(
6626 __isl_take isl_union_pw_multi_aff *upma,
6627 __isl_take isl_set *context);
6628 __isl_give isl_union_pw_multi_aff *
6629 isl_union_pw_multi_aff_gist(
6630 __isl_take isl_union_pw_multi_aff *upma,
6631 __isl_take isl_union_set *context);
6632 __isl_give isl_multi_union_pw_aff *
6633 isl_multi_union_pw_aff_gist_params(
6634 __isl_take isl_multi_union_pw_aff *aff,
6635 __isl_take isl_set *context);
6636 __isl_give isl_multi_union_pw_aff *
6637 isl_multi_union_pw_aff_gist(
6638 __isl_take isl_multi_union_pw_aff *aff,
6639 __isl_take isl_union_set *context);
6641 #include <isl/polynomial.h>
6642 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6643 __isl_take isl_qpolynomial *qp,
6644 __isl_take isl_set *context);
6645 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6646 __isl_take isl_qpolynomial *qp,
6647 __isl_take isl_set *context);
6648 __isl_give isl_qpolynomial_fold *
6649 isl_qpolynomial_fold_gist_params(
6650 __isl_take isl_qpolynomial_fold *fold,
6651 __isl_take isl_set *context);
6652 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6653 __isl_take isl_qpolynomial_fold *fold,
6654 __isl_take isl_set *context);
6655 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6656 __isl_take isl_pw_qpolynomial *pwqp,
6657 __isl_take isl_set *context);
6658 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6659 __isl_take isl_pw_qpolynomial *pwqp,
6660 __isl_take isl_set *context);
6661 __isl_give isl_pw_qpolynomial_fold *
6662 isl_pw_qpolynomial_fold_gist(
6663 __isl_take isl_pw_qpolynomial_fold *pwf,
6664 __isl_take isl_set *context);
6665 __isl_give isl_pw_qpolynomial_fold *
6666 isl_pw_qpolynomial_fold_gist_params(
6667 __isl_take isl_pw_qpolynomial_fold *pwf,
6668 __isl_take isl_set *context);
6669 __isl_give isl_union_pw_qpolynomial *
6670 isl_union_pw_qpolynomial_gist_params(
6671 __isl_take isl_union_pw_qpolynomial *upwqp,
6672 __isl_take isl_set *context);
6673 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6674 __isl_take isl_union_pw_qpolynomial *upwqp,
6675 __isl_take isl_union_set *context);
6676 __isl_give isl_union_pw_qpolynomial_fold *
6677 isl_union_pw_qpolynomial_fold_gist(
6678 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6679 __isl_take isl_union_set *context);
6680 __isl_give isl_union_pw_qpolynomial_fold *
6681 isl_union_pw_qpolynomial_fold_gist_params(
6682 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6683 __isl_take isl_set *context);
6685 =item * Binary Arithmetic Operations
6687 #include <isl/set.h>
6688 __isl_give isl_set *isl_set_sum(
6689 __isl_take isl_set *set1,
6690 __isl_take isl_set *set2);
6691 #include <isl/map.h>
6692 __isl_give isl_map *isl_map_sum(
6693 __isl_take isl_map *map1,
6694 __isl_take isl_map *map2);
6696 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6697 i.e., the set containing the sums of pairs of elements from
6698 C<set1> and C<set2>.
6699 The domain of the result of C<isl_map_sum> is the intersection
6700 of the domains of its two arguments. The corresponding range
6701 elements are the sums of the corresponding range elements
6702 in the two arguments.
6704 #include <isl/val.h>
6705 __isl_give isl_multi_val *isl_multi_val_add(
6706 __isl_take isl_multi_val *mv1,
6707 __isl_take isl_multi_val *mv2);
6708 __isl_give isl_multi_val *isl_multi_val_sub(
6709 __isl_take isl_multi_val *mv1,
6710 __isl_take isl_multi_val *mv2);
6712 #include <isl/aff.h>
6713 __isl_give isl_aff *isl_aff_add(
6714 __isl_take isl_aff *aff1,
6715 __isl_take isl_aff *aff2);
6716 __isl_give isl_multi_aff *isl_multi_aff_add(
6717 __isl_take isl_multi_aff *maff1,
6718 __isl_take isl_multi_aff *maff2);
6719 __isl_give isl_pw_aff *isl_pw_aff_add(
6720 __isl_take isl_pw_aff *pwaff1,
6721 __isl_take isl_pw_aff *pwaff2);
6722 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6723 __isl_take isl_multi_pw_aff *mpa1,
6724 __isl_take isl_multi_pw_aff *mpa2);
6725 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6726 __isl_take isl_pw_multi_aff *pma1,
6727 __isl_take isl_pw_multi_aff *pma2);
6728 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6729 __isl_take isl_union_pw_aff *upa1,
6730 __isl_take isl_union_pw_aff *upa2);
6731 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6732 __isl_take isl_union_pw_multi_aff *upma1,
6733 __isl_take isl_union_pw_multi_aff *upma2);
6734 __isl_give isl_multi_union_pw_aff *
6735 isl_multi_union_pw_aff_add(
6736 __isl_take isl_multi_union_pw_aff *mupa1,
6737 __isl_take isl_multi_union_pw_aff *mupa2);
6738 __isl_give isl_pw_aff *isl_pw_aff_min(
6739 __isl_take isl_pw_aff *pwaff1,
6740 __isl_take isl_pw_aff *pwaff2);
6741 __isl_give isl_pw_aff *isl_pw_aff_max(
6742 __isl_take isl_pw_aff *pwaff1,
6743 __isl_take isl_pw_aff *pwaff2);
6744 __isl_give isl_aff *isl_aff_sub(
6745 __isl_take isl_aff *aff1,
6746 __isl_take isl_aff *aff2);
6747 __isl_give isl_multi_aff *isl_multi_aff_sub(
6748 __isl_take isl_multi_aff *ma1,
6749 __isl_take isl_multi_aff *ma2);
6750 __isl_give isl_pw_aff *isl_pw_aff_sub(
6751 __isl_take isl_pw_aff *pwaff1,
6752 __isl_take isl_pw_aff *pwaff2);
6753 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6754 __isl_take isl_multi_pw_aff *mpa1,
6755 __isl_take isl_multi_pw_aff *mpa2);
6756 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6757 __isl_take isl_pw_multi_aff *pma1,
6758 __isl_take isl_pw_multi_aff *pma2);
6759 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6760 __isl_take isl_union_pw_aff *upa1,
6761 __isl_take isl_union_pw_aff *upa2);
6762 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6763 __isl_take isl_union_pw_multi_aff *upma1,
6764 __isl_take isl_union_pw_multi_aff *upma2);
6765 __isl_give isl_multi_union_pw_aff *
6766 isl_multi_union_pw_aff_sub(
6767 __isl_take isl_multi_union_pw_aff *mupa1,
6768 __isl_take isl_multi_union_pw_aff *mupa2);
6770 C<isl_aff_sub> subtracts the second argument from the first.
6772 #include <isl/polynomial.h>
6773 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6774 __isl_take isl_qpolynomial *qp1,
6775 __isl_take isl_qpolynomial *qp2);
6776 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6777 __isl_take isl_pw_qpolynomial *pwqp1,
6778 __isl_take isl_pw_qpolynomial *pwqp2);
6779 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6780 __isl_take isl_pw_qpolynomial *pwqp1,
6781 __isl_take isl_pw_qpolynomial *pwqp2);
6782 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6783 __isl_take isl_pw_qpolynomial_fold *pwf1,
6784 __isl_take isl_pw_qpolynomial_fold *pwf2);
6785 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6786 __isl_take isl_union_pw_qpolynomial *upwqp1,
6787 __isl_take isl_union_pw_qpolynomial *upwqp2);
6788 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6789 __isl_take isl_qpolynomial *qp1,
6790 __isl_take isl_qpolynomial *qp2);
6791 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6792 __isl_take isl_pw_qpolynomial *pwqp1,
6793 __isl_take isl_pw_qpolynomial *pwqp2);
6794 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6795 __isl_take isl_union_pw_qpolynomial *upwqp1,
6796 __isl_take isl_union_pw_qpolynomial *upwqp2);
6797 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6798 __isl_take isl_pw_qpolynomial_fold *pwf1,
6799 __isl_take isl_pw_qpolynomial_fold *pwf2);
6800 __isl_give isl_union_pw_qpolynomial_fold *
6801 isl_union_pw_qpolynomial_fold_fold(
6802 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6803 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6805 #include <isl/aff.h>
6806 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6807 __isl_take isl_pw_aff *pwaff1,
6808 __isl_take isl_pw_aff *pwaff2);
6809 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6810 __isl_take isl_pw_multi_aff *pma1,
6811 __isl_take isl_pw_multi_aff *pma2);
6812 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6813 __isl_take isl_union_pw_aff *upa1,
6814 __isl_take isl_union_pw_aff *upa2);
6815 __isl_give isl_union_pw_multi_aff *
6816 isl_union_pw_multi_aff_union_add(
6817 __isl_take isl_union_pw_multi_aff *upma1,
6818 __isl_take isl_union_pw_multi_aff *upma2);
6819 __isl_give isl_multi_union_pw_aff *
6820 isl_multi_union_pw_aff_union_add(
6821 __isl_take isl_multi_union_pw_aff *mupa1,
6822 __isl_take isl_multi_union_pw_aff *mupa2);
6823 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6824 __isl_take isl_pw_aff *pwaff1,
6825 __isl_take isl_pw_aff *pwaff2);
6826 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6827 __isl_take isl_pw_aff *pwaff1,
6828 __isl_take isl_pw_aff *pwaff2);
6830 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6831 expression with a domain that is the union of those of C<pwaff1> and
6832 C<pwaff2> and such that on each cell, the quasi-affine expression is
6833 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6834 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6835 associated expression is the defined one.
6836 This in contrast to the C<isl_pw_aff_max> function, which is
6837 only defined on the shared definition domain of the arguments.
6839 #include <isl/val.h>
6840 __isl_give isl_multi_val *isl_multi_val_add_val(
6841 __isl_take isl_multi_val *mv,
6842 __isl_take isl_val *v);
6843 __isl_give isl_multi_val *isl_multi_val_mod_val(
6844 __isl_take isl_multi_val *mv,
6845 __isl_take isl_val *v);
6846 __isl_give isl_multi_val *isl_multi_val_scale_val(
6847 __isl_take isl_multi_val *mv,
6848 __isl_take isl_val *v);
6849 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6850 __isl_take isl_multi_val *mv,
6851 __isl_take isl_val *v);
6853 #include <isl/aff.h>
6854 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6855 __isl_take isl_val *mod);
6856 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6857 __isl_take isl_pw_aff *pa,
6858 __isl_take isl_val *mod);
6859 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6860 __isl_take isl_union_pw_aff *upa,
6861 __isl_take isl_val *f);
6862 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6863 __isl_take isl_val *v);
6864 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6865 __isl_take isl_multi_aff *ma,
6866 __isl_take isl_val *v);
6867 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6868 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6869 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6870 __isl_take isl_multi_pw_aff *mpa,
6871 __isl_take isl_val *v);
6872 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6873 __isl_take isl_pw_multi_aff *pma,
6874 __isl_take isl_val *v);
6875 __isl_give isl_union_pw_multi_aff *
6876 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6877 __isl_take isl_union_pw_aff *upa,
6878 __isl_take isl_val *f);
6879 isl_union_pw_multi_aff_scale_val(
6880 __isl_take isl_union_pw_multi_aff *upma,
6881 __isl_take isl_val *val);
6882 __isl_give isl_multi_union_pw_aff *
6883 isl_multi_union_pw_aff_scale_val(
6884 __isl_take isl_multi_union_pw_aff *mupa,
6885 __isl_take isl_val *v);
6886 __isl_give isl_aff *isl_aff_scale_down_ui(
6887 __isl_take isl_aff *aff, unsigned f);
6888 __isl_give isl_aff *isl_aff_scale_down_val(
6889 __isl_take isl_aff *aff, __isl_take isl_val *v);
6890 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6891 __isl_take isl_multi_aff *ma,
6892 __isl_take isl_val *v);
6893 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6894 __isl_take isl_pw_aff *pa,
6895 __isl_take isl_val *f);
6896 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6897 __isl_take isl_multi_pw_aff *mpa,
6898 __isl_take isl_val *v);
6899 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6900 __isl_take isl_pw_multi_aff *pma,
6901 __isl_take isl_val *v);
6902 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6903 __isl_take isl_union_pw_aff *upa,
6904 __isl_take isl_val *v);
6905 __isl_give isl_union_pw_multi_aff *
6906 isl_union_pw_multi_aff_scale_down_val(
6907 __isl_take isl_union_pw_multi_aff *upma,
6908 __isl_take isl_val *val);
6909 __isl_give isl_multi_union_pw_aff *
6910 isl_multi_union_pw_aff_scale_down_val(
6911 __isl_take isl_multi_union_pw_aff *mupa,
6912 __isl_take isl_val *v);
6914 #include <isl/polynomial.h>
6915 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6916 __isl_take isl_qpolynomial *qp,
6917 __isl_take isl_val *v);
6918 __isl_give isl_qpolynomial_fold *
6919 isl_qpolynomial_fold_scale_val(
6920 __isl_take isl_qpolynomial_fold *fold,
6921 __isl_take isl_val *v);
6922 __isl_give isl_pw_qpolynomial *
6923 isl_pw_qpolynomial_scale_val(
6924 __isl_take isl_pw_qpolynomial *pwqp,
6925 __isl_take isl_val *v);
6926 __isl_give isl_pw_qpolynomial_fold *
6927 isl_pw_qpolynomial_fold_scale_val(
6928 __isl_take isl_pw_qpolynomial_fold *pwf,
6929 __isl_take isl_val *v);
6930 __isl_give isl_union_pw_qpolynomial *
6931 isl_union_pw_qpolynomial_scale_val(
6932 __isl_take isl_union_pw_qpolynomial *upwqp,
6933 __isl_take isl_val *v);
6934 __isl_give isl_union_pw_qpolynomial_fold *
6935 isl_union_pw_qpolynomial_fold_scale_val(
6936 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6937 __isl_take isl_val *v);
6938 __isl_give isl_qpolynomial *
6939 isl_qpolynomial_scale_down_val(
6940 __isl_take isl_qpolynomial *qp,
6941 __isl_take isl_val *v);
6942 __isl_give isl_qpolynomial_fold *
6943 isl_qpolynomial_fold_scale_down_val(
6944 __isl_take isl_qpolynomial_fold *fold,
6945 __isl_take isl_val *v);
6946 __isl_give isl_pw_qpolynomial *
6947 isl_pw_qpolynomial_scale_down_val(
6948 __isl_take isl_pw_qpolynomial *pwqp,
6949 __isl_take isl_val *v);
6950 __isl_give isl_pw_qpolynomial_fold *
6951 isl_pw_qpolynomial_fold_scale_down_val(
6952 __isl_take isl_pw_qpolynomial_fold *pwf,
6953 __isl_take isl_val *v);
6954 __isl_give isl_union_pw_qpolynomial *
6955 isl_union_pw_qpolynomial_scale_down_val(
6956 __isl_take isl_union_pw_qpolynomial *upwqp,
6957 __isl_take isl_val *v);
6958 __isl_give isl_union_pw_qpolynomial_fold *
6959 isl_union_pw_qpolynomial_fold_scale_down_val(
6960 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6961 __isl_take isl_val *v);
6963 #include <isl/val.h>
6964 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6965 __isl_take isl_multi_val *mv1,
6966 __isl_take isl_multi_val *mv2);
6967 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6968 __isl_take isl_multi_val *mv1,
6969 __isl_take isl_multi_val *mv2);
6970 __isl_give isl_multi_val *
6971 isl_multi_val_scale_down_multi_val(
6972 __isl_take isl_multi_val *mv1,
6973 __isl_take isl_multi_val *mv2);
6975 #include <isl/aff.h>
6976 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6977 __isl_take isl_multi_aff *ma,
6978 __isl_take isl_multi_val *mv);
6979 __isl_give isl_multi_union_pw_aff *
6980 isl_multi_union_pw_aff_mod_multi_val(
6981 __isl_take isl_multi_union_pw_aff *upma,
6982 __isl_take isl_multi_val *mv);
6983 __isl_give isl_multi_pw_aff *
6984 isl_multi_pw_aff_mod_multi_val(
6985 __isl_take isl_multi_pw_aff *mpa,
6986 __isl_take isl_multi_val *mv);
6987 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6988 __isl_take isl_multi_aff *ma,
6989 __isl_take isl_multi_val *mv);
6990 __isl_give isl_pw_multi_aff *
6991 isl_pw_multi_aff_scale_multi_val(
6992 __isl_take isl_pw_multi_aff *pma,
6993 __isl_take isl_multi_val *mv);
6994 __isl_give isl_multi_pw_aff *
6995 isl_multi_pw_aff_scale_multi_val(
6996 __isl_take isl_multi_pw_aff *mpa,
6997 __isl_take isl_multi_val *mv);
6998 __isl_give isl_multi_union_pw_aff *
6999 isl_multi_union_pw_aff_scale_multi_val(
7000 __isl_take isl_multi_union_pw_aff *mupa,
7001 __isl_take isl_multi_val *mv);
7002 __isl_give isl_union_pw_multi_aff *
7003 isl_union_pw_multi_aff_scale_multi_val(
7004 __isl_take isl_union_pw_multi_aff *upma,
7005 __isl_take isl_multi_val *mv);
7006 __isl_give isl_multi_aff *
7007 isl_multi_aff_scale_down_multi_val(
7008 __isl_take isl_multi_aff *ma,
7009 __isl_take isl_multi_val *mv);
7010 __isl_give isl_multi_pw_aff *
7011 isl_multi_pw_aff_scale_down_multi_val(
7012 __isl_take isl_multi_pw_aff *mpa,
7013 __isl_take isl_multi_val *mv);
7014 __isl_give isl_multi_union_pw_aff *
7015 isl_multi_union_pw_aff_scale_down_multi_val(
7016 __isl_take isl_multi_union_pw_aff *mupa,
7017 __isl_take isl_multi_val *mv);
7019 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7020 by the corresponding elements of C<mv>.
7022 #include <isl/aff.h>
7023 __isl_give isl_aff *isl_aff_mul(
7024 __isl_take isl_aff *aff1,
7025 __isl_take isl_aff *aff2);
7026 __isl_give isl_aff *isl_aff_div(
7027 __isl_take isl_aff *aff1,
7028 __isl_take isl_aff *aff2);
7029 __isl_give isl_pw_aff *isl_pw_aff_mul(
7030 __isl_take isl_pw_aff *pwaff1,
7031 __isl_take isl_pw_aff *pwaff2);
7032 __isl_give isl_pw_aff *isl_pw_aff_div(
7033 __isl_take isl_pw_aff *pa1,
7034 __isl_take isl_pw_aff *pa2);
7035 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7036 __isl_take isl_pw_aff *pa1,
7037 __isl_take isl_pw_aff *pa2);
7038 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7039 __isl_take isl_pw_aff *pa1,
7040 __isl_take isl_pw_aff *pa2);
7042 When multiplying two affine expressions, at least one of the two needs
7043 to be a constant. Similarly, when dividing an affine expression by another,
7044 the second expression needs to be a constant.
7045 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7046 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7049 #include <isl/polynomial.h>
7050 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7051 __isl_take isl_qpolynomial *qp1,
7052 __isl_take isl_qpolynomial *qp2);
7053 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7054 __isl_take isl_pw_qpolynomial *pwqp1,
7055 __isl_take isl_pw_qpolynomial *pwqp2);
7056 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7057 __isl_take isl_union_pw_qpolynomial *upwqp1,
7058 __isl_take isl_union_pw_qpolynomial *upwqp2);
7062 =head3 Lexicographic Optimization
7064 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7065 the following functions
7066 compute a set that contains the lexicographic minimum or maximum
7067 of the elements in C<set> (or C<bset>) for those values of the parameters
7068 that satisfy C<dom>.
7069 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7070 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7072 In other words, the union of the parameter values
7073 for which the result is non-empty and of C<*empty>
7076 #include <isl/set.h>
7077 __isl_give isl_set *isl_basic_set_partial_lexmin(
7078 __isl_take isl_basic_set *bset,
7079 __isl_take isl_basic_set *dom,
7080 __isl_give isl_set **empty);
7081 __isl_give isl_set *isl_basic_set_partial_lexmax(
7082 __isl_take isl_basic_set *bset,
7083 __isl_take isl_basic_set *dom,
7084 __isl_give isl_set **empty);
7085 __isl_give isl_set *isl_set_partial_lexmin(
7086 __isl_take isl_set *set, __isl_take isl_set *dom,
7087 __isl_give isl_set **empty);
7088 __isl_give isl_set *isl_set_partial_lexmax(
7089 __isl_take isl_set *set, __isl_take isl_set *dom,
7090 __isl_give isl_set **empty);
7092 Given a (basic) set C<set> (or C<bset>), the following functions simply
7093 return a set containing the lexicographic minimum or maximum
7094 of the elements in C<set> (or C<bset>).
7095 In case of union sets, the optimum is computed per space.
7097 #include <isl/set.h>
7098 __isl_give isl_set *isl_basic_set_lexmin(
7099 __isl_take isl_basic_set *bset);
7100 __isl_give isl_set *isl_basic_set_lexmax(
7101 __isl_take isl_basic_set *bset);
7102 __isl_give isl_set *isl_set_lexmin(
7103 __isl_take isl_set *set);
7104 __isl_give isl_set *isl_set_lexmax(
7105 __isl_take isl_set *set);
7106 __isl_give isl_union_set *isl_union_set_lexmin(
7107 __isl_take isl_union_set *uset);
7108 __isl_give isl_union_set *isl_union_set_lexmax(
7109 __isl_take isl_union_set *uset);
7111 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7112 the following functions
7113 compute a relation that maps each element of C<dom>
7114 to the single lexicographic minimum or maximum
7115 of the elements that are associated to that same
7116 element in C<map> (or C<bmap>).
7117 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7118 that contains the elements in C<dom> that do not map
7119 to any elements in C<map> (or C<bmap>).
7120 In other words, the union of the domain of the result and of C<*empty>
7123 #include <isl/map.h>
7124 __isl_give isl_map *isl_basic_map_partial_lexmax(
7125 __isl_take isl_basic_map *bmap,
7126 __isl_take isl_basic_set *dom,
7127 __isl_give isl_set **empty);
7128 __isl_give isl_map *isl_basic_map_partial_lexmin(
7129 __isl_take isl_basic_map *bmap,
7130 __isl_take isl_basic_set *dom,
7131 __isl_give isl_set **empty);
7132 __isl_give isl_map *isl_map_partial_lexmax(
7133 __isl_take isl_map *map, __isl_take isl_set *dom,
7134 __isl_give isl_set **empty);
7135 __isl_give isl_map *isl_map_partial_lexmin(
7136 __isl_take isl_map *map, __isl_take isl_set *dom,
7137 __isl_give isl_set **empty);
7139 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7140 return a map mapping each element in the domain of
7141 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7142 of all elements associated to that element.
7143 In case of union relations, the optimum is computed per space.
7145 #include <isl/map.h>
7146 __isl_give isl_map *isl_basic_map_lexmin(
7147 __isl_take isl_basic_map *bmap);
7148 __isl_give isl_map *isl_basic_map_lexmax(
7149 __isl_take isl_basic_map *bmap);
7150 __isl_give isl_map *isl_map_lexmin(
7151 __isl_take isl_map *map);
7152 __isl_give isl_map *isl_map_lexmax(
7153 __isl_take isl_map *map);
7154 __isl_give isl_union_map *isl_union_map_lexmin(
7155 __isl_take isl_union_map *umap);
7156 __isl_give isl_union_map *isl_union_map_lexmax(
7157 __isl_take isl_union_map *umap);
7159 The following functions return their result in the form of
7160 a piecewise multi-affine expression,
7161 but are otherwise equivalent to the corresponding functions
7162 returning a basic set or relation.
7164 #include <isl/set.h>
7165 __isl_give isl_pw_multi_aff *
7166 isl_basic_set_partial_lexmin_pw_multi_aff(
7167 __isl_take isl_basic_set *bset,
7168 __isl_take isl_basic_set *dom,
7169 __isl_give isl_set **empty);
7170 __isl_give isl_pw_multi_aff *
7171 isl_basic_set_partial_lexmax_pw_multi_aff(
7172 __isl_take isl_basic_set *bset,
7173 __isl_take isl_basic_set *dom,
7174 __isl_give isl_set **empty);
7175 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7176 __isl_take isl_set *set);
7177 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7178 __isl_take isl_set *set);
7180 #include <isl/map.h>
7181 __isl_give isl_pw_multi_aff *
7182 isl_basic_map_lexmin_pw_multi_aff(
7183 __isl_take isl_basic_map *bmap);
7184 __isl_give isl_pw_multi_aff *
7185 isl_basic_map_partial_lexmin_pw_multi_aff(
7186 __isl_take isl_basic_map *bmap,
7187 __isl_take isl_basic_set *dom,
7188 __isl_give isl_set **empty);
7189 __isl_give isl_pw_multi_aff *
7190 isl_basic_map_partial_lexmax_pw_multi_aff(
7191 __isl_take isl_basic_map *bmap,
7192 __isl_take isl_basic_set *dom,
7193 __isl_give isl_set **empty);
7194 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7195 __isl_take isl_map *map);
7196 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7197 __isl_take isl_map *map);
7199 The following functions return the lexicographic minimum or maximum
7200 on the shared domain of the inputs and the single defined function
7201 on those parts of the domain where only a single function is defined.
7203 #include <isl/aff.h>
7204 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7205 __isl_take isl_pw_multi_aff *pma1,
7206 __isl_take isl_pw_multi_aff *pma2);
7207 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7208 __isl_take isl_pw_multi_aff *pma1,
7209 __isl_take isl_pw_multi_aff *pma2);
7211 =head2 Ternary Operations
7213 #include <isl/aff.h>
7214 __isl_give isl_pw_aff *isl_pw_aff_cond(
7215 __isl_take isl_pw_aff *cond,
7216 __isl_take isl_pw_aff *pwaff_true,
7217 __isl_take isl_pw_aff *pwaff_false);
7219 The function C<isl_pw_aff_cond> performs a conditional operator
7220 and returns an expression that is equal to C<pwaff_true>
7221 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7222 where C<cond> is zero.
7226 Lists are defined over several element types, including
7227 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7228 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7229 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7230 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7231 Here we take lists of C<isl_set>s as an example.
7232 Lists can be created, copied, modified and freed using the following functions.
7234 #include <isl/set.h>
7235 __isl_give isl_set_list *isl_set_list_from_set(
7236 __isl_take isl_set *el);
7237 __isl_give isl_set_list *isl_set_list_alloc(
7238 isl_ctx *ctx, int n);
7239 __isl_give isl_set_list *isl_set_list_copy(
7240 __isl_keep isl_set_list *list);
7241 __isl_give isl_set_list *isl_set_list_insert(
7242 __isl_take isl_set_list *list, unsigned pos,
7243 __isl_take isl_set *el);
7244 __isl_give isl_set_list *isl_set_list_add(
7245 __isl_take isl_set_list *list,
7246 __isl_take isl_set *el);
7247 __isl_give isl_set_list *isl_set_list_drop(
7248 __isl_take isl_set_list *list,
7249 unsigned first, unsigned n);
7250 __isl_give isl_set_list *isl_set_list_set_set(
7251 __isl_take isl_set_list *list, int index,
7252 __isl_take isl_set *set);
7253 __isl_give isl_set_list *isl_set_list_concat(
7254 __isl_take isl_set_list *list1,
7255 __isl_take isl_set_list *list2);
7256 __isl_give isl_set_list *isl_set_list_sort(
7257 __isl_take isl_set_list *list,
7258 int (*cmp)(__isl_keep isl_set *a,
7259 __isl_keep isl_set *b, void *user),
7261 __isl_null isl_set_list *isl_set_list_free(
7262 __isl_take isl_set_list *list);
7264 C<isl_set_list_alloc> creates an empty list with an initial capacity
7265 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7266 add elements to a list, increasing its capacity as needed.
7267 C<isl_set_list_from_set> creates a list with a single element.
7269 Lists can be inspected using the following functions.
7271 #include <isl/set.h>
7272 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7273 __isl_give isl_set *isl_set_list_get_set(
7274 __isl_keep isl_set_list *list, int index);
7275 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7276 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7278 isl_stat isl_set_list_foreach_scc(
7279 __isl_keep isl_set_list *list,
7280 isl_bool (*follows)(__isl_keep isl_set *a,
7281 __isl_keep isl_set *b, void *user),
7283 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7286 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7287 strongly connected components of the graph with as vertices the elements
7288 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7289 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
7290 should return C<-1> on error.
7292 Lists can be printed using
7294 #include <isl/set.h>
7295 __isl_give isl_printer *isl_printer_print_set_list(
7296 __isl_take isl_printer *p,
7297 __isl_keep isl_set_list *list);
7299 =head2 Associative arrays
7301 Associative arrays map isl objects of a specific type to isl objects
7302 of some (other) specific type. They are defined for several pairs
7303 of types, including (C<isl_map>, C<isl_basic_set>),
7304 (C<isl_id>, C<isl_ast_expr>),
7305 (C<isl_id>, C<isl_id>) and
7306 (C<isl_id>, C<isl_pw_aff>).
7307 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7310 Associative arrays can be created, copied and freed using
7311 the following functions.
7313 #include <isl/id_to_ast_expr.h>
7314 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7315 isl_ctx *ctx, int min_size);
7316 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7317 __isl_keep isl_id_to_ast_expr *id2expr);
7318 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7319 __isl_take isl_id_to_ast_expr *id2expr);
7321 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7322 to specify the expected size of the associative array.
7323 The associative array will be grown automatically as needed.
7325 Associative arrays can be inspected using the following functions.
7327 #include <isl/id_to_ast_expr.h>
7328 __isl_give isl_maybe_isl_ast_expr
7329 isl_id_to_ast_expr_try_get(
7330 __isl_keep isl_id_to_ast_expr *id2expr,
7331 __isl_keep isl_id *key);
7332 isl_bool isl_id_to_ast_expr_has(
7333 __isl_keep isl_id_to_ast_expr *id2expr,
7334 __isl_keep isl_id *key);
7335 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7336 __isl_keep isl_id_to_ast_expr *id2expr,
7337 __isl_take isl_id *key);
7338 isl_stat isl_id_to_ast_expr_foreach(
7339 __isl_keep isl_id_to_ast_expr *id2expr,
7340 isl_stat (*fn)(__isl_take isl_id *key,
7341 __isl_take isl_ast_expr *val, void *user),
7344 The function C<isl_id_to_ast_expr_try_get> returns a structure
7345 containing two elements, C<valid> and C<value>.
7346 If there is a value associated to the key, then C<valid>
7347 is set to C<isl_bool_true> and C<value> contains a copy of
7348 the associated value. Otherwise C<value> is C<NULL> and
7349 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7350 on whether some error has occurred or there simply is no associated value.
7351 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7352 in the structure and
7353 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7355 Associative arrays can be modified using the following functions.
7357 #include <isl/id_to_ast_expr.h>
7358 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7359 __isl_take isl_id_to_ast_expr *id2expr,
7360 __isl_take isl_id *key,
7361 __isl_take isl_ast_expr *val);
7362 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7363 __isl_take isl_id_to_ast_expr *id2expr,
7364 __isl_take isl_id *key);
7366 Associative arrays can be printed using the following function.
7368 #include <isl/id_to_ast_expr.h>
7369 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7370 __isl_take isl_printer *p,
7371 __isl_keep isl_id_to_ast_expr *id2expr);
7375 Vectors can be created, copied and freed using the following functions.
7377 #include <isl/vec.h>
7378 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7380 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7381 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7383 Note that the elements of a newly created vector may have arbitrary values.
7384 The elements can be changed and inspected using the following functions.
7386 int isl_vec_size(__isl_keep isl_vec *vec);
7387 __isl_give isl_val *isl_vec_get_element_val(
7388 __isl_keep isl_vec *vec, int pos);
7389 __isl_give isl_vec *isl_vec_set_element_si(
7390 __isl_take isl_vec *vec, int pos, int v);
7391 __isl_give isl_vec *isl_vec_set_element_val(
7392 __isl_take isl_vec *vec, int pos,
7393 __isl_take isl_val *v);
7394 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7396 __isl_give isl_vec *isl_vec_set_val(
7397 __isl_take isl_vec *vec, __isl_take isl_val *v);
7398 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7399 __isl_keep isl_vec *vec2, int pos);
7401 C<isl_vec_get_element> will return a negative value if anything went wrong.
7402 In that case, the value of C<*v> is undefined.
7404 The following function can be used to concatenate two vectors.
7406 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7407 __isl_take isl_vec *vec2);
7411 Matrices can be created, copied and freed using the following functions.
7413 #include <isl/mat.h>
7414 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7415 unsigned n_row, unsigned n_col);
7416 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7417 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7419 Note that the elements of a newly created matrix may have arbitrary values.
7420 The elements can be changed and inspected using the following functions.
7422 int isl_mat_rows(__isl_keep isl_mat *mat);
7423 int isl_mat_cols(__isl_keep isl_mat *mat);
7424 __isl_give isl_val *isl_mat_get_element_val(
7425 __isl_keep isl_mat *mat, int row, int col);
7426 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7427 int row, int col, int v);
7428 __isl_give isl_mat *isl_mat_set_element_val(
7429 __isl_take isl_mat *mat, int row, int col,
7430 __isl_take isl_val *v);
7432 C<isl_mat_get_element> will return a negative value if anything went wrong.
7433 In that case, the value of C<*v> is undefined.
7435 The following function can be used to compute the (right) inverse
7436 of a matrix, i.e., a matrix such that the product of the original
7437 and the inverse (in that order) is a multiple of the identity matrix.
7438 The input matrix is assumed to be of full row-rank.
7440 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7442 The following function can be used to compute the (right) kernel
7443 (or null space) of a matrix, i.e., a matrix such that the product of
7444 the original and the kernel (in that order) is the zero matrix.
7446 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7448 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7450 The following functions determine
7451 an upper or lower bound on a quasipolynomial over its domain.
7453 __isl_give isl_pw_qpolynomial_fold *
7454 isl_pw_qpolynomial_bound(
7455 __isl_take isl_pw_qpolynomial *pwqp,
7456 enum isl_fold type, int *tight);
7458 __isl_give isl_union_pw_qpolynomial_fold *
7459 isl_union_pw_qpolynomial_bound(
7460 __isl_take isl_union_pw_qpolynomial *upwqp,
7461 enum isl_fold type, int *tight);
7463 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7464 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7465 is the returned bound is known be tight, i.e., for each value
7466 of the parameters there is at least
7467 one element in the domain that reaches the bound.
7468 If the domain of C<pwqp> is not wrapping, then the bound is computed
7469 over all elements in that domain and the result has a purely parametric
7470 domain. If the domain of C<pwqp> is wrapping, then the bound is
7471 computed over the range of the wrapped relation. The domain of the
7472 wrapped relation becomes the domain of the result.
7474 =head2 Parametric Vertex Enumeration
7476 The parametric vertex enumeration described in this section
7477 is mainly intended to be used internally and by the C<barvinok>
7480 #include <isl/vertices.h>
7481 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7482 __isl_keep isl_basic_set *bset);
7484 The function C<isl_basic_set_compute_vertices> performs the
7485 actual computation of the parametric vertices and the chamber
7486 decomposition and store the result in an C<isl_vertices> object.
7487 This information can be queried by either iterating over all
7488 the vertices or iterating over all the chambers or cells
7489 and then iterating over all vertices that are active on the chamber.
7491 isl_stat isl_vertices_foreach_vertex(
7492 __isl_keep isl_vertices *vertices,
7493 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7494 void *user), void *user);
7496 isl_stat isl_vertices_foreach_cell(
7497 __isl_keep isl_vertices *vertices,
7498 isl_stat (*fn)(__isl_take isl_cell *cell,
7499 void *user), void *user);
7500 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7501 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7502 void *user), void *user);
7504 Other operations that can be performed on an C<isl_vertices> object are
7507 int isl_vertices_get_n_vertices(
7508 __isl_keep isl_vertices *vertices);
7509 void isl_vertices_free(__isl_take isl_vertices *vertices);
7511 Vertices can be inspected and destroyed using the following functions.
7513 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7514 __isl_give isl_basic_set *isl_vertex_get_domain(
7515 __isl_keep isl_vertex *vertex);
7516 __isl_give isl_multi_aff *isl_vertex_get_expr(
7517 __isl_keep isl_vertex *vertex);
7518 void isl_vertex_free(__isl_take isl_vertex *vertex);
7520 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7521 describing the vertex in terms of the parameters,
7522 while C<isl_vertex_get_domain> returns the activity domain
7525 Chambers can be inspected and destroyed using the following functions.
7527 __isl_give isl_basic_set *isl_cell_get_domain(
7528 __isl_keep isl_cell *cell);
7529 void isl_cell_free(__isl_take isl_cell *cell);
7531 =head1 Polyhedral Compilation Library
7533 This section collects functionality in C<isl> that has been specifically
7534 designed for use during polyhedral compilation.
7536 =head2 Schedule Trees
7538 A schedule tree is a structured representation of a schedule,
7539 assigning a relative order to a set of domain elements.
7540 The relative order expressed by the schedule tree is
7541 defined recursively. In particular, the order between
7542 two domain elements is determined by the node that is closest
7543 to the root that refers to both elements and that orders them apart.
7544 Each node in the tree is of one of several types.
7545 The root node is always of type C<isl_schedule_node_domain>
7546 (or C<isl_schedule_node_extension>)
7547 and it describes the (extra) domain elements to which the schedule applies.
7548 The other types of nodes are as follows.
7552 =item C<isl_schedule_node_band>
7554 A band of schedule dimensions. Each schedule dimension is represented
7555 by a union piecewise quasi-affine expression. If this expression
7556 assigns a different value to two domain elements, while all previous
7557 schedule dimensions in the same band assign them the same value,
7558 then the two domain elements are ordered according to these two
7560 Each expression is required to be total in the domain elements
7561 that reach the band node.
7563 =item C<isl_schedule_node_expansion>
7565 An expansion node maps each of the domain elements that reach the node
7566 to one or more domain elements. The image of this mapping forms
7567 the set of domain elements that reach the child of the expansion node.
7568 The function that maps each of the expanded domain elements
7569 to the original domain element from which it was expanded
7570 is called the contraction.
7572 =item C<isl_schedule_node_filter>
7574 A filter node does not impose any ordering, but rather intersects
7575 the set of domain elements that the current subtree refers to
7576 with a given union set. The subtree of the filter node only
7577 refers to domain elements in the intersection.
7578 A filter node is typically only used a child of a sequence or
7581 =item C<isl_schedule_node_leaf>
7583 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7585 =item C<isl_schedule_node_mark>
7587 A mark node can be used to attach any kind of information to a subtree
7588 of the schedule tree.
7590 =item C<isl_schedule_node_sequence>
7592 A sequence node has one or more children, each of which is a filter node.
7593 The filters on these filter nodes form a partition of
7594 the domain elements that the current subtree refers to.
7595 If two domain elements appear in distinct filters then the sequence
7596 node orders them according to the child positions of the corresponding
7599 =item C<isl_schedule_node_set>
7601 A set node is similar to a sequence node, except that
7602 it expresses that domain elements appearing in distinct filters
7603 may have any order. The order of the children of a set node
7604 is therefore also immaterial.
7608 The following node types are only supported by the AST generator.
7612 =item C<isl_schedule_node_context>
7614 The context describes constraints on the parameters and
7615 the schedule dimensions of outer
7616 bands that the AST generator may assume to hold. It is also the only
7617 kind of node that may introduce additional parameters.
7618 The space of the context is that of the flat product of the outer
7619 band nodes. In particular, if there are no outer band nodes, then
7620 this space is the unnamed zero-dimensional space.
7621 Since a context node references the outer band nodes, any tree
7622 containing a context node is considered to be anchored.
7624 =item C<isl_schedule_node_extension>
7626 An extension node instructs the AST generator to add additional
7627 domain elements that need to be scheduled.
7628 The additional domain elements are described by the range of
7629 the extension map in terms of the outer schedule dimensions,
7630 i.e., the flat product of the outer band nodes.
7631 Note that domain elements are added whenever the AST generator
7632 reaches the extension node, meaning that there are still some
7633 active domain elements for which an AST needs to be generated.
7634 The conditions under which some domain elements are still active
7635 may however not be completely described by the outer AST nodes
7636 generated at that point.
7638 An extension node may also appear as the root of a schedule tree,
7639 when it is intended to be inserted into another tree
7640 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7641 In this case, the domain of the extension node should
7642 correspond to the flat product of the outer band nodes
7643 in this other schedule tree at the point where the extension tree
7646 =item C<isl_schedule_node_guard>
7648 The guard describes constraints on the parameters and
7649 the schedule dimensions of outer
7650 bands that need to be enforced by the outer nodes
7651 in the generated AST.
7652 The space of the guard is that of the flat product of the outer
7653 band nodes. In particular, if there are no outer band nodes, then
7654 this space is the unnamed zero-dimensional space.
7655 Since a guard node references the outer band nodes, any tree
7656 containing a guard node is considered to be anchored.
7660 Except for the C<isl_schedule_node_context> nodes,
7661 none of the nodes may introduce any parameters that were not
7662 already present in the root domain node.
7664 A schedule tree is encapsulated in an C<isl_schedule> object.
7665 The simplest such objects, those with a tree consisting of single domain node,
7666 can be created using the following functions with either an empty
7667 domain or a given domain.
7669 #include <isl/schedule.h>
7670 __isl_give isl_schedule *isl_schedule_empty(
7671 __isl_take isl_space *space);
7672 __isl_give isl_schedule *isl_schedule_from_domain(
7673 __isl_take isl_union_set *domain);
7675 The function C<isl_schedule_constraints_compute_schedule> described
7676 in L</"Scheduling"> can also be used to construct schedules.
7678 C<isl_schedule> objects may be copied and freed using the following functions.
7680 #include <isl/schedule.h>
7681 __isl_give isl_schedule *isl_schedule_copy(
7682 __isl_keep isl_schedule *sched);
7683 __isl_null isl_schedule *isl_schedule_free(
7684 __isl_take isl_schedule *sched);
7686 The following functions checks whether two C<isl_schedule> objects
7687 are obviously the same.
7689 #include <isl/schedule.h>
7690 isl_bool isl_schedule_plain_is_equal(
7691 __isl_keep isl_schedule *schedule1,
7692 __isl_keep isl_schedule *schedule2);
7694 The domain of the schedule, i.e., the domain described by the root node,
7695 can be obtained using the following function.
7697 #include <isl/schedule.h>
7698 __isl_give isl_union_set *isl_schedule_get_domain(
7699 __isl_keep isl_schedule *schedule);
7701 An extra top-level band node (right underneath the domain node) can
7702 be introduced into the schedule using the following function.
7703 The schedule tree is assumed not to have any anchored nodes.
7705 #include <isl/schedule.h>
7706 __isl_give isl_schedule *
7707 isl_schedule_insert_partial_schedule(
7708 __isl_take isl_schedule *schedule,
7709 __isl_take isl_multi_union_pw_aff *partial);
7711 A top-level context node (right underneath the domain node) can
7712 be introduced into the schedule using the following function.
7714 #include <isl/schedule.h>
7715 __isl_give isl_schedule *isl_schedule_insert_context(
7716 __isl_take isl_schedule *schedule,
7717 __isl_take isl_set *context)
7719 A top-level guard node (right underneath the domain node) can
7720 be introduced into the schedule using the following function.
7722 #include <isl/schedule.h>
7723 __isl_give isl_schedule *isl_schedule_insert_guard(
7724 __isl_take isl_schedule *schedule,
7725 __isl_take isl_set *guard)
7727 A schedule that combines two schedules either in the given
7728 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7729 or an C<isl_schedule_node_set> node,
7730 can be created using the following functions.
7732 #include <isl/schedule.h>
7733 __isl_give isl_schedule *isl_schedule_sequence(
7734 __isl_take isl_schedule *schedule1,
7735 __isl_take isl_schedule *schedule2);
7736 __isl_give isl_schedule *isl_schedule_set(
7737 __isl_take isl_schedule *schedule1,
7738 __isl_take isl_schedule *schedule2);
7740 The domains of the two input schedules need to be disjoint.
7742 The following function can be used to restrict the domain
7743 of a schedule with a domain node as root to be a subset of the given union set.
7744 This operation may remove nodes in the tree that have become
7747 #include <isl/schedule.h>
7748 __isl_give isl_schedule *isl_schedule_intersect_domain(
7749 __isl_take isl_schedule *schedule,
7750 __isl_take isl_union_set *domain);
7752 The following function can be used to simplify the domain
7753 of a schedule with a domain node as root with respect to the given
7756 #include <isl/schedule.h>
7757 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7758 __isl_take isl_schedule *schedule,
7759 __isl_take isl_set *context);
7761 The following function resets the user pointers on all parameter
7762 and tuple identifiers referenced by the nodes of the given schedule.
7764 #include <isl/schedule.h>
7765 __isl_give isl_schedule *isl_schedule_reset_user(
7766 __isl_take isl_schedule *schedule);
7768 The following function aligns the parameters of all nodes
7769 in the given schedule to the given space.
7771 #include <isl/schedule.h>
7772 __isl_give isl_schedule *isl_schedule_align_params(
7773 __isl_take isl_schedule *schedule,
7774 __isl_take isl_space *space);
7776 The following function allows the user to plug in a given function
7777 in the iteration domains. The input schedule is not allowed to contain
7778 any expansion nodes.
7780 #include <isl/schedule.h>
7781 __isl_give isl_schedule *
7782 isl_schedule_pullback_union_pw_multi_aff(
7783 __isl_take isl_schedule *schedule,
7784 __isl_take isl_union_pw_multi_aff *upma);
7786 An C<isl_union_map> representation of the schedule can be obtained
7787 from an C<isl_schedule> using the following function.
7789 #include <isl/schedule.h>
7790 __isl_give isl_union_map *isl_schedule_get_map(
7791 __isl_keep isl_schedule *sched);
7793 The resulting relation encodes the same relative ordering as
7794 the schedule by mapping the domain elements to a common schedule space.
7795 If the schedule_separate_components option is set, then the order
7796 of the children of a set node is explicitly encoded in the result.
7797 If the tree contains any expansion nodes, then the relation
7798 is formulated in terms of the expanded domain elements.
7800 Schedules can be read from input using the following functions.
7802 #include <isl/schedule.h>
7803 __isl_give isl_schedule *isl_schedule_read_from_file(
7804 isl_ctx *ctx, FILE *input);
7805 __isl_give isl_schedule *isl_schedule_read_from_str(
7806 isl_ctx *ctx, const char *str);
7808 A representation of the schedule can be printed using
7810 #include <isl/schedule.h>
7811 __isl_give isl_printer *isl_printer_print_schedule(
7812 __isl_take isl_printer *p,
7813 __isl_keep isl_schedule *schedule);
7814 __isl_give char *isl_schedule_to_str(
7815 __isl_keep isl_schedule *schedule);
7817 C<isl_schedule_to_str> prints the schedule in flow format.
7819 The schedule tree can be traversed through the use of
7820 C<isl_schedule_node> objects that point to a particular
7821 position in the schedule tree. Whenever a C<isl_schedule_node>
7822 is use to modify a node in the schedule tree, the original schedule
7823 tree is left untouched and the modifications are performed to a copy
7824 of the tree. The returned C<isl_schedule_node> then points to
7825 this modified copy of the tree.
7827 The root of the schedule tree can be obtained using the following function.
7829 #include <isl/schedule.h>
7830 __isl_give isl_schedule_node *isl_schedule_get_root(
7831 __isl_keep isl_schedule *schedule);
7833 A pointer to a newly created schedule tree with a single domain
7834 node can be created using the following functions.
7836 #include <isl/schedule_node.h>
7837 __isl_give isl_schedule_node *
7838 isl_schedule_node_from_domain(
7839 __isl_take isl_union_set *domain);
7840 __isl_give isl_schedule_node *
7841 isl_schedule_node_from_extension(
7842 __isl_take isl_union_map *extension);
7844 C<isl_schedule_node_from_extension> creates a tree with an extension
7847 Schedule nodes can be copied and freed using the following functions.
7849 #include <isl/schedule_node.h>
7850 __isl_give isl_schedule_node *isl_schedule_node_copy(
7851 __isl_keep isl_schedule_node *node);
7852 __isl_null isl_schedule_node *isl_schedule_node_free(
7853 __isl_take isl_schedule_node *node);
7855 The following functions can be used to check if two schedule
7856 nodes point to the same position in the same schedule.
7858 #include <isl/schedule_node.h>
7859 isl_bool isl_schedule_node_is_equal(
7860 __isl_keep isl_schedule_node *node1,
7861 __isl_keep isl_schedule_node *node2);
7863 The following properties can be obtained from a schedule node.
7865 #include <isl/schedule_node.h>
7866 enum isl_schedule_node_type isl_schedule_node_get_type(
7867 __isl_keep isl_schedule_node *node);
7868 enum isl_schedule_node_type
7869 isl_schedule_node_get_parent_type(
7870 __isl_keep isl_schedule_node *node);
7871 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7872 __isl_keep isl_schedule_node *node);
7874 The function C<isl_schedule_node_get_type> returns the type of
7875 the node, while C<isl_schedule_node_get_parent_type> returns
7876 type of the parent of the node, which is required to exist.
7877 The function C<isl_schedule_node_get_schedule> returns a copy
7878 to the schedule to which the node belongs.
7880 The following functions can be used to move the schedule node
7881 to a different position in the tree or to check if such a position
7884 #include <isl/schedule_node.h>
7885 isl_bool isl_schedule_node_has_parent(
7886 __isl_keep isl_schedule_node *node);
7887 __isl_give isl_schedule_node *isl_schedule_node_parent(
7888 __isl_take isl_schedule_node *node);
7889 __isl_give isl_schedule_node *isl_schedule_node_root(
7890 __isl_take isl_schedule_node *node);
7891 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
7892 __isl_take isl_schedule_node *node,
7894 int isl_schedule_node_n_children(
7895 __isl_keep isl_schedule_node *node);
7896 __isl_give isl_schedule_node *isl_schedule_node_child(
7897 __isl_take isl_schedule_node *node, int pos);
7898 isl_bool isl_schedule_node_has_children(
7899 __isl_keep isl_schedule_node *node);
7900 __isl_give isl_schedule_node *isl_schedule_node_first_child(
7901 __isl_take isl_schedule_node *node);
7902 isl_bool isl_schedule_node_has_previous_sibling(
7903 __isl_keep isl_schedule_node *node);
7904 __isl_give isl_schedule_node *
7905 isl_schedule_node_previous_sibling(
7906 __isl_take isl_schedule_node *node);
7907 isl_bool isl_schedule_node_has_next_sibling(
7908 __isl_keep isl_schedule_node *node);
7909 __isl_give isl_schedule_node *
7910 isl_schedule_node_next_sibling(
7911 __isl_take isl_schedule_node *node);
7913 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
7914 is the node itself, the ancestor of generation 1 is its parent and so on.
7916 It is also possible to query the number of ancestors of a node,
7917 the position of the current node
7918 within the children of its parent, the position of the subtree
7919 containing a node within the children of an ancestor
7920 or to obtain a copy of a given
7921 child without destroying the current node.
7922 Given two nodes that point to the same schedule, their closest
7923 shared ancestor can be obtained using
7924 C<isl_schedule_node_get_shared_ancestor>.
7926 #include <isl/schedule_node.h>
7927 int isl_schedule_node_get_tree_depth(
7928 __isl_keep isl_schedule_node *node);
7929 int isl_schedule_node_get_child_position(
7930 __isl_keep isl_schedule_node *node);
7931 int isl_schedule_node_get_ancestor_child_position(
7932 __isl_keep isl_schedule_node *node,
7933 __isl_keep isl_schedule_node *ancestor);
7934 __isl_give isl_schedule_node *isl_schedule_node_get_child(
7935 __isl_keep isl_schedule_node *node, int pos);
7936 __isl_give isl_schedule_node *
7937 isl_schedule_node_get_shared_ancestor(
7938 __isl_keep isl_schedule_node *node1,
7939 __isl_keep isl_schedule_node *node2);
7941 All nodes in a schedule tree or
7942 all descendants of a specific node (including the node) can be visited
7943 in depth-first pre-order using the following functions.
7945 #include <isl/schedule.h>
7946 isl_stat isl_schedule_foreach_schedule_node_top_down(
7947 __isl_keep isl_schedule *sched,
7948 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7949 void *user), void *user);
7951 #include <isl/schedule_node.h>
7952 isl_stat isl_schedule_node_foreach_descendant_top_down(
7953 __isl_keep isl_schedule_node *node,
7954 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7955 void *user), void *user);
7957 The callback function is slightly different from the usual
7958 callbacks in that it not only indicates success (non-negative result)
7959 or failure (negative result), but also indicates whether the children
7960 of the given node should be visited. In particular, if the callback
7961 returns a positive value, then the children are visited, but if
7962 the callback returns zero, then the children are not visited.
7964 The ancestors of a node in a schedule tree can be visited from
7965 the root down to and including the parent of the node using
7966 the following function.
7968 #include <isl/schedule_node.h>
7969 isl_stat isl_schedule_node_foreach_ancestor_top_down(
7970 __isl_keep isl_schedule_node *node,
7971 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
7972 void *user), void *user);
7974 The following functions allows for a depth-first post-order
7975 traversal of the nodes in a schedule tree or
7976 of the descendants of a specific node (including the node
7977 itself), where the user callback is allowed to modify the
7980 #include <isl/schedule.h>
7981 __isl_give isl_schedule *
7982 isl_schedule_map_schedule_node_bottom_up(
7983 __isl_take isl_schedule *schedule,
7984 __isl_give isl_schedule_node *(*fn)(
7985 __isl_take isl_schedule_node *node,
7986 void *user), void *user);
7988 #include <isl/schedule_node.h>
7989 __isl_give isl_schedule_node *
7990 isl_schedule_node_map_descendant_bottom_up(
7991 __isl_take isl_schedule_node *node,
7992 __isl_give isl_schedule_node *(*fn)(
7993 __isl_take isl_schedule_node *node,
7994 void *user), void *user);
7996 The traversal continues from the node returned by the callback function.
7997 It is the responsibility of the user to ensure that this does not
7998 lead to an infinite loop. It is safest to always return a pointer
7999 to the same position (same ancestors and child positions) as the input node.
8001 The following function removes a node (along with its descendants)
8002 from a schedule tree and returns a pointer to the leaf at the
8003 same position in the updated tree.
8004 It is not allowed to remove the root of a schedule tree or
8005 a child of a set or sequence node.
8007 #include <isl/schedule_node.h>
8008 __isl_give isl_schedule_node *isl_schedule_node_cut(
8009 __isl_take isl_schedule_node *node);
8011 The following function removes a single node
8012 from a schedule tree and returns a pointer to the child
8013 of the node, now located at the position of the original node
8014 or to a leaf node at that position if there was no child.
8015 It is not allowed to remove the root of a schedule tree,
8016 a set or sequence node, a child of a set or sequence node or
8017 a band node with an anchored subtree.
8019 #include <isl/schedule_node.h>
8020 __isl_give isl_schedule_node *isl_schedule_node_delete(
8021 __isl_take isl_schedule_node *node);
8023 Most nodes in a schedule tree only contain local information.
8024 In some cases, however, a node may also refer to outer band nodes.
8025 This means that the position of the node within the tree should
8026 not be changed, or at least that no changes are performed to the
8027 outer band nodes. The following function can be used to test
8028 whether the subtree rooted at a given node contains any such nodes.
8030 #include <isl/schedule_node.h>
8031 isl_bool isl_schedule_node_is_subtree_anchored(
8032 __isl_keep isl_schedule_node *node);
8034 The following function resets the user pointers on all parameter
8035 and tuple identifiers referenced by the given schedule node.
8037 #include <isl/schedule_node.h>
8038 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8039 __isl_take isl_schedule_node *node);
8041 The following function aligns the parameters of the given schedule
8042 node to the given space.
8044 #include <isl/schedule_node.h>
8045 __isl_give isl_schedule_node *
8046 isl_schedule_node_align_params(
8047 __isl_take isl_schedule_node *node,
8048 __isl_take isl_space *space);
8050 Several node types have their own functions for querying
8051 (and in some cases setting) some node type specific properties.
8053 #include <isl/schedule_node.h>
8054 __isl_give isl_space *isl_schedule_node_band_get_space(
8055 __isl_keep isl_schedule_node *node);
8056 __isl_give isl_multi_union_pw_aff *
8057 isl_schedule_node_band_get_partial_schedule(
8058 __isl_keep isl_schedule_node *node);
8059 __isl_give isl_union_map *
8060 isl_schedule_node_band_get_partial_schedule_union_map(
8061 __isl_keep isl_schedule_node *node);
8062 unsigned isl_schedule_node_band_n_member(
8063 __isl_keep isl_schedule_node *node);
8064 isl_bool isl_schedule_node_band_member_get_coincident(
8065 __isl_keep isl_schedule_node *node, int pos);
8066 __isl_give isl_schedule_node *
8067 isl_schedule_node_band_member_set_coincident(
8068 __isl_take isl_schedule_node *node, int pos,
8070 isl_bool isl_schedule_node_band_get_permutable(
8071 __isl_keep isl_schedule_node *node);
8072 __isl_give isl_schedule_node *
8073 isl_schedule_node_band_set_permutable(
8074 __isl_take isl_schedule_node *node, int permutable);
8075 enum isl_ast_loop_type
8076 isl_schedule_node_band_member_get_ast_loop_type(
8077 __isl_keep isl_schedule_node *node, int pos);
8078 __isl_give isl_schedule_node *
8079 isl_schedule_node_band_member_set_ast_loop_type(
8080 __isl_take isl_schedule_node *node, int pos,
8081 enum isl_ast_loop_type type);
8082 __isl_give isl_union_set *
8083 enum isl_ast_loop_type
8084 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8085 __isl_keep isl_schedule_node *node, int pos);
8086 __isl_give isl_schedule_node *
8087 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8088 __isl_take isl_schedule_node *node, int pos,
8089 enum isl_ast_loop_type type);
8090 isl_schedule_node_band_get_ast_build_options(
8091 __isl_keep isl_schedule_node *node);
8092 __isl_give isl_schedule_node *
8093 isl_schedule_node_band_set_ast_build_options(
8094 __isl_take isl_schedule_node *node,
8095 __isl_take isl_union_set *options);
8097 The function C<isl_schedule_node_band_get_space> returns the space
8098 of the partial schedule of the band.
8099 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8100 returns a representation of the partial schedule of the band node
8101 in the form of an C<isl_union_map>.
8102 The coincident and permutable properties are set by
8103 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8105 A scheduling dimension is considered to be ``coincident''
8106 if it satisfies the coincidence constraints within its band.
8107 That is, if the dependence distances of the coincidence
8108 constraints are all zero in that direction (for fixed
8109 iterations of outer bands).
8110 A band is marked permutable if it was produced using the Pluto-like scheduler.
8111 Note that the scheduler may have to resort to a Feautrier style scheduling
8112 step even if the default scheduler is used.
8113 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8114 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8115 For the meaning of these loop AST generation types and the difference
8116 between the regular loop AST generation type and the isolate
8117 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8118 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8119 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8120 may return C<isl_ast_loop_error> if an error occurs.
8121 The AST build options govern how an AST is generated for
8122 the individual schedule dimensions during AST generation.
8123 See L</"AST Generation Options (Schedule Tree)">.
8125 #include <isl/schedule_node.h>
8126 __isl_give isl_set *
8127 isl_schedule_node_context_get_context(
8128 __isl_keep isl_schedule_node *node);
8130 #include <isl/schedule_node.h>
8131 __isl_give isl_union_set *
8132 isl_schedule_node_domain_get_domain(
8133 __isl_keep isl_schedule_node *node);
8135 #include <isl/schedule_node.h>
8136 __isl_give isl_union_map *
8137 isl_schedule_node_expansion_get_expansion(
8138 __isl_keep isl_schedule_node *node);
8139 __isl_give isl_union_pw_multi_aff *
8140 isl_schedule_node_expansion_get_contraction(
8141 __isl_keep isl_schedule_node *node);
8143 #include <isl/schedule_node.h>
8144 __isl_give isl_union_map *
8145 isl_schedule_node_extension_get_extension(
8146 __isl_keep isl_schedule_node *node);
8148 #include <isl/schedule_node.h>
8149 __isl_give isl_union_set *
8150 isl_schedule_node_filter_get_filter(
8151 __isl_keep isl_schedule_node *node);
8153 #include <isl/schedule_node.h>
8154 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8155 __isl_keep isl_schedule_node *node);
8157 #include <isl/schedule_node.h>
8158 __isl_give isl_id *isl_schedule_node_mark_get_id(
8159 __isl_keep isl_schedule_node *node);
8161 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8162 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8163 partial schedules related to the node.
8165 #include <isl/schedule_node.h>
8166 __isl_give isl_multi_union_pw_aff *
8167 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8168 __isl_keep isl_schedule_node *node);
8169 __isl_give isl_union_pw_multi_aff *
8170 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8171 __isl_keep isl_schedule_node *node);
8172 __isl_give isl_union_map *
8173 isl_schedule_node_get_prefix_schedule_union_map(
8174 __isl_keep isl_schedule_node *node);
8175 __isl_give isl_union_map *
8176 isl_schedule_node_get_prefix_schedule_relation(
8177 __isl_keep isl_schedule_node *node);
8178 __isl_give isl_union_map *
8179 isl_schedule_node_get_subtree_schedule_union_map(
8180 __isl_keep isl_schedule_node *node);
8182 In particular, the functions
8183 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8184 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8185 and C<isl_schedule_node_get_prefix_schedule_union_map>
8186 return a relative ordering on the domain elements that reach the given
8187 node determined by its ancestors.
8188 The function C<isl_schedule_node_get_prefix_schedule_relation>
8189 additionally includes the domain constraints in the result.
8190 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8191 returns a representation of the partial schedule defined by the
8192 subtree rooted at the given node.
8193 If the tree contains any expansion nodes, then the subtree schedule
8194 is formulated in terms of the expanded domain elements.
8195 The tree passed to functions returning a prefix schedule
8196 may only contain extension nodes if these would not affect
8197 the result of these functions. That is, if one of the ancestors
8198 is an extension node, then all of the domain elements that were
8199 added by the extension node need to have been filtered out
8200 by filter nodes between the extension node and the input node.
8201 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8202 may not contain in extension nodes in the selected subtree.
8204 The expansion/contraction defined by an entire subtree, combining
8205 the expansions/contractions
8206 on the expansion nodes in the subtree, can be obtained using
8207 the following functions.
8209 #include <isl/schedule_node.h>
8210 __isl_give isl_union_map *
8211 isl_schedule_node_get_subtree_expansion(
8212 __isl_keep isl_schedule_node *node);
8213 __isl_give isl_union_pw_multi_aff *
8214 isl_schedule_node_get_subtree_contraction(
8215 __isl_keep isl_schedule_node *node);
8217 The total number of outer band members of given node, i.e.,
8218 the shared output dimension of the maps in the result
8219 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8220 using the following function.
8222 #include <isl/schedule_node.h>
8223 int isl_schedule_node_get_schedule_depth(
8224 __isl_keep isl_schedule_node *node);
8226 The following functions return the elements that reach the given node
8227 or the union of universes in the spaces that contain these elements.
8229 #include <isl/schedule_node.h>
8230 __isl_give isl_union_set *
8231 isl_schedule_node_get_domain(
8232 __isl_keep isl_schedule_node *node);
8233 __isl_give isl_union_set *
8234 isl_schedule_node_get_universe_domain(
8235 __isl_keep isl_schedule_node *node);
8237 The input tree of C<isl_schedule_node_get_domain>
8238 may only contain extension nodes if these would not affect
8239 the result of this function. That is, if one of the ancestors
8240 is an extension node, then all of the domain elements that were
8241 added by the extension node need to have been filtered out
8242 by filter nodes between the extension node and the input node.
8244 The following functions can be used to introduce additional nodes
8245 in the schedule tree. The new node is introduced at the point
8246 in the tree where the C<isl_schedule_node> points to and
8247 the results points to the new node.
8249 #include <isl/schedule_node.h>
8250 __isl_give isl_schedule_node *
8251 isl_schedule_node_insert_partial_schedule(
8252 __isl_take isl_schedule_node *node,
8253 __isl_take isl_multi_union_pw_aff *schedule);
8255 This function inserts a new band node with (the greatest integer
8256 part of) the given partial schedule.
8257 The subtree rooted at the given node is assumed not to have
8260 #include <isl/schedule_node.h>
8261 __isl_give isl_schedule_node *
8262 isl_schedule_node_insert_context(
8263 __isl_take isl_schedule_node *node,
8264 __isl_take isl_set *context);
8266 This function inserts a new context node with the given context constraints.
8268 #include <isl/schedule_node.h>
8269 __isl_give isl_schedule_node *
8270 isl_schedule_node_insert_filter(
8271 __isl_take isl_schedule_node *node,
8272 __isl_take isl_union_set *filter);
8274 This function inserts a new filter node with the given filter.
8275 If the original node already pointed to a filter node, then the
8276 two filter nodes are merged into one.
8278 #include <isl/schedule_node.h>
8279 __isl_give isl_schedule_node *
8280 isl_schedule_node_insert_guard(
8281 __isl_take isl_schedule_node *node,
8282 __isl_take isl_set *guard);
8284 This function inserts a new guard node with the given guard constraints.
8286 #include <isl/schedule_node.h>
8287 __isl_give isl_schedule_node *
8288 isl_schedule_node_insert_mark(
8289 __isl_take isl_schedule_node *node,
8290 __isl_take isl_id *mark);
8292 This function inserts a new mark node with the give mark identifier.
8294 #include <isl/schedule_node.h>
8295 __isl_give isl_schedule_node *
8296 isl_schedule_node_insert_sequence(
8297 __isl_take isl_schedule_node *node,
8298 __isl_take isl_union_set_list *filters);
8299 __isl_give isl_schedule_node *
8300 isl_schedule_node_insert_set(
8301 __isl_take isl_schedule_node *node,
8302 __isl_take isl_union_set_list *filters);
8304 These functions insert a new sequence or set node with the given
8305 filters as children.
8307 #include <isl/schedule_node.h>
8308 __isl_give isl_schedule_node *isl_schedule_node_group(
8309 __isl_take isl_schedule_node *node,
8310 __isl_take isl_id *group_id);
8312 This function introduces an expansion node in between the current
8313 node and its parent that expands instances of a space with tuple
8314 identifier C<group_id> to the original domain elements that reach
8315 the node. The group instances are identified by the prefix schedule
8316 of those domain elements. The ancestors of the node are adjusted
8317 to refer to the group instances instead of the original domain
8318 elements. The return value points to the same node in the updated
8319 schedule tree as the input node, i.e., to the child of the newly
8320 introduced expansion node. Grouping instances of different statements
8321 ensures that they will be treated as a single statement by the
8322 AST generator up to the point of the expansion node.
8324 The following function can be used to flatten a nested
8327 #include <isl/schedule_node.h>
8328 __isl_give isl_schedule_node *
8329 isl_schedule_node_sequence_splice_child(
8330 __isl_take isl_schedule_node *node, int pos);
8332 That is, given a sequence node C<node> that has another sequence node
8333 in its child at position C<pos> (in particular, the child of that filter
8334 node is a sequence node), attach the children of that other sequence
8335 node as children of C<node>, replacing the original child at position
8338 The partial schedule of a band node can be scaled (down) or reduced using
8339 the following functions.
8341 #include <isl/schedule_node.h>
8342 __isl_give isl_schedule_node *
8343 isl_schedule_node_band_scale(
8344 __isl_take isl_schedule_node *node,
8345 __isl_take isl_multi_val *mv);
8346 __isl_give isl_schedule_node *
8347 isl_schedule_node_band_scale_down(
8348 __isl_take isl_schedule_node *node,
8349 __isl_take isl_multi_val *mv);
8350 __isl_give isl_schedule_node *
8351 isl_schedule_node_band_mod(
8352 __isl_take isl_schedule_node *node,
8353 __isl_take isl_multi_val *mv);
8355 The spaces of the two arguments need to match.
8356 After scaling, the partial schedule is replaced by its greatest
8357 integer part to ensure that the schedule remains integral.
8359 The partial schedule of a band node can be shifted by an
8360 C<isl_multi_union_pw_aff> with a domain that is a superset
8361 of the domain of the partial schedule using
8362 the following function.
8364 #include <isl/schedule_node.h>
8365 __isl_give isl_schedule_node *
8366 isl_schedule_node_band_shift(
8367 __isl_take isl_schedule_node *node,
8368 __isl_take isl_multi_union_pw_aff *shift);
8370 A band node can be tiled using the following function.
8372 #include <isl/schedule_node.h>
8373 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8374 __isl_take isl_schedule_node *node,
8375 __isl_take isl_multi_val *sizes);
8377 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8379 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8380 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8382 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8384 The C<isl_schedule_node_band_tile> function tiles
8385 the band using the given tile sizes inside its schedule.
8386 A new child band node is created to represent the point loops and it is
8387 inserted between the modified band and its children.
8388 The subtree rooted at the given node is assumed not to have
8390 The C<tile_scale_tile_loops> option specifies whether the tile
8391 loops iterators should be scaled by the tile sizes.
8392 If the C<tile_shift_point_loops> option is set, then the point loops
8393 are shifted to start at zero.
8395 A band node can be split into two nested band nodes
8396 using the following function.
8398 #include <isl/schedule_node.h>
8399 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8400 __isl_take isl_schedule_node *node, int pos);
8402 The resulting outer band node contains the first C<pos> dimensions of
8403 the schedule of C<node> while the inner band contains the remaining dimensions.
8404 The schedules of the two band nodes live in anonymous spaces.
8406 A band node can be moved down to the leaves of the subtree rooted
8407 at the band node using the following function.
8409 #include <isl/schedule_node.h>
8410 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8411 __isl_take isl_schedule_node *node);
8413 The subtree rooted at the given node is assumed not to have
8415 The result points to the node in the resulting tree that is in the same
8416 position as the node pointed to by C<node> in the original tree.
8418 #include <isl/schedule_node.h>
8419 __isl_give isl_schedule_node *
8420 isl_schedule_node_order_before(
8421 __isl_take isl_schedule_node *node,
8422 __isl_take isl_union_set *filter);
8423 __isl_give isl_schedule_node *
8424 isl_schedule_node_order_after(
8425 __isl_take isl_schedule_node *node,
8426 __isl_take isl_union_set *filter);
8428 These functions split the domain elements that reach C<node>
8429 into those that satisfy C<filter> and those that do not and
8430 arranges for the elements that do satisfy the filter to be
8431 executed before (in case of C<isl_schedule_node_order_before>)
8432 or after (in case of C<isl_schedule_node_order_after>)
8433 those that do not. The order is imposed by
8434 a sequence node, possibly reusing the grandparent of C<node>
8435 on two copies of the subtree attached to the original C<node>.
8436 Both copies are simplified with respect to their filter.
8438 Return a pointer to the copy of the subtree that does not
8439 satisfy C<filter>. If there is no such copy (because all
8440 reaching domain elements satisfy the filter), then return
8441 the original pointer.
8443 #include <isl/schedule_node.h>
8444 __isl_give isl_schedule_node *
8445 isl_schedule_node_graft_before(
8446 __isl_take isl_schedule_node *node,
8447 __isl_take isl_schedule_node *graft);
8448 __isl_give isl_schedule_node *
8449 isl_schedule_node_graft_after(
8450 __isl_take isl_schedule_node *node,
8451 __isl_take isl_schedule_node *graft);
8453 This function inserts the C<graft> tree into the tree containing C<node>
8454 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8455 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8456 The root node of C<graft>
8457 should be an extension node where the domain of the extension
8458 is the flat product of all outer band nodes of C<node>.
8459 The root node may also be a domain node.
8460 The elements of the domain or the range of the extension may not
8461 intersect with the domain elements that reach "node".
8462 The schedule tree of C<graft> may not be anchored.
8464 The schedule tree of C<node> is modified to include an extension node
8465 corresponding to the root node of C<graft> as a child of the original
8466 parent of C<node>. The original node that C<node> points to and the
8467 child of the root node of C<graft> are attached to this extension node
8468 through a sequence, with appropriate filters and with the child
8469 of C<graft> appearing before or after the original C<node>.
8471 If C<node> already appears inside a sequence that is the child of
8472 an extension node and if the spaces of the new domain elements
8473 do not overlap with those of the original domain elements,
8474 then that extension node is extended with the new extension
8475 rather than introducing a new segment of extension and sequence nodes.
8477 Return a pointer to the same node in the modified tree that
8478 C<node> pointed to in the original tree.
8480 A representation of the schedule node can be printed using
8482 #include <isl/schedule_node.h>
8483 __isl_give isl_printer *isl_printer_print_schedule_node(
8484 __isl_take isl_printer *p,
8485 __isl_keep isl_schedule_node *node);
8486 __isl_give char *isl_schedule_node_to_str(
8487 __isl_keep isl_schedule_node *node);
8489 C<isl_schedule_node_to_str> prints the schedule node in block format.
8491 =head2 Dependence Analysis
8493 C<isl> contains specialized functionality for performing
8494 array dataflow analysis. That is, given a I<sink> access relation
8495 and a collection of possible I<source> access relations,
8496 C<isl> can compute relations that describe
8497 for each iteration of the sink access, which iteration
8498 of which of the source access relations was the last
8499 to access the same data element before the given iteration
8501 The resulting dependence relations map source iterations
8502 to either the corresponding sink iterations or
8503 pairs of corresponding sink iterations and accessed data elements.
8504 To compute standard flow dependences, the sink should be
8505 a read, while the sources should be writes.
8506 If any of the source accesses are marked as being I<may>
8507 accesses, then there will be a dependence from the last
8508 I<must> access B<and> from any I<may> access that follows
8509 this last I<must> access.
8510 In particular, if I<all> sources are I<may> accesses,
8511 then memory based dependence analysis is performed.
8512 If, on the other hand, all sources are I<must> accesses,
8513 then value based dependence analysis is performed.
8515 =head3 High-level Interface
8517 A high-level interface to dependence analysis is provided
8518 by the following function.
8520 #include <isl/flow.h>
8521 __isl_give isl_union_flow *
8522 isl_union_access_info_compute_flow(
8523 __isl_take isl_union_access_info *access);
8525 The input C<isl_union_access_info> object describes the sink
8526 access relations, the source access relations and a schedule,
8527 while the output C<isl_union_flow> object describes
8528 the resulting dependence relations and the subsets of the
8529 sink relations for which no source was found.
8531 An C<isl_union_access_info> is created, modified, copied and freed using
8532 the following functions.
8534 #include <isl/flow.h>
8535 __isl_give isl_union_access_info *
8536 isl_union_access_info_from_sink(
8537 __isl_take isl_union_map *sink);
8538 __isl_give isl_union_access_info *
8539 isl_union_access_info_set_must_source(
8540 __isl_take isl_union_access_info *access,
8541 __isl_take isl_union_map *must_source);
8542 __isl_give isl_union_access_info *
8543 isl_union_access_info_set_may_source(
8544 __isl_take isl_union_access_info *access,
8545 __isl_take isl_union_map *may_source);
8546 __isl_give isl_union_access_info *
8547 isl_union_access_info_set_schedule(
8548 __isl_take isl_union_access_info *access,
8549 __isl_take isl_schedule *schedule);
8550 __isl_give isl_union_access_info *
8551 isl_union_access_info_set_schedule_map(
8552 __isl_take isl_union_access_info *access,
8553 __isl_take isl_union_map *schedule_map);
8554 __isl_give isl_union_access_info *
8555 isl_union_access_info_copy(
8556 __isl_keep isl_union_access_info *access);
8557 __isl_null isl_union_access_info *
8558 isl_union_access_info_free(
8559 __isl_take isl_union_access_info *access);
8561 The may sources set by C<isl_union_access_info_set_may_source>
8562 do not need to include the must sources set by
8563 C<isl_union_access_info_set_must_source> as a subset.
8564 The user is free not to call one (or both) of these functions,
8565 in which case the corresponding set is kept to its empty default.
8566 Similarly, the default schedule initialized by
8567 C<isl_union_access_info_from_sink> is empty.
8568 The current schedule is determined by the last call to either
8569 C<isl_union_access_info_set_schedule> or
8570 C<isl_union_access_info_set_schedule_map>.
8571 The domain of the schedule corresponds to the domains of
8572 the access relations. In particular, the domains of the access
8573 relations are effectively intersected with the domain of the schedule
8574 and only the resulting accesses are considered by the dependence analysis.
8576 A representation of the information contained in an object
8577 of type C<isl_union_access_info> can be obtained using
8579 #include <isl/flow.h>
8580 __isl_give isl_printer *
8581 isl_printer_print_union_access_info(
8582 __isl_take isl_printer *p,
8583 __isl_keep isl_union_access_info *access);
8584 __isl_give char *isl_union_access_info_to_str(
8585 __isl_keep isl_union_access_info *access);
8587 C<isl_union_access_info_to_str> prints the information in flow format.
8589 The output of C<isl_union_access_info_compute_flow> can be examined
8590 and freed using the following functions.
8592 #include <isl/flow.h>
8593 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8594 __isl_keep isl_union_flow *flow);
8595 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8596 __isl_keep isl_union_flow *flow);
8597 __isl_give isl_union_map *
8598 isl_union_flow_get_full_must_dependence(
8599 __isl_keep isl_union_flow *flow);
8600 __isl_give isl_union_map *
8601 isl_union_flow_get_full_may_dependence(
8602 __isl_keep isl_union_flow *flow);
8603 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8604 __isl_keep isl_union_flow *flow);
8605 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8606 __isl_keep isl_union_flow *flow);
8607 __isl_null isl_union_flow *isl_union_flow_free(
8608 __isl_take isl_union_flow *flow);
8610 The relation returned by C<isl_union_flow_get_must_dependence>
8611 relates domain elements of must sources to domain elements of the sink.
8612 The relation returned by C<isl_union_flow_get_may_dependence>
8613 relates domain elements of must or may sources to domain elements of the sink
8614 and includes the previous relation as a subset.
8615 The relation returned by C<isl_union_flow_get_full_must_dependence>
8616 relates domain elements of must sources to pairs of domain elements of the sink
8617 and accessed data elements.
8618 The relation returned by C<isl_union_flow_get_full_may_dependence>
8619 relates domain elements of must or may sources to pairs of
8620 domain elements of the sink and accessed data elements.
8621 This relation includes the previous relation as a subset.
8622 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8623 of the sink relation for which no dependences have been found.
8624 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8625 of the sink relation for which no definite dependences have been found.
8626 That is, it contains those sink access that do not contribute to any
8627 of the elements in the relation returned
8628 by C<isl_union_flow_get_must_dependence>.
8630 A representation of the information contained in an object
8631 of type C<isl_union_flow> can be obtained using
8633 #include <isl/flow.h>
8634 __isl_give isl_printer *isl_printer_print_union_flow(
8635 __isl_take isl_printer *p,
8636 __isl_keep isl_union_flow *flow);
8637 __isl_give char *isl_union_flow_to_str(
8638 __isl_keep isl_union_flow *flow);
8640 C<isl_union_flow_to_str> prints the information in flow format.
8642 =head3 Low-level Interface
8644 A lower-level interface is provided by the following functions.
8646 #include <isl/flow.h>
8648 typedef int (*isl_access_level_before)(void *first, void *second);
8650 __isl_give isl_access_info *isl_access_info_alloc(
8651 __isl_take isl_map *sink,
8652 void *sink_user, isl_access_level_before fn,
8654 __isl_give isl_access_info *isl_access_info_add_source(
8655 __isl_take isl_access_info *acc,
8656 __isl_take isl_map *source, int must,
8658 __isl_null isl_access_info *isl_access_info_free(
8659 __isl_take isl_access_info *acc);
8661 __isl_give isl_flow *isl_access_info_compute_flow(
8662 __isl_take isl_access_info *acc);
8664 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8665 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8666 void *dep_user, void *user),
8668 __isl_give isl_map *isl_flow_get_no_source(
8669 __isl_keep isl_flow *deps, int must);
8670 void isl_flow_free(__isl_take isl_flow *deps);
8672 The function C<isl_access_info_compute_flow> performs the actual
8673 dependence analysis. The other functions are used to construct
8674 the input for this function or to read off the output.
8676 The input is collected in an C<isl_access_info>, which can
8677 be created through a call to C<isl_access_info_alloc>.
8678 The arguments to this functions are the sink access relation
8679 C<sink>, a token C<sink_user> used to identify the sink
8680 access to the user, a callback function for specifying the
8681 relative order of source and sink accesses, and the number
8682 of source access relations that will be added.
8683 The callback function has type C<int (*)(void *first, void *second)>.
8684 The function is called with two user supplied tokens identifying
8685 either a source or the sink and it should return the shared nesting
8686 level and the relative order of the two accesses.
8687 In particular, let I<n> be the number of loops shared by
8688 the two accesses. If C<first> precedes C<second> textually,
8689 then the function should return I<2 * n + 1>; otherwise,
8690 it should return I<2 * n>.
8691 The sources can be added to the C<isl_access_info> by performing
8692 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8693 C<must> indicates whether the source is a I<must> access
8694 or a I<may> access. Note that a multi-valued access relation
8695 should only be marked I<must> if every iteration in the domain
8696 of the relation accesses I<all> elements in its image.
8697 The C<source_user> token is again used to identify
8698 the source access. The range of the source access relation
8699 C<source> should have the same dimension as the range
8700 of the sink access relation.
8701 The C<isl_access_info_free> function should usually not be
8702 called explicitly, because it is called implicitly by
8703 C<isl_access_info_compute_flow>.
8705 The result of the dependence analysis is collected in an
8706 C<isl_flow>. There may be elements of
8707 the sink access for which no preceding source access could be
8708 found or for which all preceding sources are I<may> accesses.
8709 The relations containing these elements can be obtained through
8710 calls to C<isl_flow_get_no_source>, the first with C<must> set
8711 and the second with C<must> unset.
8712 In the case of standard flow dependence analysis,
8713 with the sink a read and the sources I<must> writes,
8714 the first relation corresponds to the reads from uninitialized
8715 array elements and the second relation is empty.
8716 The actual flow dependences can be extracted using
8717 C<isl_flow_foreach>. This function will call the user-specified
8718 callback function C<fn> for each B<non-empty> dependence between
8719 a source and the sink. The callback function is called
8720 with four arguments, the actual flow dependence relation
8721 mapping source iterations to sink iterations, a boolean that
8722 indicates whether it is a I<must> or I<may> dependence, a token
8723 identifying the source and an additional C<void *> with value
8724 equal to the third argument of the C<isl_flow_foreach> call.
8725 A dependence is marked I<must> if it originates from a I<must>
8726 source and if it is not followed by any I<may> sources.
8728 After finishing with an C<isl_flow>, the user should call
8729 C<isl_flow_free> to free all associated memory.
8731 =head3 Interaction with the Low-level Interface
8733 During the dependence analysis, we frequently need to perform
8734 the following operation. Given a relation between sink iterations
8735 and potential source iterations from a particular source domain,
8736 what is the last potential source iteration corresponding to each
8737 sink iteration. It can sometimes be convenient to adjust
8738 the set of potential source iterations before or after each such operation.
8739 The prototypical example is fuzzy array dataflow analysis,
8740 where we need to analyze if, based on data-dependent constraints,
8741 the sink iteration can ever be executed without one or more of
8742 the corresponding potential source iterations being executed.
8743 If so, we can introduce extra parameters and select an unknown
8744 but fixed source iteration from the potential source iterations.
8745 To be able to perform such manipulations, C<isl> provides the following
8748 #include <isl/flow.h>
8750 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8751 __isl_keep isl_map *source_map,
8752 __isl_keep isl_set *sink, void *source_user,
8754 __isl_give isl_access_info *isl_access_info_set_restrict(
8755 __isl_take isl_access_info *acc,
8756 isl_access_restrict fn, void *user);
8758 The function C<isl_access_info_set_restrict> should be called
8759 before calling C<isl_access_info_compute_flow> and registers a callback function
8760 that will be called any time C<isl> is about to compute the last
8761 potential source. The first argument is the (reverse) proto-dependence,
8762 mapping sink iterations to potential source iterations.
8763 The second argument represents the sink iterations for which
8764 we want to compute the last source iteration.
8765 The third argument is the token corresponding to the source
8766 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8767 The callback is expected to return a restriction on either the input or
8768 the output of the operation computing the last potential source.
8769 If the input needs to be restricted then restrictions are needed
8770 for both the source and the sink iterations. The sink iterations
8771 and the potential source iterations will be intersected with these sets.
8772 If the output needs to be restricted then only a restriction on the source
8773 iterations is required.
8774 If any error occurs, the callback should return C<NULL>.
8775 An C<isl_restriction> object can be created, freed and inspected
8776 using the following functions.
8778 #include <isl/flow.h>
8780 __isl_give isl_restriction *isl_restriction_input(
8781 __isl_take isl_set *source_restr,
8782 __isl_take isl_set *sink_restr);
8783 __isl_give isl_restriction *isl_restriction_output(
8784 __isl_take isl_set *source_restr);
8785 __isl_give isl_restriction *isl_restriction_none(
8786 __isl_take isl_map *source_map);
8787 __isl_give isl_restriction *isl_restriction_empty(
8788 __isl_take isl_map *source_map);
8789 __isl_null isl_restriction *isl_restriction_free(
8790 __isl_take isl_restriction *restr);
8792 C<isl_restriction_none> and C<isl_restriction_empty> are special
8793 cases of C<isl_restriction_input>. C<isl_restriction_none>
8794 is essentially equivalent to
8796 isl_restriction_input(isl_set_universe(
8797 isl_space_range(isl_map_get_space(source_map))),
8799 isl_space_domain(isl_map_get_space(source_map))));
8801 whereas C<isl_restriction_empty> is essentially equivalent to
8803 isl_restriction_input(isl_set_empty(
8804 isl_space_range(isl_map_get_space(source_map))),
8806 isl_space_domain(isl_map_get_space(source_map))));
8810 B<The functionality described in this section is fairly new
8811 and may be subject to change.>
8813 #include <isl/schedule.h>
8814 __isl_give isl_schedule *
8815 isl_schedule_constraints_compute_schedule(
8816 __isl_take isl_schedule_constraints *sc);
8818 The function C<isl_schedule_constraints_compute_schedule> can be
8819 used to compute a schedule that satisfies the given schedule constraints.
8820 These schedule constraints include the iteration domain for which
8821 a schedule should be computed and dependences between pairs of
8822 iterations. In particular, these dependences include
8823 I<validity> dependences and I<proximity> dependences.
8824 By default, the algorithm used to construct the schedule is similar
8825 to that of C<Pluto>.
8826 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8828 The generated schedule respects all validity dependences.
8829 That is, all dependence distances over these dependences in the
8830 scheduled space are lexicographically positive.
8832 The default algorithm tries to ensure that the dependence distances
8833 over coincidence constraints are zero and to minimize the
8834 dependence distances over proximity dependences.
8835 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8836 for groups of domains where the dependence distances over validity
8837 dependences have only non-negative values.
8838 Note that when minimizing the maximal dependence distance
8839 over proximity dependences, a single affine expression in the parameters
8840 is constructed that bounds all dependence distances. If no such expression
8841 exists, then the algorithm will fail and resort to an alternative
8842 scheduling algorithm. In particular, this means that adding proximity
8843 dependences may eliminate valid solutions. A typical example where this
8844 phenomenon may occur is when some subset of the proximity dependences
8845 has no restriction on some parameter, forcing the coefficient of that
8846 parameter to be zero, while some other subset forces the dependence
8847 distance to depend on that parameter, requiring the same coefficient
8849 When using Feautrier's algorithm, the coincidence and proximity constraints
8850 are only taken into account during the extension to a
8851 full-dimensional schedule.
8853 An C<isl_schedule_constraints> object can be constructed
8854 and manipulated using the following functions.
8856 #include <isl/schedule.h>
8857 __isl_give isl_schedule_constraints *
8858 isl_schedule_constraints_copy(
8859 __isl_keep isl_schedule_constraints *sc);
8860 __isl_give isl_schedule_constraints *
8861 isl_schedule_constraints_on_domain(
8862 __isl_take isl_union_set *domain);
8863 __isl_give isl_schedule_constraints *
8864 isl_schedule_constraints_set_context(
8865 __isl_take isl_schedule_constraints *sc,
8866 __isl_take isl_set *context);
8867 __isl_give isl_schedule_constraints *
8868 isl_schedule_constraints_set_validity(
8869 __isl_take isl_schedule_constraints *sc,
8870 __isl_take isl_union_map *validity);
8871 __isl_give isl_schedule_constraints *
8872 isl_schedule_constraints_set_coincidence(
8873 __isl_take isl_schedule_constraints *sc,
8874 __isl_take isl_union_map *coincidence);
8875 __isl_give isl_schedule_constraints *
8876 isl_schedule_constraints_set_proximity(
8877 __isl_take isl_schedule_constraints *sc,
8878 __isl_take isl_union_map *proximity);
8879 __isl_give isl_schedule_constraints *
8880 isl_schedule_constraints_set_conditional_validity(
8881 __isl_take isl_schedule_constraints *sc,
8882 __isl_take isl_union_map *condition,
8883 __isl_take isl_union_map *validity);
8884 __isl_null isl_schedule_constraints *
8885 isl_schedule_constraints_free(
8886 __isl_take isl_schedule_constraints *sc);
8888 The initial C<isl_schedule_constraints> object created by
8889 C<isl_schedule_constraints_on_domain> does not impose any constraints.
8890 That is, it has an empty set of dependences.
8891 The function C<isl_schedule_constraints_set_context> allows the user
8892 to specify additional constraints on the parameters that may
8893 be assumed to hold during the construction of the schedule.
8894 The function C<isl_schedule_constraints_set_validity> replaces the
8895 validity dependences, mapping domain elements I<i> to domain
8896 elements that should be scheduled after I<i>.
8897 The function C<isl_schedule_constraints_set_coincidence> replaces the
8898 coincidence dependences, mapping domain elements I<i> to domain
8899 elements that should be scheduled together with I<I>, if possible.
8900 The function C<isl_schedule_constraints_set_proximity> replaces the
8901 proximity dependences, mapping domain elements I<i> to domain
8902 elements that should be scheduled either before I<I>
8903 or as early as possible after I<i>.
8905 The function C<isl_schedule_constraints_set_conditional_validity>
8906 replaces the conditional validity constraints.
8907 A conditional validity constraint is only imposed when any of the corresponding
8908 conditions is satisfied, i.e., when any of them is non-zero.
8909 That is, the scheduler ensures that within each band if the dependence
8910 distances over the condition constraints are not all zero
8911 then all corresponding conditional validity constraints are respected.
8912 A conditional validity constraint corresponds to a condition
8913 if the two are adjacent, i.e., if the domain of one relation intersect
8914 the range of the other relation.
8915 The typical use case of conditional validity constraints is
8916 to allow order constraints between live ranges to be violated
8917 as long as the live ranges themselves are local to the band.
8918 To allow more fine-grained control over which conditions correspond
8919 to which conditional validity constraints, the domains and ranges
8920 of these relations may include I<tags>. That is, the domains and
8921 ranges of those relation may themselves be wrapped relations
8922 where the iteration domain appears in the domain of those wrapped relations
8923 and the range of the wrapped relations can be arbitrarily chosen
8924 by the user. Conditions and conditional validity constraints are only
8925 considered adjacent to each other if the entire wrapped relation matches.
8926 In particular, a relation with a tag will never be considered adjacent
8927 to a relation without a tag.
8929 An C<isl_schedule_constraints> object can be inspected
8930 using the following functions.
8932 #include <isl/schedule.h>
8933 __isl_give isl_union_set *
8934 isl_schedule_constraints_get_domain(
8935 __isl_keep isl_schedule_constraints *sc);
8936 __isl_give isl_union_map *
8937 isl_schedule_constraints_get_validity(
8938 __isl_keep isl_schedule_constraints *sc);
8939 __isl_give isl_union_map *
8940 isl_schedule_constraints_get_coincidence(
8941 __isl_keep isl_schedule_constraints *sc);
8942 __isl_give isl_union_map *
8943 isl_schedule_constraints_get_conditional_validity(
8944 __isl_keep isl_schedule_constraints *sc);
8945 __isl_give isl_union_map *
8946 isl_schedule_constraints_get_conditional_validity_condition(
8947 __isl_keep isl_schedule_constraints *sc);
8949 The following function computes a schedule directly from
8950 an iteration domain and validity and proximity dependences
8951 and is implemented in terms of the functions described above.
8952 The use of C<isl_union_set_compute_schedule> is discouraged.
8954 #include <isl/schedule.h>
8955 __isl_give isl_schedule *isl_union_set_compute_schedule(
8956 __isl_take isl_union_set *domain,
8957 __isl_take isl_union_map *validity,
8958 __isl_take isl_union_map *proximity);
8960 The generated schedule represents a schedule tree.
8961 For more information on schedule trees, see
8962 L</"Schedule Trees">.
8966 #include <isl/schedule.h>
8967 isl_stat isl_options_set_schedule_max_coefficient(
8968 isl_ctx *ctx, int val);
8969 int isl_options_get_schedule_max_coefficient(
8971 isl_stat isl_options_set_schedule_max_constant_term(
8972 isl_ctx *ctx, int val);
8973 int isl_options_get_schedule_max_constant_term(
8975 isl_stat isl_options_set_schedule_serialize_sccs(
8976 isl_ctx *ctx, int val);
8977 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
8978 isl_stat isl_options_set_schedule_whole_component(
8979 isl_ctx *ctx, int val);
8980 int isl_options_get_schedule_whole_component(
8982 isl_stat isl_options_set_schedule_maximize_band_depth(
8983 isl_ctx *ctx, int val);
8984 int isl_options_get_schedule_maximize_band_depth(
8986 isl_stat isl_options_set_schedule_outer_coincidence(
8987 isl_ctx *ctx, int val);
8988 int isl_options_get_schedule_outer_coincidence(
8990 isl_stat isl_options_set_schedule_split_scaled(
8991 isl_ctx *ctx, int val);
8992 int isl_options_get_schedule_split_scaled(
8994 isl_stat isl_options_set_schedule_algorithm(
8995 isl_ctx *ctx, int val);
8996 int isl_options_get_schedule_algorithm(
8998 isl_stat isl_options_set_schedule_separate_components(
8999 isl_ctx *ctx, int val);
9000 int isl_options_get_schedule_separate_components(
9005 =item * schedule_max_coefficient
9007 This option enforces that the coefficients for variable and parameter
9008 dimensions in the calculated schedule are not larger than the specified value.
9009 This option can significantly increase the speed of the scheduling calculation
9010 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9011 this option does not introduce bounds on the variable or parameter
9014 =item * schedule_max_constant_term
9016 This option enforces that the constant coefficients in the calculated schedule
9017 are not larger than the maximal constant term. This option can significantly
9018 increase the speed of the scheduling calculation and may also prevent fusing of
9019 unrelated dimensions. A value of -1 means that this option does not introduce
9020 bounds on the constant coefficients.
9022 =item * schedule_serialize_sccs
9024 If this option is set, then all strongly connected components
9025 in the dependence graph are serialized as soon as they are detected.
9026 This means in particular that instances of statements will only
9027 appear in the same band node if these statements belong
9028 to the same strongly connected component at the point where
9029 the band node is constructed.
9031 =item * schedule_whole_component
9033 If this option is set, then entire (weakly) connected
9034 components in the dependence graph are scheduled together
9036 Otherwise, each strongly connected component within
9037 such a weakly connected component is first scheduled separately
9038 and then combined with other strongly connected components.
9039 This option has no effect if C<schedule_serialize_sccs> is set.
9041 =item * schedule_maximize_band_depth
9043 If this option is set, then the scheduler tries to maximize
9044 the width of the bands. Wider bands give more possibilities for tiling.
9045 In particular, if the C<schedule_whole_component> option is set,
9046 then bands are split if this might result in wider bands.
9047 Otherwise, the effect of this option is to only allow
9048 strongly connected components to be combined if this does
9049 not reduce the width of the bands.
9050 Note that if the C<schedule_serialize_sccs> options is set, then
9051 the C<schedule_maximize_band_depth> option therefore has no effect.
9053 =item * schedule_maximize_coincidence
9055 This option is only effective if the C<schedule_whole_component>
9056 option is turned off.
9057 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9058 strongly connected components are only combined with each other
9059 if this does not reduce the number of coincident band members.
9061 =item * schedule_outer_coincidence
9063 If this option is set, then we try to construct schedules
9064 where the outermost scheduling dimension in each band
9065 satisfies the coincidence constraints.
9067 =item * schedule_split_scaled
9069 If this option is set, then we try to construct schedules in which the
9070 constant term is split off from the linear part if the linear parts of
9071 the scheduling rows for all nodes in the graphs have a common non-trivial
9073 The constant term is then placed in a separate band and the linear
9076 =item * schedule_algorithm
9078 Selects the scheduling algorithm to be used.
9079 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9080 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9082 =item * schedule_separate_components
9084 If this option is set then the function C<isl_schedule_get_map>
9085 will treat set nodes in the same way as sequence nodes.
9089 =head2 AST Generation
9091 This section describes the C<isl> functionality for generating
9092 ASTs that visit all the elements
9093 in a domain in an order specified by a schedule tree or
9095 In case the schedule given as a C<isl_union_map>, an AST is generated
9096 that visits all the elements in the domain of the C<isl_union_map>
9097 according to the lexicographic order of the corresponding image
9098 element(s). If the range of the C<isl_union_map> consists of
9099 elements in more than one space, then each of these spaces is handled
9100 separately in an arbitrary order.
9101 It should be noted that the schedule tree or the image elements
9102 in a schedule map only specify the I<order>
9103 in which the corresponding domain elements should be visited.
9104 No direct relation between the partial schedule values
9105 or the image elements on the one hand and the loop iterators
9106 in the generated AST on the other hand should be assumed.
9108 Each AST is generated within a build. The initial build
9109 simply specifies the constraints on the parameters (if any)
9110 and can be created, inspected, copied and freed using the following functions.
9112 #include <isl/ast_build.h>
9113 __isl_give isl_ast_build *isl_ast_build_alloc(
9115 __isl_give isl_ast_build *isl_ast_build_from_context(
9116 __isl_take isl_set *set);
9117 __isl_give isl_ast_build *isl_ast_build_copy(
9118 __isl_keep isl_ast_build *build);
9119 __isl_null isl_ast_build *isl_ast_build_free(
9120 __isl_take isl_ast_build *build);
9122 The C<set> argument is usually a parameter set with zero or more parameters.
9123 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9124 this set is required to be a parameter set.
9125 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9126 specify any parameter constraints.
9127 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9128 and L</"Fine-grained Control over AST Generation">.
9129 Finally, the AST itself can be constructed using one of the following
9132 #include <isl/ast_build.h>
9133 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9134 __isl_keep isl_ast_build *build,
9135 __isl_take isl_schedule *schedule);
9136 __isl_give isl_ast_node *
9137 isl_ast_build_node_from_schedule_map(
9138 __isl_keep isl_ast_build *build,
9139 __isl_take isl_union_map *schedule);
9141 =head3 Inspecting the AST
9143 The basic properties of an AST node can be obtained as follows.
9145 #include <isl/ast.h>
9146 enum isl_ast_node_type isl_ast_node_get_type(
9147 __isl_keep isl_ast_node *node);
9149 The type of an AST node is one of
9150 C<isl_ast_node_for>,
9152 C<isl_ast_node_block>,
9153 C<isl_ast_node_mark> or
9154 C<isl_ast_node_user>.
9155 An C<isl_ast_node_for> represents a for node.
9156 An C<isl_ast_node_if> represents an if node.
9157 An C<isl_ast_node_block> represents a compound node.
9158 An C<isl_ast_node_mark> introduces a mark in the AST.
9159 An C<isl_ast_node_user> represents an expression statement.
9160 An expression statement typically corresponds to a domain element, i.e.,
9161 one of the elements that is visited by the AST.
9163 Each type of node has its own additional properties.
9165 #include <isl/ast.h>
9166 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9167 __isl_keep isl_ast_node *node);
9168 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9169 __isl_keep isl_ast_node *node);
9170 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9171 __isl_keep isl_ast_node *node);
9172 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9173 __isl_keep isl_ast_node *node);
9174 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9175 __isl_keep isl_ast_node *node);
9176 isl_bool isl_ast_node_for_is_degenerate(
9177 __isl_keep isl_ast_node *node);
9179 An C<isl_ast_for> is considered degenerate if it is known to execute
9182 #include <isl/ast.h>
9183 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9184 __isl_keep isl_ast_node *node);
9185 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9186 __isl_keep isl_ast_node *node);
9187 isl_bool isl_ast_node_if_has_else(
9188 __isl_keep isl_ast_node *node);
9189 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9190 __isl_keep isl_ast_node *node);
9192 __isl_give isl_ast_node_list *
9193 isl_ast_node_block_get_children(
9194 __isl_keep isl_ast_node *node);
9196 __isl_give isl_id *isl_ast_node_mark_get_id(
9197 __isl_keep isl_ast_node *node);
9198 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9199 __isl_keep isl_ast_node *node);
9201 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9202 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9204 #include <isl/ast.h>
9205 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9206 __isl_keep isl_ast_node *node);
9208 All descendants of a specific node in the AST (including the node itself)
9210 in depth-first pre-order using the following function.
9212 #include <isl/ast.h>
9213 isl_stat isl_ast_node_foreach_descendant_top_down(
9214 __isl_keep isl_ast_node *node,
9215 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9216 void *user), void *user);
9218 The callback function should return C<isl_bool_true> if the children
9219 of the given node should be visited and C<isl_bool_false> if they should not.
9220 It should return C<isl_bool_error> in case of failure, in which case
9221 the entire traversal is aborted.
9223 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9224 the following functions.
9226 #include <isl/ast.h>
9227 enum isl_ast_expr_type isl_ast_expr_get_type(
9228 __isl_keep isl_ast_expr *expr);
9230 The type of an AST expression is one of
9232 C<isl_ast_expr_id> or
9233 C<isl_ast_expr_int>.
9234 An C<isl_ast_expr_op> represents the result of an operation.
9235 An C<isl_ast_expr_id> represents an identifier.
9236 An C<isl_ast_expr_int> represents an integer value.
9238 Each type of expression has its own additional properties.
9240 #include <isl/ast.h>
9241 enum isl_ast_op_type isl_ast_expr_get_op_type(
9242 __isl_keep isl_ast_expr *expr);
9243 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9244 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9245 __isl_keep isl_ast_expr *expr, int pos);
9246 isl_stat isl_ast_expr_foreach_ast_op_type(
9247 __isl_keep isl_ast_expr *expr,
9248 isl_stat (*fn)(enum isl_ast_op_type type,
9249 void *user), void *user);
9250 isl_stat isl_ast_node_foreach_ast_op_type(
9251 __isl_keep isl_ast_node *node,
9252 isl_stat (*fn)(enum isl_ast_op_type type,
9253 void *user), void *user);
9255 C<isl_ast_expr_get_op_type> returns the type of the operation
9256 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9257 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9259 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9260 C<isl_ast_op_type> that appears in C<expr>.
9261 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9262 C<isl_ast_op_type> that appears in C<node>.
9263 The operation type is one of the following.
9267 =item C<isl_ast_op_and>
9269 Logical I<and> of two arguments.
9270 Both arguments can be evaluated.
9272 =item C<isl_ast_op_and_then>
9274 Logical I<and> of two arguments.
9275 The second argument can only be evaluated if the first evaluates to true.
9277 =item C<isl_ast_op_or>
9279 Logical I<or> of two arguments.
9280 Both arguments can be evaluated.
9282 =item C<isl_ast_op_or_else>
9284 Logical I<or> of two arguments.
9285 The second argument can only be evaluated if the first evaluates to false.
9287 =item C<isl_ast_op_max>
9289 Maximum of two or more arguments.
9291 =item C<isl_ast_op_min>
9293 Minimum of two or more arguments.
9295 =item C<isl_ast_op_minus>
9299 =item C<isl_ast_op_add>
9301 Sum of two arguments.
9303 =item C<isl_ast_op_sub>
9305 Difference of two arguments.
9307 =item C<isl_ast_op_mul>
9309 Product of two arguments.
9311 =item C<isl_ast_op_div>
9313 Exact division. That is, the result is known to be an integer.
9315 =item C<isl_ast_op_fdiv_q>
9317 Result of integer division, rounded towards negative
9320 =item C<isl_ast_op_pdiv_q>
9322 Result of integer division, where dividend is known to be non-negative.
9324 =item C<isl_ast_op_pdiv_r>
9326 Remainder of integer division, where dividend is known to be non-negative.
9328 =item C<isl_ast_op_zdiv_r>
9330 Equal to zero iff the remainder on integer division is zero.
9332 =item C<isl_ast_op_cond>
9334 Conditional operator defined on three arguments.
9335 If the first argument evaluates to true, then the result
9336 is equal to the second argument. Otherwise, the result
9337 is equal to the third argument.
9338 The second and third argument may only be evaluated if
9339 the first argument evaluates to true and false, respectively.
9340 Corresponds to C<a ? b : c> in C.
9342 =item C<isl_ast_op_select>
9344 Conditional operator defined on three arguments.
9345 If the first argument evaluates to true, then the result
9346 is equal to the second argument. Otherwise, the result
9347 is equal to the third argument.
9348 The second and third argument may be evaluated independently
9349 of the value of the first argument.
9350 Corresponds to C<a * b + (1 - a) * c> in C.
9352 =item C<isl_ast_op_eq>
9356 =item C<isl_ast_op_le>
9358 Less than or equal relation.
9360 =item C<isl_ast_op_lt>
9364 =item C<isl_ast_op_ge>
9366 Greater than or equal relation.
9368 =item C<isl_ast_op_gt>
9370 Greater than relation.
9372 =item C<isl_ast_op_call>
9375 The number of arguments of the C<isl_ast_expr> is one more than
9376 the number of arguments in the function call, the first argument
9377 representing the function being called.
9379 =item C<isl_ast_op_access>
9382 The number of arguments of the C<isl_ast_expr> is one more than
9383 the number of index expressions in the array access, the first argument
9384 representing the array being accessed.
9386 =item C<isl_ast_op_member>
9389 This operation has two arguments, a structure and the name of
9390 the member of the structure being accessed.
9394 #include <isl/ast.h>
9395 __isl_give isl_id *isl_ast_expr_get_id(
9396 __isl_keep isl_ast_expr *expr);
9398 Return the identifier represented by the AST expression.
9400 #include <isl/ast.h>
9401 __isl_give isl_val *isl_ast_expr_get_val(
9402 __isl_keep isl_ast_expr *expr);
9404 Return the integer represented by the AST expression.
9406 =head3 Properties of ASTs
9408 #include <isl/ast.h>
9409 isl_bool isl_ast_expr_is_equal(
9410 __isl_keep isl_ast_expr *expr1,
9411 __isl_keep isl_ast_expr *expr2);
9413 Check if two C<isl_ast_expr>s are equal to each other.
9415 =head3 Manipulating and printing the AST
9417 AST nodes can be copied and freed using the following functions.
9419 #include <isl/ast.h>
9420 __isl_give isl_ast_node *isl_ast_node_copy(
9421 __isl_keep isl_ast_node *node);
9422 __isl_null isl_ast_node *isl_ast_node_free(
9423 __isl_take isl_ast_node *node);
9425 AST expressions can be copied and freed using the following functions.
9427 #include <isl/ast.h>
9428 __isl_give isl_ast_expr *isl_ast_expr_copy(
9429 __isl_keep isl_ast_expr *expr);
9430 __isl_null isl_ast_expr *isl_ast_expr_free(
9431 __isl_take isl_ast_expr *expr);
9433 New AST expressions can be created either directly or within
9434 the context of an C<isl_ast_build>.
9436 #include <isl/ast.h>
9437 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9438 __isl_take isl_val *v);
9439 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9440 __isl_take isl_id *id);
9441 __isl_give isl_ast_expr *isl_ast_expr_neg(
9442 __isl_take isl_ast_expr *expr);
9443 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9444 __isl_take isl_ast_expr *expr);
9445 __isl_give isl_ast_expr *isl_ast_expr_add(
9446 __isl_take isl_ast_expr *expr1,
9447 __isl_take isl_ast_expr *expr2);
9448 __isl_give isl_ast_expr *isl_ast_expr_sub(
9449 __isl_take isl_ast_expr *expr1,
9450 __isl_take isl_ast_expr *expr2);
9451 __isl_give isl_ast_expr *isl_ast_expr_mul(
9452 __isl_take isl_ast_expr *expr1,
9453 __isl_take isl_ast_expr *expr2);
9454 __isl_give isl_ast_expr *isl_ast_expr_div(
9455 __isl_take isl_ast_expr *expr1,
9456 __isl_take isl_ast_expr *expr2);
9457 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9458 __isl_take isl_ast_expr *expr1,
9459 __isl_take isl_ast_expr *expr2);
9460 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9461 __isl_take isl_ast_expr *expr1,
9462 __isl_take isl_ast_expr *expr2);
9463 __isl_give isl_ast_expr *isl_ast_expr_and(
9464 __isl_take isl_ast_expr *expr1,
9465 __isl_take isl_ast_expr *expr2)
9466 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9467 __isl_take isl_ast_expr *expr1,
9468 __isl_take isl_ast_expr *expr2)
9469 __isl_give isl_ast_expr *isl_ast_expr_or(
9470 __isl_take isl_ast_expr *expr1,
9471 __isl_take isl_ast_expr *expr2)
9472 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9473 __isl_take isl_ast_expr *expr1,
9474 __isl_take isl_ast_expr *expr2)
9475 __isl_give isl_ast_expr *isl_ast_expr_eq(
9476 __isl_take isl_ast_expr *expr1,
9477 __isl_take isl_ast_expr *expr2);
9478 __isl_give isl_ast_expr *isl_ast_expr_le(
9479 __isl_take isl_ast_expr *expr1,
9480 __isl_take isl_ast_expr *expr2);
9481 __isl_give isl_ast_expr *isl_ast_expr_lt(
9482 __isl_take isl_ast_expr *expr1,
9483 __isl_take isl_ast_expr *expr2);
9484 __isl_give isl_ast_expr *isl_ast_expr_ge(
9485 __isl_take isl_ast_expr *expr1,
9486 __isl_take isl_ast_expr *expr2);
9487 __isl_give isl_ast_expr *isl_ast_expr_gt(
9488 __isl_take isl_ast_expr *expr1,
9489 __isl_take isl_ast_expr *expr2);
9490 __isl_give isl_ast_expr *isl_ast_expr_access(
9491 __isl_take isl_ast_expr *array,
9492 __isl_take isl_ast_expr_list *indices);
9493 __isl_give isl_ast_expr *isl_ast_expr_call(
9494 __isl_take isl_ast_expr *function,
9495 __isl_take isl_ast_expr_list *arguments);
9497 The function C<isl_ast_expr_address_of> can be applied to an
9498 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9499 to represent the address of the C<isl_ast_expr_access>. The function
9500 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9501 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9503 #include <isl/ast_build.h>
9504 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9505 __isl_keep isl_ast_build *build,
9506 __isl_take isl_set *set);
9507 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9508 __isl_keep isl_ast_build *build,
9509 __isl_take isl_pw_aff *pa);
9510 __isl_give isl_ast_expr *
9511 isl_ast_build_access_from_pw_multi_aff(
9512 __isl_keep isl_ast_build *build,
9513 __isl_take isl_pw_multi_aff *pma);
9514 __isl_give isl_ast_expr *
9515 isl_ast_build_access_from_multi_pw_aff(
9516 __isl_keep isl_ast_build *build,
9517 __isl_take isl_multi_pw_aff *mpa);
9518 __isl_give isl_ast_expr *
9519 isl_ast_build_call_from_pw_multi_aff(
9520 __isl_keep isl_ast_build *build,
9521 __isl_take isl_pw_multi_aff *pma);
9522 __isl_give isl_ast_expr *
9523 isl_ast_build_call_from_multi_pw_aff(
9524 __isl_keep isl_ast_build *build,
9525 __isl_take isl_multi_pw_aff *mpa);
9528 the domains of C<pa>, C<mpa> and C<pma> should correspond
9529 to the schedule space of C<build>.
9530 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9531 the function being called.
9532 If the accessed space is a nested relation, then it is taken
9533 to represent an access of the member specified by the range
9534 of this nested relation of the structure specified by the domain
9535 of the nested relation.
9537 The following functions can be used to modify an C<isl_ast_expr>.
9539 #include <isl/ast.h>
9540 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9541 __isl_take isl_ast_expr *expr, int pos,
9542 __isl_take isl_ast_expr *arg);
9544 Replace the argument of C<expr> at position C<pos> by C<arg>.
9546 #include <isl/ast.h>
9547 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9548 __isl_take isl_ast_expr *expr,
9549 __isl_take isl_id_to_ast_expr *id2expr);
9551 The function C<isl_ast_expr_substitute_ids> replaces the
9552 subexpressions of C<expr> of type C<isl_ast_expr_id>
9553 by the corresponding expression in C<id2expr>, if there is any.
9556 User specified data can be attached to an C<isl_ast_node> and obtained
9557 from the same C<isl_ast_node> using the following functions.
9559 #include <isl/ast.h>
9560 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9561 __isl_take isl_ast_node *node,
9562 __isl_take isl_id *annotation);
9563 __isl_give isl_id *isl_ast_node_get_annotation(
9564 __isl_keep isl_ast_node *node);
9566 Basic printing can be performed using the following functions.
9568 #include <isl/ast.h>
9569 __isl_give isl_printer *isl_printer_print_ast_expr(
9570 __isl_take isl_printer *p,
9571 __isl_keep isl_ast_expr *expr);
9572 __isl_give isl_printer *isl_printer_print_ast_node(
9573 __isl_take isl_printer *p,
9574 __isl_keep isl_ast_node *node);
9575 __isl_give char *isl_ast_expr_to_str(
9576 __isl_keep isl_ast_expr *expr);
9578 More advanced printing can be performed using the following functions.
9580 #include <isl/ast.h>
9581 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9582 __isl_take isl_printer *p,
9583 enum isl_ast_op_type type,
9584 __isl_keep const char *name);
9585 isl_stat isl_options_set_ast_print_macro_once(
9586 isl_ctx *ctx, int val);
9587 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9588 __isl_give isl_printer *isl_ast_op_type_print_macro(
9589 enum isl_ast_op_type type,
9590 __isl_take isl_printer *p);
9591 __isl_give isl_printer *isl_ast_expr_print_macros(
9592 __isl_keep isl_ast_expr *expr,
9593 __isl_take isl_printer *p);
9594 __isl_give isl_printer *isl_ast_node_print_macros(
9595 __isl_keep isl_ast_node *node,
9596 __isl_take isl_printer *p);
9597 __isl_give isl_printer *isl_ast_node_print(
9598 __isl_keep isl_ast_node *node,
9599 __isl_take isl_printer *p,
9600 __isl_take isl_ast_print_options *options);
9601 __isl_give isl_printer *isl_ast_node_for_print(
9602 __isl_keep isl_ast_node *node,
9603 __isl_take isl_printer *p,
9604 __isl_take isl_ast_print_options *options);
9605 __isl_give isl_printer *isl_ast_node_if_print(
9606 __isl_keep isl_ast_node *node,
9607 __isl_take isl_printer *p,
9608 __isl_take isl_ast_print_options *options);
9610 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9611 C<isl> may print out an AST that makes use of macros such
9612 as C<floord>, C<min> and C<max>.
9613 The names of these macros may be modified by a call
9614 to C<isl_ast_op_type_set_print_name>. The user-specified
9615 names are associated to the printer object.
9616 C<isl_ast_op_type_print_macro> prints out the macro
9617 corresponding to a specific C<isl_ast_op_type>.
9618 If the print-macro-once option is set, then a given macro definition
9619 is only printed once to any given printer object.
9620 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9621 for subexpressions where these macros would be used and prints
9622 out the required macro definitions.
9623 Essentially, C<isl_ast_expr_print_macros> calls
9624 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9625 as function argument.
9626 C<isl_ast_node_print_macros> does the same
9627 for expressions in its C<isl_ast_node> argument.
9628 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9629 C<isl_ast_node_if_print> print an C<isl_ast_node>
9630 in C<ISL_FORMAT_C>, but allow for some extra control
9631 through an C<isl_ast_print_options> object.
9632 This object can be created using the following functions.
9634 #include <isl/ast.h>
9635 __isl_give isl_ast_print_options *
9636 isl_ast_print_options_alloc(isl_ctx *ctx);
9637 __isl_give isl_ast_print_options *
9638 isl_ast_print_options_copy(
9639 __isl_keep isl_ast_print_options *options);
9640 __isl_null isl_ast_print_options *
9641 isl_ast_print_options_free(
9642 __isl_take isl_ast_print_options *options);
9644 __isl_give isl_ast_print_options *
9645 isl_ast_print_options_set_print_user(
9646 __isl_take isl_ast_print_options *options,
9647 __isl_give isl_printer *(*print_user)(
9648 __isl_take isl_printer *p,
9649 __isl_take isl_ast_print_options *options,
9650 __isl_keep isl_ast_node *node, void *user),
9652 __isl_give isl_ast_print_options *
9653 isl_ast_print_options_set_print_for(
9654 __isl_take isl_ast_print_options *options,
9655 __isl_give isl_printer *(*print_for)(
9656 __isl_take isl_printer *p,
9657 __isl_take isl_ast_print_options *options,
9658 __isl_keep isl_ast_node *node, void *user),
9661 The callback set by C<isl_ast_print_options_set_print_user>
9662 is called whenever a node of type C<isl_ast_node_user> needs to
9664 The callback set by C<isl_ast_print_options_set_print_for>
9665 is called whenever a node of type C<isl_ast_node_for> needs to
9667 Note that C<isl_ast_node_for_print> will I<not> call the
9668 callback set by C<isl_ast_print_options_set_print_for> on the node
9669 on which C<isl_ast_node_for_print> is called, but only on nested
9670 nodes of type C<isl_ast_node_for>. It is therefore safe to
9671 call C<isl_ast_node_for_print> from within the callback set by
9672 C<isl_ast_print_options_set_print_for>.
9674 The following option determines the type to be used for iterators
9675 while printing the AST.
9677 isl_stat isl_options_set_ast_iterator_type(
9678 isl_ctx *ctx, const char *val);
9679 const char *isl_options_get_ast_iterator_type(
9682 The AST printer only prints body nodes as blocks if these
9683 blocks cannot be safely omitted.
9684 For example, a C<for> node with one body node will not be
9685 surrounded with braces in C<ISL_FORMAT_C>.
9686 A block will always be printed by setting the following option.
9688 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9690 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9694 #include <isl/ast_build.h>
9695 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9696 isl_ctx *ctx, int val);
9697 int isl_options_get_ast_build_atomic_upper_bound(
9699 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9701 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9702 isl_stat isl_options_set_ast_build_detect_min_max(
9703 isl_ctx *ctx, int val);
9704 int isl_options_get_ast_build_detect_min_max(
9706 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9707 isl_ctx *ctx, int val);
9708 int isl_options_get_ast_build_exploit_nested_bounds(
9710 isl_stat isl_options_set_ast_build_group_coscheduled(
9711 isl_ctx *ctx, int val);
9712 int isl_options_get_ast_build_group_coscheduled(
9714 isl_stat isl_options_set_ast_build_scale_strides(
9715 isl_ctx *ctx, int val);
9716 int isl_options_get_ast_build_scale_strides(
9718 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9720 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9721 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9723 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9727 =item * ast_build_atomic_upper_bound
9729 Generate loop upper bounds that consist of the current loop iterator,
9730 an operator and an expression not involving the iterator.
9731 If this option is not set, then the current loop iterator may appear
9732 several times in the upper bound.
9733 For example, when this option is turned off, AST generation
9736 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9740 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9743 When the option is turned on, the following AST is generated
9745 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9748 =item * ast_build_prefer_pdiv
9750 If this option is turned off, then the AST generation will
9751 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9752 operators, but no C<isl_ast_op_pdiv_q> or
9753 C<isl_ast_op_pdiv_r> operators.
9754 If this option is turned on, then C<isl> will try to convert
9755 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9756 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9758 =item * ast_build_detect_min_max
9760 If this option is turned on, then C<isl> will try and detect
9761 min or max-expressions when building AST expressions from
9762 piecewise affine expressions.
9764 =item * ast_build_exploit_nested_bounds
9766 Simplify conditions based on bounds of nested for loops.
9767 In particular, remove conditions that are implied by the fact
9768 that one or more nested loops have at least one iteration,
9769 meaning that the upper bound is at least as large as the lower bound.
9770 For example, when this option is turned off, AST generation
9773 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
9779 for (int c0 = 0; c0 <= N; c0 += 1)
9780 for (int c1 = 0; c1 <= M; c1 += 1)
9783 When the option is turned on, the following AST is generated
9785 for (int c0 = 0; c0 <= N; c0 += 1)
9786 for (int c1 = 0; c1 <= M; c1 += 1)
9789 =item * ast_build_group_coscheduled
9791 If two domain elements are assigned the same schedule point, then
9792 they may be executed in any order and they may even appear in different
9793 loops. If this options is set, then the AST generator will make
9794 sure that coscheduled domain elements do not appear in separate parts
9795 of the AST. This is useful in case of nested AST generation
9796 if the outer AST generation is given only part of a schedule
9797 and the inner AST generation should handle the domains that are
9798 coscheduled by this initial part of the schedule together.
9799 For example if an AST is generated for a schedule
9801 { A[i] -> [0]; B[i] -> [0] }
9803 then the C<isl_ast_build_set_create_leaf> callback described
9804 below may get called twice, once for each domain.
9805 Setting this option ensures that the callback is only called once
9806 on both domains together.
9808 =item * ast_build_separation_bounds
9810 This option specifies which bounds to use during separation.
9811 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
9812 then all (possibly implicit) bounds on the current dimension will
9813 be used during separation.
9814 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
9815 then only those bounds that are explicitly available will
9816 be used during separation.
9818 =item * ast_build_scale_strides
9820 This option specifies whether the AST generator is allowed
9821 to scale down iterators of strided loops.
9823 =item * ast_build_allow_else
9825 This option specifies whether the AST generator is allowed
9826 to construct if statements with else branches.
9828 =item * ast_build_allow_or
9830 This option specifies whether the AST generator is allowed
9831 to construct if conditions with disjunctions.
9835 =head3 AST Generation Options (Schedule Tree)
9837 In case of AST construction from a schedule tree, the options
9838 that control how an AST is created from the individual schedule
9839 dimensions are stored in the band nodes of the tree
9840 (see L</"Schedule Trees">).
9842 In particular, a schedule dimension can be handled in four
9843 different ways, atomic, separate, unroll or the default.
9844 This loop AST generation type can be set using
9845 C<isl_schedule_node_band_member_set_ast_loop_type>.
9847 the first three can be selected by including a one-dimensional
9848 element with as value the position of the schedule dimension
9849 within the band and as name one of C<atomic>, C<separate>
9850 or C<unroll> in the options
9851 set by C<isl_schedule_node_band_set_ast_build_options>.
9852 Only one of these three may be specified for
9853 any given schedule dimension within a band node.
9854 If none of these is specified, then the default
9855 is used. The meaning of the options is as follows.
9861 When this option is specified, the AST generator will make
9862 sure that a given domains space only appears in a single
9863 loop at the specified level.
9865 For example, for the schedule tree
9867 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9869 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9870 options: "{ atomic[x] }"
9872 the following AST will be generated
9874 for (int c0 = 0; c0 <= 10; c0 += 1) {
9881 On the other hand, for the schedule tree
9883 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9885 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9886 options: "{ separate[x] }"
9888 the following AST will be generated
9892 for (int c0 = 1; c0 <= 9; c0 += 1) {
9899 If neither C<atomic> nor C<separate> is specified, then the AST generator
9900 may produce either of these two results or some intermediate form.
9904 When this option is specified, the AST generator will
9905 split the domain of the specified schedule dimension
9906 into pieces with a fixed set of statements for which
9907 instances need to be executed by the iterations in
9908 the schedule domain part. This option tends to avoid
9909 the generation of guards inside the corresponding loops.
9910 See also the C<atomic> option.
9914 When this option is specified, the AST generator will
9915 I<completely> unroll the corresponding schedule dimension.
9916 It is the responsibility of the user to ensure that such
9917 unrolling is possible.
9918 To obtain a partial unrolling, the user should apply an additional
9919 strip-mining to the schedule and fully unroll the inner schedule
9924 The C<isolate> option is a bit more involved. It allows the user
9925 to isolate a range of schedule dimension values from smaller and
9926 greater values. Additionally, the user may specify a different
9927 atomic/separate/unroll choice for the isolated part and the remaining
9928 parts. The typical use case of the C<isolate> option is to isolate
9929 full tiles from partial tiles.
9930 The part that needs to be isolated may depend on outer schedule dimensions.
9931 The option therefore needs to be able to reference those outer schedule
9932 dimensions. In particular, the space of the C<isolate> option is that
9933 of a wrapped map with as domain the flat product of all outer band nodes
9934 and as range the space of the current band node.
9935 The atomic/separate/unroll choice for the isolated part is determined
9936 by an option that lives in an unnamed wrapped space with as domain
9937 a zero-dimensional C<isolate> space and as range the regular
9938 C<atomic>, C<separate> or C<unroll> space.
9939 This option may also be set directly using
9940 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
9941 The atomic/separate/unroll choice for the remaining part is determined
9942 by the regular C<atomic>, C<separate> or C<unroll> option.
9943 The use of the C<isolate> option causes any tree containing the node
9944 to be considered anchored.
9946 As an example, consider the isolation of full tiles from partial tiles
9947 in a tiling of a triangular domain. The original schedule is as follows.
9949 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9951 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9952 { A[i,j] -> [floor(j/10)] }, \
9953 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9957 for (int c0 = 0; c0 <= 10; c0 += 1)
9958 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9959 for (int c2 = 10 * c0;
9960 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9961 for (int c3 = 10 * c1;
9962 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9965 Isolating the full tiles, we have the following input
9967 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9969 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9970 { A[i,j] -> [floor(j/10)] }, \
9971 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9972 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9973 10a+9+10b+9 <= 100 }"
9978 for (int c0 = 0; c0 <= 8; c0 += 1) {
9979 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9980 for (int c2 = 10 * c0;
9981 c2 <= 10 * c0 + 9; c2 += 1)
9982 for (int c3 = 10 * c1;
9983 c3 <= 10 * c1 + 9; c3 += 1)
9985 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9986 for (int c2 = 10 * c0;
9987 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9988 for (int c3 = 10 * c1;
9989 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9992 for (int c0 = 9; c0 <= 10; c0 += 1)
9993 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9994 for (int c2 = 10 * c0;
9995 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9996 for (int c3 = 10 * c1;
9997 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10001 We may then additionally unroll the innermost loop of the isolated part
10003 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10005 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10006 { A[i,j] -> [floor(j/10)] }, \
10007 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10008 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10009 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10014 for (int c0 = 0; c0 <= 8; c0 += 1) {
10015 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10016 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10018 A(c2, 10 * c1 + 1);
10019 A(c2, 10 * c1 + 2);
10020 A(c2, 10 * c1 + 3);
10021 A(c2, 10 * c1 + 4);
10022 A(c2, 10 * c1 + 5);
10023 A(c2, 10 * c1 + 6);
10024 A(c2, 10 * c1 + 7);
10025 A(c2, 10 * c1 + 8);
10026 A(c2, 10 * c1 + 9);
10028 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10029 for (int c2 = 10 * c0;
10030 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10031 for (int c3 = 10 * c1;
10032 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10035 for (int c0 = 9; c0 <= 10; c0 += 1)
10036 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10037 for (int c2 = 10 * c0;
10038 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10039 for (int c3 = 10 * c1;
10040 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10045 =head3 AST Generation Options (Schedule Map)
10047 In case of AST construction using
10048 C<isl_ast_build_node_from_schedule_map>, the options
10049 that control how an AST is created from the individual schedule
10050 dimensions are stored in the C<isl_ast_build>.
10051 They can be set using the following function.
10053 #include <isl/ast_build.h>
10054 __isl_give isl_ast_build *
10055 isl_ast_build_set_options(
10056 __isl_take isl_ast_build *control,
10057 __isl_take isl_union_map *options);
10059 The options are encoded in an C<isl_union_map>.
10060 The domain of this union relation refers to the schedule domain,
10061 i.e., the range of the schedule passed
10062 to C<isl_ast_build_node_from_schedule_map>.
10063 In the case of nested AST generation (see L</"Nested AST Generation">),
10064 the domain of C<options> should refer to the extra piece of the schedule.
10065 That is, it should be equal to the range of the wrapped relation in the
10066 range of the schedule.
10067 The range of the options can consist of elements in one or more spaces,
10068 the names of which determine the effect of the option.
10069 The values of the range typically also refer to the schedule dimension
10070 to which the option applies. In case of nested AST generation
10071 (see L</"Nested AST Generation">), these values refer to the position
10072 of the schedule dimension within the innermost AST generation.
10073 The constraints on the domain elements of
10074 the option should only refer to this dimension and earlier dimensions.
10075 We consider the following spaces.
10079 =item C<separation_class>
10081 B<This option has been deprecated. Use the isolate option on
10082 schedule trees instead.>
10084 This space is a wrapped relation between two one dimensional spaces.
10085 The input space represents the schedule dimension to which the option
10086 applies and the output space represents the separation class.
10087 While constructing a loop corresponding to the specified schedule
10088 dimension(s), the AST generator will try to generate separate loops
10089 for domain elements that are assigned different classes.
10090 If only some of the elements are assigned a class, then those elements
10091 that are not assigned any class will be treated as belonging to a class
10092 that is separate from the explicitly assigned classes.
10093 The typical use case for this option is to separate full tiles from
10095 The other options, described below, are applied after the separation
10098 As an example, consider the separation into full and partial tiles
10099 of a tiling of a triangular domain.
10100 Take, for example, the domain
10102 { A[i,j] : 0 <= i,j and i + j <= 100 }
10104 and a tiling into tiles of 10 by 10. The input to the AST generator
10105 is then the schedule
10107 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10110 Without any options, the following AST is generated
10112 for (int c0 = 0; c0 <= 10; c0 += 1)
10113 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10114 for (int c2 = 10 * c0;
10115 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10117 for (int c3 = 10 * c1;
10118 c3 <= min(10 * c1 + 9, -c2 + 100);
10122 Separation into full and partial tiles can be obtained by assigning
10123 a class, say C<0>, to the full tiles. The full tiles are represented by those
10124 values of the first and second schedule dimensions for which there are
10125 values of the third and fourth dimensions to cover an entire tile.
10126 That is, we need to specify the following option
10128 { [a,b,c,d] -> separation_class[[0]->[0]] :
10129 exists b': 0 <= 10a,10b' and
10130 10a+9+10b'+9 <= 100;
10131 [a,b,c,d] -> separation_class[[1]->[0]] :
10132 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10134 which simplifies to
10136 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10137 a >= 0 and b >= 0 and b <= 8 - a;
10138 [a, b, c, d] -> separation_class[[0] -> [0]] :
10139 a >= 0 and a <= 8 }
10141 With this option, the generated AST is as follows
10144 for (int c0 = 0; c0 <= 8; c0 += 1) {
10145 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10146 for (int c2 = 10 * c0;
10147 c2 <= 10 * c0 + 9; c2 += 1)
10148 for (int c3 = 10 * c1;
10149 c3 <= 10 * c1 + 9; c3 += 1)
10151 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10152 for (int c2 = 10 * c0;
10153 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10155 for (int c3 = 10 * c1;
10156 c3 <= min(-c2 + 100, 10 * c1 + 9);
10160 for (int c0 = 9; c0 <= 10; c0 += 1)
10161 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10162 for (int c2 = 10 * c0;
10163 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10165 for (int c3 = 10 * c1;
10166 c3 <= min(10 * c1 + 9, -c2 + 100);
10173 This is a single-dimensional space representing the schedule dimension(s)
10174 to which ``separation'' should be applied. Separation tries to split
10175 a loop into several pieces if this can avoid the generation of guards
10177 See also the C<atomic> option.
10181 This is a single-dimensional space representing the schedule dimension(s)
10182 for which the domains should be considered ``atomic''. That is, the
10183 AST generator will make sure that any given domain space will only appear
10184 in a single loop at the specified level.
10186 Consider the following schedule
10188 { a[i] -> [i] : 0 <= i < 10;
10189 b[i] -> [i+1] : 0 <= i < 10 }
10191 If the following option is specified
10193 { [i] -> separate[x] }
10195 then the following AST will be generated
10199 for (int c0 = 1; c0 <= 9; c0 += 1) {
10206 If, on the other hand, the following option is specified
10208 { [i] -> atomic[x] }
10210 then the following AST will be generated
10212 for (int c0 = 0; c0 <= 10; c0 += 1) {
10219 If neither C<atomic> nor C<separate> is specified, then the AST generator
10220 may produce either of these two results or some intermediate form.
10224 This is a single-dimensional space representing the schedule dimension(s)
10225 that should be I<completely> unrolled.
10226 To obtain a partial unrolling, the user should apply an additional
10227 strip-mining to the schedule and fully unroll the inner loop.
10231 =head3 Fine-grained Control over AST Generation
10233 Besides specifying the constraints on the parameters,
10234 an C<isl_ast_build> object can be used to control
10235 various aspects of the AST generation process.
10236 In case of AST construction using
10237 C<isl_ast_build_node_from_schedule_map>,
10238 the most prominent way of control is through ``options'',
10239 as explained above.
10241 Additional control is available through the following functions.
10243 #include <isl/ast_build.h>
10244 __isl_give isl_ast_build *
10245 isl_ast_build_set_iterators(
10246 __isl_take isl_ast_build *control,
10247 __isl_take isl_id_list *iterators);
10249 The function C<isl_ast_build_set_iterators> allows the user to
10250 specify a list of iterator C<isl_id>s to be used as iterators.
10251 If the input schedule is injective, then
10252 the number of elements in this list should be as large as the dimension
10253 of the schedule space, but no direct correspondence should be assumed
10254 between dimensions and elements.
10255 If the input schedule is not injective, then an additional number
10256 of C<isl_id>s equal to the largest dimension of the input domains
10258 If the number of provided C<isl_id>s is insufficient, then additional
10259 names are automatically generated.
10261 #include <isl/ast_build.h>
10262 __isl_give isl_ast_build *
10263 isl_ast_build_set_create_leaf(
10264 __isl_take isl_ast_build *control,
10265 __isl_give isl_ast_node *(*fn)(
10266 __isl_take isl_ast_build *build,
10267 void *user), void *user);
10270 C<isl_ast_build_set_create_leaf> function allows for the
10271 specification of a callback that should be called whenever the AST
10272 generator arrives at an element of the schedule domain.
10273 The callback should return an AST node that should be inserted
10274 at the corresponding position of the AST. The default action (when
10275 the callback is not set) is to continue generating parts of the AST to scan
10276 all the domain elements associated to the schedule domain element
10277 and to insert user nodes, ``calling'' the domain element, for each of them.
10278 The C<build> argument contains the current state of the C<isl_ast_build>.
10279 To ease nested AST generation (see L</"Nested AST Generation">),
10280 all control information that is
10281 specific to the current AST generation such as the options and
10282 the callbacks has been removed from this C<isl_ast_build>.
10283 The callback would typically return the result of a nested
10284 AST generation or a
10285 user defined node created using the following function.
10287 #include <isl/ast.h>
10288 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10289 __isl_take isl_ast_expr *expr);
10291 #include <isl/ast_build.h>
10292 __isl_give isl_ast_build *
10293 isl_ast_build_set_at_each_domain(
10294 __isl_take isl_ast_build *build,
10295 __isl_give isl_ast_node *(*fn)(
10296 __isl_take isl_ast_node *node,
10297 __isl_keep isl_ast_build *build,
10298 void *user), void *user);
10299 __isl_give isl_ast_build *
10300 isl_ast_build_set_before_each_for(
10301 __isl_take isl_ast_build *build,
10302 __isl_give isl_id *(*fn)(
10303 __isl_keep isl_ast_build *build,
10304 void *user), void *user);
10305 __isl_give isl_ast_build *
10306 isl_ast_build_set_after_each_for(
10307 __isl_take isl_ast_build *build,
10308 __isl_give isl_ast_node *(*fn)(
10309 __isl_take isl_ast_node *node,
10310 __isl_keep isl_ast_build *build,
10311 void *user), void *user);
10312 __isl_give isl_ast_build *
10313 isl_ast_build_set_before_each_mark(
10314 __isl_take isl_ast_build *build,
10315 isl_stat (*fn)(__isl_keep isl_id *mark,
10316 __isl_keep isl_ast_build *build,
10317 void *user), void *user);
10318 __isl_give isl_ast_build *
10319 isl_ast_build_set_after_each_mark(
10320 __isl_take isl_ast_build *build,
10321 __isl_give isl_ast_node *(*fn)(
10322 __isl_take isl_ast_node *node,
10323 __isl_keep isl_ast_build *build,
10324 void *user), void *user);
10326 The callback set by C<isl_ast_build_set_at_each_domain> will
10327 be called for each domain AST node.
10328 The callbacks set by C<isl_ast_build_set_before_each_for>
10329 and C<isl_ast_build_set_after_each_for> will be called
10330 for each for AST node. The first will be called in depth-first
10331 pre-order, while the second will be called in depth-first post-order.
10332 Since C<isl_ast_build_set_before_each_for> is called before the for
10333 node is actually constructed, it is only passed an C<isl_ast_build>.
10334 The returned C<isl_id> will be added as an annotation (using
10335 C<isl_ast_node_set_annotation>) to the constructed for node.
10336 In particular, if the user has also specified an C<after_each_for>
10337 callback, then the annotation can be retrieved from the node passed to
10338 that callback using C<isl_ast_node_get_annotation>.
10339 The callbacks set by C<isl_ast_build_set_before_each_mark>
10340 and C<isl_ast_build_set_after_each_mark> will be called for each
10341 mark AST node that is created, i.e., for each mark schedule node
10342 in the input schedule tree. The first will be called in depth-first
10343 pre-order, while the second will be called in depth-first post-order.
10344 Since the callback set by C<isl_ast_build_set_before_each_mark>
10345 is called before the mark AST node is actually constructed, it is passed
10346 the identifier of the mark node.
10347 All callbacks should C<NULL> (or -1) on failure.
10348 The given C<isl_ast_build> can be used to create new
10349 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10350 or C<isl_ast_build_call_from_pw_multi_aff>.
10352 =head3 Nested AST Generation
10354 C<isl> allows the user to create an AST within the context
10355 of another AST. These nested ASTs are created using the
10356 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10357 the outer AST. The C<build> argument should be an C<isl_ast_build>
10358 passed to a callback set by
10359 C<isl_ast_build_set_create_leaf>.
10360 The space of the range of the C<schedule> argument should refer
10361 to this build. In particular, the space should be a wrapped
10362 relation and the domain of this wrapped relation should be the
10363 same as that of the range of the schedule returned by
10364 C<isl_ast_build_get_schedule> below.
10365 In practice, the new schedule is typically
10366 created by calling C<isl_union_map_range_product> on the old schedule
10367 and some extra piece of the schedule.
10368 The space of the schedule domain is also available from
10369 the C<isl_ast_build>.
10371 #include <isl/ast_build.h>
10372 __isl_give isl_union_map *isl_ast_build_get_schedule(
10373 __isl_keep isl_ast_build *build);
10374 __isl_give isl_space *isl_ast_build_get_schedule_space(
10375 __isl_keep isl_ast_build *build);
10376 __isl_give isl_ast_build *isl_ast_build_restrict(
10377 __isl_take isl_ast_build *build,
10378 __isl_take isl_set *set);
10380 The C<isl_ast_build_get_schedule> function returns a (partial)
10381 schedule for the domains elements for which part of the AST still needs to
10382 be generated in the current build.
10383 In particular, the domain elements are mapped to those iterations of the loops
10384 enclosing the current point of the AST generation inside which
10385 the domain elements are executed.
10386 No direct correspondence between
10387 the input schedule and this schedule should be assumed.
10388 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10389 to create a set for C<isl_ast_build_restrict> to intersect
10390 with the current build. In particular, the set passed to
10391 C<isl_ast_build_restrict> can have additional parameters.
10392 The ids of the set dimensions in the space returned by
10393 C<isl_ast_build_get_schedule_space> correspond to the
10394 iterators of the already generated loops.
10395 The user should not rely on the ids of the output dimensions
10396 of the relations in the union relation returned by
10397 C<isl_ast_build_get_schedule> having any particular value.
10399 =head1 Applications
10401 Although C<isl> is mainly meant to be used as a library,
10402 it also contains some basic applications that use some
10403 of the functionality of C<isl>.
10404 The input may be specified in either the L<isl format>
10405 or the L<PolyLib format>.
10407 =head2 C<isl_polyhedron_sample>
10409 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10410 an integer element of the polyhedron, if there is any.
10411 The first column in the output is the denominator and is always
10412 equal to 1. If the polyhedron contains no integer points,
10413 then a vector of length zero is printed.
10417 C<isl_pip> takes the same input as the C<example> program
10418 from the C<piplib> distribution, i.e., a set of constraints
10419 on the parameters, a line containing only -1 and finally a set
10420 of constraints on a parametric polyhedron.
10421 The coefficients of the parameters appear in the last columns
10422 (but before the final constant column).
10423 The output is the lexicographic minimum of the parametric polyhedron.
10424 As C<isl> currently does not have its own output format, the output
10425 is just a dump of the internal state.
10427 =head2 C<isl_polyhedron_minimize>
10429 C<isl_polyhedron_minimize> computes the minimum of some linear
10430 or affine objective function over the integer points in a polyhedron.
10431 If an affine objective function
10432 is given, then the constant should appear in the last column.
10434 =head2 C<isl_polytope_scan>
10436 Given a polytope, C<isl_polytope_scan> prints
10437 all integer points in the polytope.
10439 =head2 C<isl_codegen>
10441 Given a schedule, a context set and an options relation,
10442 C<isl_codegen> prints out an AST that scans the domain elements
10443 of the schedule in the order of their image(s) taking into account
10444 the constraints in the context set.