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.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
273 =head3 Changes since isl-0.19
277 =item * Zero-dimensional objects of type C<isl_multi_pw_aff> or
278 C<isl_multi_union_pw_aff> can now keep track of an explicit domain.
279 This explicit domain, if present, is taken into account
280 by various operations that take such objects as input.
286 C<isl> is released under the MIT license.
290 Permission is hereby granted, free of charge, to any person obtaining a copy of
291 this software and associated documentation files (the "Software"), to deal in
292 the Software without restriction, including without limitation the rights to
293 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
294 of the Software, and to permit persons to whom the Software is furnished to do
295 so, subject to the following conditions:
297 The above copyright notice and this permission notice shall be included in all
298 copies or substantial portions of the Software.
300 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
301 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
302 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
303 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
304 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
305 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
310 Note that by default C<isl> requires C<GMP>, which is released
311 under the GNU Lesser General Public License (LGPL). This means
312 that code linked against C<isl> is also linked against LGPL code.
314 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
315 will link against C<imath>, a library for exact integer arithmetic released
316 under the MIT license.
320 The source of C<isl> can be obtained either as a tarball
321 or from the git repository. Both are available from
322 L<http://isl.gforge.inria.fr/>.
323 The installation process depends on how you obtained
326 =head2 Installation from the git repository
330 =item 1 Clone or update the repository
332 The first time the source is obtained, you need to clone
335 git clone git://repo.or.cz/isl.git
337 To obtain updates, you need to pull in the latest changes
341 =item 2 Optionally get C<imath> submodule
343 To build C<isl> with C<imath>, you need to obtain the C<imath>
344 submodule by running in the git source tree of C<isl>
349 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
351 =item 2 Generate C<configure>
357 After performing the above steps, continue
358 with the L<Common installation instructions>.
360 =head2 Common installation instructions
364 =item 1 Obtain C<GMP>
366 By default, building C<isl> requires C<GMP>, including its headers files.
367 Your distribution may not provide these header files by default
368 and you may need to install a package called C<gmp-devel> or something
369 similar. Alternatively, C<GMP> can be built from
370 source, available from L<http://gmplib.org/>.
371 C<GMP> is not needed if you build C<isl> with C<imath>.
375 C<isl> uses the standard C<autoconf> C<configure> script.
380 optionally followed by some configure options.
381 A complete list of options can be obtained by running
385 Below we discuss some of the more common options.
391 Installation prefix for C<isl>
393 =item C<--with-int=[gmp|imath|imath-32]>
395 Select the integer library to be used by C<isl>, the default is C<gmp>.
396 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
397 for values out of the 32 bit range. In most applications, C<isl> will run
398 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
401 =item C<--with-gmp-prefix>
403 Installation prefix for C<GMP> (architecture-independent files).
405 =item C<--with-gmp-exec-prefix>
407 Installation prefix for C<GMP> (architecture-dependent files).
415 =item 4 Install (optional)
421 =head1 Integer Set Library
423 =head2 Memory Management
425 Since a high-level operation on isl objects usually involves
426 several substeps and since the user is usually not interested in
427 the intermediate results, most functions that return a new object
428 will also release all the objects passed as arguments.
429 If the user still wants to use one or more of these arguments
430 after the function call, she should pass along a copy of the
431 object rather than the object itself.
432 The user is then responsible for making sure that the original
433 object gets used somewhere else or is explicitly freed.
435 The arguments and return values of all documented functions are
436 annotated to make clear which arguments are released and which
437 arguments are preserved. In particular, the following annotations
444 C<__isl_give> means that a new object is returned.
445 The user should make sure that the returned pointer is
446 used exactly once as a value for an C<__isl_take> argument.
447 In between, it can be used as a value for as many
448 C<__isl_keep> arguments as the user likes.
449 There is one exception, and that is the case where the
450 pointer returned is C<NULL>. Is this case, the user
451 is free to use it as an C<__isl_take> argument or not.
452 When applied to a C<char *>, the returned pointer needs to be
457 C<__isl_null> means that a C<NULL> value is returned.
461 C<__isl_take> means that the object the argument points to
462 is taken over by the function and may no longer be used
463 by the user as an argument to any other function.
464 The pointer value must be one returned by a function
465 returning an C<__isl_give> pointer.
466 If the user passes in a C<NULL> value, then this will
467 be treated as an error in the sense that the function will
468 not perform its usual operation. However, it will still
469 make sure that all the other C<__isl_take> arguments
474 C<__isl_keep> means that the function will only use the object
475 temporarily. After the function has finished, the user
476 can still use it as an argument to other functions.
477 A C<NULL> value will be treated in the same way as
478 a C<NULL> value for an C<__isl_take> argument.
479 This annotation may also be used on return values of
480 type C<const char *>, in which case the returned pointer should
481 not be freed by the user and is only valid until the object
482 from which it was derived is updated or freed.
486 =head2 Initialization
488 All manipulations of integer sets and relations occur within
489 the context of an C<isl_ctx>.
490 A given C<isl_ctx> can only be used within a single thread.
491 All arguments of a function are required to have been allocated
492 within the same context.
493 There are currently no functions available for moving an object
494 from one C<isl_ctx> to another C<isl_ctx>. This means that
495 there is currently no way of safely moving an object from one
496 thread to another, unless the whole C<isl_ctx> is moved.
498 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
499 freed using C<isl_ctx_free>.
500 All objects allocated within an C<isl_ctx> should be freed
501 before the C<isl_ctx> itself is freed.
503 isl_ctx *isl_ctx_alloc();
504 void isl_ctx_free(isl_ctx *ctx);
506 The user can impose a bound on the number of low-level I<operations>
507 that can be performed by an C<isl_ctx>. This bound can be set and
508 retrieved using the following functions. A bound of zero means that
509 no bound is imposed. The number of operations performed can be
510 reset using C<isl_ctx_reset_operations>. Note that the number
511 of low-level operations needed to perform a high-level computation
512 may differ significantly across different versions
513 of C<isl>, but it should be the same across different platforms
514 for the same version of C<isl>.
516 Warning: This feature is experimental. C<isl> has good support to abort and
517 bail out during the computation, but this feature may exercise error code paths
518 that are normally not used that much. Consequently, it is not unlikely that
519 hidden bugs will be exposed.
521 void isl_ctx_set_max_operations(isl_ctx *ctx,
522 unsigned long max_operations);
523 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
524 void isl_ctx_reset_operations(isl_ctx *ctx);
526 In order to be able to create an object in the same context
527 as another object, most object types (described later in
528 this document) provide a function to obtain the context
529 in which the object was created.
532 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
533 isl_ctx *isl_multi_val_get_ctx(
534 __isl_keep isl_multi_val *mv);
537 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
539 #include <isl/local_space.h>
540 isl_ctx *isl_local_space_get_ctx(
541 __isl_keep isl_local_space *ls);
544 isl_ctx *isl_set_list_get_ctx(
545 __isl_keep isl_set_list *list);
548 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
549 isl_ctx *isl_multi_aff_get_ctx(
550 __isl_keep isl_multi_aff *maff);
551 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
552 isl_ctx *isl_pw_multi_aff_get_ctx(
553 __isl_keep isl_pw_multi_aff *pma);
554 isl_ctx *isl_multi_pw_aff_get_ctx(
555 __isl_keep isl_multi_pw_aff *mpa);
556 isl_ctx *isl_union_pw_aff_get_ctx(
557 __isl_keep isl_union_pw_aff *upa);
558 isl_ctx *isl_union_pw_multi_aff_get_ctx(
559 __isl_keep isl_union_pw_multi_aff *upma);
560 isl_ctx *isl_multi_union_pw_aff_get_ctx(
561 __isl_keep isl_multi_union_pw_aff *mupa);
563 #include <isl/id_to_ast_expr.h>
564 isl_ctx *isl_id_to_ast_expr_get_ctx(
565 __isl_keep isl_id_to_ast_expr *id2expr);
567 #include <isl/point.h>
568 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
571 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
574 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
576 #include <isl/vertices.h>
577 isl_ctx *isl_vertices_get_ctx(
578 __isl_keep isl_vertices *vertices);
579 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
580 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
582 #include <isl/flow.h>
583 isl_ctx *isl_restriction_get_ctx(
584 __isl_keep isl_restriction *restr);
585 isl_ctx *isl_union_access_info_get_ctx(
586 __isl_keep isl_union_access_info *access);
587 isl_ctx *isl_union_flow_get_ctx(
588 __isl_keep isl_union_flow *flow);
590 #include <isl/schedule.h>
591 isl_ctx *isl_schedule_get_ctx(
592 __isl_keep isl_schedule *sched);
593 isl_ctx *isl_schedule_constraints_get_ctx(
594 __isl_keep isl_schedule_constraints *sc);
596 #include <isl/schedule_node.h>
597 isl_ctx *isl_schedule_node_get_ctx(
598 __isl_keep isl_schedule_node *node);
600 #include <isl/ast_build.h>
601 isl_ctx *isl_ast_build_get_ctx(
602 __isl_keep isl_ast_build *build);
605 isl_ctx *isl_ast_expr_get_ctx(
606 __isl_keep isl_ast_expr *expr);
607 isl_ctx *isl_ast_node_get_ctx(
608 __isl_keep isl_ast_node *node);
610 #include <isl/stride_info.h>
611 isl_ctx *isl_stride_info_get_ctx(
612 __isl_keep isl_stride_info *si);
614 #include <isl/fixed_box.h>
615 isl_ctx *isl_fixed_box_get_ctx(
616 __isl_keep isl_fixed_box *box);
620 C<isl> uses two special return types for functions that either return
621 a boolean or that in principle do not return anything.
622 In particular, the C<isl_bool> type has three possible values:
623 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
624 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
625 C<isl_bool_error> (a negative integer value), indicating that something
626 went wrong. The following function can be used to negate an C<isl_bool>,
627 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
630 isl_bool isl_bool_not(isl_bool b);
632 The C<isl_stat> type has two possible values:
633 C<isl_stat_ok> (the integer value zero), indicating a successful
635 C<isl_stat_error> (a negative integer value), indicating that something
637 See L</"Error Handling"> for more information on
638 C<isl_bool_error> and C<isl_stat_error>.
642 An C<isl_val> represents an integer value, a rational value
643 or one of three special values, infinity, negative infinity and NaN.
644 Some predefined values can be created using the following functions.
647 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
648 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
649 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
650 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
651 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
652 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
654 Specific integer values can be created using the following functions.
657 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
659 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
661 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
662 size_t n, size_t size, const void *chunks);
664 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
665 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
666 The least significant digit is assumed to be stored first.
668 Value objects can be copied and freed using the following functions.
671 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
672 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
674 They can be inspected using the following functions.
677 long isl_val_get_num_si(__isl_keep isl_val *v);
678 long isl_val_get_den_si(__isl_keep isl_val *v);
679 __isl_give isl_val *isl_val_get_den_val(
680 __isl_keep isl_val *v);
681 double isl_val_get_d(__isl_keep isl_val *v);
682 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
684 isl_stat isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
685 size_t size, void *chunks);
687 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
688 of C<size> bytes needed to store the absolute value of the
690 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
691 which is assumed to have been preallocated by the caller.
692 The least significant digit is stored first.
693 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
694 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
695 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
697 An C<isl_val> can be modified using the following function.
700 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
703 The following unary properties are defined on C<isl_val>s.
706 int isl_val_sgn(__isl_keep isl_val *v);
707 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
708 isl_bool isl_val_is_one(__isl_keep isl_val *v);
709 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
710 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
711 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
712 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
713 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
714 isl_bool isl_val_is_int(__isl_keep isl_val *v);
715 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
716 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
717 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
718 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
720 Note that the sign of NaN is undefined.
722 The following binary properties are defined on pairs of C<isl_val>s.
725 isl_bool isl_val_lt(__isl_keep isl_val *v1,
726 __isl_keep isl_val *v2);
727 isl_bool isl_val_le(__isl_keep isl_val *v1,
728 __isl_keep isl_val *v2);
729 isl_bool isl_val_gt(__isl_keep isl_val *v1,
730 __isl_keep isl_val *v2);
731 isl_bool isl_val_ge(__isl_keep isl_val *v1,
732 __isl_keep isl_val *v2);
733 isl_bool isl_val_eq(__isl_keep isl_val *v1,
734 __isl_keep isl_val *v2);
735 isl_bool isl_val_ne(__isl_keep isl_val *v1,
736 __isl_keep isl_val *v2);
737 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
738 __isl_keep isl_val *v2);
740 Comparisons to NaN always return false.
741 That is, a NaN is not considered to hold any relative position
742 with respect to any value. In particular, a NaN
743 is neither considered to be equal to nor to be different from
744 any value (including another NaN).
745 The function C<isl_val_abs_eq> checks whether its two arguments
746 are equal in absolute value.
748 For integer C<isl_val>s we additionally have the following binary property.
751 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
752 __isl_keep isl_val *v2);
754 An C<isl_val> can also be compared to an integer using the following
755 functions. The result of C<isl_val_cmp_si> undefined for NaN.
758 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
759 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
761 The following unary operations are available on C<isl_val>s.
764 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
765 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
766 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
767 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
768 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
769 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
771 The following binary operations are available on C<isl_val>s.
774 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
775 __isl_take isl_val *v2);
776 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
777 __isl_take isl_val *v2);
778 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
779 __isl_take isl_val *v2);
780 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
782 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
783 __isl_take isl_val *v2);
784 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
786 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
787 __isl_take isl_val *v2);
788 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
790 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
791 __isl_take isl_val *v2);
792 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
795 On integer values, we additionally have the following operations.
798 __isl_give isl_val *isl_val_pow2(__isl_take isl_val *v);
799 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
800 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
801 __isl_take isl_val *v2);
802 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
803 __isl_take isl_val *v2);
804 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
805 __isl_take isl_val *v2, __isl_give isl_val **x,
806 __isl_give isl_val **y);
808 C<isl_val_2exp> is an alternative name for C<isl_val_pow2>.
809 The function C<isl_val_gcdext> returns the greatest common divisor g
810 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
811 that C<*x> * C<v1> + C<*y> * C<v2> = g.
813 =head3 GMP specific functions
815 These functions are only available if C<isl> has been compiled with C<GMP>
818 Specific integer and rational values can be created from C<GMP> values using
819 the following functions.
821 #include <isl/val_gmp.h>
822 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
824 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
825 const mpz_t n, const mpz_t d);
827 The numerator and denominator of a rational value can be extracted as
828 C<GMP> values using the following functions.
830 #include <isl/val_gmp.h>
831 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
832 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
834 =head2 Sets and Relations
836 C<isl> uses six types of objects for representing sets and relations,
837 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
838 C<isl_union_set> and C<isl_union_map>.
839 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
840 can be described as a conjunction of affine constraints, while
841 C<isl_set> and C<isl_map> represent unions of
842 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
843 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
844 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
845 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
846 where spaces are considered different if they have a different number
847 of dimensions and/or different names (see L<"Spaces">).
848 The difference between sets and relations (maps) is that sets have
849 one set of variables, while relations have two sets of variables,
850 input variables and output variables.
852 =head2 Error Handling
854 C<isl> supports different ways to react in case a runtime error is triggered.
855 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
856 with two maps that have incompatible spaces. There are three possible ways
857 to react on error: to warn, to continue or to abort.
859 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
860 the last error in the corresponding C<isl_ctx> and the function in which the
861 error was triggered returns a value indicating that some error has
862 occurred. In case of functions returning a pointer, this value is
863 C<NULL>. In case of functions returning an C<isl_bool> or an
864 C<isl_stat>, this value is C<isl_bool_error> or C<isl_stat_error>.
865 An error does not corrupt internal state,
866 such that isl can continue to be used. C<isl> also provides functions to
867 read the last error, including the specific error message,
868 the isl source file where the error occurred and the line number,
869 and to reset all information about the last error. The
870 last error is only stored for information purposes. Its presence does not
871 change the behavior of C<isl>. Hence, resetting an error is not required to
872 continue to use isl, but only to observe new errors.
875 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
876 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
877 const char *isl_ctx_last_error_file(isl_ctx *ctx);
878 int isl_ctx_last_error_line(isl_ctx *ctx);
879 void isl_ctx_reset_error(isl_ctx *ctx);
881 If no error has occurred since the last call to C<isl_ctx_reset_error>,
882 then the functions C<isl_ctx_last_error_msg> and
883 C<isl_ctx_last_error_file> return C<NULL>.
885 Another option is to continue on error. This is similar to warn on error mode,
886 except that C<isl> does not print any warning. This allows a program to
887 implement its own error reporting.
889 The last option is to directly abort the execution of the program from within
890 the isl library. This makes it obviously impossible to recover from an error,
891 but it allows to directly spot the error location. By aborting on error,
892 debuggers break at the location the error occurred and can provide a stack
893 trace. Other tools that automatically provide stack traces on abort or that do
894 not want to continue execution after an error was triggered may also prefer to
897 The on error behavior of isl can be specified by calling
898 C<isl_options_set_on_error> or by setting the command line option
899 C<--isl-on-error>. Valid arguments for the function call are
900 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
901 choices for the command line option are C<warn>, C<continue> and C<abort>.
902 It is also possible to query the current error mode.
904 #include <isl/options.h>
905 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
906 int isl_options_get_on_error(isl_ctx *ctx);
910 Identifiers are used to identify both individual dimensions
911 and tuples of dimensions. They consist of an optional name and an optional
912 user pointer. The name and the user pointer cannot both be C<NULL>, however.
913 Identifiers with the same name but different pointer values
914 are considered to be distinct.
915 Similarly, identifiers with different names but the same pointer value
916 are also considered to be distinct.
917 Equal identifiers are represented using the same object.
918 Pairs of identifiers can therefore be tested for equality using the
920 Identifiers can be constructed, copied, freed, inspected and printed
921 using the following functions.
924 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
925 __isl_keep const char *name, void *user);
926 __isl_give isl_id *isl_id_set_free_user(
927 __isl_take isl_id *id,
928 void (*free_user)(void *user));
929 __isl_give isl_id *isl_id_copy(isl_id *id);
930 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
932 void *isl_id_get_user(__isl_keep isl_id *id);
933 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
935 __isl_give isl_printer *isl_printer_print_id(
936 __isl_take isl_printer *p, __isl_keep isl_id *id);
938 The callback set by C<isl_id_set_free_user> is called on the user
939 pointer when the last reference to the C<isl_id> is freed.
940 Note that C<isl_id_get_name> returns a pointer to some internal
941 data structure, so the result can only be used while the
942 corresponding C<isl_id> is alive.
946 Whenever a new set, relation or similar object is created from scratch,
947 the space in which it lives needs to be specified using an C<isl_space>.
948 Each space involves zero or more parameters and zero, one or two
949 tuples of set or input/output dimensions. The parameters and dimensions
950 are identified by an C<isl_dim_type> and a position.
951 The type C<isl_dim_param> refers to parameters,
952 the type C<isl_dim_set> refers to set dimensions (for spaces
953 with a single tuple of dimensions) and the types C<isl_dim_in>
954 and C<isl_dim_out> refer to input and output dimensions
955 (for spaces with two tuples of dimensions).
956 Local spaces (see L</"Local Spaces">) also contain dimensions
957 of type C<isl_dim_div>.
958 Note that parameters are only identified by their position within
959 a given object. Across different objects, parameters are (usually)
960 identified by their names or identifiers. Only unnamed parameters
961 are identified by their positions across objects. The use of unnamed
962 parameters is discouraged.
964 #include <isl/space.h>
965 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
966 unsigned nparam, unsigned n_in, unsigned n_out);
967 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
969 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
970 unsigned nparam, unsigned dim);
971 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
972 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
974 The space used for creating a parameter domain
975 needs to be created using C<isl_space_params_alloc>.
976 For other sets, the space
977 needs to be created using C<isl_space_set_alloc>, while
978 for a relation, the space
979 needs to be created using C<isl_space_alloc>.
981 To check whether a given space is that of a set or a map
982 or whether it is a parameter space, use these functions:
984 #include <isl/space.h>
985 isl_bool isl_space_is_params(__isl_keep isl_space *space);
986 isl_bool isl_space_is_set(__isl_keep isl_space *space);
987 isl_bool isl_space_is_map(__isl_keep isl_space *space);
989 Spaces can be compared using the following functions:
991 #include <isl/space.h>
992 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
993 __isl_keep isl_space *space2);
994 isl_bool isl_space_has_equal_params(
995 __isl_keep isl_space *space1,
996 __isl_keep isl_space *space2);
997 isl_bool isl_space_has_equal_tuples(
998 __isl_keep isl_space *space1,
999 __isl_keep isl_space *space2);
1000 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
1001 __isl_keep isl_space *space2);
1002 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
1003 __isl_keep isl_space *space2);
1004 isl_bool isl_space_tuple_is_equal(
1005 __isl_keep isl_space *space1,
1006 enum isl_dim_type type1,
1007 __isl_keep isl_space *space2,
1008 enum isl_dim_type type2);
1010 C<isl_space_is_domain> checks whether the first argument is equal
1011 to the domain of the second argument. This requires in particular that
1012 the first argument is a set space and that the second argument
1013 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1014 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1015 spaces are the same. That is, it checks if they have the same
1016 identifier (if any), the same dimension and the same internal structure
1019 C<isl_space_has_equal_params> checks whether two spaces
1020 have the same parameters in the same order.
1021 C<isl_space_has_equal_tuples> check whether two spaces have
1022 the same tuples. In contrast to C<isl_space_is_equal> below,
1023 it does not check the
1024 parameters. This is useful because many C<isl> functions align the
1025 parameters before they perform their operations, such that equivalence
1027 C<isl_space_is_equal> checks whether two spaces are identical,
1028 meaning that they have the same parameters and the same tuples.
1029 That is, it checks whether both C<isl_space_has_equal_params> and
1030 C<isl_space_has_equal_tuples> hold.
1032 It is often useful to create objects that live in the
1033 same space as some other object. This can be accomplished
1034 by creating the new objects
1035 (see L</"Creating New Sets and Relations"> or
1036 L</"Functions">) based on the space
1037 of the original object.
1039 #include <isl/set.h>
1040 __isl_give isl_space *isl_basic_set_get_space(
1041 __isl_keep isl_basic_set *bset);
1042 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1044 #include <isl/union_set.h>
1045 __isl_give isl_space *isl_union_set_get_space(
1046 __isl_keep isl_union_set *uset);
1048 #include <isl/map.h>
1049 __isl_give isl_space *isl_basic_map_get_space(
1050 __isl_keep isl_basic_map *bmap);
1051 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1053 #include <isl/union_map.h>
1054 __isl_give isl_space *isl_union_map_get_space(
1055 __isl_keep isl_union_map *umap);
1057 #include <isl/constraint.h>
1058 __isl_give isl_space *isl_constraint_get_space(
1059 __isl_keep isl_constraint *constraint);
1061 #include <isl/polynomial.h>
1062 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1063 __isl_keep isl_qpolynomial *qp);
1064 __isl_give isl_space *isl_qpolynomial_get_space(
1065 __isl_keep isl_qpolynomial *qp);
1066 __isl_give isl_space *
1067 isl_qpolynomial_fold_get_domain_space(
1068 __isl_keep isl_qpolynomial_fold *fold);
1069 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1070 __isl_keep isl_qpolynomial_fold *fold);
1071 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1072 __isl_keep isl_pw_qpolynomial *pwqp);
1073 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1074 __isl_keep isl_pw_qpolynomial *pwqp);
1075 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1076 __isl_keep isl_pw_qpolynomial_fold *pwf);
1077 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1078 __isl_keep isl_pw_qpolynomial_fold *pwf);
1079 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1080 __isl_keep isl_union_pw_qpolynomial *upwqp);
1081 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1082 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1084 #include <isl/val.h>
1085 __isl_give isl_space *isl_multi_val_get_space(
1086 __isl_keep isl_multi_val *mv);
1088 #include <isl/aff.h>
1089 __isl_give isl_space *isl_aff_get_domain_space(
1090 __isl_keep isl_aff *aff);
1091 __isl_give isl_space *isl_aff_get_space(
1092 __isl_keep isl_aff *aff);
1093 __isl_give isl_space *isl_pw_aff_get_domain_space(
1094 __isl_keep isl_pw_aff *pwaff);
1095 __isl_give isl_space *isl_pw_aff_get_space(
1096 __isl_keep isl_pw_aff *pwaff);
1097 __isl_give isl_space *isl_multi_aff_get_domain_space(
1098 __isl_keep isl_multi_aff *maff);
1099 __isl_give isl_space *isl_multi_aff_get_space(
1100 __isl_keep isl_multi_aff *maff);
1101 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1102 __isl_keep isl_pw_multi_aff *pma);
1103 __isl_give isl_space *isl_pw_multi_aff_get_space(
1104 __isl_keep isl_pw_multi_aff *pma);
1105 __isl_give isl_space *isl_union_pw_aff_get_space(
1106 __isl_keep isl_union_pw_aff *upa);
1107 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1108 __isl_keep isl_union_pw_multi_aff *upma);
1109 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1110 __isl_keep isl_multi_pw_aff *mpa);
1111 __isl_give isl_space *isl_multi_pw_aff_get_space(
1112 __isl_keep isl_multi_pw_aff *mpa);
1113 __isl_give isl_space *
1114 isl_multi_union_pw_aff_get_domain_space(
1115 __isl_keep isl_multi_union_pw_aff *mupa);
1116 __isl_give isl_space *
1117 isl_multi_union_pw_aff_get_space(
1118 __isl_keep isl_multi_union_pw_aff *mupa);
1120 #include <isl/point.h>
1121 __isl_give isl_space *isl_point_get_space(
1122 __isl_keep isl_point *pnt);
1124 #include <isl/fixed_box.h>
1125 __isl_give isl_space *isl_fixed_box_get_space(
1126 __isl_keep isl_fixed_box *box);
1128 The number of dimensions of a given type of space
1129 may be read off from a space or an object that lives
1130 in a space using the following functions.
1131 In case of C<isl_space_dim>, type may be
1132 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1133 C<isl_dim_out> (only for relations), C<isl_dim_set>
1134 (only for sets) or C<isl_dim_all>.
1136 #include <isl/space.h>
1137 unsigned isl_space_dim(__isl_keep isl_space *space,
1138 enum isl_dim_type type);
1140 #include <isl/local_space.h>
1141 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1142 enum isl_dim_type type);
1144 #include <isl/set.h>
1145 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1146 enum isl_dim_type type);
1147 unsigned isl_set_dim(__isl_keep isl_set *set,
1148 enum isl_dim_type type);
1150 #include <isl/union_set.h>
1151 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1152 enum isl_dim_type type);
1154 #include <isl/map.h>
1155 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1156 enum isl_dim_type type);
1157 unsigned isl_map_dim(__isl_keep isl_map *map,
1158 enum isl_dim_type type);
1160 #include <isl/union_map.h>
1161 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1162 enum isl_dim_type type);
1164 #include <isl/val.h>
1165 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1166 enum isl_dim_type type);
1168 #include <isl/aff.h>
1169 int isl_aff_dim(__isl_keep isl_aff *aff,
1170 enum isl_dim_type type);
1171 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1172 enum isl_dim_type type);
1173 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1174 enum isl_dim_type type);
1175 unsigned isl_pw_multi_aff_dim(
1176 __isl_keep isl_pw_multi_aff *pma,
1177 enum isl_dim_type type);
1178 unsigned isl_multi_pw_aff_dim(
1179 __isl_keep isl_multi_pw_aff *mpa,
1180 enum isl_dim_type type);
1181 unsigned isl_union_pw_aff_dim(
1182 __isl_keep isl_union_pw_aff *upa,
1183 enum isl_dim_type type);
1184 unsigned isl_union_pw_multi_aff_dim(
1185 __isl_keep isl_union_pw_multi_aff *upma,
1186 enum isl_dim_type type);
1187 unsigned isl_multi_union_pw_aff_dim(
1188 __isl_keep isl_multi_union_pw_aff *mupa,
1189 enum isl_dim_type type);
1191 #include <isl/polynomial.h>
1192 unsigned isl_union_pw_qpolynomial_dim(
1193 __isl_keep isl_union_pw_qpolynomial *upwqp,
1194 enum isl_dim_type type);
1195 unsigned isl_union_pw_qpolynomial_fold_dim(
1196 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1197 enum isl_dim_type type);
1199 Note that an C<isl_union_set>, an C<isl_union_map>,
1200 an C<isl_union_pw_multi_aff>,
1201 an C<isl_union_pw_qpolynomial> and
1202 an C<isl_union_pw_qpolynomial_fold>
1203 only have parameters.
1205 Additional parameters can be added to a space using the following function.
1207 #include <isl/space.h>
1208 __isl_give isl_space *isl_space_add_param_id(
1209 __isl_take isl_space *space,
1210 __isl_take isl_id *id);
1212 If a parameter with the given identifier already appears in the space,
1213 then it is not added again.
1215 Conversely, all parameters can be removed from a space
1216 using the following function.
1218 #include <isl/space.h>
1219 __isl_give isl_space *isl_space_drop_all_params(
1220 __isl_take isl_space *space);
1222 The identifiers or names of the individual dimensions of spaces
1223 may be set or read off using the following functions on spaces
1224 or objects that live in spaces.
1225 These functions are mostly useful to obtain the identifiers, positions
1226 or names of the parameters. Identifiers of individual dimensions are
1227 essentially only useful for printing. They are ignored by all other
1228 operations and may not be preserved across those operations.
1230 #include <isl/space.h>
1231 __isl_give isl_space *isl_space_set_dim_id(
1232 __isl_take isl_space *space,
1233 enum isl_dim_type type, unsigned pos,
1234 __isl_take isl_id *id);
1235 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1236 enum isl_dim_type type, unsigned pos);
1237 __isl_give isl_id *isl_space_get_dim_id(
1238 __isl_keep isl_space *space,
1239 enum isl_dim_type type, unsigned pos);
1240 __isl_give isl_space *isl_space_set_dim_name(
1241 __isl_take isl_space *space,
1242 enum isl_dim_type type, unsigned pos,
1243 __isl_keep const char *name);
1244 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1245 enum isl_dim_type type, unsigned pos);
1246 __isl_keep const char *isl_space_get_dim_name(
1247 __isl_keep isl_space *space,
1248 enum isl_dim_type type, unsigned pos);
1250 #include <isl/local_space.h>
1251 __isl_give isl_local_space *isl_local_space_set_dim_id(
1252 __isl_take isl_local_space *ls,
1253 enum isl_dim_type type, unsigned pos,
1254 __isl_take isl_id *id);
1255 isl_bool isl_local_space_has_dim_id(
1256 __isl_keep isl_local_space *ls,
1257 enum isl_dim_type type, unsigned pos);
1258 __isl_give isl_id *isl_local_space_get_dim_id(
1259 __isl_keep isl_local_space *ls,
1260 enum isl_dim_type type, unsigned pos);
1261 __isl_give isl_local_space *isl_local_space_set_dim_name(
1262 __isl_take isl_local_space *ls,
1263 enum isl_dim_type type, unsigned pos, const char *s);
1264 isl_bool isl_local_space_has_dim_name(
1265 __isl_keep isl_local_space *ls,
1266 enum isl_dim_type type, unsigned pos)
1267 const char *isl_local_space_get_dim_name(
1268 __isl_keep isl_local_space *ls,
1269 enum isl_dim_type type, unsigned pos);
1271 #include <isl/constraint.h>
1272 const char *isl_constraint_get_dim_name(
1273 __isl_keep isl_constraint *constraint,
1274 enum isl_dim_type type, unsigned pos);
1276 #include <isl/set.h>
1277 __isl_give isl_id *isl_basic_set_get_dim_id(
1278 __isl_keep isl_basic_set *bset,
1279 enum isl_dim_type type, unsigned pos);
1280 __isl_give isl_set *isl_set_set_dim_id(
1281 __isl_take isl_set *set, enum isl_dim_type type,
1282 unsigned pos, __isl_take isl_id *id);
1283 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1284 enum isl_dim_type type, unsigned pos);
1285 __isl_give isl_id *isl_set_get_dim_id(
1286 __isl_keep isl_set *set, enum isl_dim_type type,
1288 const char *isl_basic_set_get_dim_name(
1289 __isl_keep isl_basic_set *bset,
1290 enum isl_dim_type type, unsigned pos);
1291 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1292 enum isl_dim_type type, unsigned pos);
1293 const char *isl_set_get_dim_name(
1294 __isl_keep isl_set *set,
1295 enum isl_dim_type type, unsigned pos);
1297 #include <isl/map.h>
1298 __isl_give isl_map *isl_map_set_dim_id(
1299 __isl_take isl_map *map, enum isl_dim_type type,
1300 unsigned pos, __isl_take isl_id *id);
1301 isl_bool isl_basic_map_has_dim_id(
1302 __isl_keep isl_basic_map *bmap,
1303 enum isl_dim_type type, unsigned pos);
1304 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1305 enum isl_dim_type type, unsigned pos);
1306 __isl_give isl_id *isl_map_get_dim_id(
1307 __isl_keep isl_map *map, enum isl_dim_type type,
1309 __isl_give isl_id *isl_union_map_get_dim_id(
1310 __isl_keep isl_union_map *umap,
1311 enum isl_dim_type type, unsigned pos);
1312 const char *isl_basic_map_get_dim_name(
1313 __isl_keep isl_basic_map *bmap,
1314 enum isl_dim_type type, unsigned pos);
1315 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1316 enum isl_dim_type type, unsigned pos);
1317 const char *isl_map_get_dim_name(
1318 __isl_keep isl_map *map,
1319 enum isl_dim_type type, unsigned pos);
1321 #include <isl/val.h>
1322 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1323 __isl_take isl_multi_val *mv,
1324 enum isl_dim_type type, unsigned pos,
1325 __isl_take isl_id *id);
1326 __isl_give isl_id *isl_multi_val_get_dim_id(
1327 __isl_keep isl_multi_val *mv,
1328 enum isl_dim_type type, unsigned pos);
1329 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1330 __isl_take isl_multi_val *mv,
1331 enum isl_dim_type type, unsigned pos, const char *s);
1333 #include <isl/aff.h>
1334 __isl_give isl_aff *isl_aff_set_dim_id(
1335 __isl_take isl_aff *aff, enum isl_dim_type type,
1336 unsigned pos, __isl_take isl_id *id);
1337 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1338 __isl_take isl_multi_aff *maff,
1339 enum isl_dim_type type, unsigned pos,
1340 __isl_take isl_id *id);
1341 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1342 __isl_take isl_pw_aff *pma,
1343 enum isl_dim_type type, unsigned pos,
1344 __isl_take isl_id *id);
1345 __isl_give isl_multi_pw_aff *
1346 isl_multi_pw_aff_set_dim_id(
1347 __isl_take isl_multi_pw_aff *mpa,
1348 enum isl_dim_type type, unsigned pos,
1349 __isl_take isl_id *id);
1350 __isl_give isl_multi_union_pw_aff *
1351 isl_multi_union_pw_aff_set_dim_id(
1352 __isl_take isl_multi_union_pw_aff *mupa,
1353 enum isl_dim_type type, unsigned pos,
1354 __isl_take isl_id *id);
1355 __isl_give isl_id *isl_multi_aff_get_dim_id(
1356 __isl_keep isl_multi_aff *ma,
1357 enum isl_dim_type type, unsigned pos);
1358 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1359 enum isl_dim_type type, unsigned pos);
1360 __isl_give isl_id *isl_pw_aff_get_dim_id(
1361 __isl_keep isl_pw_aff *pa,
1362 enum isl_dim_type type, unsigned pos);
1363 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1364 __isl_keep isl_pw_multi_aff *pma,
1365 enum isl_dim_type type, unsigned pos);
1366 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1367 __isl_keep isl_multi_pw_aff *mpa,
1368 enum isl_dim_type type, unsigned pos);
1369 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1370 __isl_keep isl_multi_union_pw_aff *mupa,
1371 enum isl_dim_type type, unsigned pos);
1372 __isl_give isl_aff *isl_aff_set_dim_name(
1373 __isl_take isl_aff *aff, enum isl_dim_type type,
1374 unsigned pos, const char *s);
1375 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1376 __isl_take isl_multi_aff *maff,
1377 enum isl_dim_type type, unsigned pos, const char *s);
1378 __isl_give isl_multi_pw_aff *
1379 isl_multi_pw_aff_set_dim_name(
1380 __isl_take isl_multi_pw_aff *mpa,
1381 enum isl_dim_type type, unsigned pos, const char *s);
1382 __isl_give isl_union_pw_aff *
1383 isl_union_pw_aff_set_dim_name(
1384 __isl_take isl_union_pw_aff *upa,
1385 enum isl_dim_type type, unsigned pos,
1387 __isl_give isl_union_pw_multi_aff *
1388 isl_union_pw_multi_aff_set_dim_name(
1389 __isl_take isl_union_pw_multi_aff *upma,
1390 enum isl_dim_type type, unsigned pos,
1392 __isl_give isl_multi_union_pw_aff *
1393 isl_multi_union_pw_aff_set_dim_name(
1394 __isl_take isl_multi_union_pw_aff *mupa,
1395 enum isl_dim_type type, unsigned pos,
1396 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1397 enum isl_dim_type type, unsigned pos);
1398 const char *isl_pw_aff_get_dim_name(
1399 __isl_keep isl_pw_aff *pa,
1400 enum isl_dim_type type, unsigned pos);
1401 const char *isl_pw_multi_aff_get_dim_name(
1402 __isl_keep isl_pw_multi_aff *pma,
1403 enum isl_dim_type type, unsigned pos);
1405 #include <isl/polynomial.h>
1406 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1407 __isl_take isl_qpolynomial *qp,
1408 enum isl_dim_type type, unsigned pos,
1410 __isl_give isl_pw_qpolynomial *
1411 isl_pw_qpolynomial_set_dim_name(
1412 __isl_take isl_pw_qpolynomial *pwqp,
1413 enum isl_dim_type type, unsigned pos,
1415 __isl_give isl_pw_qpolynomial_fold *
1416 isl_pw_qpolynomial_fold_set_dim_name(
1417 __isl_take isl_pw_qpolynomial_fold *pwf,
1418 enum isl_dim_type type, unsigned pos,
1420 __isl_give isl_union_pw_qpolynomial *
1421 isl_union_pw_qpolynomial_set_dim_name(
1422 __isl_take isl_union_pw_qpolynomial *upwqp,
1423 enum isl_dim_type type, unsigned pos,
1425 __isl_give isl_union_pw_qpolynomial_fold *
1426 isl_union_pw_qpolynomial_fold_set_dim_name(
1427 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1428 enum isl_dim_type type, unsigned pos,
1431 Note that C<isl_space_get_name> returns a pointer to some internal
1432 data structure, so the result can only be used while the
1433 corresponding C<isl_space> is alive.
1434 Also note that every function that operates on two sets or relations
1435 requires that both arguments have the same parameters. This also
1436 means that if one of the arguments has named parameters, then the
1437 other needs to have named parameters too and the names need to match.
1438 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1439 arguments may have different parameters (as long as they are named),
1440 in which case the result will have as parameters the union of the parameters of
1443 Given the identifier or name of a dimension (typically a parameter),
1444 its position can be obtained from the following functions.
1446 #include <isl/space.h>
1447 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1448 enum isl_dim_type type, __isl_keep isl_id *id);
1449 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1450 enum isl_dim_type type, const char *name);
1452 #include <isl/local_space.h>
1453 int isl_local_space_find_dim_by_name(
1454 __isl_keep isl_local_space *ls,
1455 enum isl_dim_type type, const char *name);
1457 #include <isl/val.h>
1458 int isl_multi_val_find_dim_by_id(
1459 __isl_keep isl_multi_val *mv,
1460 enum isl_dim_type type, __isl_keep isl_id *id);
1461 int isl_multi_val_find_dim_by_name(
1462 __isl_keep isl_multi_val *mv,
1463 enum isl_dim_type type, const char *name);
1465 #include <isl/set.h>
1466 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1467 enum isl_dim_type type, __isl_keep isl_id *id);
1468 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1469 enum isl_dim_type type, const char *name);
1471 #include <isl/map.h>
1472 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1473 enum isl_dim_type type, __isl_keep isl_id *id);
1474 int isl_basic_map_find_dim_by_name(
1475 __isl_keep isl_basic_map *bmap,
1476 enum isl_dim_type type, const char *name);
1477 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1478 enum isl_dim_type type, const char *name);
1479 int isl_union_map_find_dim_by_name(
1480 __isl_keep isl_union_map *umap,
1481 enum isl_dim_type type, const char *name);
1483 #include <isl/aff.h>
1484 int isl_multi_aff_find_dim_by_id(
1485 __isl_keep isl_multi_aff *ma,
1486 enum isl_dim_type type, __isl_keep isl_id *id);
1487 int isl_multi_pw_aff_find_dim_by_id(
1488 __isl_keep isl_multi_pw_aff *mpa,
1489 enum isl_dim_type type, __isl_keep isl_id *id);
1490 int isl_multi_union_pw_aff_find_dim_by_id(
1491 __isl_keep isl_union_multi_pw_aff *mupa,
1492 enum isl_dim_type type, __isl_keep isl_id *id);
1493 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1494 enum isl_dim_type type, const char *name);
1495 int isl_multi_aff_find_dim_by_name(
1496 __isl_keep isl_multi_aff *ma,
1497 enum isl_dim_type type, const char *name);
1498 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1499 enum isl_dim_type type, const char *name);
1500 int isl_multi_pw_aff_find_dim_by_name(
1501 __isl_keep isl_multi_pw_aff *mpa,
1502 enum isl_dim_type type, const char *name);
1503 int isl_pw_multi_aff_find_dim_by_name(
1504 __isl_keep isl_pw_multi_aff *pma,
1505 enum isl_dim_type type, const char *name);
1506 int isl_union_pw_aff_find_dim_by_name(
1507 __isl_keep isl_union_pw_aff *upa,
1508 enum isl_dim_type type, const char *name);
1509 int isl_union_pw_multi_aff_find_dim_by_name(
1510 __isl_keep isl_union_pw_multi_aff *upma,
1511 enum isl_dim_type type, const char *name);
1512 int isl_multi_union_pw_aff_find_dim_by_name(
1513 __isl_keep isl_multi_union_pw_aff *mupa,
1514 enum isl_dim_type type, const char *name);
1516 #include <isl/polynomial.h>
1517 int isl_pw_qpolynomial_find_dim_by_name(
1518 __isl_keep isl_pw_qpolynomial *pwqp,
1519 enum isl_dim_type type, const char *name);
1520 int isl_pw_qpolynomial_fold_find_dim_by_name(
1521 __isl_keep isl_pw_qpolynomial_fold *pwf,
1522 enum isl_dim_type type, const char *name);
1523 int isl_union_pw_qpolynomial_find_dim_by_name(
1524 __isl_keep isl_union_pw_qpolynomial *upwqp,
1525 enum isl_dim_type type, const char *name);
1526 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1527 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1528 enum isl_dim_type type, const char *name);
1530 The identifiers or names of entire spaces may be set or read off
1531 using the following functions.
1533 #include <isl/space.h>
1534 __isl_give isl_space *isl_space_set_tuple_id(
1535 __isl_take isl_space *space,
1536 enum isl_dim_type type, __isl_take isl_id *id);
1537 __isl_give isl_space *isl_space_reset_tuple_id(
1538 __isl_take isl_space *space, enum isl_dim_type type);
1539 isl_bool isl_space_has_tuple_id(
1540 __isl_keep isl_space *space,
1541 enum isl_dim_type type);
1542 __isl_give isl_id *isl_space_get_tuple_id(
1543 __isl_keep isl_space *space, enum isl_dim_type type);
1544 __isl_give isl_space *isl_space_set_tuple_name(
1545 __isl_take isl_space *space,
1546 enum isl_dim_type type, const char *s);
1547 isl_bool isl_space_has_tuple_name(
1548 __isl_keep isl_space *space,
1549 enum isl_dim_type type);
1550 __isl_keep const char *isl_space_get_tuple_name(
1551 __isl_keep isl_space *space,
1552 enum isl_dim_type type);
1554 #include <isl/local_space.h>
1555 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1556 __isl_take isl_local_space *ls,
1557 enum isl_dim_type type, __isl_take isl_id *id);
1559 #include <isl/set.h>
1560 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1561 __isl_take isl_basic_set *bset,
1562 __isl_take isl_id *id);
1563 __isl_give isl_set *isl_set_set_tuple_id(
1564 __isl_take isl_set *set, __isl_take isl_id *id);
1565 __isl_give isl_set *isl_set_reset_tuple_id(
1566 __isl_take isl_set *set);
1567 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1568 __isl_give isl_id *isl_set_get_tuple_id(
1569 __isl_keep isl_set *set);
1570 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1571 __isl_take isl_basic_set *set, const char *s);
1572 __isl_give isl_set *isl_set_set_tuple_name(
1573 __isl_take isl_set *set, const char *s);
1574 const char *isl_basic_set_get_tuple_name(
1575 __isl_keep isl_basic_set *bset);
1576 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1577 const char *isl_set_get_tuple_name(
1578 __isl_keep isl_set *set);
1580 #include <isl/map.h>
1581 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1582 __isl_take isl_basic_map *bmap,
1583 enum isl_dim_type type, __isl_take isl_id *id);
1584 __isl_give isl_map *isl_map_set_tuple_id(
1585 __isl_take isl_map *map, enum isl_dim_type type,
1586 __isl_take isl_id *id);
1587 __isl_give isl_map *isl_map_reset_tuple_id(
1588 __isl_take isl_map *map, enum isl_dim_type type);
1589 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1590 enum isl_dim_type type);
1591 __isl_give isl_id *isl_map_get_tuple_id(
1592 __isl_keep isl_map *map, enum isl_dim_type type);
1593 __isl_give isl_map *isl_map_set_tuple_name(
1594 __isl_take isl_map *map,
1595 enum isl_dim_type type, const char *s);
1596 const char *isl_basic_map_get_tuple_name(
1597 __isl_keep isl_basic_map *bmap,
1598 enum isl_dim_type type);
1599 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1600 __isl_take isl_basic_map *bmap,
1601 enum isl_dim_type type, const char *s);
1602 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1603 enum isl_dim_type type);
1604 const char *isl_map_get_tuple_name(
1605 __isl_keep isl_map *map,
1606 enum isl_dim_type type);
1608 #include <isl/val.h>
1609 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1610 __isl_take isl_multi_val *mv,
1611 enum isl_dim_type type, __isl_take isl_id *id);
1612 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1613 __isl_take isl_multi_val *mv,
1614 enum isl_dim_type type);
1615 isl_bool isl_multi_val_has_tuple_id(
1616 __isl_keep isl_multi_val *mv,
1617 enum isl_dim_type type);
1618 __isl_give isl_id *isl_multi_val_get_tuple_id(
1619 __isl_keep isl_multi_val *mv,
1620 enum isl_dim_type type);
1621 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1622 __isl_take isl_multi_val *mv,
1623 enum isl_dim_type type, const char *s);
1624 const char *isl_multi_val_get_tuple_name(
1625 __isl_keep isl_multi_val *mv,
1626 enum isl_dim_type type);
1628 #include <isl/aff.h>
1629 __isl_give isl_aff *isl_aff_set_tuple_id(
1630 __isl_take isl_aff *aff,
1631 enum isl_dim_type type, __isl_take isl_id *id);
1632 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1633 __isl_take isl_multi_aff *maff,
1634 enum isl_dim_type type, __isl_take isl_id *id);
1635 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1636 __isl_take isl_pw_aff *pwaff,
1637 enum isl_dim_type type, __isl_take isl_id *id);
1638 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1639 __isl_take isl_pw_multi_aff *pma,
1640 enum isl_dim_type type, __isl_take isl_id *id);
1641 __isl_give isl_multi_union_pw_aff *
1642 isl_multi_union_pw_aff_set_tuple_id(
1643 __isl_take isl_multi_union_pw_aff *mupa,
1644 enum isl_dim_type type, __isl_take isl_id *id);
1645 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1646 __isl_take isl_multi_aff *ma,
1647 enum isl_dim_type type);
1648 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1649 __isl_take isl_pw_aff *pa,
1650 enum isl_dim_type type);
1651 __isl_give isl_multi_pw_aff *
1652 isl_multi_pw_aff_reset_tuple_id(
1653 __isl_take isl_multi_pw_aff *mpa,
1654 enum isl_dim_type type);
1655 __isl_give isl_pw_multi_aff *
1656 isl_pw_multi_aff_reset_tuple_id(
1657 __isl_take isl_pw_multi_aff *pma,
1658 enum isl_dim_type type);
1659 __isl_give isl_multi_union_pw_aff *
1660 isl_multi_union_pw_aff_reset_tuple_id(
1661 __isl_take isl_multi_union_pw_aff *mupa,
1662 enum isl_dim_type type);
1663 isl_bool isl_multi_aff_has_tuple_id(
1664 __isl_keep isl_multi_aff *ma,
1665 enum isl_dim_type type);
1666 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1667 __isl_keep isl_multi_aff *ma,
1668 enum isl_dim_type type);
1669 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1670 enum isl_dim_type type);
1671 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1672 __isl_keep isl_pw_aff *pa,
1673 enum isl_dim_type type);
1674 isl_bool isl_pw_multi_aff_has_tuple_id(
1675 __isl_keep isl_pw_multi_aff *pma,
1676 enum isl_dim_type type);
1677 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1678 __isl_keep isl_pw_multi_aff *pma,
1679 enum isl_dim_type type);
1680 isl_bool isl_multi_pw_aff_has_tuple_id(
1681 __isl_keep isl_multi_pw_aff *mpa,
1682 enum isl_dim_type type);
1683 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1684 __isl_keep isl_multi_pw_aff *mpa,
1685 enum isl_dim_type type);
1686 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1687 __isl_keep isl_multi_union_pw_aff *mupa,
1688 enum isl_dim_type type);
1689 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1690 __isl_keep isl_multi_union_pw_aff *mupa,
1691 enum isl_dim_type type);
1692 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1693 __isl_take isl_multi_aff *maff,
1694 enum isl_dim_type type, const char *s);
1695 __isl_give isl_multi_pw_aff *
1696 isl_multi_pw_aff_set_tuple_name(
1697 __isl_take isl_multi_pw_aff *mpa,
1698 enum isl_dim_type type, const char *s);
1699 __isl_give isl_multi_union_pw_aff *
1700 isl_multi_union_pw_aff_set_tuple_name(
1701 __isl_take isl_multi_union_pw_aff *mupa,
1702 enum isl_dim_type type, const char *s);
1703 const char *isl_multi_aff_get_tuple_name(
1704 __isl_keep isl_multi_aff *multi,
1705 enum isl_dim_type type);
1706 isl_bool isl_pw_multi_aff_has_tuple_name(
1707 __isl_keep isl_pw_multi_aff *pma,
1708 enum isl_dim_type type);
1709 const char *isl_pw_multi_aff_get_tuple_name(
1710 __isl_keep isl_pw_multi_aff *pma,
1711 enum isl_dim_type type);
1712 const char *isl_multi_union_pw_aff_get_tuple_name(
1713 __isl_keep isl_multi_union_pw_aff *mupa,
1714 enum isl_dim_type type);
1716 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1717 or C<isl_dim_set>. As with C<isl_space_get_name>,
1718 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1720 Binary operations require the corresponding spaces of their arguments
1721 to have the same name.
1723 To keep the names of all parameters and tuples, but reset the user pointers
1724 of all the corresponding identifiers, use the following function.
1726 #include <isl/space.h>
1727 __isl_give isl_space *isl_space_reset_user(
1728 __isl_take isl_space *space);
1730 #include <isl/set.h>
1731 __isl_give isl_set *isl_set_reset_user(
1732 __isl_take isl_set *set);
1734 #include <isl/map.h>
1735 __isl_give isl_map *isl_map_reset_user(
1736 __isl_take isl_map *map);
1738 #include <isl/union_set.h>
1739 __isl_give isl_union_set *isl_union_set_reset_user(
1740 __isl_take isl_union_set *uset);
1742 #include <isl/union_map.h>
1743 __isl_give isl_union_map *isl_union_map_reset_user(
1744 __isl_take isl_union_map *umap);
1746 #include <isl/val.h>
1747 __isl_give isl_multi_val *isl_multi_val_reset_user(
1748 __isl_take isl_multi_val *mv);
1750 #include <isl/aff.h>
1751 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1752 __isl_take isl_multi_aff *ma);
1753 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1754 __isl_take isl_pw_aff *pa);
1755 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1756 __isl_take isl_multi_pw_aff *mpa);
1757 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1758 __isl_take isl_pw_multi_aff *pma);
1759 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1760 __isl_take isl_union_pw_aff *upa);
1761 __isl_give isl_multi_union_pw_aff *
1762 isl_multi_union_pw_aff_reset_user(
1763 __isl_take isl_multi_union_pw_aff *mupa);
1764 __isl_give isl_union_pw_multi_aff *
1765 isl_union_pw_multi_aff_reset_user(
1766 __isl_take isl_union_pw_multi_aff *upma);
1768 #include <isl/polynomial.h>
1769 __isl_give isl_pw_qpolynomial *
1770 isl_pw_qpolynomial_reset_user(
1771 __isl_take isl_pw_qpolynomial *pwqp);
1772 __isl_give isl_union_pw_qpolynomial *
1773 isl_union_pw_qpolynomial_reset_user(
1774 __isl_take isl_union_pw_qpolynomial *upwqp);
1775 __isl_give isl_pw_qpolynomial_fold *
1776 isl_pw_qpolynomial_fold_reset_user(
1777 __isl_take isl_pw_qpolynomial_fold *pwf);
1778 __isl_give isl_union_pw_qpolynomial_fold *
1779 isl_union_pw_qpolynomial_fold_reset_user(
1780 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1782 Spaces can be nested. In particular, the domain of a set or
1783 the domain or range of a relation can be a nested relation.
1784 This process is also called I<wrapping>.
1785 The functions for detecting, constructing and deconstructing
1786 such nested spaces can be found in the wrapping properties
1787 of L</"Unary Properties">, the wrapping operations
1788 of L</"Unary Operations"> and the Cartesian product operations
1789 of L</"Basic Operations">.
1791 Spaces can be created from other spaces
1792 using the functions described in L</"Unary Operations">
1793 and L</"Binary Operations">.
1797 A local space is essentially a space with
1798 zero or more existentially quantified variables.
1799 The local space of various objects can be obtained
1800 using the following functions.
1802 #include <isl/constraint.h>
1803 __isl_give isl_local_space *isl_constraint_get_local_space(
1804 __isl_keep isl_constraint *constraint);
1806 #include <isl/set.h>
1807 __isl_give isl_local_space *isl_basic_set_get_local_space(
1808 __isl_keep isl_basic_set *bset);
1810 #include <isl/map.h>
1811 __isl_give isl_local_space *isl_basic_map_get_local_space(
1812 __isl_keep isl_basic_map *bmap);
1814 #include <isl/aff.h>
1815 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1816 __isl_keep isl_aff *aff);
1817 __isl_give isl_local_space *isl_aff_get_local_space(
1818 __isl_keep isl_aff *aff);
1820 A new local space can be created from a space using
1822 #include <isl/local_space.h>
1823 __isl_give isl_local_space *isl_local_space_from_space(
1824 __isl_take isl_space *space);
1826 They can be inspected, modified, copied and freed using the following functions.
1828 #include <isl/local_space.h>
1829 isl_bool isl_local_space_is_params(
1830 __isl_keep isl_local_space *ls);
1831 isl_bool isl_local_space_is_set(
1832 __isl_keep isl_local_space *ls);
1833 __isl_give isl_space *isl_local_space_get_space(
1834 __isl_keep isl_local_space *ls);
1835 __isl_give isl_aff *isl_local_space_get_div(
1836 __isl_keep isl_local_space *ls, int pos);
1837 __isl_give isl_local_space *isl_local_space_copy(
1838 __isl_keep isl_local_space *ls);
1839 __isl_null isl_local_space *isl_local_space_free(
1840 __isl_take isl_local_space *ls);
1842 Note that C<isl_local_space_get_div> can only be used on local spaces
1845 Two local spaces can be compared using
1847 isl_bool isl_local_space_is_equal(
1848 __isl_keep isl_local_space *ls1,
1849 __isl_keep isl_local_space *ls2);
1851 Local spaces can be created from other local spaces
1852 using the functions described in L</"Unary Operations">
1853 and L</"Binary Operations">.
1855 =head2 Creating New Sets and Relations
1857 C<isl> has functions for creating some standard sets and relations.
1861 =item * Empty sets and relations
1863 __isl_give isl_basic_set *isl_basic_set_empty(
1864 __isl_take isl_space *space);
1865 __isl_give isl_basic_map *isl_basic_map_empty(
1866 __isl_take isl_space *space);
1867 __isl_give isl_set *isl_set_empty(
1868 __isl_take isl_space *space);
1869 __isl_give isl_map *isl_map_empty(
1870 __isl_take isl_space *space);
1871 __isl_give isl_union_set *isl_union_set_empty(
1872 __isl_take isl_space *space);
1873 __isl_give isl_union_map *isl_union_map_empty(
1874 __isl_take isl_space *space);
1876 For C<isl_union_set>s and C<isl_union_map>s, the space
1877 is only used to specify the parameters.
1879 =item * Universe sets and relations
1881 __isl_give isl_basic_set *isl_basic_set_universe(
1882 __isl_take isl_space *space);
1883 __isl_give isl_basic_map *isl_basic_map_universe(
1884 __isl_take isl_space *space);
1885 __isl_give isl_set *isl_set_universe(
1886 __isl_take isl_space *space);
1887 __isl_give isl_map *isl_map_universe(
1888 __isl_take isl_space *space);
1889 __isl_give isl_union_set *isl_union_set_universe(
1890 __isl_take isl_union_set *uset);
1891 __isl_give isl_union_map *isl_union_map_universe(
1892 __isl_take isl_union_map *umap);
1894 The sets and relations constructed by the functions above
1895 contain all integer values, while those constructed by the
1896 functions below only contain non-negative values.
1898 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1899 __isl_take isl_space *space);
1900 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1901 __isl_take isl_space *space);
1902 __isl_give isl_set *isl_set_nat_universe(
1903 __isl_take isl_space *space);
1904 __isl_give isl_map *isl_map_nat_universe(
1905 __isl_take isl_space *space);
1907 =item * Identity relations
1909 __isl_give isl_basic_map *isl_basic_map_identity(
1910 __isl_take isl_space *space);
1911 __isl_give isl_map *isl_map_identity(
1912 __isl_take isl_space *space);
1914 The number of input and output dimensions in C<space> needs
1917 =item * Lexicographic order
1919 __isl_give isl_map *isl_map_lex_lt(
1920 __isl_take isl_space *set_space);
1921 __isl_give isl_map *isl_map_lex_le(
1922 __isl_take isl_space *set_space);
1923 __isl_give isl_map *isl_map_lex_gt(
1924 __isl_take isl_space *set_space);
1925 __isl_give isl_map *isl_map_lex_ge(
1926 __isl_take isl_space *set_space);
1927 __isl_give isl_map *isl_map_lex_lt_first(
1928 __isl_take isl_space *space, unsigned n);
1929 __isl_give isl_map *isl_map_lex_le_first(
1930 __isl_take isl_space *space, unsigned n);
1931 __isl_give isl_map *isl_map_lex_gt_first(
1932 __isl_take isl_space *space, unsigned n);
1933 __isl_give isl_map *isl_map_lex_ge_first(
1934 __isl_take isl_space *space, unsigned n);
1936 The first four functions take a space for a B<set>
1937 and return relations that express that the elements in the domain
1938 are lexicographically less
1939 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1940 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1941 than the elements in the range.
1942 The last four functions take a space for a map
1943 and return relations that express that the first C<n> dimensions
1944 in the domain are lexicographically less
1945 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1946 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1947 than the first C<n> dimensions in the range.
1951 A basic set or relation can be converted to a set or relation
1952 using the following functions.
1954 __isl_give isl_set *isl_set_from_basic_set(
1955 __isl_take isl_basic_set *bset);
1956 __isl_give isl_map *isl_map_from_basic_map(
1957 __isl_take isl_basic_map *bmap);
1959 Sets and relations can be converted to union sets and relations
1960 using the following functions.
1962 __isl_give isl_union_set *isl_union_set_from_basic_set(
1963 __isl_take isl_basic_set *bset);
1964 __isl_give isl_union_map *isl_union_map_from_basic_map(
1965 __isl_take isl_basic_map *bmap);
1966 __isl_give isl_union_set *isl_union_set_from_set(
1967 __isl_take isl_set *set);
1968 __isl_give isl_union_map *isl_union_map_from_map(
1969 __isl_take isl_map *map);
1971 The inverse conversions below can only be used if the input
1972 union set or relation is known to contain elements in exactly one
1975 __isl_give isl_set *isl_set_from_union_set(
1976 __isl_take isl_union_set *uset);
1977 __isl_give isl_map *isl_map_from_union_map(
1978 __isl_take isl_union_map *umap);
1980 Sets and relations can be copied and freed again using the following
1983 __isl_give isl_basic_set *isl_basic_set_copy(
1984 __isl_keep isl_basic_set *bset);
1985 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1986 __isl_give isl_union_set *isl_union_set_copy(
1987 __isl_keep isl_union_set *uset);
1988 __isl_give isl_basic_map *isl_basic_map_copy(
1989 __isl_keep isl_basic_map *bmap);
1990 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1991 __isl_give isl_union_map *isl_union_map_copy(
1992 __isl_keep isl_union_map *umap);
1993 __isl_null isl_basic_set *isl_basic_set_free(
1994 __isl_take isl_basic_set *bset);
1995 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1996 __isl_null isl_union_set *isl_union_set_free(
1997 __isl_take isl_union_set *uset);
1998 __isl_null isl_basic_map *isl_basic_map_free(
1999 __isl_take isl_basic_map *bmap);
2000 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
2001 __isl_null isl_union_map *isl_union_map_free(
2002 __isl_take isl_union_map *umap);
2004 Other sets and relations can be constructed by starting
2005 from a universe set or relation, adding equality and/or
2006 inequality constraints and then projecting out the
2007 existentially quantified variables, if any.
2008 Constraints can be constructed, manipulated and
2009 added to (or removed from) (basic) sets and relations
2010 using the following functions.
2012 #include <isl/constraint.h>
2013 __isl_give isl_constraint *isl_constraint_alloc_equality(
2014 __isl_take isl_local_space *ls);
2015 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2016 __isl_take isl_local_space *ls);
2017 __isl_give isl_constraint *isl_constraint_set_constant_si(
2018 __isl_take isl_constraint *constraint, int v);
2019 __isl_give isl_constraint *isl_constraint_set_constant_val(
2020 __isl_take isl_constraint *constraint,
2021 __isl_take isl_val *v);
2022 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2023 __isl_take isl_constraint *constraint,
2024 enum isl_dim_type type, int pos, int v);
2025 __isl_give isl_constraint *
2026 isl_constraint_set_coefficient_val(
2027 __isl_take isl_constraint *constraint,
2028 enum isl_dim_type type, int pos,
2029 __isl_take isl_val *v);
2030 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2031 __isl_take isl_basic_map *bmap,
2032 __isl_take isl_constraint *constraint);
2033 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2034 __isl_take isl_basic_set *bset,
2035 __isl_take isl_constraint *constraint);
2036 __isl_give isl_map *isl_map_add_constraint(
2037 __isl_take isl_map *map,
2038 __isl_take isl_constraint *constraint);
2039 __isl_give isl_set *isl_set_add_constraint(
2040 __isl_take isl_set *set,
2041 __isl_take isl_constraint *constraint);
2043 For example, to create a set containing the even integers
2044 between 10 and 42, you would use the following code.
2047 isl_local_space *ls;
2049 isl_basic_set *bset;
2051 space = isl_space_set_alloc(ctx, 0, 2);
2052 bset = isl_basic_set_universe(isl_space_copy(space));
2053 ls = isl_local_space_from_space(space);
2055 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2056 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2057 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2058 bset = isl_basic_set_add_constraint(bset, c);
2060 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2061 c = isl_constraint_set_constant_si(c, -10);
2062 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2063 bset = isl_basic_set_add_constraint(bset, c);
2065 c = isl_constraint_alloc_inequality(ls);
2066 c = isl_constraint_set_constant_si(c, 42);
2067 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2068 bset = isl_basic_set_add_constraint(bset, c);
2070 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2074 isl_basic_set *bset;
2075 bset = isl_basic_set_read_from_str(ctx,
2076 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2078 A basic set or relation can also be constructed from two matrices
2079 describing the equalities and the inequalities.
2081 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2082 __isl_take isl_space *space,
2083 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2084 enum isl_dim_type c1,
2085 enum isl_dim_type c2, enum isl_dim_type c3,
2086 enum isl_dim_type c4);
2087 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2088 __isl_take isl_space *space,
2089 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2090 enum isl_dim_type c1,
2091 enum isl_dim_type c2, enum isl_dim_type c3,
2092 enum isl_dim_type c4, enum isl_dim_type c5);
2094 The C<isl_dim_type> arguments indicate the order in which
2095 different kinds of variables appear in the input matrices
2096 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2097 C<isl_dim_set> and C<isl_dim_div> for sets and
2098 of C<isl_dim_cst>, C<isl_dim_param>,
2099 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2101 A (basic or union) set or relation can also be constructed from a
2102 (union) (piecewise) (multiple) affine expression
2103 or a list of affine expressions
2104 (See L</"Functions">), provided these affine expressions do not
2107 #include <isl/set.h>
2108 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2109 __isl_take isl_multi_aff *ma);
2110 __isl_give isl_set *isl_set_from_multi_aff(
2111 __isl_take isl_multi_aff *ma);
2113 #include <isl/map.h>
2114 __isl_give isl_basic_map *isl_basic_map_from_aff(
2115 __isl_take isl_aff *aff);
2116 __isl_give isl_map *isl_map_from_aff(
2117 __isl_take isl_aff *aff);
2118 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2119 __isl_take isl_space *domain_space,
2120 __isl_take isl_aff_list *list);
2121 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2122 __isl_take isl_multi_aff *maff)
2123 __isl_give isl_map *isl_map_from_multi_aff(
2124 __isl_take isl_multi_aff *maff)
2126 #include <isl/aff.h>
2127 __isl_give isl_set *isl_set_from_pw_aff(
2128 __isl_take isl_pw_aff *pwaff);
2129 __isl_give isl_map *isl_map_from_pw_aff(
2130 __isl_take isl_pw_aff *pwaff);
2131 __isl_give isl_set *isl_set_from_pw_multi_aff(
2132 __isl_take isl_pw_multi_aff *pma);
2133 __isl_give isl_map *isl_map_from_pw_multi_aff(
2134 __isl_take isl_pw_multi_aff *pma);
2135 __isl_give isl_set *isl_set_from_multi_pw_aff(
2136 __isl_take isl_multi_pw_aff *mpa);
2137 __isl_give isl_map *isl_map_from_multi_pw_aff(
2138 __isl_take isl_multi_pw_aff *mpa);
2139 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2140 __isl_take isl_union_pw_aff *upa);
2141 __isl_give isl_union_map *
2142 isl_union_map_from_union_pw_multi_aff(
2143 __isl_take isl_union_pw_multi_aff *upma);
2144 __isl_give isl_union_map *
2145 isl_union_map_from_multi_union_pw_aff(
2146 __isl_take isl_multi_union_pw_aff *mupa);
2148 The C<domain_space> argument describes the domain of the resulting
2149 basic relation. It is required because the C<list> may consist
2150 of zero affine expressions.
2151 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2152 is not allowed to be zero-dimensional. The domain of the result
2153 is the shared domain of the union piecewise affine elements.
2155 =head2 Inspecting Sets and Relations
2157 Usually, the user should not have to care about the actual constraints
2158 of the sets and maps, but should instead apply the abstract operations
2159 explained in the following sections.
2160 Occasionally, however, it may be required to inspect the individual
2161 coefficients of the constraints. This section explains how to do so.
2162 In these cases, it may also be useful to have C<isl> compute
2163 an explicit representation of the existentially quantified variables.
2165 __isl_give isl_set *isl_set_compute_divs(
2166 __isl_take isl_set *set);
2167 __isl_give isl_map *isl_map_compute_divs(
2168 __isl_take isl_map *map);
2169 __isl_give isl_union_set *isl_union_set_compute_divs(
2170 __isl_take isl_union_set *uset);
2171 __isl_give isl_union_map *isl_union_map_compute_divs(
2172 __isl_take isl_union_map *umap);
2174 This explicit representation defines the existentially quantified
2175 variables as integer divisions of the other variables, possibly
2176 including earlier existentially quantified variables.
2177 An explicitly represented existentially quantified variable therefore
2178 has a unique value when the values of the other variables are known.
2180 Alternatively, the existentially quantified variables can be removed
2181 using the following functions, which compute an overapproximation.
2183 #include <isl/set.h>
2184 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2185 __isl_take isl_basic_set *bset);
2186 __isl_give isl_set *isl_set_remove_divs(
2187 __isl_take isl_set *set);
2189 #include <isl/map.h>
2190 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2191 __isl_take isl_basic_map *bmap);
2192 __isl_give isl_map *isl_map_remove_divs(
2193 __isl_take isl_map *map);
2195 #include <isl/union_set.h>
2196 __isl_give isl_union_set *isl_union_set_remove_divs(
2197 __isl_take isl_union_set *bset);
2199 #include <isl/union_map.h>
2200 __isl_give isl_union_map *isl_union_map_remove_divs(
2201 __isl_take isl_union_map *bmap);
2203 It is also possible to only remove those divs that are defined
2204 in terms of a given range of dimensions or only those for which
2205 no explicit representation is known.
2207 __isl_give isl_basic_set *
2208 isl_basic_set_remove_divs_involving_dims(
2209 __isl_take isl_basic_set *bset,
2210 enum isl_dim_type type,
2211 unsigned first, unsigned n);
2212 __isl_give isl_basic_map *
2213 isl_basic_map_remove_divs_involving_dims(
2214 __isl_take isl_basic_map *bmap,
2215 enum isl_dim_type type,
2216 unsigned first, unsigned n);
2217 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2218 __isl_take isl_set *set, enum isl_dim_type type,
2219 unsigned first, unsigned n);
2220 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2221 __isl_take isl_map *map, enum isl_dim_type type,
2222 unsigned first, unsigned n);
2224 __isl_give isl_basic_set *
2225 isl_basic_set_remove_unknown_divs(
2226 __isl_take isl_basic_set *bset);
2227 __isl_give isl_set *isl_set_remove_unknown_divs(
2228 __isl_take isl_set *set);
2229 __isl_give isl_map *isl_map_remove_unknown_divs(
2230 __isl_take isl_map *map);
2232 To iterate over all the sets or maps in a union set or map, use
2234 #include <isl/union_set.h>
2235 isl_stat isl_union_set_foreach_set(
2236 __isl_keep isl_union_set *uset,
2237 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2239 isl_bool isl_union_set_every_set(
2240 __isl_keep isl_union_set *uset,
2241 isl_bool (*test)(__isl_keep isl_set *set,
2245 #include <isl/union_map.h>
2246 isl_stat isl_union_map_foreach_map(
2247 __isl_keep isl_union_map *umap,
2248 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2250 isl_bool isl_union_map_every_map(
2251 __isl_keep isl_union_map *umap,
2252 isl_bool (*test)(__isl_keep isl_map *map,
2256 These functions call the callback function once for each
2257 (pair of) space(s) for which there are elements in the input.
2258 The argument to the callback contains all elements in the input
2259 with that (pair of) space(s).
2260 The C<isl_union_set_every_set> and
2261 C<isl_union_map_every_map> variants check whether each
2262 call to the callback returns true and stops checking as soon as one
2263 of these calls returns false.
2265 The number of sets or maps in a union set or map can be obtained
2268 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2269 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2271 To extract the set or map in a given space from a union, use
2273 __isl_give isl_set *isl_union_set_extract_set(
2274 __isl_keep isl_union_set *uset,
2275 __isl_take isl_space *space);
2276 __isl_give isl_map *isl_union_map_extract_map(
2277 __isl_keep isl_union_map *umap,
2278 __isl_take isl_space *space);
2280 To iterate over all the basic sets or maps in a set or map, use
2282 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2283 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2286 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2287 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2291 The callback function C<fn> should return C<isl_stat_ok> if successful and
2292 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2293 occurs, the above functions will return C<isl_stat_error>.
2295 It should be noted that C<isl> does not guarantee that
2296 the basic sets or maps passed to C<fn> are disjoint.
2297 If this is required, then the user should call one of
2298 the following functions first.
2300 __isl_give isl_set *isl_set_make_disjoint(
2301 __isl_take isl_set *set);
2302 __isl_give isl_map *isl_map_make_disjoint(
2303 __isl_take isl_map *map);
2305 The number of basic sets in a set can be obtained
2306 or the number of basic maps in a map can be obtained
2309 #include <isl/set.h>
2310 int isl_set_n_basic_set(__isl_keep isl_set *set);
2312 #include <isl/map.h>
2313 int isl_map_n_basic_map(__isl_keep isl_map *map);
2315 It is also possible to obtain a list of (basic) sets from a set
2316 or union set, a list of basic maps from a map and a list of maps from a union
2319 #include <isl/set.h>
2320 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2321 __isl_keep isl_set *set);
2323 #include <isl/union_set.h>
2324 __isl_give isl_basic_set_list *
2325 isl_union_set_get_basic_set_list(
2326 __isl_keep isl_union_set *uset);
2327 __isl_give isl_set_list *isl_union_set_get_set_list(
2328 __isl_keep isl_union_set *uset);
2330 #include <isl/map.h>
2331 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2332 __isl_keep isl_map *map);
2334 #include <isl/union_map.h>
2335 __isl_give isl_map_list *isl_union_map_get_map_list(
2336 __isl_keep isl_union_map *umap);
2338 The returned list can be manipulated using the functions in L<"Lists">.
2340 To iterate over the constraints of a basic set or map, use
2342 #include <isl/constraint.h>
2344 int isl_basic_set_n_constraint(
2345 __isl_keep isl_basic_set *bset);
2346 isl_stat isl_basic_set_foreach_constraint(
2347 __isl_keep isl_basic_set *bset,
2348 isl_stat (*fn)(__isl_take isl_constraint *c,
2351 int isl_basic_map_n_constraint(
2352 __isl_keep isl_basic_map *bmap);
2353 isl_stat isl_basic_map_foreach_constraint(
2354 __isl_keep isl_basic_map *bmap,
2355 isl_stat (*fn)(__isl_take isl_constraint *c,
2358 __isl_null isl_constraint *isl_constraint_free(
2359 __isl_take isl_constraint *c);
2361 Again, the callback function C<fn> should return C<isl_stat_ok>
2363 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2364 occurs, the above functions will return C<isl_stat_error>.
2365 The constraint C<c> represents either an equality or an inequality.
2366 Use the following function to find out whether a constraint
2367 represents an equality. If not, it represents an inequality.
2369 isl_bool isl_constraint_is_equality(
2370 __isl_keep isl_constraint *constraint);
2372 It is also possible to obtain a list of constraints from a basic
2375 #include <isl/constraint.h>
2376 __isl_give isl_constraint_list *
2377 isl_basic_map_get_constraint_list(
2378 __isl_keep isl_basic_map *bmap);
2379 __isl_give isl_constraint_list *
2380 isl_basic_set_get_constraint_list(
2381 __isl_keep isl_basic_set *bset);
2383 These functions require that all existentially quantified variables
2384 have an explicit representation.
2385 The returned list can be manipulated using the functions in L<"Lists">.
2387 The coefficients of the constraints can be inspected using
2388 the following functions.
2390 isl_bool isl_constraint_is_lower_bound(
2391 __isl_keep isl_constraint *constraint,
2392 enum isl_dim_type type, unsigned pos);
2393 isl_bool isl_constraint_is_upper_bound(
2394 __isl_keep isl_constraint *constraint,
2395 enum isl_dim_type type, unsigned pos);
2396 __isl_give isl_val *isl_constraint_get_constant_val(
2397 __isl_keep isl_constraint *constraint);
2398 __isl_give isl_val *isl_constraint_get_coefficient_val(
2399 __isl_keep isl_constraint *constraint,
2400 enum isl_dim_type type, int pos);
2402 The explicit representations of the existentially quantified
2403 variables can be inspected using the following function.
2404 Note that the user is only allowed to use this function
2405 if the inspected set or map is the result of a call
2406 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2407 The existentially quantified variable is equal to the floor
2408 of the returned affine expression. The affine expression
2409 itself can be inspected using the functions in
2412 __isl_give isl_aff *isl_constraint_get_div(
2413 __isl_keep isl_constraint *constraint, int pos);
2415 To obtain the constraints of a basic set or map in matrix
2416 form, use the following functions.
2418 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2419 __isl_keep isl_basic_set *bset,
2420 enum isl_dim_type c1, enum isl_dim_type c2,
2421 enum isl_dim_type c3, enum isl_dim_type c4);
2422 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2423 __isl_keep isl_basic_set *bset,
2424 enum isl_dim_type c1, enum isl_dim_type c2,
2425 enum isl_dim_type c3, enum isl_dim_type c4);
2426 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2427 __isl_keep isl_basic_map *bmap,
2428 enum isl_dim_type c1,
2429 enum isl_dim_type c2, enum isl_dim_type c3,
2430 enum isl_dim_type c4, enum isl_dim_type c5);
2431 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2432 __isl_keep isl_basic_map *bmap,
2433 enum isl_dim_type c1,
2434 enum isl_dim_type c2, enum isl_dim_type c3,
2435 enum isl_dim_type c4, enum isl_dim_type c5);
2437 The C<isl_dim_type> arguments dictate the order in which
2438 different kinds of variables appear in the resulting matrix.
2439 For set inputs, they should be a permutation of
2440 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2441 For map inputs, they should be a permutation of
2442 C<isl_dim_cst>, C<isl_dim_param>,
2443 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2447 Points are elements of a set. They can be used to construct
2448 simple sets (boxes) or they can be used to represent the
2449 individual elements of a set.
2450 The zero point (the origin) can be created using
2452 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2454 The coordinates of a point can be inspected, set and changed
2457 __isl_give isl_val *isl_point_get_coordinate_val(
2458 __isl_keep isl_point *pnt,
2459 enum isl_dim_type type, int pos);
2460 __isl_give isl_point *isl_point_set_coordinate_val(
2461 __isl_take isl_point *pnt,
2462 enum isl_dim_type type, int pos,
2463 __isl_take isl_val *v);
2465 __isl_give isl_point *isl_point_add_ui(
2466 __isl_take isl_point *pnt,
2467 enum isl_dim_type type, int pos, unsigned val);
2468 __isl_give isl_point *isl_point_sub_ui(
2469 __isl_take isl_point *pnt,
2470 enum isl_dim_type type, int pos, unsigned val);
2472 Points can be copied or freed using
2474 __isl_give isl_point *isl_point_copy(
2475 __isl_keep isl_point *pnt);
2476 __isl_null isl_point *isl_point_free(
2477 __isl_take isl_point *pnt);
2479 A singleton set can be created from a point using
2481 __isl_give isl_basic_set *isl_basic_set_from_point(
2482 __isl_take isl_point *pnt);
2483 __isl_give isl_set *isl_set_from_point(
2484 __isl_take isl_point *pnt);
2485 __isl_give isl_union_set *isl_union_set_from_point(
2486 __isl_take isl_point *pnt);
2488 and a box can be created from two opposite extremal points using
2490 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2491 __isl_take isl_point *pnt1,
2492 __isl_take isl_point *pnt2);
2493 __isl_give isl_set *isl_set_box_from_points(
2494 __isl_take isl_point *pnt1,
2495 __isl_take isl_point *pnt2);
2497 All elements of a B<bounded> (union) set can be enumerated using
2498 the following functions.
2500 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2501 isl_stat (*fn)(__isl_take isl_point *pnt,
2504 isl_stat isl_union_set_foreach_point(
2505 __isl_keep isl_union_set *uset,
2506 isl_stat (*fn)(__isl_take isl_point *pnt,
2510 The function C<fn> is called for each integer point in
2511 C<set> with as second argument the last argument of
2512 the C<isl_set_foreach_point> call. The function C<fn>
2513 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2514 In the latter case, C<isl_set_foreach_point> will stop
2515 enumerating and return C<isl_stat_error> as well.
2516 If the enumeration is performed successfully and to completion,
2517 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2519 To obtain a single point of a (basic or union) set, use
2521 __isl_give isl_point *isl_basic_set_sample_point(
2522 __isl_take isl_basic_set *bset);
2523 __isl_give isl_point *isl_set_sample_point(
2524 __isl_take isl_set *set);
2525 __isl_give isl_point *isl_union_set_sample_point(
2526 __isl_take isl_union_set *uset);
2528 If C<set> does not contain any (integer) points, then the
2529 resulting point will be ``void'', a property that can be
2532 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2536 Besides sets and relation, C<isl> also supports various types of functions.
2537 Each of these types is derived from the value type (see L</"Values">)
2538 or from one of two primitive function types
2539 through the application of zero or more type constructors.
2540 We first describe the primitive type and then we describe
2541 the types derived from these primitive types.
2543 =head3 Primitive Functions
2545 C<isl> support two primitive function types, quasi-affine
2546 expressions and quasipolynomials.
2547 A quasi-affine expression is defined either over a parameter
2548 space or over a set and is composed of integer constants,
2549 parameters and set variables, addition, subtraction and
2550 integer division by an integer constant.
2551 For example, the quasi-affine expression
2553 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2555 maps C<x> to C<2*floor((4 n + x)/9>.
2556 A quasipolynomial is a polynomial expression in quasi-affine
2557 expression. That is, it additionally allows for multiplication.
2558 Note, though, that it is not allowed to construct an integer
2559 division of an expression involving multiplications.
2560 Here is an example of a quasipolynomial that is not
2561 quasi-affine expression
2563 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2565 Note that the external representations of quasi-affine expressions
2566 and quasipolynomials are different. Quasi-affine expressions
2567 use a notation with square brackets just like binary relations,
2568 while quasipolynomials do not. This might change at some point.
2570 If a primitive function is defined over a parameter space,
2571 then the space of the function itself is that of a set.
2572 If it is defined over a set, then the space of the function
2573 is that of a relation. In both cases, the set space (or
2574 the output space) is single-dimensional, anonymous and unstructured.
2575 To create functions with multiple dimensions or with other kinds
2576 of set or output spaces, use multiple expressions
2577 (see L</"Multiple Expressions">).
2581 =item * Quasi-affine Expressions
2583 Besides the expressions described above, a quasi-affine
2584 expression can also be set to NaN. Such expressions
2585 typically represent a failure to represent a result
2586 as a quasi-affine expression.
2588 The zero quasi affine expression or the quasi affine expression
2589 that is equal to a given value, parameter or
2590 a specified dimension on a given domain can be created using
2592 #include <isl/aff.h>
2593 __isl_give isl_aff *isl_aff_zero_on_domain(
2594 __isl_take isl_local_space *ls);
2595 __isl_give isl_aff *isl_aff_val_on_domain(
2596 __isl_take isl_local_space *ls,
2597 __isl_take isl_val *val);
2598 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2599 __isl_take isl_space *space,
2600 __isl_take isl_id *id);
2601 __isl_give isl_aff *isl_aff_var_on_domain(
2602 __isl_take isl_local_space *ls,
2603 enum isl_dim_type type, unsigned pos);
2604 __isl_give isl_aff *isl_aff_nan_on_domain(
2605 __isl_take isl_local_space *ls);
2607 The space passed to C<isl_aff_param_on_domain_space_id>
2608 is required to have a parameter with the given identifier.
2610 Quasi affine expressions can be copied and freed using
2612 #include <isl/aff.h>
2613 __isl_give isl_aff *isl_aff_copy(
2614 __isl_keep isl_aff *aff);
2615 __isl_null isl_aff *isl_aff_free(
2616 __isl_take isl_aff *aff);
2618 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2619 using the following function. The constraint is required to have
2620 a non-zero coefficient for the specified dimension.
2622 #include <isl/constraint.h>
2623 __isl_give isl_aff *isl_constraint_get_bound(
2624 __isl_keep isl_constraint *constraint,
2625 enum isl_dim_type type, int pos);
2627 The entire affine expression of the constraint can also be extracted
2628 using the following function.
2630 #include <isl/constraint.h>
2631 __isl_give isl_aff *isl_constraint_get_aff(
2632 __isl_keep isl_constraint *constraint);
2634 Conversely, an equality constraint equating
2635 the affine expression to zero or an inequality constraint enforcing
2636 the affine expression to be non-negative, can be constructed using
2638 __isl_give isl_constraint *isl_equality_from_aff(
2639 __isl_take isl_aff *aff);
2640 __isl_give isl_constraint *isl_inequality_from_aff(
2641 __isl_take isl_aff *aff);
2643 The coefficients and the integer divisions of an affine expression
2644 can be inspected using the following functions.
2646 #include <isl/aff.h>
2647 __isl_give isl_val *isl_aff_get_constant_val(
2648 __isl_keep isl_aff *aff);
2649 __isl_give isl_val *isl_aff_get_coefficient_val(
2650 __isl_keep isl_aff *aff,
2651 enum isl_dim_type type, int pos);
2652 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2653 enum isl_dim_type type, int pos);
2654 __isl_give isl_val *isl_aff_get_denominator_val(
2655 __isl_keep isl_aff *aff);
2656 __isl_give isl_aff *isl_aff_get_div(
2657 __isl_keep isl_aff *aff, int pos);
2659 They can be modified using the following functions.
2661 #include <isl/aff.h>
2662 __isl_give isl_aff *isl_aff_set_constant_si(
2663 __isl_take isl_aff *aff, int v);
2664 __isl_give isl_aff *isl_aff_set_constant_val(
2665 __isl_take isl_aff *aff, __isl_take isl_val *v);
2666 __isl_give isl_aff *isl_aff_set_coefficient_si(
2667 __isl_take isl_aff *aff,
2668 enum isl_dim_type type, int pos, int v);
2669 __isl_give isl_aff *isl_aff_set_coefficient_val(
2670 __isl_take isl_aff *aff,
2671 enum isl_dim_type type, int pos,
2672 __isl_take isl_val *v);
2674 __isl_give isl_aff *isl_aff_add_constant_si(
2675 __isl_take isl_aff *aff, int v);
2676 __isl_give isl_aff *isl_aff_add_constant_val(
2677 __isl_take isl_aff *aff, __isl_take isl_val *v);
2678 __isl_give isl_aff *isl_aff_add_constant_num_si(
2679 __isl_take isl_aff *aff, int v);
2680 __isl_give isl_aff *isl_aff_add_coefficient_si(
2681 __isl_take isl_aff *aff,
2682 enum isl_dim_type type, int pos, int v);
2683 __isl_give isl_aff *isl_aff_add_coefficient_val(
2684 __isl_take isl_aff *aff,
2685 enum isl_dim_type type, int pos,
2686 __isl_take isl_val *v);
2688 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2689 set the I<numerator> of the constant or coefficient, while
2690 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2691 the constant or coefficient as a whole.
2692 The C<add_constant> and C<add_coefficient> functions add an integer
2693 or rational value to
2694 the possibly rational constant or coefficient.
2695 The C<add_constant_num> functions add an integer value to
2698 =item * Quasipolynomials
2700 Some simple quasipolynomials can be created using the following functions.
2702 #include <isl/polynomial.h>
2703 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2704 __isl_take isl_space *domain);
2705 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2706 __isl_take isl_space *domain);
2707 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2708 __isl_take isl_space *domain);
2709 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2710 __isl_take isl_space *domain);
2711 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2712 __isl_take isl_space *domain);
2713 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2714 __isl_take isl_space *domain,
2715 __isl_take isl_val *val);
2716 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2717 __isl_take isl_space *domain,
2718 enum isl_dim_type type, unsigned pos);
2719 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2720 __isl_take isl_aff *aff);
2722 Recall that the space in which a quasipolynomial lives is a map space
2723 with a one-dimensional range. The C<domain> argument in some of
2724 the functions above corresponds to the domain of this map space.
2726 Quasipolynomials can be copied and freed again using the following
2729 #include <isl/polynomial.h>
2730 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2731 __isl_keep isl_qpolynomial *qp);
2732 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2733 __isl_take isl_qpolynomial *qp);
2735 The constant term of a quasipolynomial can be extracted using
2737 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2738 __isl_keep isl_qpolynomial *qp);
2740 To iterate over all terms in a quasipolynomial,
2743 isl_stat isl_qpolynomial_foreach_term(
2744 __isl_keep isl_qpolynomial *qp,
2745 isl_stat (*fn)(__isl_take isl_term *term,
2746 void *user), void *user);
2748 The terms themselves can be inspected and freed using
2751 unsigned isl_term_dim(__isl_keep isl_term *term,
2752 enum isl_dim_type type);
2753 __isl_give isl_val *isl_term_get_coefficient_val(
2754 __isl_keep isl_term *term);
2755 int isl_term_get_exp(__isl_keep isl_term *term,
2756 enum isl_dim_type type, unsigned pos);
2757 __isl_give isl_aff *isl_term_get_div(
2758 __isl_keep isl_term *term, unsigned pos);
2759 __isl_null isl_term *isl_term_free(
2760 __isl_take isl_term *term);
2762 Each term is a product of parameters, set variables and
2763 integer divisions. The function C<isl_term_get_exp>
2764 returns the exponent of a given dimensions in the given term.
2770 A reduction represents a maximum or a minimum of its
2772 The only reduction type defined by C<isl> is
2773 C<isl_qpolynomial_fold>.
2775 There are currently no functions to directly create such
2776 objects, but they do appear in the piecewise quasipolynomial
2777 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2779 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2781 Reductions can be copied and freed using
2782 the following functions.
2784 #include <isl/polynomial.h>
2785 __isl_give isl_qpolynomial_fold *
2786 isl_qpolynomial_fold_copy(
2787 __isl_keep isl_qpolynomial_fold *fold);
2788 __isl_null isl_qpolynomial_fold *
2789 isl_qpolynomial_fold_free(
2790 __isl_take isl_qpolynomial_fold *fold);
2792 To iterate over all quasipolynomials in a reduction, use
2794 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2795 __isl_keep isl_qpolynomial_fold *fold,
2796 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2797 void *user), void *user);
2799 =head3 Multiple Expressions
2801 A multiple expression represents a sequence of zero or
2802 more base expressions, all defined on the same domain space.
2803 The domain space of the multiple expression is the same
2804 as that of the base expressions, but the range space
2805 can be any space. In case the base expressions have
2806 a set space, the corresponding multiple expression
2807 also has a set space.
2808 Objects of the value type do not have an associated space.
2809 The space of a multiple value is therefore always a set space.
2810 Similarly, the space of a multiple union piecewise
2811 affine expression is always a set space.
2812 If the base expressions are not total, then
2813 a corresponding zero-dimensional multiple expression may
2814 have an explicit domain that keeps track of the domain
2815 outside of any base expressions.
2817 The multiple expression types defined by C<isl>
2818 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2819 C<isl_multi_union_pw_aff>.
2821 A multiple expression with the value zero for
2822 each output (or set) dimension can be created
2823 using the following functions.
2825 #include <isl/val.h>
2826 __isl_give isl_multi_val *isl_multi_val_zero(
2827 __isl_take isl_space *space);
2829 #include <isl/aff.h>
2830 __isl_give isl_multi_aff *isl_multi_aff_zero(
2831 __isl_take isl_space *space);
2832 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2833 __isl_take isl_space *space);
2834 __isl_give isl_multi_union_pw_aff *
2835 isl_multi_union_pw_aff_zero(
2836 __isl_take isl_space *space);
2838 Since there is no canonical way of representing a zero
2839 value of type C<isl_union_pw_aff>, the space passed
2840 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2842 An identity function can be created using the following
2843 functions. The space needs to be that of a relation
2844 with the same number of input and output dimensions.
2846 #include <isl/aff.h>
2847 __isl_give isl_multi_aff *isl_multi_aff_identity(
2848 __isl_take isl_space *space);
2849 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2850 __isl_take isl_space *space);
2852 A function that performs a projection on a universe
2853 relation or set can be created using the following functions.
2854 See also the corresponding
2855 projection operations in L</"Unary Operations">.
2857 #include <isl/aff.h>
2858 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2859 __isl_take isl_space *space);
2860 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2861 __isl_take isl_space *space);
2862 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2863 __isl_take isl_space *space,
2864 enum isl_dim_type type,
2865 unsigned first, unsigned n);
2867 A multiple expression can be created from a single
2868 base expression using the following functions.
2869 The space of the created multiple expression is the same
2870 as that of the base expression, except for
2871 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2872 lives in a parameter space and the output lives
2873 in a single-dimensional set space.
2875 #include <isl/aff.h>
2876 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2877 __isl_take isl_aff *aff);
2878 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2879 __isl_take isl_pw_aff *pa);
2880 __isl_give isl_multi_union_pw_aff *
2881 isl_multi_union_pw_aff_from_union_pw_aff(
2882 __isl_take isl_union_pw_aff *upa);
2884 A multiple expression can be created from a list
2885 of base expression in a specified space.
2886 The domain of this space needs to be the same
2887 as the domains of the base expressions in the list.
2888 If the base expressions have a set space (or no associated space),
2889 then this space also needs to be a set space.
2891 #include <isl/val.h>
2892 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2893 __isl_take isl_space *space,
2894 __isl_take isl_val_list *list);
2896 #include <isl/aff.h>
2897 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2898 __isl_take isl_space *space,
2899 __isl_take isl_aff_list *list);
2900 __isl_give isl_multi_pw_aff *
2901 isl_multi_pw_aff_from_pw_aff_list(
2902 __isl_take isl_space *space,
2903 __isl_take isl_pw_aff_list *list);
2904 __isl_give isl_multi_union_pw_aff *
2905 isl_multi_union_pw_aff_from_union_pw_aff_list(
2906 __isl_take isl_space *space,
2907 __isl_take isl_union_pw_aff_list *list);
2909 As a convenience, a multiple piecewise expression can
2910 also be created from a multiple expression.
2911 Each piecewise expression in the result has a single
2914 #include <isl/aff.h>
2915 __isl_give isl_multi_pw_aff *
2916 isl_multi_pw_aff_from_multi_aff(
2917 __isl_take isl_multi_aff *ma);
2919 Similarly, a multiple union expression can be
2920 created from a multiple expression.
2922 #include <isl/aff.h>
2923 __isl_give isl_multi_union_pw_aff *
2924 isl_multi_union_pw_aff_from_multi_aff(
2925 __isl_take isl_multi_aff *ma);
2926 __isl_give isl_multi_union_pw_aff *
2927 isl_multi_union_pw_aff_from_multi_pw_aff(
2928 __isl_take isl_multi_pw_aff *mpa);
2930 A multiple quasi-affine expression can be created from
2931 a multiple value with a given domain space using the following
2934 #include <isl/aff.h>
2935 __isl_give isl_multi_aff *
2936 isl_multi_aff_multi_val_on_space(
2937 __isl_take isl_space *space,
2938 __isl_take isl_multi_val *mv);
2941 a multiple union piecewise affine expression can be created from
2942 a multiple value with a given domain or
2943 a (piecewise) multiple affine expression with a given domain
2944 using the following functions.
2946 #include <isl/aff.h>
2947 __isl_give isl_multi_union_pw_aff *
2948 isl_multi_union_pw_aff_multi_val_on_domain(
2949 __isl_take isl_union_set *domain,
2950 __isl_take isl_multi_val *mv);
2951 __isl_give isl_multi_union_pw_aff *
2952 isl_multi_union_pw_aff_multi_aff_on_domain(
2953 __isl_take isl_union_set *domain,
2954 __isl_take isl_multi_aff *ma);
2955 __isl_give isl_multi_union_pw_aff *
2956 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2957 __isl_take isl_union_set *domain,
2958 __isl_take isl_pw_multi_aff *pma);
2960 Multiple expressions can be copied and freed using
2961 the following functions.
2963 #include <isl/val.h>
2964 __isl_give isl_multi_val *isl_multi_val_copy(
2965 __isl_keep isl_multi_val *mv);
2966 __isl_null isl_multi_val *isl_multi_val_free(
2967 __isl_take isl_multi_val *mv);
2969 #include <isl/aff.h>
2970 __isl_give isl_multi_aff *isl_multi_aff_copy(
2971 __isl_keep isl_multi_aff *maff);
2972 __isl_null isl_multi_aff *isl_multi_aff_free(
2973 __isl_take isl_multi_aff *maff);
2974 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2975 __isl_keep isl_multi_pw_aff *mpa);
2976 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2977 __isl_take isl_multi_pw_aff *mpa);
2978 __isl_give isl_multi_union_pw_aff *
2979 isl_multi_union_pw_aff_copy(
2980 __isl_keep isl_multi_union_pw_aff *mupa);
2981 __isl_null isl_multi_union_pw_aff *
2982 isl_multi_union_pw_aff_free(
2983 __isl_take isl_multi_union_pw_aff *mupa);
2985 The base expression at a given position of a multiple
2986 expression can be extracted using the following functions.
2988 #include <isl/val.h>
2989 __isl_give isl_val *isl_multi_val_get_val(
2990 __isl_keep isl_multi_val *mv, int pos);
2992 #include <isl/aff.h>
2993 __isl_give isl_aff *isl_multi_aff_get_aff(
2994 __isl_keep isl_multi_aff *multi, int pos);
2995 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2996 __isl_keep isl_multi_pw_aff *mpa, int pos);
2997 __isl_give isl_union_pw_aff *
2998 isl_multi_union_pw_aff_get_union_pw_aff(
2999 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3001 It can be replaced using the following functions.
3003 #include <isl/val.h>
3004 __isl_give isl_multi_val *isl_multi_val_set_val(
3005 __isl_take isl_multi_val *mv, int pos,
3006 __isl_take isl_val *val);
3008 #include <isl/aff.h>
3009 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3010 __isl_take isl_multi_aff *multi, int pos,
3011 __isl_take isl_aff *aff);
3012 __isl_give isl_multi_union_pw_aff *
3013 isl_multi_union_pw_aff_set_union_pw_aff(
3014 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3015 __isl_take isl_union_pw_aff *upa);
3017 As a convenience, a sequence of base expressions that have
3018 their domains in a given space can be extracted from a sequence
3019 of union expressions using the following function.
3021 #include <isl/aff.h>
3022 __isl_give isl_multi_pw_aff *
3023 isl_multi_union_pw_aff_extract_multi_pw_aff(
3024 __isl_keep isl_multi_union_pw_aff *mupa,
3025 __isl_take isl_space *space);
3027 Note that there is a difference between C<isl_multi_union_pw_aff>
3028 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3029 of unions of piecewise expressions, while the second is a union
3030 of piecewise sequences. In particular, multiple affine expressions
3031 in an C<isl_union_pw_multi_aff> may live in different spaces,
3032 while there is only a single multiple expression in
3033 an C<isl_multi_union_pw_aff>, which can therefore only live
3034 in a single space. This means that not every
3035 C<isl_union_pw_multi_aff> can be converted to
3036 an C<isl_multi_union_pw_aff>. Conversely, the elements
3037 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3038 while each multiple expression inside an C<isl_union_pw_multi_aff>
3039 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3040 of dimension greater than one may therefore not be exact.
3041 The following functions can
3042 be used to perform these conversions when they are possible.
3044 #include <isl/aff.h>
3045 __isl_give isl_multi_union_pw_aff *
3046 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3047 __isl_take isl_union_pw_multi_aff *upma);
3048 __isl_give isl_union_pw_multi_aff *
3049 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3050 __isl_take isl_multi_union_pw_aff *mupa);
3052 =head3 Piecewise Expressions
3054 A piecewise expression is an expression that is described
3055 using zero or more base expression defined over the same
3056 number of cells in the domain space of the base expressions.
3057 All base expressions are defined over the same
3058 domain space and the cells are disjoint.
3059 The space of a piecewise expression is the same as
3060 that of the base expressions.
3061 If the union of the cells is a strict subset of the domain
3062 space, then the value of the piecewise expression outside
3063 this union is different for types derived from quasi-affine
3064 expressions and those derived from quasipolynomials.
3065 Piecewise expressions derived from quasi-affine expressions
3066 are considered to be undefined outside the union of their cells.
3067 Piecewise expressions derived from quasipolynomials
3068 are considered to be zero outside the union of their cells.
3070 Piecewise quasipolynomials are mainly used by the C<barvinok>
3071 library for representing the number of elements in a parametric set or map.
3072 For example, the piecewise quasipolynomial
3074 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3076 represents the number of points in the map
3078 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3080 The piecewise expression types defined by C<isl>
3081 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3082 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3084 A piecewise expression with no cells can be created using
3085 the following functions.
3087 #include <isl/aff.h>
3088 __isl_give isl_pw_aff *isl_pw_aff_empty(
3089 __isl_take isl_space *space);
3090 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3091 __isl_take isl_space *space);
3093 A piecewise expression with a single universe cell can be
3094 created using the following functions.
3096 #include <isl/aff.h>
3097 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3098 __isl_take isl_aff *aff);
3099 __isl_give isl_pw_multi_aff *
3100 isl_pw_multi_aff_from_multi_aff(
3101 __isl_take isl_multi_aff *ma);
3103 #include <isl/polynomial.h>
3104 __isl_give isl_pw_qpolynomial *
3105 isl_pw_qpolynomial_from_qpolynomial(
3106 __isl_take isl_qpolynomial *qp);
3108 A piecewise expression with a single specified cell can be
3109 created using the following functions.
3111 #include <isl/aff.h>
3112 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3113 __isl_take isl_set *set, __isl_take isl_aff *aff);
3114 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3115 __isl_take isl_set *set,
3116 __isl_take isl_multi_aff *maff);
3118 #include <isl/polynomial.h>
3119 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3120 __isl_take isl_set *set,
3121 __isl_take isl_qpolynomial *qp);
3123 The following convenience functions first create a base expression and
3124 then create a piecewise expression over a universe domain.
3126 #include <isl/aff.h>
3127 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3128 __isl_take isl_local_space *ls);
3129 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3130 __isl_take isl_local_space *ls,
3131 enum isl_dim_type type, unsigned pos);
3132 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3133 __isl_take isl_local_space *ls);
3134 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3135 __isl_take isl_space *space);
3136 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3137 __isl_take isl_space *space);
3138 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3139 __isl_take isl_space *space);
3140 __isl_give isl_pw_multi_aff *
3141 isl_pw_multi_aff_project_out_map(
3142 __isl_take isl_space *space,
3143 enum isl_dim_type type,
3144 unsigned first, unsigned n);
3146 #include <isl/polynomial.h>
3147 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3148 __isl_take isl_space *space);
3150 The following convenience functions first create a base expression and
3151 then create a piecewise expression over a given domain.
3153 #include <isl/aff.h>
3154 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3155 __isl_take isl_set *domain,
3156 __isl_take isl_val *v);
3157 __isl_give isl_pw_multi_aff *
3158 isl_pw_multi_aff_multi_val_on_domain(
3159 __isl_take isl_set *domain,
3160 __isl_take isl_multi_val *mv);
3162 As a convenience, a piecewise multiple expression can
3163 also be created from a piecewise expression.
3164 Each multiple expression in the result is derived
3165 from the corresponding base expression.
3167 #include <isl/aff.h>
3168 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3169 __isl_take isl_pw_aff *pa);
3171 Similarly, a piecewise quasipolynomial can be
3172 created from a piecewise quasi-affine expression using
3173 the following function.
3175 #include <isl/polynomial.h>
3176 __isl_give isl_pw_qpolynomial *
3177 isl_pw_qpolynomial_from_pw_aff(
3178 __isl_take isl_pw_aff *pwaff);
3180 Piecewise expressions can be copied and freed using the following functions.
3182 #include <isl/aff.h>
3183 __isl_give isl_pw_aff *isl_pw_aff_copy(
3184 __isl_keep isl_pw_aff *pwaff);
3185 __isl_null isl_pw_aff *isl_pw_aff_free(
3186 __isl_take isl_pw_aff *pwaff);
3187 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3188 __isl_keep isl_pw_multi_aff *pma);
3189 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3190 __isl_take isl_pw_multi_aff *pma);
3192 #include <isl/polynomial.h>
3193 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3194 __isl_keep isl_pw_qpolynomial *pwqp);
3195 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3196 __isl_take isl_pw_qpolynomial *pwqp);
3197 __isl_give isl_pw_qpolynomial_fold *
3198 isl_pw_qpolynomial_fold_copy(
3199 __isl_keep isl_pw_qpolynomial_fold *pwf);
3200 __isl_null isl_pw_qpolynomial_fold *
3201 isl_pw_qpolynomial_fold_free(
3202 __isl_take isl_pw_qpolynomial_fold *pwf);
3204 To iterate over the different cells of a piecewise expression,
3205 use the following functions.
3207 #include <isl/aff.h>
3208 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3209 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3210 isl_stat isl_pw_aff_foreach_piece(
3211 __isl_keep isl_pw_aff *pwaff,
3212 isl_stat (*fn)(__isl_take isl_set *set,
3213 __isl_take isl_aff *aff,
3214 void *user), void *user);
3215 int isl_pw_multi_aff_n_piece(
3216 __isl_keep isl_pw_multi_aff *pma);
3217 isl_stat isl_pw_multi_aff_foreach_piece(
3218 __isl_keep isl_pw_multi_aff *pma,
3219 isl_stat (*fn)(__isl_take isl_set *set,
3220 __isl_take isl_multi_aff *maff,
3221 void *user), void *user);
3223 #include <isl/polynomial.h>
3224 int isl_pw_qpolynomial_n_piece(
3225 __isl_keep isl_pw_qpolynomial *pwqp);
3226 isl_stat isl_pw_qpolynomial_foreach_piece(
3227 __isl_keep isl_pw_qpolynomial *pwqp,
3228 isl_stat (*fn)(__isl_take isl_set *set,
3229 __isl_take isl_qpolynomial *qp,
3230 void *user), void *user);
3231 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3232 __isl_keep isl_pw_qpolynomial *pwqp,
3233 isl_stat (*fn)(__isl_take isl_set *set,
3234 __isl_take isl_qpolynomial *qp,
3235 void *user), void *user);
3236 int isl_pw_qpolynomial_fold_n_piece(
3237 __isl_keep isl_pw_qpolynomial_fold *pwf);
3238 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3239 __isl_keep isl_pw_qpolynomial_fold *pwf,
3240 isl_stat (*fn)(__isl_take isl_set *set,
3241 __isl_take isl_qpolynomial_fold *fold,
3242 void *user), void *user);
3243 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3244 __isl_keep isl_pw_qpolynomial_fold *pwf,
3245 isl_stat (*fn)(__isl_take isl_set *set,
3246 __isl_take isl_qpolynomial_fold *fold,
3247 void *user), void *user);
3249 As usual, the function C<fn> should return C<isl_stat_ok> on success
3250 and C<isl_stat_error> on failure. The difference between
3251 C<isl_pw_qpolynomial_foreach_piece> and
3252 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3253 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3254 compute unique representations for all existentially quantified
3255 variables and then turn these existentially quantified variables
3256 into extra set variables, adapting the associated quasipolynomial
3257 accordingly. This means that the C<set> passed to C<fn>
3258 will not have any existentially quantified variables, but that
3259 the dimensions of the sets may be different for different
3260 invocations of C<fn>.
3261 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3262 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3264 A piecewise expression consisting of the expressions at a given
3265 position of a piecewise multiple expression can be extracted
3266 using the following function.
3268 #include <isl/aff.h>
3269 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3270 __isl_keep isl_pw_multi_aff *pma, int pos);
3272 These expressions can be replaced using the following function.
3274 #include <isl/aff.h>
3275 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3276 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3277 __isl_take isl_pw_aff *pa);
3279 Note that there is a difference between C<isl_multi_pw_aff> and
3280 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3281 affine expressions, while the second is a piecewise sequence
3282 of affine expressions. In particular, each of the piecewise
3283 affine expressions in an C<isl_multi_pw_aff> may have a different
3284 domain, while all multiple expressions associated to a cell
3285 in an C<isl_pw_multi_aff> have the same domain.
3286 It is possible to convert between the two, but when converting
3287 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3288 of the result is the intersection of the domains of the input.
3289 The reverse conversion is exact.
3291 #include <isl/aff.h>
3292 __isl_give isl_pw_multi_aff *
3293 isl_pw_multi_aff_from_multi_pw_aff(
3294 __isl_take isl_multi_pw_aff *mpa);
3295 __isl_give isl_multi_pw_aff *
3296 isl_multi_pw_aff_from_pw_multi_aff(
3297 __isl_take isl_pw_multi_aff *pma);
3299 =head3 Union Expressions
3301 A union expression collects base expressions defined
3302 over different domains. The space of a union expression
3303 is that of the shared parameter space.
3305 The union expression types defined by C<isl>
3306 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3307 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3309 C<isl_union_pw_aff>,
3310 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3311 there can be at most one base expression for a given domain space.
3313 C<isl_union_pw_multi_aff>,
3314 there can be multiple such expressions for a given domain space,
3315 but the domains of these expressions need to be disjoint.
3317 An empty union expression can be created using the following functions.
3319 #include <isl/aff.h>
3320 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3321 __isl_take isl_space *space);
3322 __isl_give isl_union_pw_multi_aff *
3323 isl_union_pw_multi_aff_empty(
3324 __isl_take isl_space *space);
3326 #include <isl/polynomial.h>
3327 __isl_give isl_union_pw_qpolynomial *
3328 isl_union_pw_qpolynomial_zero(
3329 __isl_take isl_space *space);
3331 A union expression containing a single base expression
3332 can be created using the following functions.
3334 #include <isl/aff.h>
3335 __isl_give isl_union_pw_aff *
3336 isl_union_pw_aff_from_pw_aff(
3337 __isl_take isl_pw_aff *pa);
3338 __isl_give isl_union_pw_multi_aff *
3339 isl_union_pw_multi_aff_from_aff(
3340 __isl_take isl_aff *aff);
3341 __isl_give isl_union_pw_multi_aff *
3342 isl_union_pw_multi_aff_from_pw_multi_aff(
3343 __isl_take isl_pw_multi_aff *pma);
3345 #include <isl/polynomial.h>
3346 __isl_give isl_union_pw_qpolynomial *
3347 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3348 __isl_take isl_pw_qpolynomial *pwqp);
3350 The following functions create a base expression on each
3351 of the sets in the union set and collect the results.
3353 #include <isl/aff.h>
3354 __isl_give isl_union_pw_multi_aff *
3355 isl_union_pw_multi_aff_from_union_pw_aff(
3356 __isl_take isl_union_pw_aff *upa);
3357 __isl_give isl_union_pw_aff *
3358 isl_union_pw_multi_aff_get_union_pw_aff(
3359 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3360 __isl_give isl_union_pw_aff *
3361 isl_union_pw_aff_val_on_domain(
3362 __isl_take isl_union_set *domain,
3363 __isl_take isl_val *v);
3364 __isl_give isl_union_pw_multi_aff *
3365 isl_union_pw_multi_aff_multi_val_on_domain(
3366 __isl_take isl_union_set *domain,
3367 __isl_take isl_multi_val *mv);
3368 __isl_give isl_union_pw_aff *
3369 isl_union_pw_aff_param_on_domain_id(
3370 __isl_take isl_union_set *domain,
3371 __isl_take isl_id *id);
3373 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3374 is the identifier of a parameter that may or may not already
3375 be present in C<domain>.
3377 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3379 expression on a given domain can be created using the following
3382 #include <isl/aff.h>
3383 __isl_give isl_union_pw_aff *
3384 isl_union_pw_aff_aff_on_domain(
3385 __isl_take isl_union_set *domain,
3386 __isl_take isl_aff *aff);
3387 __isl_give isl_union_pw_aff *
3388 isl_union_pw_aff_pw_aff_on_domain(
3389 __isl_take isl_union_set *domain,
3390 __isl_take isl_pw_aff *pa);
3392 A base expression can be added to a union expression using
3393 the following functions.
3395 #include <isl/aff.h>
3396 __isl_give isl_union_pw_aff *
3397 isl_union_pw_aff_add_pw_aff(
3398 __isl_take isl_union_pw_aff *upa,
3399 __isl_take isl_pw_aff *pa);
3400 __isl_give isl_union_pw_multi_aff *
3401 isl_union_pw_multi_aff_add_pw_multi_aff(
3402 __isl_take isl_union_pw_multi_aff *upma,
3403 __isl_take isl_pw_multi_aff *pma);
3405 #include <isl/polynomial.h>
3406 __isl_give isl_union_pw_qpolynomial *
3407 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3408 __isl_take isl_union_pw_qpolynomial *upwqp,
3409 __isl_take isl_pw_qpolynomial *pwqp);
3411 Union expressions can be copied and freed using
3412 the following functions.
3414 #include <isl/aff.h>
3415 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3416 __isl_keep isl_union_pw_aff *upa);
3417 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3418 __isl_take isl_union_pw_aff *upa);
3419 __isl_give isl_union_pw_multi_aff *
3420 isl_union_pw_multi_aff_copy(
3421 __isl_keep isl_union_pw_multi_aff *upma);
3422 __isl_null isl_union_pw_multi_aff *
3423 isl_union_pw_multi_aff_free(
3424 __isl_take isl_union_pw_multi_aff *upma);
3426 #include <isl/polynomial.h>
3427 __isl_give isl_union_pw_qpolynomial *
3428 isl_union_pw_qpolynomial_copy(
3429 __isl_keep isl_union_pw_qpolynomial *upwqp);
3430 __isl_null isl_union_pw_qpolynomial *
3431 isl_union_pw_qpolynomial_free(
3432 __isl_take isl_union_pw_qpolynomial *upwqp);
3433 __isl_give isl_union_pw_qpolynomial_fold *
3434 isl_union_pw_qpolynomial_fold_copy(
3435 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3436 __isl_null isl_union_pw_qpolynomial_fold *
3437 isl_union_pw_qpolynomial_fold_free(
3438 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3440 To iterate over the base expressions in a union expression,
3441 use the following functions.
3443 #include <isl/aff.h>
3444 int isl_union_pw_aff_n_pw_aff(
3445 __isl_keep isl_union_pw_aff *upa);
3446 isl_stat isl_union_pw_aff_foreach_pw_aff(
3447 __isl_keep isl_union_pw_aff *upa,
3448 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3449 void *user), void *user);
3450 int isl_union_pw_multi_aff_n_pw_multi_aff(
3451 __isl_keep isl_union_pw_multi_aff *upma);
3452 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3453 __isl_keep isl_union_pw_multi_aff *upma,
3454 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3455 void *user), void *user);
3457 #include <isl/polynomial.h>
3458 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3459 __isl_keep isl_union_pw_qpolynomial *upwqp);
3460 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3461 __isl_keep isl_union_pw_qpolynomial *upwqp,
3462 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3463 void *user), void *user);
3464 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3465 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3466 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3467 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3468 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3469 void *user), void *user);
3471 To extract the base expression in a given space from a union, use
3472 the following functions.
3474 #include <isl/aff.h>
3475 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3476 __isl_keep isl_union_pw_aff *upa,
3477 __isl_take isl_space *space);
3478 __isl_give isl_pw_multi_aff *
3479 isl_union_pw_multi_aff_extract_pw_multi_aff(
3480 __isl_keep isl_union_pw_multi_aff *upma,
3481 __isl_take isl_space *space);
3483 #include <isl/polynomial.h>
3484 __isl_give isl_pw_qpolynomial *
3485 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3486 __isl_keep isl_union_pw_qpolynomial *upwqp,
3487 __isl_take isl_space *space);
3489 It is also possible to obtain a list of the base expressions using
3490 the following functions.
3492 #include <isl/aff.h>
3493 __isl_give isl_pw_aff_list *
3494 isl_union_pw_aff_get_pw_aff_list(
3495 __isl_keep isl_union_pw_aff *upa);
3496 __isl_give isl_pw_multi_aff_list *
3497 isl_union_pw_multi_aff_get_pw_multi_aff_list(
3498 __isl_keep isl_union_pw_multi_aff *upma);
3500 #include <isl/polynomial.h>
3501 __isl_give isl_pw_qpolynomial_list *
3502 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
3503 __isl_keep isl_union_pw_qpolynomial *upwqp);
3504 __isl_give isl_pw_qpolynomial_fold_list *
3505 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
3506 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3508 The returned list can be manipulated using the functions in L<"Lists">.
3510 =head2 Input and Output
3512 For set and relation,
3513 C<isl> supports its own input/output format, which is similar
3514 to the C<Omega> format, but also supports the C<PolyLib> format
3516 For other object types, typically only an C<isl> format is supported.
3518 =head3 C<isl> format
3520 The C<isl> format is similar to that of C<Omega>, but has a different
3521 syntax for describing the parameters and allows for the definition
3522 of an existentially quantified variable as the integer division
3523 of an affine expression.
3524 For example, the set of integers C<i> between C<0> and C<n>
3525 such that C<i % 10 <= 6> can be described as
3527 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3530 A set or relation can have several disjuncts, separated
3531 by the keyword C<or>. Each disjunct is either a conjunction
3532 of constraints or a projection (C<exists>) of a conjunction
3533 of constraints. The constraints are separated by the keyword
3536 =head3 C<PolyLib> format
3538 If the represented set is a union, then the first line
3539 contains a single number representing the number of disjuncts.
3540 Otherwise, a line containing the number C<1> is optional.
3542 Each disjunct is represented by a matrix of constraints.
3543 The first line contains two numbers representing
3544 the number of rows and columns,
3545 where the number of rows is equal to the number of constraints
3546 and the number of columns is equal to two plus the number of variables.
3547 The following lines contain the actual rows of the constraint matrix.
3548 In each row, the first column indicates whether the constraint
3549 is an equality (C<0>) or inequality (C<1>). The final column
3550 corresponds to the constant term.
3552 If the set is parametric, then the coefficients of the parameters
3553 appear in the last columns before the constant column.
3554 The coefficients of any existentially quantified variables appear
3555 between those of the set variables and those of the parameters.
3557 =head3 Extended C<PolyLib> format
3559 The extended C<PolyLib> format is nearly identical to the
3560 C<PolyLib> format. The only difference is that the line
3561 containing the number of rows and columns of a constraint matrix
3562 also contains four additional numbers:
3563 the number of output dimensions, the number of input dimensions,
3564 the number of local dimensions (i.e., the number of existentially
3565 quantified variables) and the number of parameters.
3566 For sets, the number of ``output'' dimensions is equal
3567 to the number of set dimensions, while the number of ``input''
3572 Objects can be read from input using the following functions.
3574 #include <isl/val.h>
3575 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3577 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3578 isl_ctx *ctx, const char *str);
3580 #include <isl/set.h>
3581 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3582 isl_ctx *ctx, FILE *input);
3583 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3584 isl_ctx *ctx, const char *str);
3585 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3587 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3590 #include <isl/map.h>
3591 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3592 isl_ctx *ctx, FILE *input);
3593 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3594 isl_ctx *ctx, const char *str);
3595 __isl_give isl_map *isl_map_read_from_file(
3596 isl_ctx *ctx, FILE *input);
3597 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3600 #include <isl/union_set.h>
3601 __isl_give isl_union_set *isl_union_set_read_from_file(
3602 isl_ctx *ctx, FILE *input);
3603 __isl_give isl_union_set *isl_union_set_read_from_str(
3604 isl_ctx *ctx, const char *str);
3606 #include <isl/union_map.h>
3607 __isl_give isl_union_map *isl_union_map_read_from_file(
3608 isl_ctx *ctx, FILE *input);
3609 __isl_give isl_union_map *isl_union_map_read_from_str(
3610 isl_ctx *ctx, const char *str);
3612 #include <isl/aff.h>
3613 __isl_give isl_aff *isl_aff_read_from_str(
3614 isl_ctx *ctx, const char *str);
3615 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3616 isl_ctx *ctx, const char *str);
3617 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3618 isl_ctx *ctx, const char *str);
3619 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3620 isl_ctx *ctx, const char *str);
3621 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3622 isl_ctx *ctx, const char *str);
3623 __isl_give isl_union_pw_aff *
3624 isl_union_pw_aff_read_from_str(
3625 isl_ctx *ctx, const char *str);
3626 __isl_give isl_union_pw_multi_aff *
3627 isl_union_pw_multi_aff_read_from_str(
3628 isl_ctx *ctx, const char *str);
3629 __isl_give isl_multi_union_pw_aff *
3630 isl_multi_union_pw_aff_read_from_str(
3631 isl_ctx *ctx, const char *str);
3633 #include <isl/polynomial.h>
3634 __isl_give isl_union_pw_qpolynomial *
3635 isl_union_pw_qpolynomial_read_from_str(
3636 isl_ctx *ctx, const char *str);
3638 For sets and relations,
3639 the input format is autodetected and may be either the C<PolyLib> format
3640 or the C<isl> format.
3644 Before anything can be printed, an C<isl_printer> needs to
3647 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3649 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3650 __isl_null isl_printer *isl_printer_free(
3651 __isl_take isl_printer *printer);
3653 C<isl_printer_to_file> prints to the given file, while
3654 C<isl_printer_to_str> prints to a string that can be extracted
3655 using the following function.
3657 #include <isl/printer.h>
3658 __isl_give char *isl_printer_get_str(
3659 __isl_keep isl_printer *printer);
3661 The printer can be inspected using the following functions.
3663 FILE *isl_printer_get_file(
3664 __isl_keep isl_printer *printer);
3665 int isl_printer_get_output_format(
3666 __isl_keep isl_printer *p);
3667 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3669 The behavior of the printer can be modified in various ways
3671 __isl_give isl_printer *isl_printer_set_output_format(
3672 __isl_take isl_printer *p, int output_format);
3673 __isl_give isl_printer *isl_printer_set_indent(
3674 __isl_take isl_printer *p, int indent);
3675 __isl_give isl_printer *isl_printer_set_indent_prefix(
3676 __isl_take isl_printer *p, const char *prefix);
3677 __isl_give isl_printer *isl_printer_indent(
3678 __isl_take isl_printer *p, int indent);
3679 __isl_give isl_printer *isl_printer_set_prefix(
3680 __isl_take isl_printer *p, const char *prefix);
3681 __isl_give isl_printer *isl_printer_set_suffix(
3682 __isl_take isl_printer *p, const char *suffix);
3683 __isl_give isl_printer *isl_printer_set_yaml_style(
3684 __isl_take isl_printer *p, int yaml_style);
3686 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3687 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3688 and defaults to C<ISL_FORMAT_ISL>.
3689 Each line in the output is prefixed by C<indent_prefix>,
3690 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3691 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3692 In the C<PolyLib> format output,
3693 the coefficients of the existentially quantified variables
3694 appear between those of the set variables and those
3696 The function C<isl_printer_indent> increases the indentation
3697 by the specified amount (which may be negative).
3698 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3699 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3702 To actually print something, use
3704 #include <isl/printer.h>
3705 __isl_give isl_printer *isl_printer_print_double(
3706 __isl_take isl_printer *p, double d);
3708 #include <isl/val.h>
3709 __isl_give isl_printer *isl_printer_print_val(
3710 __isl_take isl_printer *p, __isl_keep isl_val *v);
3712 #include <isl/set.h>
3713 __isl_give isl_printer *isl_printer_print_basic_set(
3714 __isl_take isl_printer *printer,
3715 __isl_keep isl_basic_set *bset);
3716 __isl_give isl_printer *isl_printer_print_set(
3717 __isl_take isl_printer *printer,
3718 __isl_keep isl_set *set);
3720 #include <isl/map.h>
3721 __isl_give isl_printer *isl_printer_print_basic_map(
3722 __isl_take isl_printer *printer,
3723 __isl_keep isl_basic_map *bmap);
3724 __isl_give isl_printer *isl_printer_print_map(
3725 __isl_take isl_printer *printer,
3726 __isl_keep isl_map *map);
3728 #include <isl/union_set.h>
3729 __isl_give isl_printer *isl_printer_print_union_set(
3730 __isl_take isl_printer *p,
3731 __isl_keep isl_union_set *uset);
3733 #include <isl/union_map.h>
3734 __isl_give isl_printer *isl_printer_print_union_map(
3735 __isl_take isl_printer *p,
3736 __isl_keep isl_union_map *umap);
3738 #include <isl/val.h>
3739 __isl_give isl_printer *isl_printer_print_multi_val(
3740 __isl_take isl_printer *p,
3741 __isl_keep isl_multi_val *mv);
3743 #include <isl/aff.h>
3744 __isl_give isl_printer *isl_printer_print_aff(
3745 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3746 __isl_give isl_printer *isl_printer_print_multi_aff(
3747 __isl_take isl_printer *p,
3748 __isl_keep isl_multi_aff *maff);
3749 __isl_give isl_printer *isl_printer_print_pw_aff(
3750 __isl_take isl_printer *p,
3751 __isl_keep isl_pw_aff *pwaff);
3752 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3753 __isl_take isl_printer *p,
3754 __isl_keep isl_pw_multi_aff *pma);
3755 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3756 __isl_take isl_printer *p,
3757 __isl_keep isl_multi_pw_aff *mpa);
3758 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3759 __isl_take isl_printer *p,
3760 __isl_keep isl_union_pw_aff *upa);
3761 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3762 __isl_take isl_printer *p,
3763 __isl_keep isl_union_pw_multi_aff *upma);
3764 __isl_give isl_printer *
3765 isl_printer_print_multi_union_pw_aff(
3766 __isl_take isl_printer *p,
3767 __isl_keep isl_multi_union_pw_aff *mupa);
3769 #include <isl/polynomial.h>
3770 __isl_give isl_printer *isl_printer_print_qpolynomial(
3771 __isl_take isl_printer *p,
3772 __isl_keep isl_qpolynomial *qp);
3773 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3774 __isl_take isl_printer *p,
3775 __isl_keep isl_pw_qpolynomial *pwqp);
3776 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3777 __isl_take isl_printer *p,
3778 __isl_keep isl_union_pw_qpolynomial *upwqp);
3780 __isl_give isl_printer *
3781 isl_printer_print_pw_qpolynomial_fold(
3782 __isl_take isl_printer *p,
3783 __isl_keep isl_pw_qpolynomial_fold *pwf);
3784 __isl_give isl_printer *
3785 isl_printer_print_union_pw_qpolynomial_fold(
3786 __isl_take isl_printer *p,
3787 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3789 For C<isl_printer_print_qpolynomial>,
3790 C<isl_printer_print_pw_qpolynomial> and
3791 C<isl_printer_print_pw_qpolynomial_fold>,
3792 the output format of the printer
3793 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3794 For C<isl_printer_print_union_pw_qpolynomial> and
3795 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3797 In case of printing in C<ISL_FORMAT_C>, the user may want
3798 to set the names of all dimensions first.
3800 C<isl> also provides limited support for printing YAML documents,
3801 just enough for the internal use for printing such documents.
3803 #include <isl/printer.h>
3804 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3805 __isl_take isl_printer *p);
3806 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3807 __isl_take isl_printer *p);
3808 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3809 __isl_take isl_printer *p);
3810 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3811 __isl_take isl_printer *p);
3812 __isl_give isl_printer *isl_printer_yaml_next(
3813 __isl_take isl_printer *p);
3815 A document is started by a call to either
3816 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3817 Anything printed to the printer after such a call belong to the
3818 first key of the mapping or the first element in the sequence.
3819 The function C<isl_printer_yaml_next> moves to the value if
3820 we are currently printing a mapping key, the next key if we
3821 are printing a value or the next element if we are printing
3822 an element in a sequence.
3823 Nested mappings and sequences are initiated by the same
3824 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3825 Each call to these functions needs to have a corresponding call to
3826 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3828 When called on a file printer, the following function flushes
3829 the file. When called on a string printer, the buffer is cleared.
3831 __isl_give isl_printer *isl_printer_flush(
3832 __isl_take isl_printer *p);
3834 The following functions allow the user to attach
3835 notes to a printer in order to keep track of additional state.
3837 #include <isl/printer.h>
3838 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3839 __isl_keep isl_id *id);
3840 __isl_give isl_id *isl_printer_get_note(
3841 __isl_keep isl_printer *p, __isl_take isl_id *id);
3842 __isl_give isl_printer *isl_printer_set_note(
3843 __isl_take isl_printer *p,
3844 __isl_take isl_id *id, __isl_take isl_id *note);
3846 C<isl_printer_set_note> associates the given note to the given
3847 identifier in the printer.
3848 C<isl_printer_get_note> retrieves a note associated to an
3850 C<isl_printer_has_note> checks if there is such a note.
3851 C<isl_printer_get_note> fails if the requested note does not exist.
3853 Alternatively, a string representation can be obtained
3854 directly using the following functions, which always print
3858 __isl_give char *isl_id_to_str(
3859 __isl_keep isl_id *id);
3861 #include <isl/space.h>
3862 __isl_give char *isl_space_to_str(
3863 __isl_keep isl_space *space);
3865 #include <isl/val.h>
3866 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3867 __isl_give char *isl_multi_val_to_str(
3868 __isl_keep isl_multi_val *mv);
3870 #include <isl/set.h>
3871 __isl_give char *isl_basic_set_to_str(
3872 __isl_keep isl_basic_set *bset);
3873 __isl_give char *isl_set_to_str(
3874 __isl_keep isl_set *set);
3876 #include <isl/union_set.h>
3877 __isl_give char *isl_union_set_to_str(
3878 __isl_keep isl_union_set *uset);
3880 #include <isl/map.h>
3881 __isl_give char *isl_basic_map_to_str(
3882 __isl_keep isl_basic_map *bmap);
3883 __isl_give char *isl_map_to_str(
3884 __isl_keep isl_map *map);
3886 #include <isl/union_map.h>
3887 __isl_give char *isl_union_map_to_str(
3888 __isl_keep isl_union_map *umap);
3890 #include <isl/aff.h>
3891 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3892 __isl_give char *isl_pw_aff_to_str(
3893 __isl_keep isl_pw_aff *pa);
3894 __isl_give char *isl_multi_aff_to_str(
3895 __isl_keep isl_multi_aff *ma);
3896 __isl_give char *isl_pw_multi_aff_to_str(
3897 __isl_keep isl_pw_multi_aff *pma);
3898 __isl_give char *isl_multi_pw_aff_to_str(
3899 __isl_keep isl_multi_pw_aff *mpa);
3900 __isl_give char *isl_union_pw_aff_to_str(
3901 __isl_keep isl_union_pw_aff *upa);
3902 __isl_give char *isl_union_pw_multi_aff_to_str(
3903 __isl_keep isl_union_pw_multi_aff *upma);
3904 __isl_give char *isl_multi_union_pw_aff_to_str(
3905 __isl_keep isl_multi_union_pw_aff *mupa);
3907 #include <isl/point.h>
3908 __isl_give char *isl_point_to_str(
3909 __isl_keep isl_point *pnt);
3911 #include <isl/polynomial.h>
3912 __isl_give char *isl_pw_qpolynomial_to_str(
3913 __isl_keep isl_pw_qpolynomial *pwqp);
3914 __isl_give char *isl_union_pw_qpolynomial_to_str(
3915 __isl_keep isl_union_pw_qpolynomial *upwqp);
3919 =head3 Unary Properties
3925 The following functions test whether the given set or relation
3926 contains any integer points. The ``plain'' variants do not perform
3927 any computations, but simply check if the given set or relation
3928 is already known to be empty.
3930 #include <isl/set.h>
3931 isl_bool isl_basic_set_plain_is_empty(
3932 __isl_keep isl_basic_set *bset);
3933 isl_bool isl_basic_set_is_empty(
3934 __isl_keep isl_basic_set *bset);
3935 isl_bool isl_set_plain_is_empty(
3936 __isl_keep isl_set *set);
3937 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3939 #include <isl/union_set.h>
3940 isl_bool isl_union_set_is_empty(
3941 __isl_keep isl_union_set *uset);
3943 #include <isl/map.h>
3944 isl_bool isl_basic_map_plain_is_empty(
3945 __isl_keep isl_basic_map *bmap);
3946 isl_bool isl_basic_map_is_empty(
3947 __isl_keep isl_basic_map *bmap);
3948 isl_bool isl_map_plain_is_empty(
3949 __isl_keep isl_map *map);
3950 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3952 #include <isl/union_map.h>
3953 isl_bool isl_union_map_plain_is_empty(
3954 __isl_keep isl_union_map *umap);
3955 isl_bool isl_union_map_is_empty(
3956 __isl_keep isl_union_map *umap);
3958 =item * Universality
3960 isl_bool isl_basic_set_plain_is_universe(
3961 __isl_keep isl_basic_set *bset);
3962 isl_bool isl_basic_set_is_universe(
3963 __isl_keep isl_basic_set *bset);
3964 isl_bool isl_basic_map_plain_is_universe(
3965 __isl_keep isl_basic_map *bmap);
3966 isl_bool isl_basic_map_is_universe(
3967 __isl_keep isl_basic_map *bmap);
3968 isl_bool isl_set_plain_is_universe(
3969 __isl_keep isl_set *set);
3970 isl_bool isl_map_plain_is_universe(
3971 __isl_keep isl_map *map);
3973 =item * Single-valuedness
3975 #include <isl/set.h>
3976 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3978 #include <isl/map.h>
3979 isl_bool isl_basic_map_is_single_valued(
3980 __isl_keep isl_basic_map *bmap);
3981 isl_bool isl_map_plain_is_single_valued(
3982 __isl_keep isl_map *map);
3983 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3985 #include <isl/union_map.h>
3986 isl_bool isl_union_map_is_single_valued(
3987 __isl_keep isl_union_map *umap);
3991 isl_bool isl_map_plain_is_injective(
3992 __isl_keep isl_map *map);
3993 isl_bool isl_map_is_injective(
3994 __isl_keep isl_map *map);
3995 isl_bool isl_union_map_plain_is_injective(
3996 __isl_keep isl_union_map *umap);
3997 isl_bool isl_union_map_is_injective(
3998 __isl_keep isl_union_map *umap);
4002 isl_bool isl_map_is_bijective(
4003 __isl_keep isl_map *map);
4004 isl_bool isl_union_map_is_bijective(
4005 __isl_keep isl_union_map *umap);
4009 The following functions test whether the given relation
4010 only maps elements to themselves.
4012 #include <isl/map.h>
4013 isl_bool isl_map_is_identity(
4014 __isl_keep isl_map *map);
4016 #include <isl/union_map.h>
4017 isl_bool isl_union_map_is_identity(
4018 __isl_keep isl_union_map *umap);
4022 __isl_give isl_val *
4023 isl_basic_map_plain_get_val_if_fixed(
4024 __isl_keep isl_basic_map *bmap,
4025 enum isl_dim_type type, unsigned pos);
4026 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4027 __isl_keep isl_set *set,
4028 enum isl_dim_type type, unsigned pos);
4029 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4030 __isl_keep isl_map *map,
4031 enum isl_dim_type type, unsigned pos);
4033 If the set or relation obviously lies on a hyperplane where the given dimension
4034 has a fixed value, then return that value.
4035 Otherwise return NaN.
4039 isl_stat isl_set_dim_residue_class_val(
4040 __isl_keep isl_set *set,
4041 int pos, __isl_give isl_val **modulo,
4042 __isl_give isl_val **residue);
4044 Check if the values of the given set dimension are equal to a fixed
4045 value modulo some integer value. If so, assign the modulo to C<*modulo>
4046 and the fixed value to C<*residue>. If the given dimension attains only
4047 a single value, then assign C<0> to C<*modulo> and the fixed value to
4049 If the dimension does not attain only a single value and if no modulo
4050 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4052 #include <isl/set.h>
4053 __isl_give isl_stride_info *isl_set_get_stride_info(
4054 __isl_keep isl_set *set, int pos);
4055 __isl_give isl_val *isl_set_get_stride(
4056 __isl_keep isl_set *set, int pos);
4058 #include <isl/map.h>
4059 __isl_give isl_stride_info *
4060 isl_map_get_range_stride_info(
4061 __isl_keep isl_map *map, int pos);
4063 Check if the values of the given set dimension are equal to
4064 some affine expression of the other dimensions (the offset)
4065 modulo some integer stride or
4066 check if the values of the given output dimensions are equal to
4067 some affine expression of the input dimensions (the offset)
4068 modulo some integer stride.
4069 If no more specific information can be found, then the stride
4070 is taken to be one and the offset is taken to be the zero expression.
4071 The function C<isl_set_get_stride> performs the same
4072 computation as C<isl_set_get_stride_info> but only returns the stride.
4073 For the other functions,
4074 the stride and offset can be extracted from the returned object
4075 using the following functions.
4077 #include <isl/stride_info.h>
4078 __isl_give isl_val *isl_stride_info_get_stride(
4079 __isl_keep isl_stride_info *si);
4080 __isl_give isl_aff *isl_stride_info_get_offset(
4081 __isl_keep isl_stride_info *si);
4083 The stride info object can be copied and released using the following
4086 #include <isl/stride_info.h>
4087 __isl_give isl_stride_info *isl_stride_info_copy(
4088 __isl_keep isl_stride_info *si);
4089 __isl_null isl_stride_info *isl_stride_info_free(
4090 __isl_take isl_stride_info *si);
4094 To check whether the description of a set, relation or function depends
4095 on one or more given dimensions,
4096 the following functions can be used.
4098 #include <isl/constraint.h>
4099 isl_bool isl_constraint_involves_dims(
4100 __isl_keep isl_constraint *constraint,
4101 enum isl_dim_type type, unsigned first, unsigned n);
4103 #include <isl/set.h>
4104 isl_bool isl_basic_set_involves_dims(
4105 __isl_keep isl_basic_set *bset,
4106 enum isl_dim_type type, unsigned first, unsigned n);
4107 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4108 enum isl_dim_type type, unsigned first, unsigned n);
4110 #include <isl/map.h>
4111 isl_bool isl_basic_map_involves_dims(
4112 __isl_keep isl_basic_map *bmap,
4113 enum isl_dim_type type, unsigned first, unsigned n);
4114 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4115 enum isl_dim_type type, unsigned first, unsigned n);
4117 #include <isl/union_map.h>
4118 isl_bool isl_union_map_involves_dims(
4119 __isl_keep isl_union_map *umap,
4120 enum isl_dim_type type, unsigned first, unsigned n);
4122 #include <isl/aff.h>
4123 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4124 enum isl_dim_type type, unsigned first, unsigned n);
4125 isl_bool isl_pw_aff_involves_dims(
4126 __isl_keep isl_pw_aff *pwaff,
4127 enum isl_dim_type type, unsigned first, unsigned n);
4128 isl_bool isl_multi_aff_involves_dims(
4129 __isl_keep isl_multi_aff *ma,
4130 enum isl_dim_type type, unsigned first, unsigned n);
4131 isl_bool isl_pw_multi_aff_involves_dims(
4132 __isl_keep isl_pw_multi_aff *pma,
4133 enum isl_dim_type type, unsigned first, unsigned n);
4134 isl_bool isl_multi_pw_aff_involves_dims(
4135 __isl_keep isl_multi_pw_aff *mpa,
4136 enum isl_dim_type type, unsigned first, unsigned n);
4138 #include <isl/polynomial.h>
4139 isl_bool isl_qpolynomial_involves_dims(
4140 __isl_keep isl_qpolynomial *qp,
4141 enum isl_dim_type type, unsigned first, unsigned n);
4143 Similarly, the following functions can be used to check whether
4144 a given dimension is involved in any lower or upper bound.
4146 #include <isl/set.h>
4147 isl_bool isl_set_dim_has_any_lower_bound(
4148 __isl_keep isl_set *set,
4149 enum isl_dim_type type, unsigned pos);
4150 isl_bool isl_set_dim_has_any_upper_bound(
4151 __isl_keep isl_set *set,
4152 enum isl_dim_type type, unsigned pos);
4154 Note that these functions return true even if there is a bound on
4155 the dimension on only some of the basic sets of C<set>.
4156 To check if they have a bound for all of the basic sets in C<set>,
4157 use the following functions instead.
4159 #include <isl/set.h>
4160 isl_bool isl_set_dim_has_lower_bound(
4161 __isl_keep isl_set *set,
4162 enum isl_dim_type type, unsigned pos);
4163 isl_bool isl_set_dim_has_upper_bound(
4164 __isl_keep isl_set *set,
4165 enum isl_dim_type type, unsigned pos);
4169 To check whether a set is a parameter domain, use this function:
4171 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4172 isl_bool isl_union_set_is_params(
4173 __isl_keep isl_union_set *uset);
4177 The following functions check whether the space of the given
4178 (basic) set or relation domain and/or range is a wrapped relation.
4180 #include <isl/space.h>
4181 isl_bool isl_space_is_wrapping(
4182 __isl_keep isl_space *space);
4183 isl_bool isl_space_domain_is_wrapping(
4184 __isl_keep isl_space *space);
4185 isl_bool isl_space_range_is_wrapping(
4186 __isl_keep isl_space *space);
4187 isl_bool isl_space_is_product(
4188 __isl_keep isl_space *space);
4190 #include <isl/set.h>
4191 isl_bool isl_basic_set_is_wrapping(
4192 __isl_keep isl_basic_set *bset);
4193 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4195 #include <isl/map.h>
4196 isl_bool isl_map_domain_is_wrapping(
4197 __isl_keep isl_map *map);
4198 isl_bool isl_map_range_is_wrapping(
4199 __isl_keep isl_map *map);
4200 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4202 #include <isl/val.h>
4203 isl_bool isl_multi_val_range_is_wrapping(
4204 __isl_keep isl_multi_val *mv);
4206 #include <isl/aff.h>
4207 isl_bool isl_multi_aff_range_is_wrapping(
4208 __isl_keep isl_multi_aff *ma);
4209 isl_bool isl_multi_pw_aff_range_is_wrapping(
4210 __isl_keep isl_multi_pw_aff *mpa);
4211 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4212 __isl_keep isl_multi_union_pw_aff *mupa);
4214 The input to C<isl_space_is_wrapping> should
4215 be the space of a set, while that of
4216 C<isl_space_domain_is_wrapping> and
4217 C<isl_space_range_is_wrapping> should be the space of a relation.
4218 The input to C<isl_space_is_product> can be either the space
4219 of a set or that of a binary relation.
4220 In case the input is the space of a binary relation, it checks
4221 whether both domain and range are wrapping.
4223 =item * Internal Product
4225 isl_bool isl_basic_map_can_zip(
4226 __isl_keep isl_basic_map *bmap);
4227 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4229 Check whether the product of domain and range of the given relation
4231 i.e., whether both domain and range are nested relations.
4235 #include <isl/space.h>
4236 isl_bool isl_space_can_curry(
4237 __isl_keep isl_space *space);
4239 #include <isl/map.h>
4240 isl_bool isl_basic_map_can_curry(
4241 __isl_keep isl_basic_map *bmap);
4242 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4244 Check whether the domain of the (basic) relation is a wrapped relation.
4246 #include <isl/space.h>
4247 __isl_give isl_space *isl_space_uncurry(
4248 __isl_take isl_space *space);
4250 #include <isl/map.h>
4251 isl_bool isl_basic_map_can_uncurry(
4252 __isl_keep isl_basic_map *bmap);
4253 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4255 Check whether the range of the (basic) relation is a wrapped relation.
4257 #include <isl/space.h>
4258 isl_bool isl_space_can_range_curry(
4259 __isl_keep isl_space *space);
4261 #include <isl/map.h>
4262 isl_bool isl_map_can_range_curry(
4263 __isl_keep isl_map *map);
4265 Check whether the domain of the relation wrapped in the range of
4266 the input is itself a wrapped relation.
4268 =item * Special Values
4270 #include <isl/aff.h>
4271 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4272 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4273 isl_bool isl_multi_pw_aff_is_cst(
4274 __isl_keep isl_multi_pw_aff *mpa);
4276 Check whether the given expression is a constant.
4278 #include <isl/val.h>
4279 isl_bool isl_multi_val_involves_nan(
4280 __isl_keep isl_multi_val *mv);
4282 #include <isl/aff.h>
4283 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4284 isl_bool isl_multi_aff_involves_nan(
4285 __isl_keep isl_multi_aff *ma);
4286 isl_bool isl_pw_aff_involves_nan(
4287 __isl_keep isl_pw_aff *pa);
4288 isl_bool isl_pw_multi_aff_involves_nan(
4289 __isl_keep isl_pw_multi_aff *pma);
4290 isl_bool isl_multi_pw_aff_involves_nan(
4291 __isl_keep isl_multi_pw_aff *mpa);
4292 isl_bool isl_union_pw_aff_involves_nan(
4293 __isl_keep isl_union_pw_aff *upa);
4294 isl_bool isl_union_pw_multi_aff_involves_nan(
4295 __isl_keep isl_union_pw_multi_aff *upma);
4296 isl_bool isl_multi_union_pw_aff_involves_nan(
4297 __isl_keep isl_multi_union_pw_aff *mupa);
4299 #include <isl/polynomial.h>
4300 isl_bool isl_qpolynomial_is_nan(
4301 __isl_keep isl_qpolynomial *qp);
4302 isl_bool isl_qpolynomial_fold_is_nan(
4303 __isl_keep isl_qpolynomial_fold *fold);
4304 isl_bool isl_pw_qpolynomial_involves_nan(
4305 __isl_keep isl_pw_qpolynomial *pwqp);
4306 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4307 __isl_keep isl_pw_qpolynomial_fold *pwf);
4308 isl_bool isl_union_pw_qpolynomial_involves_nan(
4309 __isl_keep isl_union_pw_qpolynomial *upwqp);
4310 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4311 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4313 Check whether the given expression is equal to or involves NaN.
4315 #include <isl/aff.h>
4316 isl_bool isl_aff_plain_is_zero(
4317 __isl_keep isl_aff *aff);
4319 Check whether the affine expression is obviously zero.
4323 =head3 Binary Properties
4329 The following functions check whether two objects
4330 represent the same set, relation or function.
4331 The C<plain> variants only return true if the objects
4332 are obviously the same. That is, they may return false
4333 even if the objects are the same, but they will never
4334 return true if the objects are not the same.
4336 #include <isl/set.h>
4337 isl_bool isl_basic_set_plain_is_equal(
4338 __isl_keep isl_basic_set *bset1,
4339 __isl_keep isl_basic_set *bset2);
4340 isl_bool isl_basic_set_is_equal(
4341 __isl_keep isl_basic_set *bset1,
4342 __isl_keep isl_basic_set *bset2);
4343 isl_bool isl_set_plain_is_equal(
4344 __isl_keep isl_set *set1,
4345 __isl_keep isl_set *set2);
4346 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4347 __isl_keep isl_set *set2);
4349 #include <isl/map.h>
4350 isl_bool isl_basic_map_is_equal(
4351 __isl_keep isl_basic_map *bmap1,
4352 __isl_keep isl_basic_map *bmap2);
4353 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4354 __isl_keep isl_map *map2);
4355 isl_bool isl_map_plain_is_equal(
4356 __isl_keep isl_map *map1,
4357 __isl_keep isl_map *map2);
4359 #include <isl/union_set.h>
4360 isl_bool isl_union_set_is_equal(
4361 __isl_keep isl_union_set *uset1,
4362 __isl_keep isl_union_set *uset2);
4364 #include <isl/union_map.h>
4365 isl_bool isl_union_map_is_equal(
4366 __isl_keep isl_union_map *umap1,
4367 __isl_keep isl_union_map *umap2);
4369 #include <isl/val.h>
4370 isl_bool isl_multi_val_plain_is_equal(
4371 __isl_keep isl_multi_val *mv1,
4372 __isl_keep isl_multi_val *mv2);
4374 #include <isl/aff.h>
4375 isl_bool isl_aff_plain_is_equal(
4376 __isl_keep isl_aff *aff1,
4377 __isl_keep isl_aff *aff2);
4378 isl_bool isl_multi_aff_plain_is_equal(
4379 __isl_keep isl_multi_aff *maff1,
4380 __isl_keep isl_multi_aff *maff2);
4381 isl_bool isl_pw_aff_plain_is_equal(
4382 __isl_keep isl_pw_aff *pwaff1,
4383 __isl_keep isl_pw_aff *pwaff2);
4384 isl_bool isl_pw_aff_is_equal(
4385 __isl_keep isl_pw_aff *pa1,
4386 __isl_keep isl_pw_aff *pa2);
4387 isl_bool isl_pw_multi_aff_plain_is_equal(
4388 __isl_keep isl_pw_multi_aff *pma1,
4389 __isl_keep isl_pw_multi_aff *pma2);
4390 isl_bool isl_pw_multi_aff_is_equal(
4391 __isl_keep isl_pw_multi_aff *pma1,
4392 __isl_keep isl_pw_multi_aff *pma2);
4393 isl_bool isl_multi_pw_aff_plain_is_equal(
4394 __isl_keep isl_multi_pw_aff *mpa1,
4395 __isl_keep isl_multi_pw_aff *mpa2);
4396 isl_bool isl_multi_pw_aff_is_equal(
4397 __isl_keep isl_multi_pw_aff *mpa1,
4398 __isl_keep isl_multi_pw_aff *mpa2);
4399 isl_bool isl_union_pw_aff_plain_is_equal(
4400 __isl_keep isl_union_pw_aff *upa1,
4401 __isl_keep isl_union_pw_aff *upa2);
4402 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4403 __isl_keep isl_union_pw_multi_aff *upma1,
4404 __isl_keep isl_union_pw_multi_aff *upma2);
4405 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4406 __isl_keep isl_multi_union_pw_aff *mupa1,
4407 __isl_keep isl_multi_union_pw_aff *mupa2);
4409 #include <isl/polynomial.h>
4410 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4411 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4412 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4413 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4414 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4415 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4417 =item * Disjointness
4419 #include <isl/set.h>
4420 isl_bool isl_basic_set_is_disjoint(
4421 __isl_keep isl_basic_set *bset1,
4422 __isl_keep isl_basic_set *bset2);
4423 isl_bool isl_set_plain_is_disjoint(
4424 __isl_keep isl_set *set1,
4425 __isl_keep isl_set *set2);
4426 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4427 __isl_keep isl_set *set2);
4429 #include <isl/map.h>
4430 isl_bool isl_basic_map_is_disjoint(
4431 __isl_keep isl_basic_map *bmap1,
4432 __isl_keep isl_basic_map *bmap2);
4433 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4434 __isl_keep isl_map *map2);
4436 #include <isl/union_set.h>
4437 isl_bool isl_union_set_is_disjoint(
4438 __isl_keep isl_union_set *uset1,
4439 __isl_keep isl_union_set *uset2);
4441 #include <isl/union_map.h>
4442 isl_bool isl_union_map_is_disjoint(
4443 __isl_keep isl_union_map *umap1,
4444 __isl_keep isl_union_map *umap2);
4448 isl_bool isl_basic_set_is_subset(
4449 __isl_keep isl_basic_set *bset1,
4450 __isl_keep isl_basic_set *bset2);
4451 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4452 __isl_keep isl_set *set2);
4453 isl_bool isl_set_is_strict_subset(
4454 __isl_keep isl_set *set1,
4455 __isl_keep isl_set *set2);
4456 isl_bool isl_union_set_is_subset(
4457 __isl_keep isl_union_set *uset1,
4458 __isl_keep isl_union_set *uset2);
4459 isl_bool isl_union_set_is_strict_subset(
4460 __isl_keep isl_union_set *uset1,
4461 __isl_keep isl_union_set *uset2);
4462 isl_bool isl_basic_map_is_subset(
4463 __isl_keep isl_basic_map *bmap1,
4464 __isl_keep isl_basic_map *bmap2);
4465 isl_bool isl_basic_map_is_strict_subset(
4466 __isl_keep isl_basic_map *bmap1,
4467 __isl_keep isl_basic_map *bmap2);
4468 isl_bool isl_map_is_subset(
4469 __isl_keep isl_map *map1,
4470 __isl_keep isl_map *map2);
4471 isl_bool isl_map_is_strict_subset(
4472 __isl_keep isl_map *map1,
4473 __isl_keep isl_map *map2);
4474 isl_bool isl_union_map_is_subset(
4475 __isl_keep isl_union_map *umap1,
4476 __isl_keep isl_union_map *umap2);
4477 isl_bool isl_union_map_is_strict_subset(
4478 __isl_keep isl_union_map *umap1,
4479 __isl_keep isl_union_map *umap2);
4481 Check whether the first argument is a (strict) subset of the
4486 Every comparison function returns a negative value if the first
4487 argument is considered smaller than the second, a positive value
4488 if the first argument is considered greater and zero if the two
4489 constraints are considered the same by the comparison criterion.
4491 #include <isl/constraint.h>
4492 int isl_constraint_plain_cmp(
4493 __isl_keep isl_constraint *c1,
4494 __isl_keep isl_constraint *c2);
4496 This function is useful for sorting C<isl_constraint>s.
4497 The order depends on the internal representation of the inputs.
4498 The order is fixed over different calls to the function (assuming
4499 the internal representation of the inputs has not changed), but may
4500 change over different versions of C<isl>.
4502 #include <isl/constraint.h>
4503 int isl_constraint_cmp_last_non_zero(
4504 __isl_keep isl_constraint *c1,
4505 __isl_keep isl_constraint *c2);
4507 This function can be used to sort constraints that live in the same
4508 local space. Constraints that involve ``earlier'' dimensions or
4509 that have a smaller coefficient for the shared latest dimension
4510 are considered smaller than other constraints.
4511 This function only defines a B<partial> order.
4513 #include <isl/set.h>
4514 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4515 __isl_keep isl_set *set2);
4517 This function is useful for sorting C<isl_set>s.
4518 The order depends on the internal representation of the inputs.
4519 The order is fixed over different calls to the function (assuming
4520 the internal representation of the inputs has not changed), but may
4521 change over different versions of C<isl>.
4523 #include <isl/aff.h>
4524 int isl_multi_aff_plain_cmp(
4525 __isl_keep isl_multi_aff *ma1,
4526 __isl_keep isl_multi_aff *ma2);
4527 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4528 __isl_keep isl_pw_aff *pa2);
4530 The functions C<isl_multi_aff_plain_cmp> and
4531 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4532 C<isl_pw_aff>s. The order is not strictly defined.
4533 The current order sorts expressions that only involve
4534 earlier dimensions before those that involve later dimensions.
4538 =head2 Unary Operations
4544 __isl_give isl_set *isl_set_complement(
4545 __isl_take isl_set *set);
4546 __isl_give isl_map *isl_map_complement(
4547 __isl_take isl_map *map);
4551 #include <isl/space.h>
4552 __isl_give isl_space *isl_space_reverse(
4553 __isl_take isl_space *space);
4555 #include <isl/map.h>
4556 __isl_give isl_basic_map *isl_basic_map_reverse(
4557 __isl_take isl_basic_map *bmap);
4558 __isl_give isl_map *isl_map_reverse(
4559 __isl_take isl_map *map);
4561 #include <isl/union_map.h>
4562 __isl_give isl_union_map *isl_union_map_reverse(
4563 __isl_take isl_union_map *umap);
4567 #include <isl/space.h>
4568 __isl_give isl_space *isl_space_domain(
4569 __isl_take isl_space *space);
4570 __isl_give isl_space *isl_space_range(
4571 __isl_take isl_space *space);
4572 __isl_give isl_space *isl_space_params(
4573 __isl_take isl_space *space);
4575 #include <isl/local_space.h>
4576 __isl_give isl_local_space *isl_local_space_domain(
4577 __isl_take isl_local_space *ls);
4578 __isl_give isl_local_space *isl_local_space_range(
4579 __isl_take isl_local_space *ls);
4581 #include <isl/set.h>
4582 __isl_give isl_basic_set *isl_basic_set_project_out(
4583 __isl_take isl_basic_set *bset,
4584 enum isl_dim_type type, unsigned first, unsigned n);
4585 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4586 enum isl_dim_type type, unsigned first, unsigned n);
4587 __isl_give isl_map *isl_set_project_onto_map(
4588 __isl_take isl_set *set,
4589 enum isl_dim_type type, unsigned first,
4591 __isl_give isl_basic_set *isl_basic_set_params(
4592 __isl_take isl_basic_set *bset);
4593 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4595 The function C<isl_set_project_onto_map> returns a relation
4596 that projects the input set onto the given set dimensions.
4598 #include <isl/map.h>
4599 __isl_give isl_basic_map *isl_basic_map_project_out(
4600 __isl_take isl_basic_map *bmap,
4601 enum isl_dim_type type, unsigned first, unsigned n);
4602 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4603 enum isl_dim_type type, unsigned first, unsigned n);
4604 __isl_give isl_basic_set *isl_basic_map_domain(
4605 __isl_take isl_basic_map *bmap);
4606 __isl_give isl_basic_set *isl_basic_map_range(
4607 __isl_take isl_basic_map *bmap);
4608 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4609 __isl_give isl_set *isl_map_domain(
4610 __isl_take isl_map *bmap);
4611 __isl_give isl_set *isl_map_range(
4612 __isl_take isl_map *map);
4614 #include <isl/union_set.h>
4615 __isl_give isl_union_set *isl_union_set_project_out(
4616 __isl_take isl_union_set *uset,
4617 enum isl_dim_type type,
4618 unsigned first, unsigned n);
4619 __isl_give isl_union_set *
4620 isl_union_set_project_out_all_params(
4621 __isl_take isl_union_set *uset);
4622 __isl_give isl_set *isl_union_set_params(
4623 __isl_take isl_union_set *uset);
4625 The function C<isl_union_set_project_out> can only project out
4628 #include <isl/union_map.h>
4629 __isl_give isl_union_map *isl_union_map_project_out(
4630 __isl_take isl_union_map *umap,
4631 enum isl_dim_type type, unsigned first, unsigned n);
4632 __isl_give isl_union_map *
4633 isl_union_map_project_out_all_params(
4634 __isl_take isl_union_map *umap);
4635 __isl_give isl_set *isl_union_map_params(
4636 __isl_take isl_union_map *umap);
4637 __isl_give isl_union_set *isl_union_map_domain(
4638 __isl_take isl_union_map *umap);
4639 __isl_give isl_union_set *isl_union_map_range(
4640 __isl_take isl_union_map *umap);
4642 The function C<isl_union_map_project_out> can only project out
4645 #include <isl/aff.h>
4646 __isl_give isl_aff *isl_aff_project_domain_on_params(
4647 __isl_take isl_aff *aff);
4648 __isl_give isl_multi_aff *
4649 isl_multi_aff_project_domain_on_params(
4650 __isl_take isl_multi_aff *ma);
4651 __isl_give isl_pw_aff *
4652 isl_pw_aff_project_domain_on_params(
4653 __isl_take isl_pw_aff *pa);
4654 __isl_give isl_multi_pw_aff *
4655 isl_multi_pw_aff_project_domain_on_params(
4656 __isl_take isl_multi_pw_aff *mpa);
4657 __isl_give isl_pw_multi_aff *
4658 isl_pw_multi_aff_project_domain_on_params(
4659 __isl_take isl_pw_multi_aff *pma);
4660 __isl_give isl_set *isl_pw_aff_domain(
4661 __isl_take isl_pw_aff *pwaff);
4662 __isl_give isl_set *isl_pw_multi_aff_domain(
4663 __isl_take isl_pw_multi_aff *pma);
4664 __isl_give isl_set *isl_multi_pw_aff_domain(
4665 __isl_take isl_multi_pw_aff *mpa);
4666 __isl_give isl_union_set *isl_union_pw_aff_domain(
4667 __isl_take isl_union_pw_aff *upa);
4668 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4669 __isl_take isl_union_pw_multi_aff *upma);
4670 __isl_give isl_union_set *
4671 isl_multi_union_pw_aff_domain(
4672 __isl_take isl_multi_union_pw_aff *mupa);
4673 __isl_give isl_set *isl_pw_aff_params(
4674 __isl_take isl_pw_aff *pwa);
4676 If no explicit domain was set on a zero-dimensional input to
4677 C<isl_multi_union_pw_aff_domain>, then this function will
4678 return a parameter set.
4680 #include <isl/polynomial.h>
4681 __isl_give isl_qpolynomial *
4682 isl_qpolynomial_project_domain_on_params(
4683 __isl_take isl_qpolynomial *qp);
4684 __isl_give isl_pw_qpolynomial *
4685 isl_pw_qpolynomial_project_domain_on_params(
4686 __isl_take isl_pw_qpolynomial *pwqp);
4687 __isl_give isl_pw_qpolynomial_fold *
4688 isl_pw_qpolynomial_fold_project_domain_on_params(
4689 __isl_take isl_pw_qpolynomial_fold *pwf);
4690 __isl_give isl_set *isl_pw_qpolynomial_domain(
4691 __isl_take isl_pw_qpolynomial *pwqp);
4692 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4693 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4694 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4695 __isl_take isl_union_pw_qpolynomial *upwqp);
4697 #include <isl/space.h>
4698 __isl_give isl_space *isl_space_domain_map(
4699 __isl_take isl_space *space);
4700 __isl_give isl_space *isl_space_range_map(
4701 __isl_take isl_space *space);
4703 #include <isl/map.h>
4704 __isl_give isl_map *isl_set_wrapped_domain_map(
4705 __isl_take isl_set *set);
4706 __isl_give isl_basic_map *isl_basic_map_domain_map(
4707 __isl_take isl_basic_map *bmap);
4708 __isl_give isl_basic_map *isl_basic_map_range_map(
4709 __isl_take isl_basic_map *bmap);
4710 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4711 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4713 #include <isl/union_map.h>
4714 __isl_give isl_union_map *isl_union_map_domain_map(
4715 __isl_take isl_union_map *umap);
4716 __isl_give isl_union_pw_multi_aff *
4717 isl_union_map_domain_map_union_pw_multi_aff(
4718 __isl_take isl_union_map *umap);
4719 __isl_give isl_union_map *isl_union_map_range_map(
4720 __isl_take isl_union_map *umap);
4721 __isl_give isl_union_map *
4722 isl_union_set_wrapped_domain_map(
4723 __isl_take isl_union_set *uset);
4725 The functions above construct a (basic, regular or union) relation
4726 that maps (a wrapped version of) the input relation to its domain or range.
4727 C<isl_set_wrapped_domain_map> maps the input set to the domain
4728 of its wrapped relation.
4732 __isl_give isl_basic_set *isl_basic_set_eliminate(
4733 __isl_take isl_basic_set *bset,
4734 enum isl_dim_type type,
4735 unsigned first, unsigned n);
4736 __isl_give isl_set *isl_set_eliminate(
4737 __isl_take isl_set *set, enum isl_dim_type type,
4738 unsigned first, unsigned n);
4739 __isl_give isl_basic_map *isl_basic_map_eliminate(
4740 __isl_take isl_basic_map *bmap,
4741 enum isl_dim_type type,
4742 unsigned first, unsigned n);
4743 __isl_give isl_map *isl_map_eliminate(
4744 __isl_take isl_map *map, enum isl_dim_type type,
4745 unsigned first, unsigned n);
4747 Eliminate the coefficients for the given dimensions from the constraints,
4748 without removing the dimensions.
4750 =item * Constructing a set from a parameter domain
4752 A zero-dimensional (local) space or (basic) set can be constructed
4753 on a given parameter domain using the following functions.
4755 #include <isl/space.h>
4756 __isl_give isl_space *isl_space_set_from_params(
4757 __isl_take isl_space *space);
4759 #include <isl/local_space.h>
4760 __isl_give isl_local_space *
4761 isl_local_space_set_from_params(
4762 __isl_take isl_local_space *ls);
4764 #include <isl/set.h>
4765 __isl_give isl_basic_set *isl_basic_set_from_params(
4766 __isl_take isl_basic_set *bset);
4767 __isl_give isl_set *isl_set_from_params(
4768 __isl_take isl_set *set);
4770 =item * Constructing a relation from one or two sets
4772 Create a relation with the given set(s) as domain and/or range.
4773 If only the domain or the range is specified, then
4774 the range or domain of the created relation is a zero-dimensional
4775 flat anonymous space.
4777 #include <isl/space.h>
4778 __isl_give isl_space *isl_space_from_domain(
4779 __isl_take isl_space *space);
4780 __isl_give isl_space *isl_space_from_range(
4781 __isl_take isl_space *space);
4782 __isl_give isl_space *isl_space_map_from_set(
4783 __isl_take isl_space *space);
4784 __isl_give isl_space *isl_space_map_from_domain_and_range(
4785 __isl_take isl_space *domain,
4786 __isl_take isl_space *range);
4788 #include <isl/local_space.h>
4789 __isl_give isl_local_space *isl_local_space_from_domain(
4790 __isl_take isl_local_space *ls);
4792 #include <isl/map.h>
4793 __isl_give isl_map *isl_map_from_domain(
4794 __isl_take isl_set *set);
4795 __isl_give isl_map *isl_map_from_range(
4796 __isl_take isl_set *set);
4798 #include <isl/union_map.h>
4799 __isl_give isl_union_map *isl_union_map_from_domain(
4800 __isl_take isl_union_set *uset);
4801 __isl_give isl_union_map *isl_union_map_from_range(
4802 __isl_take isl_union_set *uset);
4803 __isl_give isl_union_map *
4804 isl_union_map_from_domain_and_range(
4805 __isl_take isl_union_set *domain,
4806 __isl_take isl_union_set *range);
4808 #include <isl/val.h>
4809 __isl_give isl_multi_val *isl_multi_val_from_range(
4810 __isl_take isl_multi_val *mv);
4812 #include <isl/aff.h>
4813 __isl_give isl_aff *isl_aff_from_range(
4814 __isl_take isl_aff *aff);
4815 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4816 __isl_take isl_multi_aff *ma);
4817 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4818 __isl_take isl_pw_aff *pwa);
4819 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4820 __isl_take isl_multi_pw_aff *mpa);
4821 __isl_give isl_multi_union_pw_aff *
4822 isl_multi_union_pw_aff_from_range(
4823 __isl_take isl_multi_union_pw_aff *mupa);
4824 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4825 __isl_take isl_set *set);
4826 __isl_give isl_union_pw_multi_aff *
4827 isl_union_pw_multi_aff_from_domain(
4828 __isl_take isl_union_set *uset);
4830 #include <isl/polynomial.h>
4831 __isl_give isl_pw_qpolynomial *
4832 isl_pw_qpolynomial_from_range(
4833 __isl_take isl_pw_qpolynomial *pwqp);
4834 __isl_give isl_pw_qpolynomial_fold *
4835 isl_pw_qpolynomial_fold_from_range(
4836 __isl_take isl_pw_qpolynomial_fold *pwf);
4840 #include <isl/set.h>
4841 __isl_give isl_basic_set *isl_basic_set_fix_si(
4842 __isl_take isl_basic_set *bset,
4843 enum isl_dim_type type, unsigned pos, int value);
4844 __isl_give isl_basic_set *isl_basic_set_fix_val(
4845 __isl_take isl_basic_set *bset,
4846 enum isl_dim_type type, unsigned pos,
4847 __isl_take isl_val *v);
4848 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4849 enum isl_dim_type type, unsigned pos, int value);
4850 __isl_give isl_set *isl_set_fix_val(
4851 __isl_take isl_set *set,
4852 enum isl_dim_type type, unsigned pos,
4853 __isl_take isl_val *v);
4855 #include <isl/map.h>
4856 __isl_give isl_basic_map *isl_basic_map_fix_si(
4857 __isl_take isl_basic_map *bmap,
4858 enum isl_dim_type type, unsigned pos, int value);
4859 __isl_give isl_basic_map *isl_basic_map_fix_val(
4860 __isl_take isl_basic_map *bmap,
4861 enum isl_dim_type type, unsigned pos,
4862 __isl_take isl_val *v);
4863 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4864 enum isl_dim_type type, unsigned pos, int value);
4865 __isl_give isl_map *isl_map_fix_val(
4866 __isl_take isl_map *map,
4867 enum isl_dim_type type, unsigned pos,
4868 __isl_take isl_val *v);
4870 #include <isl/aff.h>
4871 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4872 __isl_take isl_pw_multi_aff *pma,
4873 enum isl_dim_type type, unsigned pos, int value);
4875 #include <isl/polynomial.h>
4876 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4877 __isl_take isl_pw_qpolynomial *pwqp,
4878 enum isl_dim_type type, unsigned n,
4879 __isl_take isl_val *v);
4880 __isl_give isl_pw_qpolynomial_fold *
4881 isl_pw_qpolynomial_fold_fix_val(
4882 __isl_take isl_pw_qpolynomial_fold *pwf,
4883 enum isl_dim_type type, unsigned n,
4884 __isl_take isl_val *v);
4886 Intersect the set, relation or function domain
4887 with the hyperplane where the given
4888 dimension has the fixed given value.
4890 #include <isl/set.h>
4891 __isl_give isl_basic_set *
4892 isl_basic_set_lower_bound_val(
4893 __isl_take isl_basic_set *bset,
4894 enum isl_dim_type type, unsigned pos,
4895 __isl_take isl_val *value);
4896 __isl_give isl_basic_set *
4897 isl_basic_set_upper_bound_val(
4898 __isl_take isl_basic_set *bset,
4899 enum isl_dim_type type, unsigned pos,
4900 __isl_take isl_val *value);
4901 __isl_give isl_set *isl_set_lower_bound_si(
4902 __isl_take isl_set *set,
4903 enum isl_dim_type type, unsigned pos, int value);
4904 __isl_give isl_set *isl_set_lower_bound_val(
4905 __isl_take isl_set *set,
4906 enum isl_dim_type type, unsigned pos,
4907 __isl_take isl_val *value);
4908 __isl_give isl_set *isl_set_upper_bound_si(
4909 __isl_take isl_set *set,
4910 enum isl_dim_type type, unsigned pos, int value);
4911 __isl_give isl_set *isl_set_upper_bound_val(
4912 __isl_take isl_set *set,
4913 enum isl_dim_type type, unsigned pos,
4914 __isl_take isl_val *value);
4916 #include <isl/map.h>
4917 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4918 __isl_take isl_basic_map *bmap,
4919 enum isl_dim_type type, unsigned pos, int value);
4920 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4921 __isl_take isl_basic_map *bmap,
4922 enum isl_dim_type type, unsigned pos, int value);
4923 __isl_give isl_map *isl_map_lower_bound_si(
4924 __isl_take isl_map *map,
4925 enum isl_dim_type type, unsigned pos, int value);
4926 __isl_give isl_map *isl_map_upper_bound_si(
4927 __isl_take isl_map *map,
4928 enum isl_dim_type type, unsigned pos, int value);
4930 Intersect the set or relation with the half-space where the given
4931 dimension has a value bounded by the fixed given integer value.
4933 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4934 enum isl_dim_type type1, int pos1,
4935 enum isl_dim_type type2, int pos2);
4936 __isl_give isl_basic_map *isl_basic_map_equate(
4937 __isl_take isl_basic_map *bmap,
4938 enum isl_dim_type type1, int pos1,
4939 enum isl_dim_type type2, int pos2);
4940 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4941 enum isl_dim_type type1, int pos1,
4942 enum isl_dim_type type2, int pos2);
4944 Intersect the set or relation with the hyperplane where the given
4945 dimensions are equal to each other.
4947 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4948 enum isl_dim_type type1, int pos1,
4949 enum isl_dim_type type2, int pos2);
4951 Intersect the relation with the hyperplane where the given
4952 dimensions have opposite values.
4954 __isl_give isl_map *isl_map_order_le(
4955 __isl_take isl_map *map,
4956 enum isl_dim_type type1, int pos1,
4957 enum isl_dim_type type2, int pos2);
4958 __isl_give isl_basic_map *isl_basic_map_order_ge(
4959 __isl_take isl_basic_map *bmap,
4960 enum isl_dim_type type1, int pos1,
4961 enum isl_dim_type type2, int pos2);
4962 __isl_give isl_map *isl_map_order_ge(
4963 __isl_take isl_map *map,
4964 enum isl_dim_type type1, int pos1,
4965 enum isl_dim_type type2, int pos2);
4966 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4967 enum isl_dim_type type1, int pos1,
4968 enum isl_dim_type type2, int pos2);
4969 __isl_give isl_basic_map *isl_basic_map_order_gt(
4970 __isl_take isl_basic_map *bmap,
4971 enum isl_dim_type type1, int pos1,
4972 enum isl_dim_type type2, int pos2);
4973 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4974 enum isl_dim_type type1, int pos1,
4975 enum isl_dim_type type2, int pos2);
4977 Intersect the relation with the half-space where the given
4978 dimensions satisfy the given ordering.
4980 #include <isl/union_set.h>
4981 __isl_give isl_union_map *isl_union_map_remove_map_if(
4982 __isl_take isl_union_map *umap,
4983 isl_bool (*fn)(__isl_keep isl_map *map,
4984 void *user), void *user);
4986 This function calls the callback function once for each
4987 pair of spaces for which there are elements in the input.
4988 If the callback returns C<isl_bool_true>, then all those elements
4989 are removed from the result. The only remaining elements in the output
4990 are then those for which the callback returns C<isl_bool_false>.
4994 #include <isl/aff.h>
4995 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4996 __isl_take isl_aff *aff);
4997 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4998 __isl_take isl_aff *aff);
4999 __isl_give isl_set *isl_pw_aff_pos_set(
5000 __isl_take isl_pw_aff *pa);
5001 __isl_give isl_set *isl_pw_aff_nonneg_set(
5002 __isl_take isl_pw_aff *pwaff);
5003 __isl_give isl_set *isl_pw_aff_zero_set(
5004 __isl_take isl_pw_aff *pwaff);
5005 __isl_give isl_set *isl_pw_aff_non_zero_set(
5006 __isl_take isl_pw_aff *pwaff);
5007 __isl_give isl_union_set *
5008 isl_union_pw_aff_zero_union_set(
5009 __isl_take isl_union_pw_aff *upa);
5010 __isl_give isl_union_set *
5011 isl_multi_union_pw_aff_zero_union_set(
5012 __isl_take isl_multi_union_pw_aff *mupa);
5014 The function C<isl_aff_neg_basic_set> returns a basic set
5015 containing those elements in the domain space
5016 of C<aff> where C<aff> is negative.
5017 The function C<isl_pw_aff_nonneg_set> returns a set
5018 containing those elements in the domain
5019 of C<pwaff> where C<pwaff> is non-negative.
5020 The function C<isl_multi_union_pw_aff_zero_union_set>
5021 returns a union set containing those elements
5022 in the domains of its elements where they are all zero.
5026 __isl_give isl_map *isl_set_identity(
5027 __isl_take isl_set *set);
5028 __isl_give isl_union_map *isl_union_set_identity(
5029 __isl_take isl_union_set *uset);
5030 __isl_give isl_union_pw_multi_aff *
5031 isl_union_set_identity_union_pw_multi_aff(
5032 __isl_take isl_union_set *uset);
5034 Construct an identity relation on the given (union) set.
5036 =item * Function Extraction
5038 A piecewise quasi affine expression that is equal to 1 on a set
5039 and 0 outside the set can be created using the following function.
5041 #include <isl/aff.h>
5042 __isl_give isl_pw_aff *isl_set_indicator_function(
5043 __isl_take isl_set *set);
5045 A piecewise multiple quasi affine expression can be extracted
5046 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
5047 and the C<isl_map> is single-valued.
5048 In case of a conversion from an C<isl_union_map>
5049 to an C<isl_union_pw_multi_aff>, these properties need to hold
5050 in each domain space.
5051 A conversion to a C<isl_multi_union_pw_aff> additionally
5052 requires that the input is non-empty and involves only a single
5055 #include <isl/aff.h>
5056 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
5057 __isl_take isl_set *set);
5058 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
5059 __isl_take isl_map *map);
5061 __isl_give isl_union_pw_multi_aff *
5062 isl_union_pw_multi_aff_from_union_set(
5063 __isl_take isl_union_set *uset);
5064 __isl_give isl_union_pw_multi_aff *
5065 isl_union_pw_multi_aff_from_union_map(
5066 __isl_take isl_union_map *umap);
5068 __isl_give isl_multi_union_pw_aff *
5069 isl_multi_union_pw_aff_from_union_map(
5070 __isl_take isl_union_map *umap);
5074 __isl_give isl_basic_set *isl_basic_map_deltas(
5075 __isl_take isl_basic_map *bmap);
5076 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
5077 __isl_give isl_union_set *isl_union_map_deltas(
5078 __isl_take isl_union_map *umap);
5080 These functions return a (basic) set containing the differences
5081 between image elements and corresponding domain elements in the input.
5083 __isl_give isl_basic_map *isl_basic_map_deltas_map(
5084 __isl_take isl_basic_map *bmap);
5085 __isl_give isl_map *isl_map_deltas_map(
5086 __isl_take isl_map *map);
5087 __isl_give isl_union_map *isl_union_map_deltas_map(
5088 __isl_take isl_union_map *umap);
5090 The functions above construct a (basic, regular or union) relation
5091 that maps (a wrapped version of) the input relation to its delta set.
5095 Simplify the representation of a set, relation or functions by trying
5096 to combine pairs of basic sets or relations into a single
5097 basic set or relation.
5099 #include <isl/set.h>
5100 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
5102 #include <isl/map.h>
5103 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5105 #include <isl/union_set.h>
5106 __isl_give isl_union_set *isl_union_set_coalesce(
5107 __isl_take isl_union_set *uset);
5109 #include <isl/union_map.h>
5110 __isl_give isl_union_map *isl_union_map_coalesce(
5111 __isl_take isl_union_map *umap);
5113 #include <isl/aff.h>
5114 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5115 __isl_take isl_pw_aff *pwqp);
5116 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5117 __isl_take isl_pw_multi_aff *pma);
5118 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5119 __isl_take isl_multi_pw_aff *mpa);
5120 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5121 __isl_take isl_union_pw_aff *upa);
5122 __isl_give isl_union_pw_multi_aff *
5123 isl_union_pw_multi_aff_coalesce(
5124 __isl_take isl_union_pw_multi_aff *upma);
5125 __isl_give isl_multi_union_pw_aff *
5126 isl_multi_union_pw_aff_coalesce(
5127 __isl_take isl_multi_union_pw_aff *aff);
5129 #include <isl/polynomial.h>
5130 __isl_give isl_pw_qpolynomial_fold *
5131 isl_pw_qpolynomial_fold_coalesce(
5132 __isl_take isl_pw_qpolynomial_fold *pwf);
5133 __isl_give isl_union_pw_qpolynomial *
5134 isl_union_pw_qpolynomial_coalesce(
5135 __isl_take isl_union_pw_qpolynomial *upwqp);
5136 __isl_give isl_union_pw_qpolynomial_fold *
5137 isl_union_pw_qpolynomial_fold_coalesce(
5138 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5140 One of the methods for combining pairs of basic sets or relations
5141 can result in coefficients that are much larger than those that appear
5142 in the constraints of the input. By default, the coefficients are
5143 not allowed to grow larger, but this can be changed by unsetting
5144 the following option.
5146 isl_stat isl_options_set_coalesce_bounded_wrapping(
5147 isl_ctx *ctx, int val);
5148 int isl_options_get_coalesce_bounded_wrapping(
5151 One of the other methods tries to combine pairs of basic sets
5152 with different local variables, treating them as existentially
5153 quantified variables even if they have known (but different)
5154 integer division expressions. The result may then also have
5155 existentially quantified variables. Turning on the following
5156 option prevents this from happening.
5158 isl_stat isl_options_set_coalesce_preserve_locals(
5159 isl_ctx *ctx, int val);
5160 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
5162 =item * Detecting equalities
5164 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5165 __isl_take isl_basic_set *bset);
5166 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5167 __isl_take isl_basic_map *bmap);
5168 __isl_give isl_set *isl_set_detect_equalities(
5169 __isl_take isl_set *set);
5170 __isl_give isl_map *isl_map_detect_equalities(
5171 __isl_take isl_map *map);
5172 __isl_give isl_union_set *isl_union_set_detect_equalities(
5173 __isl_take isl_union_set *uset);
5174 __isl_give isl_union_map *isl_union_map_detect_equalities(
5175 __isl_take isl_union_map *umap);
5177 Simplify the representation of a set or relation by detecting implicit
5180 =item * Removing redundant constraints
5182 #include <isl/set.h>
5183 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5184 __isl_take isl_basic_set *bset);
5185 __isl_give isl_set *isl_set_remove_redundancies(
5186 __isl_take isl_set *set);
5188 #include <isl/union_set.h>
5189 __isl_give isl_union_set *
5190 isl_union_set_remove_redundancies(
5191 __isl_take isl_union_set *uset);
5193 #include <isl/map.h>
5194 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5195 __isl_take isl_basic_map *bmap);
5196 __isl_give isl_map *isl_map_remove_redundancies(
5197 __isl_take isl_map *map);
5199 #include <isl/union_map.h>
5200 __isl_give isl_union_map *
5201 isl_union_map_remove_redundancies(
5202 __isl_take isl_union_map *umap);
5206 __isl_give isl_basic_set *isl_set_convex_hull(
5207 __isl_take isl_set *set);
5208 __isl_give isl_basic_map *isl_map_convex_hull(
5209 __isl_take isl_map *map);
5211 If the input set or relation has any existentially quantified
5212 variables, then the result of these operations is currently undefined.
5216 #include <isl/set.h>
5217 __isl_give isl_basic_set *
5218 isl_set_unshifted_simple_hull(
5219 __isl_take isl_set *set);
5220 __isl_give isl_basic_set *isl_set_simple_hull(
5221 __isl_take isl_set *set);
5222 __isl_give isl_basic_set *
5223 isl_set_plain_unshifted_simple_hull(
5224 __isl_take isl_set *set);
5225 __isl_give isl_basic_set *
5226 isl_set_unshifted_simple_hull_from_set_list(
5227 __isl_take isl_set *set,
5228 __isl_take isl_set_list *list);
5230 #include <isl/map.h>
5231 __isl_give isl_basic_map *
5232 isl_map_unshifted_simple_hull(
5233 __isl_take isl_map *map);
5234 __isl_give isl_basic_map *isl_map_simple_hull(
5235 __isl_take isl_map *map);
5236 __isl_give isl_basic_map *
5237 isl_map_plain_unshifted_simple_hull(
5238 __isl_take isl_map *map);
5239 __isl_give isl_basic_map *
5240 isl_map_unshifted_simple_hull_from_map_list(
5241 __isl_take isl_map *map,
5242 __isl_take isl_map_list *list);
5244 #include <isl/union_map.h>
5245 __isl_give isl_union_map *isl_union_map_simple_hull(
5246 __isl_take isl_union_map *umap);
5248 These functions compute a single basic set or relation
5249 that contains the whole input set or relation.
5250 In particular, the output is described by translates
5251 of the constraints describing the basic sets or relations in the input.
5252 In case of C<isl_set_unshifted_simple_hull>, only the original
5253 constraints are used, without any translation.
5254 In case of C<isl_set_plain_unshifted_simple_hull> and
5255 C<isl_map_plain_unshifted_simple_hull>, the result is described
5256 by original constraints that are obviously satisfied
5257 by the entire input set or relation.
5258 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5259 C<isl_map_unshifted_simple_hull_from_map_list>, the
5260 constraints are taken from the elements of the second argument.
5264 (See \autoref{s:simple hull}.)
5270 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5271 __isl_take isl_basic_set *bset);
5272 __isl_give isl_basic_set *isl_set_affine_hull(
5273 __isl_take isl_set *set);
5274 __isl_give isl_union_set *isl_union_set_affine_hull(
5275 __isl_take isl_union_set *uset);
5276 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5277 __isl_take isl_basic_map *bmap);
5278 __isl_give isl_basic_map *isl_map_affine_hull(
5279 __isl_take isl_map *map);
5280 __isl_give isl_union_map *isl_union_map_affine_hull(
5281 __isl_take isl_union_map *umap);
5283 In case of union sets and relations, the affine hull is computed
5286 =item * Polyhedral hull
5288 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5289 __isl_take isl_set *set);
5290 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5291 __isl_take isl_map *map);
5292 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5293 __isl_take isl_union_set *uset);
5294 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5295 __isl_take isl_union_map *umap);
5297 These functions compute a single basic set or relation
5298 not involving any existentially quantified variables
5299 that contains the whole input set or relation.
5300 In case of union sets and relations, the polyhedral hull is computed
5305 #include <isl/map.h>
5306 __isl_give isl_fixed_box *
5307 isl_map_get_range_simple_fixed_box_hull(
5308 __isl_keep isl_map *map);
5310 This function tries to approximate the range of the map by a box of fixed size.
5311 The box is described in terms of an offset living in the same space as
5312 the input map and a size living in the range space. For any element
5313 in the input map, the range value is greater than or equal to
5314 the offset applied to the domain value and the difference with
5315 this offset is strictly smaller than the size.
5316 If no fixed-size approximation of the range can be found,
5317 an I<invalid> box is returned, i.e., one for which
5318 C<isl_fixed_box_is_valid> below returns false.
5320 The validity, the offset and the size of the box can be obtained using
5321 the following functions.
5323 #include <isl/fixed_box.h>
5324 isl_bool isl_fixed_box_is_valid(
5325 __isl_keep isl_fixed_box *box);
5326 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
5327 __isl_keep isl_fixed_box *box);
5328 __isl_give isl_multi_val *isl_fixed_box_get_size(
5329 __isl_keep isl_fixed_box *box);
5331 The box can be copied and freed using the following functions.
5333 #include <isl/fixed_box.h>
5334 __isl_give isl_fixed_box *isl_fixed_box_copy(
5335 __isl_keep isl_fixed_box *box);
5336 __isl_null isl_fixed_box *isl_fixed_box_free(
5337 __isl_take isl_fixed_box *box);
5339 =item * Other approximations
5341 #include <isl/set.h>
5342 __isl_give isl_basic_set *
5343 isl_basic_set_drop_constraints_involving_dims(
5344 __isl_take isl_basic_set *bset,
5345 enum isl_dim_type type,
5346 unsigned first, unsigned n);
5347 __isl_give isl_basic_set *
5348 isl_basic_set_drop_constraints_not_involving_dims(
5349 __isl_take isl_basic_set *bset,
5350 enum isl_dim_type type,
5351 unsigned first, unsigned n);
5352 __isl_give isl_set *
5353 isl_set_drop_constraints_involving_dims(
5354 __isl_take isl_set *set,
5355 enum isl_dim_type type,
5356 unsigned first, unsigned n);
5357 __isl_give isl_set *
5358 isl_set_drop_constraints_not_involving_dims(
5359 __isl_take isl_set *set,
5360 enum isl_dim_type type,
5361 unsigned first, unsigned n);
5363 #include <isl/map.h>
5364 __isl_give isl_basic_map *
5365 isl_basic_map_drop_constraints_involving_dims(
5366 __isl_take isl_basic_map *bmap,
5367 enum isl_dim_type type,
5368 unsigned first, unsigned n);
5369 __isl_give isl_basic_map *
5370 isl_basic_map_drop_constraints_not_involving_dims(
5371 __isl_take isl_basic_map *bmap,
5372 enum isl_dim_type type,
5373 unsigned first, unsigned n);
5374 __isl_give isl_map *
5375 isl_map_drop_constraints_involving_dims(
5376 __isl_take isl_map *map,
5377 enum isl_dim_type type,
5378 unsigned first, unsigned n);
5379 __isl_give isl_map *
5380 isl_map_drop_constraints_not_involving_dims(
5381 __isl_take isl_map *map,
5382 enum isl_dim_type type,
5383 unsigned first, unsigned n);
5385 These functions drop any constraints (not) involving the specified dimensions.
5386 Note that the result depends on the representation of the input.
5388 #include <isl/polynomial.h>
5389 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5390 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5391 __isl_give isl_union_pw_qpolynomial *
5392 isl_union_pw_qpolynomial_to_polynomial(
5393 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5395 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5396 the polynomial will be an overapproximation. If C<sign> is negative,
5397 it will be an underapproximation. If C<sign> is zero, the approximation
5398 will lie somewhere in between.
5402 __isl_give isl_basic_set *isl_basic_set_sample(
5403 __isl_take isl_basic_set *bset);
5404 __isl_give isl_basic_set *isl_set_sample(
5405 __isl_take isl_set *set);
5406 __isl_give isl_basic_map *isl_basic_map_sample(
5407 __isl_take isl_basic_map *bmap);
5408 __isl_give isl_basic_map *isl_map_sample(
5409 __isl_take isl_map *map);
5411 If the input (basic) set or relation is non-empty, then return
5412 a singleton subset of the input. Otherwise, return an empty set.
5414 =item * Optimization
5416 #include <isl/ilp.h>
5417 __isl_give isl_val *isl_basic_set_max_val(
5418 __isl_keep isl_basic_set *bset,
5419 __isl_keep isl_aff *obj);
5420 __isl_give isl_val *isl_set_min_val(
5421 __isl_keep isl_set *set,
5422 __isl_keep isl_aff *obj);
5423 __isl_give isl_val *isl_set_max_val(
5424 __isl_keep isl_set *set,
5425 __isl_keep isl_aff *obj);
5426 __isl_give isl_multi_val *
5427 isl_union_set_min_multi_union_pw_aff(
5428 __isl_keep isl_union_set *uset,
5429 __isl_keep isl_multi_union_pw_aff *obj);
5431 Compute the minimum or maximum of the integer affine expression C<obj>
5432 over the points in C<set>.
5433 The result is C<NULL> in case of an error, the optimal value in case
5434 there is one, negative infinity or infinity if the problem is unbounded and
5435 NaN if the problem is empty.
5437 #include <isl/ilp.h>
5438 __isl_give isl_val *isl_union_pw_aff_min_val(
5439 __isl_take isl_union_pw_aff *upa);
5440 __isl_give isl_val *isl_union_pw_aff_max_val(
5441 __isl_take isl_union_pw_aff *upa);
5442 __isl_give isl_multi_val *
5443 isl_multi_union_pw_aff_min_multi_val(
5444 __isl_take isl_multi_union_pw_aff *mupa);
5445 __isl_give isl_multi_val *
5446 isl_multi_union_pw_aff_max_multi_val(
5447 __isl_take isl_multi_union_pw_aff *mupa);
5449 Compute the minimum or maximum of the integer affine expression
5450 over its definition domain.
5451 The result is C<NULL> in case of an error, the optimal value in case
5452 there is one, negative infinity or infinity if the problem is unbounded and
5453 NaN if the problem is empty.
5455 #include <isl/ilp.h>
5456 __isl_give isl_val *isl_basic_set_dim_max_val(
5457 __isl_take isl_basic_set *bset, int pos);
5459 Return the maximal value attained by the given set dimension,
5460 independently of the parameter values and of any other dimensions.
5461 The result is C<NULL> in case of an error, the optimal value in case
5462 there is one, infinity if the problem is unbounded and
5463 NaN if the input is empty.
5465 =item * Parametric optimization
5467 __isl_give isl_pw_aff *isl_set_dim_min(
5468 __isl_take isl_set *set, int pos);
5469 __isl_give isl_pw_aff *isl_set_dim_max(
5470 __isl_take isl_set *set, int pos);
5471 __isl_give isl_pw_aff *isl_map_dim_min(
5472 __isl_take isl_map *map, int pos);
5473 __isl_give isl_pw_aff *isl_map_dim_max(
5474 __isl_take isl_map *map, int pos);
5476 Compute the minimum or maximum of the given set or output dimension
5477 as a function of the parameters (and input dimensions), but independently
5478 of the other set or output dimensions.
5479 For lexicographic optimization, see L<"Lexicographic Optimization">.
5483 The following functions compute either the set of (rational) coefficient
5484 values of valid constraints for the given set or the set of (rational)
5485 values satisfying the constraints with coefficients from the given set.
5486 Internally, these two sets of functions perform essentially the
5487 same operations, except that the set of coefficients is assumed to
5488 be a cone, while the set of values may be any polyhedron.
5489 The current implementation is based on the Farkas lemma and
5490 Fourier-Motzkin elimination, but this may change or be made optional
5491 in future. In particular, future implementations may use different
5492 dualization algorithms or skip the elimination step.
5494 #include <isl/set.h>
5495 __isl_give isl_basic_set *isl_basic_set_coefficients(
5496 __isl_take isl_basic_set *bset);
5497 __isl_give isl_basic_set_list *
5498 isl_basic_set_list_coefficients(
5499 __isl_take isl_basic_set_list *list);
5500 __isl_give isl_basic_set *isl_set_coefficients(
5501 __isl_take isl_set *set);
5502 __isl_give isl_union_set *isl_union_set_coefficients(
5503 __isl_take isl_union_set *bset);
5504 __isl_give isl_basic_set *isl_basic_set_solutions(
5505 __isl_take isl_basic_set *bset);
5506 __isl_give isl_basic_set *isl_set_solutions(
5507 __isl_take isl_set *set);
5508 __isl_give isl_union_set *isl_union_set_solutions(
5509 __isl_take isl_union_set *bset);
5513 __isl_give isl_map *isl_map_fixed_power_val(
5514 __isl_take isl_map *map,
5515 __isl_take isl_val *exp);
5516 __isl_give isl_union_map *
5517 isl_union_map_fixed_power_val(
5518 __isl_take isl_union_map *umap,
5519 __isl_take isl_val *exp);
5521 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5522 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5523 of C<map> is computed.
5525 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5527 __isl_give isl_union_map *isl_union_map_power(
5528 __isl_take isl_union_map *umap, int *exact);
5530 Compute a parametric representation for all positive powers I<k> of C<map>.
5531 The result maps I<k> to a nested relation corresponding to the
5532 I<k>th power of C<map>.
5533 The result may be an overapproximation. If the result is known to be exact,
5534 then C<*exact> is set to C<1>.
5536 =item * Transitive closure
5538 __isl_give isl_map *isl_map_transitive_closure(
5539 __isl_take isl_map *map, int *exact);
5540 __isl_give isl_union_map *isl_union_map_transitive_closure(
5541 __isl_take isl_union_map *umap, int *exact);
5543 Compute the transitive closure of C<map>.
5544 The result may be an overapproximation. If the result is known to be exact,
5545 then C<*exact> is set to C<1>.
5547 =item * Reaching path lengths
5549 __isl_give isl_map *isl_map_reaching_path_lengths(
5550 __isl_take isl_map *map, int *exact);
5552 Compute a relation that maps each element in the range of C<map>
5553 to the lengths of all paths composed of edges in C<map> that
5554 end up in the given element.
5555 The result may be an overapproximation. If the result is known to be exact,
5556 then C<*exact> is set to C<1>.
5557 To compute the I<maximal> path length, the resulting relation
5558 should be postprocessed by C<isl_map_lexmax>.
5559 In particular, if the input relation is a dependence relation
5560 (mapping sources to sinks), then the maximal path length corresponds
5561 to the free schedule.
5562 Note, however, that C<isl_map_lexmax> expects the maximum to be
5563 finite, so if the path lengths are unbounded (possibly due to
5564 the overapproximation), then you will get an error message.
5568 #include <isl/space.h>
5569 __isl_give isl_space *isl_space_wrap(
5570 __isl_take isl_space *space);
5571 __isl_give isl_space *isl_space_unwrap(
5572 __isl_take isl_space *space);
5574 #include <isl/local_space.h>
5575 __isl_give isl_local_space *isl_local_space_wrap(
5576 __isl_take isl_local_space *ls);
5578 #include <isl/set.h>
5579 __isl_give isl_basic_map *isl_basic_set_unwrap(
5580 __isl_take isl_basic_set *bset);
5581 __isl_give isl_map *isl_set_unwrap(
5582 __isl_take isl_set *set);
5584 #include <isl/map.h>
5585 __isl_give isl_basic_set *isl_basic_map_wrap(
5586 __isl_take isl_basic_map *bmap);
5587 __isl_give isl_set *isl_map_wrap(
5588 __isl_take isl_map *map);
5590 #include <isl/union_set.h>
5591 __isl_give isl_union_map *isl_union_set_unwrap(
5592 __isl_take isl_union_set *uset);
5594 #include <isl/union_map.h>
5595 __isl_give isl_union_set *isl_union_map_wrap(
5596 __isl_take isl_union_map *umap);
5598 The input to C<isl_space_unwrap> should
5599 be the space of a set, while that of
5600 C<isl_space_wrap> should be the space of a relation.
5601 Conversely, the output of C<isl_space_unwrap> is the space
5602 of a relation, while that of C<isl_space_wrap> is the space of a set.
5606 Remove any internal structure of domain (and range) of the given
5607 set or relation. If there is any such internal structure in the input,
5608 then the name of the space is also removed.
5610 #include <isl/space.h>
5611 __isl_give isl_space *isl_space_flatten_domain(
5612 __isl_take isl_space *space);
5613 __isl_give isl_space *isl_space_flatten_range(
5614 __isl_take isl_space *space);
5616 #include <isl/local_space.h>
5617 __isl_give isl_local_space *
5618 isl_local_space_flatten_domain(
5619 __isl_take isl_local_space *ls);
5620 __isl_give isl_local_space *
5621 isl_local_space_flatten_range(
5622 __isl_take isl_local_space *ls);
5624 #include <isl/set.h>
5625 __isl_give isl_basic_set *isl_basic_set_flatten(
5626 __isl_take isl_basic_set *bset);
5627 __isl_give isl_set *isl_set_flatten(
5628 __isl_take isl_set *set);
5630 #include <isl/map.h>
5631 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5632 __isl_take isl_basic_map *bmap);
5633 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5634 __isl_take isl_basic_map *bmap);
5635 __isl_give isl_map *isl_map_flatten_range(
5636 __isl_take isl_map *map);
5637 __isl_give isl_map *isl_map_flatten_domain(
5638 __isl_take isl_map *map);
5639 __isl_give isl_basic_map *isl_basic_map_flatten(
5640 __isl_take isl_basic_map *bmap);
5641 __isl_give isl_map *isl_map_flatten(
5642 __isl_take isl_map *map);
5644 #include <isl/val.h>
5645 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5646 __isl_take isl_multi_val *mv);
5648 #include <isl/aff.h>
5649 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5650 __isl_take isl_multi_aff *ma);
5651 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5652 __isl_take isl_multi_aff *ma);
5653 __isl_give isl_multi_pw_aff *
5654 isl_multi_pw_aff_flatten_range(
5655 __isl_take isl_multi_pw_aff *mpa);
5656 __isl_give isl_multi_union_pw_aff *
5657 isl_multi_union_pw_aff_flatten_range(
5658 __isl_take isl_multi_union_pw_aff *mupa);
5660 #include <isl/map.h>
5661 __isl_give isl_map *isl_set_flatten_map(
5662 __isl_take isl_set *set);
5664 The function above constructs a relation
5665 that maps the input set to a flattened version of the set.
5669 Lift the input set to a space with extra dimensions corresponding
5670 to the existentially quantified variables in the input.
5671 In particular, the result lives in a wrapped map where the domain
5672 is the original space and the range corresponds to the original
5673 existentially quantified variables.
5675 #include <isl/set.h>
5676 __isl_give isl_basic_set *isl_basic_set_lift(
5677 __isl_take isl_basic_set *bset);
5678 __isl_give isl_set *isl_set_lift(
5679 __isl_take isl_set *set);
5680 __isl_give isl_union_set *isl_union_set_lift(
5681 __isl_take isl_union_set *uset);
5683 Given a local space that contains the existentially quantified
5684 variables of a set, a basic relation that, when applied to
5685 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5686 can be constructed using the following function.
5688 #include <isl/local_space.h>
5689 __isl_give isl_basic_map *isl_local_space_lifting(
5690 __isl_take isl_local_space *ls);
5692 #include <isl/aff.h>
5693 __isl_give isl_multi_aff *isl_multi_aff_lift(
5694 __isl_take isl_multi_aff *maff,
5695 __isl_give isl_local_space **ls);
5697 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5698 then it is assigned the local space that lies at the basis of
5699 the lifting applied.
5701 =item * Internal Product
5703 #include <isl/space.h>
5704 __isl_give isl_space *isl_space_zip(
5705 __isl_take isl_space *space);
5707 #include <isl/map.h>
5708 __isl_give isl_basic_map *isl_basic_map_zip(
5709 __isl_take isl_basic_map *bmap);
5710 __isl_give isl_map *isl_map_zip(
5711 __isl_take isl_map *map);
5713 #include <isl/union_map.h>
5714 __isl_give isl_union_map *isl_union_map_zip(
5715 __isl_take isl_union_map *umap);
5717 Given a relation with nested relations for domain and range,
5718 interchange the range of the domain with the domain of the range.
5722 #include <isl/space.h>
5723 __isl_give isl_space *isl_space_curry(
5724 __isl_take isl_space *space);
5725 __isl_give isl_space *isl_space_uncurry(
5726 __isl_take isl_space *space);
5728 #include <isl/map.h>
5729 __isl_give isl_basic_map *isl_basic_map_curry(
5730 __isl_take isl_basic_map *bmap);
5731 __isl_give isl_basic_map *isl_basic_map_uncurry(
5732 __isl_take isl_basic_map *bmap);
5733 __isl_give isl_map *isl_map_curry(
5734 __isl_take isl_map *map);
5735 __isl_give isl_map *isl_map_uncurry(
5736 __isl_take isl_map *map);
5738 #include <isl/union_map.h>
5739 __isl_give isl_union_map *isl_union_map_curry(
5740 __isl_take isl_union_map *umap);
5741 __isl_give isl_union_map *isl_union_map_uncurry(
5742 __isl_take isl_union_map *umap);
5744 Given a relation with a nested relation for domain,
5745 the C<curry> functions
5746 move the range of the nested relation out of the domain
5747 and use it as the domain of a nested relation in the range,
5748 with the original range as range of this nested relation.
5749 The C<uncurry> functions perform the inverse operation.
5751 #include <isl/space.h>
5752 __isl_give isl_space *isl_space_range_curry(
5753 __isl_take isl_space *space);
5755 #include <isl/map.h>
5756 __isl_give isl_map *isl_map_range_curry(
5757 __isl_take isl_map *map);
5759 #include <isl/union_map.h>
5760 __isl_give isl_union_map *isl_union_map_range_curry(
5761 __isl_take isl_union_map *umap);
5763 These functions apply the currying to the relation that
5764 is nested inside the range of the input.
5766 =item * Aligning parameters
5768 Change the order of the parameters of the given set, relation
5770 such that the first parameters match those of C<model>.
5771 This may involve the introduction of extra parameters.
5772 All parameters need to be named.
5774 #include <isl/space.h>
5775 __isl_give isl_space *isl_space_align_params(
5776 __isl_take isl_space *space1,
5777 __isl_take isl_space *space2)
5779 #include <isl/set.h>
5780 __isl_give isl_basic_set *isl_basic_set_align_params(
5781 __isl_take isl_basic_set *bset,
5782 __isl_take isl_space *model);
5783 __isl_give isl_set *isl_set_align_params(
5784 __isl_take isl_set *set,
5785 __isl_take isl_space *model);
5787 #include <isl/map.h>
5788 __isl_give isl_basic_map *isl_basic_map_align_params(
5789 __isl_take isl_basic_map *bmap,
5790 __isl_take isl_space *model);
5791 __isl_give isl_map *isl_map_align_params(
5792 __isl_take isl_map *map,
5793 __isl_take isl_space *model);
5795 #include <isl/val.h>
5796 __isl_give isl_multi_val *isl_multi_val_align_params(
5797 __isl_take isl_multi_val *mv,
5798 __isl_take isl_space *model);
5800 #include <isl/aff.h>
5801 __isl_give isl_aff *isl_aff_align_params(
5802 __isl_take isl_aff *aff,
5803 __isl_take isl_space *model);
5804 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5805 __isl_take isl_multi_aff *multi,
5806 __isl_take isl_space *model);
5807 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5808 __isl_take isl_pw_aff *pwaff,
5809 __isl_take isl_space *model);
5810 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5811 __isl_take isl_pw_multi_aff *pma,
5812 __isl_take isl_space *model);
5813 __isl_give isl_union_pw_aff *
5814 isl_union_pw_aff_align_params(
5815 __isl_take isl_union_pw_aff *upa,
5816 __isl_take isl_space *model);
5817 __isl_give isl_union_pw_multi_aff *
5818 isl_union_pw_multi_aff_align_params(
5819 __isl_take isl_union_pw_multi_aff *upma,
5820 __isl_take isl_space *model);
5821 __isl_give isl_multi_union_pw_aff *
5822 isl_multi_union_pw_aff_align_params(
5823 __isl_take isl_multi_union_pw_aff *mupa,
5824 __isl_take isl_space *model);
5826 #include <isl/polynomial.h>
5827 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5828 __isl_take isl_qpolynomial *qp,
5829 __isl_take isl_space *model);
5831 =item * Drop unused parameters
5833 Drop parameters that are not referenced by the isl object.
5834 All parameters need to be named.
5836 #include <isl/set.h>
5837 __isl_give isl_basic_set *
5838 isl_basic_set_drop_unused_params(
5839 __isl_take isl_basic_set *bset);
5840 __isl_give isl_set *isl_set_drop_unused_params(
5841 __isl_take isl_set *set);
5843 #include <isl/map.h>
5844 __isl_give isl_basic_map *
5845 isl_basic_map_drop_unused_params(
5846 __isl_take isl_basic_map *bmap);
5847 __isl_give isl_map *isl_map_drop_unused_params(
5848 __isl_take isl_map *map);
5850 #include <isl/aff.h>
5851 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
5852 __isl_take isl_pw_aff *pa);
5853 __isl_give isl_pw_multi_aff *
5854 isl_pw_multi_aff_drop_unused_params(
5855 __isl_take isl_pw_multi_aff *pma);
5857 #include <isl/polynomial.h>
5858 __isl_give isl_pw_qpolynomial *
5859 isl_pw_qpolynomial_drop_unused_params(
5860 __isl_take isl_pw_qpolynomial *pwqp);
5861 __isl_give isl_pw_qpolynomial_fold *
5862 isl_pw_qpolynomial_fold_drop_unused_params(
5863 __isl_take isl_pw_qpolynomial_fold *pwf);
5865 =item * Unary Arithmetic Operations
5867 #include <isl/set.h>
5868 __isl_give isl_set *isl_set_neg(
5869 __isl_take isl_set *set);
5870 #include <isl/map.h>
5871 __isl_give isl_map *isl_map_neg(
5872 __isl_take isl_map *map);
5874 C<isl_set_neg> constructs a set containing the opposites of
5875 the elements in its argument.
5876 The domain of the result of C<isl_map_neg> is the same
5877 as the domain of its argument. The corresponding range
5878 elements are the opposites of the corresponding range
5879 elements in the argument.
5881 #include <isl/val.h>
5882 __isl_give isl_multi_val *isl_multi_val_neg(
5883 __isl_take isl_multi_val *mv);
5885 #include <isl/aff.h>
5886 __isl_give isl_aff *isl_aff_neg(
5887 __isl_take isl_aff *aff);
5888 __isl_give isl_multi_aff *isl_multi_aff_neg(
5889 __isl_take isl_multi_aff *ma);
5890 __isl_give isl_pw_aff *isl_pw_aff_neg(
5891 __isl_take isl_pw_aff *pwaff);
5892 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5893 __isl_take isl_pw_multi_aff *pma);
5894 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5895 __isl_take isl_multi_pw_aff *mpa);
5896 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5897 __isl_take isl_union_pw_aff *upa);
5898 __isl_give isl_union_pw_multi_aff *
5899 isl_union_pw_multi_aff_neg(
5900 __isl_take isl_union_pw_multi_aff *upma);
5901 __isl_give isl_multi_union_pw_aff *
5902 isl_multi_union_pw_aff_neg(
5903 __isl_take isl_multi_union_pw_aff *mupa);
5904 __isl_give isl_aff *isl_aff_ceil(
5905 __isl_take isl_aff *aff);
5906 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5907 __isl_take isl_pw_aff *pwaff);
5908 __isl_give isl_aff *isl_aff_floor(
5909 __isl_take isl_aff *aff);
5910 __isl_give isl_multi_aff *isl_multi_aff_floor(
5911 __isl_take isl_multi_aff *ma);
5912 __isl_give isl_pw_aff *isl_pw_aff_floor(
5913 __isl_take isl_pw_aff *pwaff);
5914 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5915 __isl_take isl_union_pw_aff *upa);
5916 __isl_give isl_multi_union_pw_aff *
5917 isl_multi_union_pw_aff_floor(
5918 __isl_take isl_multi_union_pw_aff *mupa);
5920 #include <isl/aff.h>
5921 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5922 __isl_take isl_pw_aff_list *list);
5923 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5924 __isl_take isl_pw_aff_list *list);
5926 #include <isl/polynomial.h>
5927 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5928 __isl_take isl_qpolynomial *qp);
5929 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5930 __isl_take isl_pw_qpolynomial *pwqp);
5931 __isl_give isl_union_pw_qpolynomial *
5932 isl_union_pw_qpolynomial_neg(
5933 __isl_take isl_union_pw_qpolynomial *upwqp);
5934 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5935 __isl_take isl_qpolynomial *qp,
5937 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5938 __isl_take isl_pw_qpolynomial *pwqp,
5943 The following functions evaluate a function in a point.
5945 #include <isl/aff.h>
5946 __isl_give isl_val *isl_aff_eval(
5947 __isl_take isl_aff *aff,
5948 __isl_take isl_point *pnt);
5949 __isl_give isl_val *isl_pw_aff_eval(
5950 __isl_take isl_pw_aff *pa,
5951 __isl_take isl_point *pnt);
5953 #include <isl/polynomial.h>
5954 __isl_give isl_val *isl_pw_qpolynomial_eval(
5955 __isl_take isl_pw_qpolynomial *pwqp,
5956 __isl_take isl_point *pnt);
5957 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5958 __isl_take isl_pw_qpolynomial_fold *pwf,
5959 __isl_take isl_point *pnt);
5960 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5961 __isl_take isl_union_pw_qpolynomial *upwqp,
5962 __isl_take isl_point *pnt);
5963 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5964 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5965 __isl_take isl_point *pnt);
5967 These functions return NaN when evaluated at a void point.
5968 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
5969 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
5970 when the function is evaluated outside its explicit domain.
5972 =item * Dimension manipulation
5974 It is usually not advisable to directly change the (input or output)
5975 space of a set or a relation as this removes the name and the internal
5976 structure of the space. However, the functions below can be useful
5977 to add new parameters, assuming
5978 C<isl_set_align_params> and C<isl_map_align_params>
5981 #include <isl/space.h>
5982 __isl_give isl_space *isl_space_add_dims(
5983 __isl_take isl_space *space,
5984 enum isl_dim_type type, unsigned n);
5985 __isl_give isl_space *isl_space_insert_dims(
5986 __isl_take isl_space *space,
5987 enum isl_dim_type type, unsigned pos, unsigned n);
5988 __isl_give isl_space *isl_space_drop_dims(
5989 __isl_take isl_space *space,
5990 enum isl_dim_type type, unsigned first, unsigned n);
5991 __isl_give isl_space *isl_space_move_dims(
5992 __isl_take isl_space *space,
5993 enum isl_dim_type dst_type, unsigned dst_pos,
5994 enum isl_dim_type src_type, unsigned src_pos,
5997 #include <isl/local_space.h>
5998 __isl_give isl_local_space *isl_local_space_add_dims(
5999 __isl_take isl_local_space *ls,
6000 enum isl_dim_type type, unsigned n);
6001 __isl_give isl_local_space *isl_local_space_insert_dims(
6002 __isl_take isl_local_space *ls,
6003 enum isl_dim_type type, unsigned first, unsigned n);
6004 __isl_give isl_local_space *isl_local_space_drop_dims(
6005 __isl_take isl_local_space *ls,
6006 enum isl_dim_type type, unsigned first, unsigned n);
6008 #include <isl/set.h>
6009 __isl_give isl_basic_set *isl_basic_set_add_dims(
6010 __isl_take isl_basic_set *bset,
6011 enum isl_dim_type type, unsigned n);
6012 __isl_give isl_set *isl_set_add_dims(
6013 __isl_take isl_set *set,
6014 enum isl_dim_type type, unsigned n);
6015 __isl_give isl_basic_set *isl_basic_set_insert_dims(
6016 __isl_take isl_basic_set *bset,
6017 enum isl_dim_type type, unsigned pos,
6019 __isl_give isl_set *isl_set_insert_dims(
6020 __isl_take isl_set *set,
6021 enum isl_dim_type type, unsigned pos, unsigned n);
6022 __isl_give isl_basic_set *isl_basic_set_move_dims(
6023 __isl_take isl_basic_set *bset,
6024 enum isl_dim_type dst_type, unsigned dst_pos,
6025 enum isl_dim_type src_type, unsigned src_pos,
6027 __isl_give isl_set *isl_set_move_dims(
6028 __isl_take isl_set *set,
6029 enum isl_dim_type dst_type, unsigned dst_pos,
6030 enum isl_dim_type src_type, unsigned src_pos,
6033 #include <isl/map.h>
6034 __isl_give isl_basic_map *isl_basic_map_add_dims(
6035 __isl_take isl_basic_map *bmap,
6036 enum isl_dim_type type, unsigned n);
6037 __isl_give isl_map *isl_map_add_dims(
6038 __isl_take isl_map *map,
6039 enum isl_dim_type type, unsigned n);
6040 __isl_give isl_basic_map *isl_basic_map_insert_dims(
6041 __isl_take isl_basic_map *bmap,
6042 enum isl_dim_type type, unsigned pos,
6044 __isl_give isl_map *isl_map_insert_dims(
6045 __isl_take isl_map *map,
6046 enum isl_dim_type type, unsigned pos, unsigned n);
6047 __isl_give isl_basic_map *isl_basic_map_move_dims(
6048 __isl_take isl_basic_map *bmap,
6049 enum isl_dim_type dst_type, unsigned dst_pos,
6050 enum isl_dim_type src_type, unsigned src_pos,
6052 __isl_give isl_map *isl_map_move_dims(
6053 __isl_take isl_map *map,
6054 enum isl_dim_type dst_type, unsigned dst_pos,
6055 enum isl_dim_type src_type, unsigned src_pos,
6058 #include <isl/val.h>
6059 __isl_give isl_multi_val *isl_multi_val_insert_dims(
6060 __isl_take isl_multi_val *mv,
6061 enum isl_dim_type type, unsigned first, unsigned n);
6062 __isl_give isl_multi_val *isl_multi_val_add_dims(
6063 __isl_take isl_multi_val *mv,
6064 enum isl_dim_type type, unsigned n);
6065 __isl_give isl_multi_val *isl_multi_val_drop_dims(
6066 __isl_take isl_multi_val *mv,
6067 enum isl_dim_type type, unsigned first, unsigned n);
6069 #include <isl/aff.h>
6070 __isl_give isl_aff *isl_aff_insert_dims(
6071 __isl_take isl_aff *aff,
6072 enum isl_dim_type type, unsigned first, unsigned n);
6073 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
6074 __isl_take isl_multi_aff *ma,
6075 enum isl_dim_type type, unsigned first, unsigned n);
6076 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
6077 __isl_take isl_pw_aff *pwaff,
6078 enum isl_dim_type type, unsigned first, unsigned n);
6079 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
6080 __isl_take isl_multi_pw_aff *mpa,
6081 enum isl_dim_type type, unsigned first, unsigned n);
6082 __isl_give isl_aff *isl_aff_add_dims(
6083 __isl_take isl_aff *aff,
6084 enum isl_dim_type type, unsigned n);
6085 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
6086 __isl_take isl_multi_aff *ma,
6087 enum isl_dim_type type, unsigned n);
6088 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
6089 __isl_take isl_pw_aff *pwaff,
6090 enum isl_dim_type type, unsigned n);
6091 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
6092 __isl_take isl_multi_pw_aff *mpa,
6093 enum isl_dim_type type, unsigned n);
6094 __isl_give isl_aff *isl_aff_drop_dims(
6095 __isl_take isl_aff *aff,
6096 enum isl_dim_type type, unsigned first, unsigned n);
6097 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
6098 __isl_take isl_multi_aff *maff,
6099 enum isl_dim_type type, unsigned first, unsigned n);
6100 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
6101 __isl_take isl_pw_aff *pwaff,
6102 enum isl_dim_type type, unsigned first, unsigned n);
6103 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
6104 __isl_take isl_pw_multi_aff *pma,
6105 enum isl_dim_type type, unsigned first, unsigned n);
6106 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
6107 __isl_take isl_union_pw_aff *upa,
6108 enum isl_dim_type type, unsigned first, unsigned n);
6109 __isl_give isl_union_pw_multi_aff *
6110 isl_union_pw_multi_aff_drop_dims(
6111 __isl_take isl_union_pw_multi_aff *upma,
6112 enum isl_dim_type type,
6113 unsigned first, unsigned n);
6114 __isl_give isl_multi_union_pw_aff *
6115 isl_multi_union_pw_aff_drop_dims(
6116 __isl_take isl_multi_union_pw_aff *mupa,
6117 enum isl_dim_type type, unsigned first,
6119 __isl_give isl_aff *isl_aff_move_dims(
6120 __isl_take isl_aff *aff,
6121 enum isl_dim_type dst_type, unsigned dst_pos,
6122 enum isl_dim_type src_type, unsigned src_pos,
6124 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
6125 __isl_take isl_multi_aff *ma,
6126 enum isl_dim_type dst_type, unsigned dst_pos,
6127 enum isl_dim_type src_type, unsigned src_pos,
6129 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
6130 __isl_take isl_pw_aff *pa,
6131 enum isl_dim_type dst_type, unsigned dst_pos,
6132 enum isl_dim_type src_type, unsigned src_pos,
6134 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
6135 __isl_take isl_multi_pw_aff *pma,
6136 enum isl_dim_type dst_type, unsigned dst_pos,
6137 enum isl_dim_type src_type, unsigned src_pos,
6140 #include <isl/polynomial.h>
6141 __isl_give isl_union_pw_qpolynomial *
6142 isl_union_pw_qpolynomial_drop_dims(
6143 __isl_take isl_union_pw_qpolynomial *upwqp,
6144 enum isl_dim_type type,
6145 unsigned first, unsigned n);
6146 __isl_give isl_union_pw_qpolynomial_fold *
6147 isl_union_pw_qpolynomial_fold_drop_dims(
6148 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6149 enum isl_dim_type type,
6150 unsigned first, unsigned n);
6152 The operations on union expressions can only manipulate parameters.
6156 =head2 Binary Operations
6158 The two arguments of a binary operation not only need to live
6159 in the same C<isl_ctx>, they currently also need to have
6160 the same (number of) parameters.
6162 =head3 Basic Operations
6166 =item * Intersection
6168 #include <isl/local_space.h>
6169 __isl_give isl_local_space *isl_local_space_intersect(
6170 __isl_take isl_local_space *ls1,
6171 __isl_take isl_local_space *ls2);
6173 #include <isl/set.h>
6174 __isl_give isl_basic_set *isl_basic_set_intersect_params(
6175 __isl_take isl_basic_set *bset1,
6176 __isl_take isl_basic_set *bset2);
6177 __isl_give isl_basic_set *isl_basic_set_intersect(
6178 __isl_take isl_basic_set *bset1,
6179 __isl_take isl_basic_set *bset2);
6180 __isl_give isl_basic_set *isl_basic_set_list_intersect(
6181 __isl_take struct isl_basic_set_list *list);
6182 __isl_give isl_set *isl_set_intersect_params(
6183 __isl_take isl_set *set,
6184 __isl_take isl_set *params);
6185 __isl_give isl_set *isl_set_intersect(
6186 __isl_take isl_set *set1,
6187 __isl_take isl_set *set2);
6189 #include <isl/map.h>
6190 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
6191 __isl_take isl_basic_map *bmap,
6192 __isl_take isl_basic_set *bset);
6193 __isl_give isl_basic_map *isl_basic_map_intersect_range(
6194 __isl_take isl_basic_map *bmap,
6195 __isl_take isl_basic_set *bset);
6196 __isl_give isl_basic_map *isl_basic_map_intersect(
6197 __isl_take isl_basic_map *bmap1,
6198 __isl_take isl_basic_map *bmap2);
6199 __isl_give isl_basic_map *isl_basic_map_list_intersect(
6200 __isl_take isl_basic_map_list *list);
6201 __isl_give isl_map *isl_map_intersect_params(
6202 __isl_take isl_map *map,
6203 __isl_take isl_set *params);
6204 __isl_give isl_map *isl_map_intersect_domain(
6205 __isl_take isl_map *map,
6206 __isl_take isl_set *set);
6207 __isl_give isl_map *isl_map_intersect_range(
6208 __isl_take isl_map *map,
6209 __isl_take isl_set *set);
6210 __isl_give isl_map *isl_map_intersect(
6211 __isl_take isl_map *map1,
6212 __isl_take isl_map *map2);
6213 __isl_give isl_map *
6214 isl_map_intersect_domain_factor_range(
6215 __isl_take isl_map *map,
6216 __isl_take isl_map *factor);
6217 __isl_give isl_map *
6218 isl_map_intersect_range_factor_range(
6219 __isl_take isl_map *map,
6220 __isl_take isl_map *factor);
6222 #include <isl/union_set.h>
6223 __isl_give isl_union_set *isl_union_set_intersect_params(
6224 __isl_take isl_union_set *uset,
6225 __isl_take isl_set *set);
6226 __isl_give isl_union_set *isl_union_set_intersect(
6227 __isl_take isl_union_set *uset1,
6228 __isl_take isl_union_set *uset2);
6230 #include <isl/union_map.h>
6231 __isl_give isl_union_map *isl_union_map_intersect_params(
6232 __isl_take isl_union_map *umap,
6233 __isl_take isl_set *set);
6234 __isl_give isl_union_map *isl_union_map_intersect_domain(
6235 __isl_take isl_union_map *umap,
6236 __isl_take isl_union_set *uset);
6237 __isl_give isl_union_map *isl_union_map_intersect_range(
6238 __isl_take isl_union_map *umap,
6239 __isl_take isl_union_set *uset);
6240 __isl_give isl_union_map *isl_union_map_intersect(
6241 __isl_take isl_union_map *umap1,
6242 __isl_take isl_union_map *umap2);
6243 __isl_give isl_union_map *
6244 isl_union_map_intersect_range_factor_range(
6245 __isl_take isl_union_map *umap,
6246 __isl_take isl_union_map *factor);
6248 #include <isl/aff.h>
6249 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6250 __isl_take isl_pw_aff *pa,
6251 __isl_take isl_set *set);
6252 __isl_give isl_multi_pw_aff *
6253 isl_multi_pw_aff_intersect_domain(
6254 __isl_take isl_multi_pw_aff *mpa,
6255 __isl_take isl_set *domain);
6256 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6257 __isl_take isl_pw_multi_aff *pma,
6258 __isl_take isl_set *set);
6259 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6260 __isl_take isl_union_pw_aff *upa,
6261 __isl_take isl_union_set *uset);
6262 __isl_give isl_union_pw_multi_aff *
6263 isl_union_pw_multi_aff_intersect_domain(
6264 __isl_take isl_union_pw_multi_aff *upma,
6265 __isl_take isl_union_set *uset);
6266 __isl_give isl_multi_union_pw_aff *
6267 isl_multi_union_pw_aff_intersect_domain(
6268 __isl_take isl_multi_union_pw_aff *mupa,
6269 __isl_take isl_union_set *uset);
6270 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6271 __isl_take isl_pw_aff *pa,
6272 __isl_take isl_set *set);
6273 __isl_give isl_multi_pw_aff *
6274 isl_multi_pw_aff_intersect_params(
6275 __isl_take isl_multi_pw_aff *mpa,
6276 __isl_take isl_set *set);
6277 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6278 __isl_take isl_pw_multi_aff *pma,
6279 __isl_take isl_set *set);
6280 __isl_give isl_union_pw_aff *
6281 isl_union_pw_aff_intersect_params(
6282 __isl_take isl_union_pw_aff *upa,
6283 __isl_give isl_union_pw_multi_aff *
6284 isl_union_pw_multi_aff_intersect_params(
6285 __isl_take isl_union_pw_multi_aff *upma,
6286 __isl_take isl_set *set);
6287 __isl_give isl_multi_union_pw_aff *
6288 isl_multi_union_pw_aff_intersect_params(
6289 __isl_take isl_multi_union_pw_aff *mupa,
6290 __isl_take isl_set *params);
6291 isl_multi_union_pw_aff_intersect_range(
6292 __isl_take isl_multi_union_pw_aff *mupa,
6293 __isl_take isl_set *set);
6295 #include <isl/polynomial.h>
6296 __isl_give isl_pw_qpolynomial *
6297 isl_pw_qpolynomial_intersect_domain(
6298 __isl_take isl_pw_qpolynomial *pwpq,
6299 __isl_take isl_set *set);
6300 __isl_give isl_union_pw_qpolynomial *
6301 isl_union_pw_qpolynomial_intersect_domain(
6302 __isl_take isl_union_pw_qpolynomial *upwpq,
6303 __isl_take isl_union_set *uset);
6304 __isl_give isl_union_pw_qpolynomial_fold *
6305 isl_union_pw_qpolynomial_fold_intersect_domain(
6306 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6307 __isl_take isl_union_set *uset);
6308 __isl_give isl_pw_qpolynomial *
6309 isl_pw_qpolynomial_intersect_params(
6310 __isl_take isl_pw_qpolynomial *pwpq,
6311 __isl_take isl_set *set);
6312 __isl_give isl_pw_qpolynomial_fold *
6313 isl_pw_qpolynomial_fold_intersect_params(
6314 __isl_take isl_pw_qpolynomial_fold *pwf,
6315 __isl_take isl_set *set);
6316 __isl_give isl_union_pw_qpolynomial *
6317 isl_union_pw_qpolynomial_intersect_params(
6318 __isl_take isl_union_pw_qpolynomial *upwpq,
6319 __isl_take isl_set *set);
6320 __isl_give isl_union_pw_qpolynomial_fold *
6321 isl_union_pw_qpolynomial_fold_intersect_params(
6322 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6323 __isl_take isl_set *set);
6325 The second argument to the C<_params> functions needs to be
6326 a parametric (basic) set. For the other functions, a parametric set
6327 for either argument is only allowed if the other argument is
6328 a parametric set as well.
6329 The list passed to C<isl_basic_set_list_intersect> needs to have
6330 at least one element and all elements need to live in the same space.
6331 The function C<isl_multi_union_pw_aff_intersect_range>
6332 restricts the input function to those shared domain elements
6333 that map to the specified range.
6337 #include <isl/set.h>
6338 __isl_give isl_set *isl_basic_set_union(
6339 __isl_take isl_basic_set *bset1,
6340 __isl_take isl_basic_set *bset2);
6341 __isl_give isl_set *isl_set_union(
6342 __isl_take isl_set *set1,
6343 __isl_take isl_set *set2);
6344 __isl_give isl_set *isl_set_list_union(
6345 __isl_take isl_set_list *list);
6347 #include <isl/map.h>
6348 __isl_give isl_map *isl_basic_map_union(
6349 __isl_take isl_basic_map *bmap1,
6350 __isl_take isl_basic_map *bmap2);
6351 __isl_give isl_map *isl_map_union(
6352 __isl_take isl_map *map1,
6353 __isl_take isl_map *map2);
6355 #include <isl/union_set.h>
6356 __isl_give isl_union_set *isl_union_set_union(
6357 __isl_take isl_union_set *uset1,
6358 __isl_take isl_union_set *uset2);
6359 __isl_give isl_union_set *isl_union_set_list_union(
6360 __isl_take isl_union_set_list *list);
6362 #include <isl/union_map.h>
6363 __isl_give isl_union_map *isl_union_map_union(
6364 __isl_take isl_union_map *umap1,
6365 __isl_take isl_union_map *umap2);
6367 The list passed to C<isl_set_list_union> needs to have
6368 at least one element and all elements need to live in the same space.
6370 =item * Set difference
6372 #include <isl/set.h>
6373 __isl_give isl_set *isl_set_subtract(
6374 __isl_take isl_set *set1,
6375 __isl_take isl_set *set2);
6377 #include <isl/map.h>
6378 __isl_give isl_map *isl_map_subtract(
6379 __isl_take isl_map *map1,
6380 __isl_take isl_map *map2);
6381 __isl_give isl_map *isl_map_subtract_domain(
6382 __isl_take isl_map *map,
6383 __isl_take isl_set *dom);
6384 __isl_give isl_map *isl_map_subtract_range(
6385 __isl_take isl_map *map,
6386 __isl_take isl_set *dom);
6388 #include <isl/union_set.h>
6389 __isl_give isl_union_set *isl_union_set_subtract(
6390 __isl_take isl_union_set *uset1,
6391 __isl_take isl_union_set *uset2);
6393 #include <isl/union_map.h>
6394 __isl_give isl_union_map *isl_union_map_subtract(
6395 __isl_take isl_union_map *umap1,
6396 __isl_take isl_union_map *umap2);
6397 __isl_give isl_union_map *isl_union_map_subtract_domain(
6398 __isl_take isl_union_map *umap,
6399 __isl_take isl_union_set *dom);
6400 __isl_give isl_union_map *isl_union_map_subtract_range(
6401 __isl_take isl_union_map *umap,
6402 __isl_take isl_union_set *dom);
6404 #include <isl/aff.h>
6405 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6406 __isl_take isl_pw_aff *pa,
6407 __isl_take isl_set *set);
6408 __isl_give isl_pw_multi_aff *
6409 isl_pw_multi_aff_subtract_domain(
6410 __isl_take isl_pw_multi_aff *pma,
6411 __isl_take isl_set *set);
6412 __isl_give isl_union_pw_aff *
6413 isl_union_pw_aff_subtract_domain(
6414 __isl_take isl_union_pw_aff *upa,
6415 __isl_take isl_union_set *uset);
6416 __isl_give isl_union_pw_multi_aff *
6417 isl_union_pw_multi_aff_subtract_domain(
6418 __isl_take isl_union_pw_multi_aff *upma,
6419 __isl_take isl_set *set);
6421 #include <isl/polynomial.h>
6422 __isl_give isl_pw_qpolynomial *
6423 isl_pw_qpolynomial_subtract_domain(
6424 __isl_take isl_pw_qpolynomial *pwpq,
6425 __isl_take isl_set *set);
6426 __isl_give isl_pw_qpolynomial_fold *
6427 isl_pw_qpolynomial_fold_subtract_domain(
6428 __isl_take isl_pw_qpolynomial_fold *pwf,
6429 __isl_take isl_set *set);
6430 __isl_give isl_union_pw_qpolynomial *
6431 isl_union_pw_qpolynomial_subtract_domain(
6432 __isl_take isl_union_pw_qpolynomial *upwpq,
6433 __isl_take isl_union_set *uset);
6434 __isl_give isl_union_pw_qpolynomial_fold *
6435 isl_union_pw_qpolynomial_fold_subtract_domain(
6436 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6437 __isl_take isl_union_set *uset);
6441 #include <isl/space.h>
6442 __isl_give isl_space *isl_space_join(
6443 __isl_take isl_space *left,
6444 __isl_take isl_space *right);
6446 #include <isl/map.h>
6447 __isl_give isl_basic_set *isl_basic_set_apply(
6448 __isl_take isl_basic_set *bset,
6449 __isl_take isl_basic_map *bmap);
6450 __isl_give isl_set *isl_set_apply(
6451 __isl_take isl_set *set,
6452 __isl_take isl_map *map);
6453 __isl_give isl_union_set *isl_union_set_apply(
6454 __isl_take isl_union_set *uset,
6455 __isl_take isl_union_map *umap);
6456 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6457 __isl_take isl_basic_map *bmap1,
6458 __isl_take isl_basic_map *bmap2);
6459 __isl_give isl_basic_map *isl_basic_map_apply_range(
6460 __isl_take isl_basic_map *bmap1,
6461 __isl_take isl_basic_map *bmap2);
6462 __isl_give isl_map *isl_map_apply_domain(
6463 __isl_take isl_map *map1,
6464 __isl_take isl_map *map2);
6465 __isl_give isl_map *isl_map_apply_range(
6466 __isl_take isl_map *map1,
6467 __isl_take isl_map *map2);
6469 #include <isl/union_map.h>
6470 __isl_give isl_union_map *isl_union_map_apply_domain(
6471 __isl_take isl_union_map *umap1,
6472 __isl_take isl_union_map *umap2);
6473 __isl_give isl_union_map *isl_union_map_apply_range(
6474 __isl_take isl_union_map *umap1,
6475 __isl_take isl_union_map *umap2);
6477 #include <isl/aff.h>
6478 __isl_give isl_union_pw_aff *
6479 isl_multi_union_pw_aff_apply_aff(
6480 __isl_take isl_multi_union_pw_aff *mupa,
6481 __isl_take isl_aff *aff);
6482 __isl_give isl_union_pw_aff *
6483 isl_multi_union_pw_aff_apply_pw_aff(
6484 __isl_take isl_multi_union_pw_aff *mupa,
6485 __isl_take isl_pw_aff *pa);
6486 __isl_give isl_multi_union_pw_aff *
6487 isl_multi_union_pw_aff_apply_multi_aff(
6488 __isl_take isl_multi_union_pw_aff *mupa,
6489 __isl_take isl_multi_aff *ma);
6490 __isl_give isl_multi_union_pw_aff *
6491 isl_multi_union_pw_aff_apply_pw_multi_aff(
6492 __isl_take isl_multi_union_pw_aff *mupa,
6493 __isl_take isl_pw_multi_aff *pma);
6495 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6496 over the shared domain of the elements of the input. The dimension is
6497 required to be greater than zero.
6498 The C<isl_multi_union_pw_aff> argument of
6499 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6500 but only if the range of the C<isl_multi_aff> argument
6501 is also zero-dimensional.
6502 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6504 #include <isl/polynomial.h>
6505 __isl_give isl_pw_qpolynomial_fold *
6506 isl_set_apply_pw_qpolynomial_fold(
6507 __isl_take isl_set *set,
6508 __isl_take isl_pw_qpolynomial_fold *pwf,
6510 __isl_give isl_pw_qpolynomial_fold *
6511 isl_map_apply_pw_qpolynomial_fold(
6512 __isl_take isl_map *map,
6513 __isl_take isl_pw_qpolynomial_fold *pwf,
6515 __isl_give isl_union_pw_qpolynomial_fold *
6516 isl_union_set_apply_union_pw_qpolynomial_fold(
6517 __isl_take isl_union_set *uset,
6518 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6520 __isl_give isl_union_pw_qpolynomial_fold *
6521 isl_union_map_apply_union_pw_qpolynomial_fold(
6522 __isl_take isl_union_map *umap,
6523 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6526 The functions taking a map
6527 compose the given map with the given piecewise quasipolynomial reduction.
6528 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6529 over all elements in the intersection of the range of the map
6530 and the domain of the piecewise quasipolynomial reduction
6531 as a function of an element in the domain of the map.
6532 The functions taking a set compute a bound over all elements in the
6533 intersection of the set and the domain of the
6534 piecewise quasipolynomial reduction.
6538 #include <isl/set.h>
6539 __isl_give isl_basic_set *
6540 isl_basic_set_preimage_multi_aff(
6541 __isl_take isl_basic_set *bset,
6542 __isl_take isl_multi_aff *ma);
6543 __isl_give isl_set *isl_set_preimage_multi_aff(
6544 __isl_take isl_set *set,
6545 __isl_take isl_multi_aff *ma);
6546 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6547 __isl_take isl_set *set,
6548 __isl_take isl_pw_multi_aff *pma);
6549 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6550 __isl_take isl_set *set,
6551 __isl_take isl_multi_pw_aff *mpa);
6553 #include <isl/union_set.h>
6554 __isl_give isl_union_set *
6555 isl_union_set_preimage_multi_aff(
6556 __isl_take isl_union_set *uset,
6557 __isl_take isl_multi_aff *ma);
6558 __isl_give isl_union_set *
6559 isl_union_set_preimage_pw_multi_aff(
6560 __isl_take isl_union_set *uset,
6561 __isl_take isl_pw_multi_aff *pma);
6562 __isl_give isl_union_set *
6563 isl_union_set_preimage_union_pw_multi_aff(
6564 __isl_take isl_union_set *uset,
6565 __isl_take isl_union_pw_multi_aff *upma);
6567 #include <isl/map.h>
6568 __isl_give isl_basic_map *
6569 isl_basic_map_preimage_domain_multi_aff(
6570 __isl_take isl_basic_map *bmap,
6571 __isl_take isl_multi_aff *ma);
6572 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6573 __isl_take isl_map *map,
6574 __isl_take isl_multi_aff *ma);
6575 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6576 __isl_take isl_map *map,
6577 __isl_take isl_multi_aff *ma);
6578 __isl_give isl_map *
6579 isl_map_preimage_domain_pw_multi_aff(
6580 __isl_take isl_map *map,
6581 __isl_take isl_pw_multi_aff *pma);
6582 __isl_give isl_map *
6583 isl_map_preimage_range_pw_multi_aff(
6584 __isl_take isl_map *map,
6585 __isl_take isl_pw_multi_aff *pma);
6586 __isl_give isl_map *
6587 isl_map_preimage_domain_multi_pw_aff(
6588 __isl_take isl_map *map,
6589 __isl_take isl_multi_pw_aff *mpa);
6590 __isl_give isl_basic_map *
6591 isl_basic_map_preimage_range_multi_aff(
6592 __isl_take isl_basic_map *bmap,
6593 __isl_take isl_multi_aff *ma);
6595 #include <isl/union_map.h>
6596 __isl_give isl_union_map *
6597 isl_union_map_preimage_domain_multi_aff(
6598 __isl_take isl_union_map *umap,
6599 __isl_take isl_multi_aff *ma);
6600 __isl_give isl_union_map *
6601 isl_union_map_preimage_range_multi_aff(
6602 __isl_take isl_union_map *umap,
6603 __isl_take isl_multi_aff *ma);
6604 __isl_give isl_union_map *
6605 isl_union_map_preimage_domain_pw_multi_aff(
6606 __isl_take isl_union_map *umap,
6607 __isl_take isl_pw_multi_aff *pma);
6608 __isl_give isl_union_map *
6609 isl_union_map_preimage_range_pw_multi_aff(
6610 __isl_take isl_union_map *umap,
6611 __isl_take isl_pw_multi_aff *pma);
6612 __isl_give isl_union_map *
6613 isl_union_map_preimage_domain_union_pw_multi_aff(
6614 __isl_take isl_union_map *umap,
6615 __isl_take isl_union_pw_multi_aff *upma);
6616 __isl_give isl_union_map *
6617 isl_union_map_preimage_range_union_pw_multi_aff(
6618 __isl_take isl_union_map *umap,
6619 __isl_take isl_union_pw_multi_aff *upma);
6621 These functions compute the preimage of the given set or map domain/range under
6622 the given function. In other words, the expression is plugged
6623 into the set description or into the domain/range of the map.
6627 #include <isl/aff.h>
6628 __isl_give isl_aff *isl_aff_pullback_aff(
6629 __isl_take isl_aff *aff1,
6630 __isl_take isl_aff *aff2);
6631 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6632 __isl_take isl_aff *aff,
6633 __isl_take isl_multi_aff *ma);
6634 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6635 __isl_take isl_pw_aff *pa,
6636 __isl_take isl_multi_aff *ma);
6637 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6638 __isl_take isl_pw_aff *pa,
6639 __isl_take isl_pw_multi_aff *pma);
6640 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6641 __isl_take isl_pw_aff *pa,
6642 __isl_take isl_multi_pw_aff *mpa);
6643 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6644 __isl_take isl_multi_aff *ma1,
6645 __isl_take isl_multi_aff *ma2);
6646 __isl_give isl_pw_multi_aff *
6647 isl_pw_multi_aff_pullback_multi_aff(
6648 __isl_take isl_pw_multi_aff *pma,
6649 __isl_take isl_multi_aff *ma);
6650 __isl_give isl_multi_pw_aff *
6651 isl_multi_pw_aff_pullback_multi_aff(
6652 __isl_take isl_multi_pw_aff *mpa,
6653 __isl_take isl_multi_aff *ma);
6654 __isl_give isl_pw_multi_aff *
6655 isl_pw_multi_aff_pullback_pw_multi_aff(
6656 __isl_take isl_pw_multi_aff *pma1,
6657 __isl_take isl_pw_multi_aff *pma2);
6658 __isl_give isl_multi_pw_aff *
6659 isl_multi_pw_aff_pullback_pw_multi_aff(
6660 __isl_take isl_multi_pw_aff *mpa,
6661 __isl_take isl_pw_multi_aff *pma);
6662 __isl_give isl_multi_pw_aff *
6663 isl_multi_pw_aff_pullback_multi_pw_aff(
6664 __isl_take isl_multi_pw_aff *mpa1,
6665 __isl_take isl_multi_pw_aff *mpa2);
6666 __isl_give isl_union_pw_aff *
6667 isl_union_pw_aff_pullback_union_pw_multi_aff(
6668 __isl_take isl_union_pw_aff *upa,
6669 __isl_take isl_union_pw_multi_aff *upma);
6670 __isl_give isl_union_pw_multi_aff *
6671 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6672 __isl_take isl_union_pw_multi_aff *upma1,
6673 __isl_take isl_union_pw_multi_aff *upma2);
6674 __isl_give isl_multi_union_pw_aff *
6675 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6676 __isl_take isl_multi_union_pw_aff *mupa,
6677 __isl_take isl_union_pw_multi_aff *upma);
6679 These functions precompose the first expression by the second function.
6680 In other words, the second function is plugged
6681 into the first expression.
6685 #include <isl/aff.h>
6686 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6687 __isl_take isl_aff *aff1,
6688 __isl_take isl_aff *aff2);
6689 __isl_give isl_set *isl_aff_eq_set(
6690 __isl_take isl_aff *aff1,
6691 __isl_take isl_aff *aff2);
6692 __isl_give isl_set *isl_aff_ne_set(
6693 __isl_take isl_aff *aff1,
6694 __isl_take isl_aff *aff2);
6695 __isl_give isl_basic_set *isl_aff_le_basic_set(
6696 __isl_take isl_aff *aff1,
6697 __isl_take isl_aff *aff2);
6698 __isl_give isl_set *isl_aff_le_set(
6699 __isl_take isl_aff *aff1,
6700 __isl_take isl_aff *aff2);
6701 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6702 __isl_take isl_aff *aff1,
6703 __isl_take isl_aff *aff2);
6704 __isl_give isl_set *isl_aff_lt_set(
6705 __isl_take isl_aff *aff1,
6706 __isl_take isl_aff *aff2);
6707 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6708 __isl_take isl_aff *aff1,
6709 __isl_take isl_aff *aff2);
6710 __isl_give isl_set *isl_aff_ge_set(
6711 __isl_take isl_aff *aff1,
6712 __isl_take isl_aff *aff2);
6713 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6714 __isl_take isl_aff *aff1,
6715 __isl_take isl_aff *aff2);
6716 __isl_give isl_set *isl_aff_gt_set(
6717 __isl_take isl_aff *aff1,
6718 __isl_take isl_aff *aff2);
6719 __isl_give isl_set *isl_pw_aff_eq_set(
6720 __isl_take isl_pw_aff *pwaff1,
6721 __isl_take isl_pw_aff *pwaff2);
6722 __isl_give isl_set *isl_pw_aff_ne_set(
6723 __isl_take isl_pw_aff *pwaff1,
6724 __isl_take isl_pw_aff *pwaff2);
6725 __isl_give isl_set *isl_pw_aff_le_set(
6726 __isl_take isl_pw_aff *pwaff1,
6727 __isl_take isl_pw_aff *pwaff2);
6728 __isl_give isl_set *isl_pw_aff_lt_set(
6729 __isl_take isl_pw_aff *pwaff1,
6730 __isl_take isl_pw_aff *pwaff2);
6731 __isl_give isl_set *isl_pw_aff_ge_set(
6732 __isl_take isl_pw_aff *pwaff1,
6733 __isl_take isl_pw_aff *pwaff2);
6734 __isl_give isl_set *isl_pw_aff_gt_set(
6735 __isl_take isl_pw_aff *pwaff1,
6736 __isl_take isl_pw_aff *pwaff2);
6738 __isl_give isl_set *isl_multi_aff_lex_le_set(
6739 __isl_take isl_multi_aff *ma1,
6740 __isl_take isl_multi_aff *ma2);
6741 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6742 __isl_take isl_multi_aff *ma1,
6743 __isl_take isl_multi_aff *ma2);
6744 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6745 __isl_take isl_multi_aff *ma1,
6746 __isl_take isl_multi_aff *ma2);
6747 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6748 __isl_take isl_multi_aff *ma1,
6749 __isl_take isl_multi_aff *ma2);
6751 __isl_give isl_set *isl_pw_aff_list_eq_set(
6752 __isl_take isl_pw_aff_list *list1,
6753 __isl_take isl_pw_aff_list *list2);
6754 __isl_give isl_set *isl_pw_aff_list_ne_set(
6755 __isl_take isl_pw_aff_list *list1,
6756 __isl_take isl_pw_aff_list *list2);
6757 __isl_give isl_set *isl_pw_aff_list_le_set(
6758 __isl_take isl_pw_aff_list *list1,
6759 __isl_take isl_pw_aff_list *list2);
6760 __isl_give isl_set *isl_pw_aff_list_lt_set(
6761 __isl_take isl_pw_aff_list *list1,
6762 __isl_take isl_pw_aff_list *list2);
6763 __isl_give isl_set *isl_pw_aff_list_ge_set(
6764 __isl_take isl_pw_aff_list *list1,
6765 __isl_take isl_pw_aff_list *list2);
6766 __isl_give isl_set *isl_pw_aff_list_gt_set(
6767 __isl_take isl_pw_aff_list *list1,
6768 __isl_take isl_pw_aff_list *list2);
6770 The function C<isl_aff_ge_basic_set> returns a basic set
6771 containing those elements in the shared space
6772 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6773 The function C<isl_pw_aff_ge_set> returns a set
6774 containing those elements in the shared domain
6775 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6776 greater than or equal to C<pwaff2>.
6777 The function C<isl_multi_aff_lex_le_set> returns a set
6778 containing those elements in the shared domain space
6779 where C<ma1> is lexicographically smaller than or
6781 The functions operating on C<isl_pw_aff_list> apply the corresponding
6782 C<isl_pw_aff> function to each pair of elements in the two lists.
6784 #include <isl/aff.h>
6785 __isl_give isl_map *isl_pw_aff_eq_map(
6786 __isl_take isl_pw_aff *pa1,
6787 __isl_take isl_pw_aff *pa2);
6788 __isl_give isl_map *isl_pw_aff_lt_map(
6789 __isl_take isl_pw_aff *pa1,
6790 __isl_take isl_pw_aff *pa2);
6791 __isl_give isl_map *isl_pw_aff_gt_map(
6792 __isl_take isl_pw_aff *pa1,
6793 __isl_take isl_pw_aff *pa2);
6795 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6796 __isl_take isl_multi_pw_aff *mpa1,
6797 __isl_take isl_multi_pw_aff *mpa2);
6798 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6799 __isl_take isl_multi_pw_aff *mpa1,
6800 __isl_take isl_multi_pw_aff *mpa2);
6801 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6802 __isl_take isl_multi_pw_aff *mpa1,
6803 __isl_take isl_multi_pw_aff *mpa2);
6805 These functions return a map between domain elements of the arguments
6806 where the function values satisfy the given relation.
6808 #include <isl/union_map.h>
6809 __isl_give isl_union_map *
6810 isl_union_map_eq_at_multi_union_pw_aff(
6811 __isl_take isl_union_map *umap,
6812 __isl_take isl_multi_union_pw_aff *mupa);
6813 __isl_give isl_union_map *
6814 isl_union_map_lex_lt_at_multi_union_pw_aff(
6815 __isl_take isl_union_map *umap,
6816 __isl_take isl_multi_union_pw_aff *mupa);
6817 __isl_give isl_union_map *
6818 isl_union_map_lex_gt_at_multi_union_pw_aff(
6819 __isl_take isl_union_map *umap,
6820 __isl_take isl_multi_union_pw_aff *mupa);
6822 These functions select the subset of elements in the union map
6823 that have an equal or lexicographically smaller function value.
6825 =item * Cartesian Product
6827 #include <isl/space.h>
6828 __isl_give isl_space *isl_space_product(
6829 __isl_take isl_space *space1,
6830 __isl_take isl_space *space2);
6831 __isl_give isl_space *isl_space_domain_product(
6832 __isl_take isl_space *space1,
6833 __isl_take isl_space *space2);
6834 __isl_give isl_space *isl_space_range_product(
6835 __isl_take isl_space *space1,
6836 __isl_take isl_space *space2);
6839 C<isl_space_product>, C<isl_space_domain_product>
6840 and C<isl_space_range_product> take pairs or relation spaces and
6841 produce a single relations space, where either the domain, the range
6842 or both domain and range are wrapped spaces of relations between
6843 the domains and/or ranges of the input spaces.
6844 If the product is only constructed over the domain or the range
6845 then the ranges or the domains of the inputs should be the same.
6846 The function C<isl_space_product> also accepts a pair of set spaces,
6847 in which case it returns a wrapped space of a relation between the
6850 #include <isl/set.h>
6851 __isl_give isl_set *isl_set_product(
6852 __isl_take isl_set *set1,
6853 __isl_take isl_set *set2);
6855 #include <isl/map.h>
6856 __isl_give isl_basic_map *isl_basic_map_domain_product(
6857 __isl_take isl_basic_map *bmap1,
6858 __isl_take isl_basic_map *bmap2);
6859 __isl_give isl_basic_map *isl_basic_map_range_product(
6860 __isl_take isl_basic_map *bmap1,
6861 __isl_take isl_basic_map *bmap2);
6862 __isl_give isl_basic_map *isl_basic_map_product(
6863 __isl_take isl_basic_map *bmap1,
6864 __isl_take isl_basic_map *bmap2);
6865 __isl_give isl_map *isl_map_domain_product(
6866 __isl_take isl_map *map1,
6867 __isl_take isl_map *map2);
6868 __isl_give isl_map *isl_map_range_product(
6869 __isl_take isl_map *map1,
6870 __isl_take isl_map *map2);
6871 __isl_give isl_map *isl_map_product(
6872 __isl_take isl_map *map1,
6873 __isl_take isl_map *map2);
6875 #include <isl/union_set.h>
6876 __isl_give isl_union_set *isl_union_set_product(
6877 __isl_take isl_union_set *uset1,
6878 __isl_take isl_union_set *uset2);
6880 #include <isl/union_map.h>
6881 __isl_give isl_union_map *isl_union_map_domain_product(
6882 __isl_take isl_union_map *umap1,
6883 __isl_take isl_union_map *umap2);
6884 __isl_give isl_union_map *isl_union_map_range_product(
6885 __isl_take isl_union_map *umap1,
6886 __isl_take isl_union_map *umap2);
6887 __isl_give isl_union_map *isl_union_map_product(
6888 __isl_take isl_union_map *umap1,
6889 __isl_take isl_union_map *umap2);
6891 #include <isl/val.h>
6892 __isl_give isl_multi_val *isl_multi_val_range_product(
6893 __isl_take isl_multi_val *mv1,
6894 __isl_take isl_multi_val *mv2);
6895 __isl_give isl_multi_val *isl_multi_val_product(
6896 __isl_take isl_multi_val *mv1,
6897 __isl_take isl_multi_val *mv2);
6899 #include <isl/aff.h>
6900 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6901 __isl_take isl_multi_aff *ma1,
6902 __isl_take isl_multi_aff *ma2);
6903 __isl_give isl_multi_aff *isl_multi_aff_product(
6904 __isl_take isl_multi_aff *ma1,
6905 __isl_take isl_multi_aff *ma2);
6906 __isl_give isl_multi_pw_aff *
6907 isl_multi_pw_aff_range_product(
6908 __isl_take isl_multi_pw_aff *mpa1,
6909 __isl_take isl_multi_pw_aff *mpa2);
6910 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6911 __isl_take isl_multi_pw_aff *mpa1,
6912 __isl_take isl_multi_pw_aff *mpa2);
6913 __isl_give isl_pw_multi_aff *
6914 isl_pw_multi_aff_range_product(
6915 __isl_take isl_pw_multi_aff *pma1,
6916 __isl_take isl_pw_multi_aff *pma2);
6917 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6918 __isl_take isl_pw_multi_aff *pma1,
6919 __isl_take isl_pw_multi_aff *pma2);
6920 __isl_give isl_multi_union_pw_aff *
6921 isl_multi_union_pw_aff_range_product(
6922 __isl_take isl_multi_union_pw_aff *mupa1,
6923 __isl_take isl_multi_union_pw_aff *mupa2);
6925 The above functions compute the cross product of the given
6926 sets, relations or functions. The domains and ranges of the results
6927 are wrapped maps between domains and ranges of the inputs.
6928 To obtain a ``flat'' product, use the following functions
6931 #include <isl/set.h>
6932 __isl_give isl_basic_set *isl_basic_set_flat_product(
6933 __isl_take isl_basic_set *bset1,
6934 __isl_take isl_basic_set *bset2);
6935 __isl_give isl_set *isl_set_flat_product(
6936 __isl_take isl_set *set1,
6937 __isl_take isl_set *set2);
6939 #include <isl/map.h>
6940 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6941 __isl_take isl_basic_map *bmap1,
6942 __isl_take isl_basic_map *bmap2);
6943 __isl_give isl_map *isl_map_flat_domain_product(
6944 __isl_take isl_map *map1,
6945 __isl_take isl_map *map2);
6946 __isl_give isl_map *isl_map_flat_range_product(
6947 __isl_take isl_map *map1,
6948 __isl_take isl_map *map2);
6949 __isl_give isl_basic_map *isl_basic_map_flat_product(
6950 __isl_take isl_basic_map *bmap1,
6951 __isl_take isl_basic_map *bmap2);
6952 __isl_give isl_map *isl_map_flat_product(
6953 __isl_take isl_map *map1,
6954 __isl_take isl_map *map2);
6956 #include <isl/union_map.h>
6957 __isl_give isl_union_map *
6958 isl_union_map_flat_domain_product(
6959 __isl_take isl_union_map *umap1,
6960 __isl_take isl_union_map *umap2);
6961 __isl_give isl_union_map *
6962 isl_union_map_flat_range_product(
6963 __isl_take isl_union_map *umap1,
6964 __isl_take isl_union_map *umap2);
6966 #include <isl/val.h>
6967 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6968 __isl_take isl_multi_val *mv1,
6969 __isl_take isl_multi_val *mv2);
6971 #include <isl/aff.h>
6972 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6973 __isl_take isl_multi_aff *ma1,
6974 __isl_take isl_multi_aff *ma2);
6975 __isl_give isl_pw_multi_aff *
6976 isl_pw_multi_aff_flat_range_product(
6977 __isl_take isl_pw_multi_aff *pma1,
6978 __isl_take isl_pw_multi_aff *pma2);
6979 __isl_give isl_multi_pw_aff *
6980 isl_multi_pw_aff_flat_range_product(
6981 __isl_take isl_multi_pw_aff *mpa1,
6982 __isl_take isl_multi_pw_aff *mpa2);
6983 __isl_give isl_union_pw_multi_aff *
6984 isl_union_pw_multi_aff_flat_range_product(
6985 __isl_take isl_union_pw_multi_aff *upma1,
6986 __isl_take isl_union_pw_multi_aff *upma2);
6987 __isl_give isl_multi_union_pw_aff *
6988 isl_multi_union_pw_aff_flat_range_product(
6989 __isl_take isl_multi_union_pw_aff *mupa1,
6990 __isl_take isl_multi_union_pw_aff *mupa2);
6992 #include <isl/space.h>
6993 __isl_give isl_space *isl_space_factor_domain(
6994 __isl_take isl_space *space);
6995 __isl_give isl_space *isl_space_factor_range(
6996 __isl_take isl_space *space);
6997 __isl_give isl_space *isl_space_domain_factor_domain(
6998 __isl_take isl_space *space);
6999 __isl_give isl_space *isl_space_domain_factor_range(
7000 __isl_take isl_space *space);
7001 __isl_give isl_space *isl_space_range_factor_domain(
7002 __isl_take isl_space *space);
7003 __isl_give isl_space *isl_space_range_factor_range(
7004 __isl_take isl_space *space);
7006 The functions C<isl_space_range_factor_domain> and
7007 C<isl_space_range_factor_range> extract the two arguments from
7008 the result of a call to C<isl_space_range_product>.
7010 The arguments of a call to a product can be extracted
7011 from the result using the following functions.
7013 #include <isl/map.h>
7014 __isl_give isl_map *isl_map_factor_domain(
7015 __isl_take isl_map *map);
7016 __isl_give isl_map *isl_map_factor_range(
7017 __isl_take isl_map *map);
7018 __isl_give isl_map *isl_map_domain_factor_domain(
7019 __isl_take isl_map *map);
7020 __isl_give isl_map *isl_map_domain_factor_range(
7021 __isl_take isl_map *map);
7022 __isl_give isl_map *isl_map_range_factor_domain(
7023 __isl_take isl_map *map);
7024 __isl_give isl_map *isl_map_range_factor_range(
7025 __isl_take isl_map *map);
7027 #include <isl/union_map.h>
7028 __isl_give isl_union_map *isl_union_map_factor_domain(
7029 __isl_take isl_union_map *umap);
7030 __isl_give isl_union_map *isl_union_map_factor_range(
7031 __isl_take isl_union_map *umap);
7032 __isl_give isl_union_map *
7033 isl_union_map_domain_factor_domain(
7034 __isl_take isl_union_map *umap);
7035 __isl_give isl_union_map *
7036 isl_union_map_domain_factor_range(
7037 __isl_take isl_union_map *umap);
7038 __isl_give isl_union_map *
7039 isl_union_map_range_factor_domain(
7040 __isl_take isl_union_map *umap);
7041 __isl_give isl_union_map *
7042 isl_union_map_range_factor_range(
7043 __isl_take isl_union_map *umap);
7045 #include <isl/val.h>
7046 __isl_give isl_multi_val *isl_multi_val_factor_range(
7047 __isl_take isl_multi_val *mv);
7048 __isl_give isl_multi_val *
7049 isl_multi_val_range_factor_domain(
7050 __isl_take isl_multi_val *mv);
7051 __isl_give isl_multi_val *
7052 isl_multi_val_range_factor_range(
7053 __isl_take isl_multi_val *mv);
7055 #include <isl/aff.h>
7056 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
7057 __isl_take isl_multi_aff *ma);
7058 __isl_give isl_multi_aff *
7059 isl_multi_aff_range_factor_domain(
7060 __isl_take isl_multi_aff *ma);
7061 __isl_give isl_multi_aff *
7062 isl_multi_aff_range_factor_range(
7063 __isl_take isl_multi_aff *ma);
7064 __isl_give isl_multi_pw_aff *
7065 isl_multi_pw_aff_factor_range(
7066 __isl_take isl_multi_pw_aff *mpa);
7067 __isl_give isl_multi_pw_aff *
7068 isl_multi_pw_aff_range_factor_domain(
7069 __isl_take isl_multi_pw_aff *mpa);
7070 __isl_give isl_multi_pw_aff *
7071 isl_multi_pw_aff_range_factor_range(
7072 __isl_take isl_multi_pw_aff *mpa);
7073 __isl_give isl_multi_union_pw_aff *
7074 isl_multi_union_pw_aff_factor_range(
7075 __isl_take isl_multi_union_pw_aff *mupa);
7076 __isl_give isl_multi_union_pw_aff *
7077 isl_multi_union_pw_aff_range_factor_domain(
7078 __isl_take isl_multi_union_pw_aff *mupa);
7079 __isl_give isl_multi_union_pw_aff *
7080 isl_multi_union_pw_aff_range_factor_range(
7081 __isl_take isl_multi_union_pw_aff *mupa);
7083 The splice functions are a generalization of the flat product functions,
7084 where the second argument may be inserted at any position inside
7085 the first argument rather than being placed at the end.
7086 The functions C<isl_multi_val_factor_range>,
7087 C<isl_multi_aff_factor_range>,
7088 C<isl_multi_pw_aff_factor_range> and
7089 C<isl_multi_union_pw_aff_factor_range>
7090 take functions that live in a set space.
7092 #include <isl/val.h>
7093 __isl_give isl_multi_val *isl_multi_val_range_splice(
7094 __isl_take isl_multi_val *mv1, unsigned pos,
7095 __isl_take isl_multi_val *mv2);
7097 #include <isl/aff.h>
7098 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
7099 __isl_take isl_multi_aff *ma1, unsigned pos,
7100 __isl_take isl_multi_aff *ma2);
7101 __isl_give isl_multi_aff *isl_multi_aff_splice(
7102 __isl_take isl_multi_aff *ma1,
7103 unsigned in_pos, unsigned out_pos,
7104 __isl_take isl_multi_aff *ma2);
7105 __isl_give isl_multi_pw_aff *
7106 isl_multi_pw_aff_range_splice(
7107 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
7108 __isl_take isl_multi_pw_aff *mpa2);
7109 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
7110 __isl_take isl_multi_pw_aff *mpa1,
7111 unsigned in_pos, unsigned out_pos,
7112 __isl_take isl_multi_pw_aff *mpa2);
7113 __isl_give isl_multi_union_pw_aff *
7114 isl_multi_union_pw_aff_range_splice(
7115 __isl_take isl_multi_union_pw_aff *mupa1,
7117 __isl_take isl_multi_union_pw_aff *mupa2);
7119 =item * Simplification
7121 When applied to a set or relation,
7122 the gist operation returns a set or relation that has the
7123 same intersection with the context as the input set or relation.
7124 Any implicit equality in the intersection is made explicit in the result,
7125 while all inequalities that are redundant with respect to the intersection
7127 In case of union sets and relations, the gist operation is performed
7130 When applied to a function,
7131 the gist operation applies the set gist operation to each of
7132 the cells in the domain of the input piecewise expression.
7133 The context is also exploited
7134 to simplify the expression associated to each cell.
7136 #include <isl/set.h>
7137 __isl_give isl_basic_set *isl_basic_set_gist(
7138 __isl_take isl_basic_set *bset,
7139 __isl_take isl_basic_set *context);
7140 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
7141 __isl_take isl_set *context);
7142 __isl_give isl_set *isl_set_gist_params(
7143 __isl_take isl_set *set,
7144 __isl_take isl_set *context);
7146 #include <isl/map.h>
7147 __isl_give isl_basic_map *isl_basic_map_gist(
7148 __isl_take isl_basic_map *bmap,
7149 __isl_take isl_basic_map *context);
7150 __isl_give isl_basic_map *isl_basic_map_gist_domain(
7151 __isl_take isl_basic_map *bmap,
7152 __isl_take isl_basic_set *context);
7153 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
7154 __isl_take isl_map *context);
7155 __isl_give isl_map *isl_map_gist_params(
7156 __isl_take isl_map *map,
7157 __isl_take isl_set *context);
7158 __isl_give isl_map *isl_map_gist_domain(
7159 __isl_take isl_map *map,
7160 __isl_take isl_set *context);
7161 __isl_give isl_map *isl_map_gist_range(
7162 __isl_take isl_map *map,
7163 __isl_take isl_set *context);
7165 #include <isl/union_set.h>
7166 __isl_give isl_union_set *isl_union_set_gist(
7167 __isl_take isl_union_set *uset,
7168 __isl_take isl_union_set *context);
7169 __isl_give isl_union_set *isl_union_set_gist_params(
7170 __isl_take isl_union_set *uset,
7171 __isl_take isl_set *set);
7173 #include <isl/union_map.h>
7174 __isl_give isl_union_map *isl_union_map_gist(
7175 __isl_take isl_union_map *umap,
7176 __isl_take isl_union_map *context);
7177 __isl_give isl_union_map *isl_union_map_gist_params(
7178 __isl_take isl_union_map *umap,
7179 __isl_take isl_set *set);
7180 __isl_give isl_union_map *isl_union_map_gist_domain(
7181 __isl_take isl_union_map *umap,
7182 __isl_take isl_union_set *uset);
7183 __isl_give isl_union_map *isl_union_map_gist_range(
7184 __isl_take isl_union_map *umap,
7185 __isl_take isl_union_set *uset);
7187 #include <isl/aff.h>
7188 __isl_give isl_aff *isl_aff_gist_params(
7189 __isl_take isl_aff *aff,
7190 __isl_take isl_set *context);
7191 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
7192 __isl_take isl_set *context);
7193 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
7194 __isl_take isl_multi_aff *maff,
7195 __isl_take isl_set *context);
7196 __isl_give isl_multi_aff *isl_multi_aff_gist(
7197 __isl_take isl_multi_aff *maff,
7198 __isl_take isl_set *context);
7199 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
7200 __isl_take isl_pw_aff *pwaff,
7201 __isl_take isl_set *context);
7202 __isl_give isl_pw_aff *isl_pw_aff_gist(
7203 __isl_take isl_pw_aff *pwaff,
7204 __isl_take isl_set *context);
7205 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
7206 __isl_take isl_pw_multi_aff *pma,
7207 __isl_take isl_set *set);
7208 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
7209 __isl_take isl_pw_multi_aff *pma,
7210 __isl_take isl_set *set);
7211 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
7212 __isl_take isl_multi_pw_aff *mpa,
7213 __isl_take isl_set *set);
7214 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
7215 __isl_take isl_multi_pw_aff *mpa,
7216 __isl_take isl_set *set);
7217 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
7218 __isl_take isl_union_pw_aff *upa,
7219 __isl_take isl_union_set *context);
7220 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
7221 __isl_take isl_union_pw_aff *upa,
7222 __isl_take isl_set *context);
7223 __isl_give isl_union_pw_multi_aff *
7224 isl_union_pw_multi_aff_gist_params(
7225 __isl_take isl_union_pw_multi_aff *upma,
7226 __isl_take isl_set *context);
7227 __isl_give isl_union_pw_multi_aff *
7228 isl_union_pw_multi_aff_gist(
7229 __isl_take isl_union_pw_multi_aff *upma,
7230 __isl_take isl_union_set *context);
7231 __isl_give isl_multi_union_pw_aff *
7232 isl_multi_union_pw_aff_gist_params(
7233 __isl_take isl_multi_union_pw_aff *aff,
7234 __isl_take isl_set *context);
7235 __isl_give isl_multi_union_pw_aff *
7236 isl_multi_union_pw_aff_gist(
7237 __isl_take isl_multi_union_pw_aff *aff,
7238 __isl_take isl_union_set *context);
7240 #include <isl/polynomial.h>
7241 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
7242 __isl_take isl_qpolynomial *qp,
7243 __isl_take isl_set *context);
7244 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
7245 __isl_take isl_qpolynomial *qp,
7246 __isl_take isl_set *context);
7247 __isl_give isl_qpolynomial_fold *
7248 isl_qpolynomial_fold_gist_params(
7249 __isl_take isl_qpolynomial_fold *fold,
7250 __isl_take isl_set *context);
7251 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7252 __isl_take isl_qpolynomial_fold *fold,
7253 __isl_take isl_set *context);
7254 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7255 __isl_take isl_pw_qpolynomial *pwqp,
7256 __isl_take isl_set *context);
7257 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7258 __isl_take isl_pw_qpolynomial *pwqp,
7259 __isl_take isl_set *context);
7260 __isl_give isl_pw_qpolynomial_fold *
7261 isl_pw_qpolynomial_fold_gist(
7262 __isl_take isl_pw_qpolynomial_fold *pwf,
7263 __isl_take isl_set *context);
7264 __isl_give isl_pw_qpolynomial_fold *
7265 isl_pw_qpolynomial_fold_gist_params(
7266 __isl_take isl_pw_qpolynomial_fold *pwf,
7267 __isl_take isl_set *context);
7268 __isl_give isl_union_pw_qpolynomial *
7269 isl_union_pw_qpolynomial_gist_params(
7270 __isl_take isl_union_pw_qpolynomial *upwqp,
7271 __isl_take isl_set *context);
7272 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7273 __isl_take isl_union_pw_qpolynomial *upwqp,
7274 __isl_take isl_union_set *context);
7275 __isl_give isl_union_pw_qpolynomial_fold *
7276 isl_union_pw_qpolynomial_fold_gist(
7277 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7278 __isl_take isl_union_set *context);
7279 __isl_give isl_union_pw_qpolynomial_fold *
7280 isl_union_pw_qpolynomial_fold_gist_params(
7281 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7282 __isl_take isl_set *context);
7284 =item * Binary Arithmetic Operations
7286 #include <isl/set.h>
7287 __isl_give isl_set *isl_set_sum(
7288 __isl_take isl_set *set1,
7289 __isl_take isl_set *set2);
7290 #include <isl/map.h>
7291 __isl_give isl_map *isl_map_sum(
7292 __isl_take isl_map *map1,
7293 __isl_take isl_map *map2);
7295 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7296 i.e., the set containing the sums of pairs of elements from
7297 C<set1> and C<set2>.
7298 The domain of the result of C<isl_map_sum> is the intersection
7299 of the domains of its two arguments. The corresponding range
7300 elements are the sums of the corresponding range elements
7301 in the two arguments.
7303 #include <isl/val.h>
7304 __isl_give isl_multi_val *isl_multi_val_add(
7305 __isl_take isl_multi_val *mv1,
7306 __isl_take isl_multi_val *mv2);
7307 __isl_give isl_multi_val *isl_multi_val_sub(
7308 __isl_take isl_multi_val *mv1,
7309 __isl_take isl_multi_val *mv2);
7311 #include <isl/aff.h>
7312 __isl_give isl_aff *isl_aff_add(
7313 __isl_take isl_aff *aff1,
7314 __isl_take isl_aff *aff2);
7315 __isl_give isl_multi_aff *isl_multi_aff_add(
7316 __isl_take isl_multi_aff *maff1,
7317 __isl_take isl_multi_aff *maff2);
7318 __isl_give isl_pw_aff *isl_pw_aff_add(
7319 __isl_take isl_pw_aff *pwaff1,
7320 __isl_take isl_pw_aff *pwaff2);
7321 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7322 __isl_take isl_multi_pw_aff *mpa1,
7323 __isl_take isl_multi_pw_aff *mpa2);
7324 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7325 __isl_take isl_pw_multi_aff *pma1,
7326 __isl_take isl_pw_multi_aff *pma2);
7327 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7328 __isl_take isl_union_pw_aff *upa1,
7329 __isl_take isl_union_pw_aff *upa2);
7330 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7331 __isl_take isl_union_pw_multi_aff *upma1,
7332 __isl_take isl_union_pw_multi_aff *upma2);
7333 __isl_give isl_multi_union_pw_aff *
7334 isl_multi_union_pw_aff_add(
7335 __isl_take isl_multi_union_pw_aff *mupa1,
7336 __isl_take isl_multi_union_pw_aff *mupa2);
7337 __isl_give isl_pw_aff *isl_pw_aff_min(
7338 __isl_take isl_pw_aff *pwaff1,
7339 __isl_take isl_pw_aff *pwaff2);
7340 __isl_give isl_pw_aff *isl_pw_aff_max(
7341 __isl_take isl_pw_aff *pwaff1,
7342 __isl_take isl_pw_aff *pwaff2);
7343 __isl_give isl_aff *isl_aff_sub(
7344 __isl_take isl_aff *aff1,
7345 __isl_take isl_aff *aff2);
7346 __isl_give isl_multi_aff *isl_multi_aff_sub(
7347 __isl_take isl_multi_aff *ma1,
7348 __isl_take isl_multi_aff *ma2);
7349 __isl_give isl_pw_aff *isl_pw_aff_sub(
7350 __isl_take isl_pw_aff *pwaff1,
7351 __isl_take isl_pw_aff *pwaff2);
7352 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7353 __isl_take isl_multi_pw_aff *mpa1,
7354 __isl_take isl_multi_pw_aff *mpa2);
7355 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7356 __isl_take isl_pw_multi_aff *pma1,
7357 __isl_take isl_pw_multi_aff *pma2);
7358 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7359 __isl_take isl_union_pw_aff *upa1,
7360 __isl_take isl_union_pw_aff *upa2);
7361 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7362 __isl_take isl_union_pw_multi_aff *upma1,
7363 __isl_take isl_union_pw_multi_aff *upma2);
7364 __isl_give isl_multi_union_pw_aff *
7365 isl_multi_union_pw_aff_sub(
7366 __isl_take isl_multi_union_pw_aff *mupa1,
7367 __isl_take isl_multi_union_pw_aff *mupa2);
7369 C<isl_aff_sub> subtracts the second argument from the first.
7371 #include <isl/polynomial.h>
7372 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7373 __isl_take isl_qpolynomial *qp1,
7374 __isl_take isl_qpolynomial *qp2);
7375 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7376 __isl_take isl_pw_qpolynomial *pwqp1,
7377 __isl_take isl_pw_qpolynomial *pwqp2);
7378 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7379 __isl_take isl_pw_qpolynomial *pwqp1,
7380 __isl_take isl_pw_qpolynomial *pwqp2);
7381 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7382 __isl_take isl_pw_qpolynomial_fold *pwf1,
7383 __isl_take isl_pw_qpolynomial_fold *pwf2);
7384 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7385 __isl_take isl_union_pw_qpolynomial *upwqp1,
7386 __isl_take isl_union_pw_qpolynomial *upwqp2);
7387 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7388 __isl_take isl_qpolynomial *qp1,
7389 __isl_take isl_qpolynomial *qp2);
7390 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7391 __isl_take isl_pw_qpolynomial *pwqp1,
7392 __isl_take isl_pw_qpolynomial *pwqp2);
7393 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7394 __isl_take isl_union_pw_qpolynomial *upwqp1,
7395 __isl_take isl_union_pw_qpolynomial *upwqp2);
7396 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7397 __isl_take isl_pw_qpolynomial_fold *pwf1,
7398 __isl_take isl_pw_qpolynomial_fold *pwf2);
7399 __isl_give isl_union_pw_qpolynomial_fold *
7400 isl_union_pw_qpolynomial_fold_fold(
7401 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7402 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7404 #include <isl/aff.h>
7405 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7406 __isl_take isl_pw_aff *pwaff1,
7407 __isl_take isl_pw_aff *pwaff2);
7408 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7409 __isl_take isl_pw_multi_aff *pma1,
7410 __isl_take isl_pw_multi_aff *pma2);
7411 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7412 __isl_take isl_union_pw_aff *upa1,
7413 __isl_take isl_union_pw_aff *upa2);
7414 __isl_give isl_union_pw_multi_aff *
7415 isl_union_pw_multi_aff_union_add(
7416 __isl_take isl_union_pw_multi_aff *upma1,
7417 __isl_take isl_union_pw_multi_aff *upma2);
7418 __isl_give isl_multi_union_pw_aff *
7419 isl_multi_union_pw_aff_union_add(
7420 __isl_take isl_multi_union_pw_aff *mupa1,
7421 __isl_take isl_multi_union_pw_aff *mupa2);
7422 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7423 __isl_take isl_pw_aff *pwaff1,
7424 __isl_take isl_pw_aff *pwaff2);
7425 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7426 __isl_take isl_pw_aff *pwaff1,
7427 __isl_take isl_pw_aff *pwaff2);
7429 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7430 expression with a domain that is the union of those of C<pwaff1> and
7431 C<pwaff2> and such that on each cell, the quasi-affine expression is
7432 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7433 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7434 associated expression is the defined one.
7435 This in contrast to the C<isl_pw_aff_max> function, which is
7436 only defined on the shared definition domain of the arguments.
7438 #include <isl/val.h>
7439 __isl_give isl_multi_val *isl_multi_val_add_val(
7440 __isl_take isl_multi_val *mv,
7441 __isl_take isl_val *v);
7442 __isl_give isl_multi_val *isl_multi_val_mod_val(
7443 __isl_take isl_multi_val *mv,
7444 __isl_take isl_val *v);
7445 __isl_give isl_multi_val *isl_multi_val_scale_val(
7446 __isl_take isl_multi_val *mv,
7447 __isl_take isl_val *v);
7448 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7449 __isl_take isl_multi_val *mv,
7450 __isl_take isl_val *v);
7452 #include <isl/aff.h>
7453 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7454 __isl_take isl_val *mod);
7455 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7456 __isl_take isl_pw_aff *pa,
7457 __isl_take isl_val *mod);
7458 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7459 __isl_take isl_union_pw_aff *upa,
7460 __isl_take isl_val *f);
7461 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7462 __isl_take isl_val *v);
7463 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7464 __isl_take isl_multi_aff *ma,
7465 __isl_take isl_val *v);
7466 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7467 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7468 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7469 __isl_take isl_multi_pw_aff *mpa,
7470 __isl_take isl_val *v);
7471 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7472 __isl_take isl_pw_multi_aff *pma,
7473 __isl_take isl_val *v);
7474 __isl_give isl_union_pw_multi_aff *
7475 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7476 __isl_take isl_union_pw_aff *upa,
7477 __isl_take isl_val *f);
7478 isl_union_pw_multi_aff_scale_val(
7479 __isl_take isl_union_pw_multi_aff *upma,
7480 __isl_take isl_val *val);
7481 __isl_give isl_multi_union_pw_aff *
7482 isl_multi_union_pw_aff_scale_val(
7483 __isl_take isl_multi_union_pw_aff *mupa,
7484 __isl_take isl_val *v);
7485 __isl_give isl_aff *isl_aff_scale_down_ui(
7486 __isl_take isl_aff *aff, unsigned f);
7487 __isl_give isl_aff *isl_aff_scale_down_val(
7488 __isl_take isl_aff *aff, __isl_take isl_val *v);
7489 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7490 __isl_take isl_multi_aff *ma,
7491 __isl_take isl_val *v);
7492 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7493 __isl_take isl_pw_aff *pa,
7494 __isl_take isl_val *f);
7495 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7496 __isl_take isl_multi_pw_aff *mpa,
7497 __isl_take isl_val *v);
7498 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7499 __isl_take isl_pw_multi_aff *pma,
7500 __isl_take isl_val *v);
7501 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7502 __isl_take isl_union_pw_aff *upa,
7503 __isl_take isl_val *v);
7504 __isl_give isl_union_pw_multi_aff *
7505 isl_union_pw_multi_aff_scale_down_val(
7506 __isl_take isl_union_pw_multi_aff *upma,
7507 __isl_take isl_val *val);
7508 __isl_give isl_multi_union_pw_aff *
7509 isl_multi_union_pw_aff_scale_down_val(
7510 __isl_take isl_multi_union_pw_aff *mupa,
7511 __isl_take isl_val *v);
7513 #include <isl/polynomial.h>
7514 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7515 __isl_take isl_qpolynomial *qp,
7516 __isl_take isl_val *v);
7517 __isl_give isl_qpolynomial_fold *
7518 isl_qpolynomial_fold_scale_val(
7519 __isl_take isl_qpolynomial_fold *fold,
7520 __isl_take isl_val *v);
7521 __isl_give isl_pw_qpolynomial *
7522 isl_pw_qpolynomial_scale_val(
7523 __isl_take isl_pw_qpolynomial *pwqp,
7524 __isl_take isl_val *v);
7525 __isl_give isl_pw_qpolynomial_fold *
7526 isl_pw_qpolynomial_fold_scale_val(
7527 __isl_take isl_pw_qpolynomial_fold *pwf,
7528 __isl_take isl_val *v);
7529 __isl_give isl_union_pw_qpolynomial *
7530 isl_union_pw_qpolynomial_scale_val(
7531 __isl_take isl_union_pw_qpolynomial *upwqp,
7532 __isl_take isl_val *v);
7533 __isl_give isl_union_pw_qpolynomial_fold *
7534 isl_union_pw_qpolynomial_fold_scale_val(
7535 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7536 __isl_take isl_val *v);
7537 __isl_give isl_qpolynomial *
7538 isl_qpolynomial_scale_down_val(
7539 __isl_take isl_qpolynomial *qp,
7540 __isl_take isl_val *v);
7541 __isl_give isl_qpolynomial_fold *
7542 isl_qpolynomial_fold_scale_down_val(
7543 __isl_take isl_qpolynomial_fold *fold,
7544 __isl_take isl_val *v);
7545 __isl_give isl_pw_qpolynomial *
7546 isl_pw_qpolynomial_scale_down_val(
7547 __isl_take isl_pw_qpolynomial *pwqp,
7548 __isl_take isl_val *v);
7549 __isl_give isl_pw_qpolynomial_fold *
7550 isl_pw_qpolynomial_fold_scale_down_val(
7551 __isl_take isl_pw_qpolynomial_fold *pwf,
7552 __isl_take isl_val *v);
7553 __isl_give isl_union_pw_qpolynomial *
7554 isl_union_pw_qpolynomial_scale_down_val(
7555 __isl_take isl_union_pw_qpolynomial *upwqp,
7556 __isl_take isl_val *v);
7557 __isl_give isl_union_pw_qpolynomial_fold *
7558 isl_union_pw_qpolynomial_fold_scale_down_val(
7559 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7560 __isl_take isl_val *v);
7562 #include <isl/val.h>
7563 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7564 __isl_take isl_multi_val *mv1,
7565 __isl_take isl_multi_val *mv2);
7566 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7567 __isl_take isl_multi_val *mv1,
7568 __isl_take isl_multi_val *mv2);
7569 __isl_give isl_multi_val *
7570 isl_multi_val_scale_down_multi_val(
7571 __isl_take isl_multi_val *mv1,
7572 __isl_take isl_multi_val *mv2);
7574 #include <isl/aff.h>
7575 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7576 __isl_take isl_multi_aff *ma,
7577 __isl_take isl_multi_val *mv);
7578 __isl_give isl_multi_union_pw_aff *
7579 isl_multi_union_pw_aff_mod_multi_val(
7580 __isl_take isl_multi_union_pw_aff *upma,
7581 __isl_take isl_multi_val *mv);
7582 __isl_give isl_multi_pw_aff *
7583 isl_multi_pw_aff_mod_multi_val(
7584 __isl_take isl_multi_pw_aff *mpa,
7585 __isl_take isl_multi_val *mv);
7586 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7587 __isl_take isl_multi_aff *ma,
7588 __isl_take isl_multi_val *mv);
7589 __isl_give isl_pw_multi_aff *
7590 isl_pw_multi_aff_scale_multi_val(
7591 __isl_take isl_pw_multi_aff *pma,
7592 __isl_take isl_multi_val *mv);
7593 __isl_give isl_multi_pw_aff *
7594 isl_multi_pw_aff_scale_multi_val(
7595 __isl_take isl_multi_pw_aff *mpa,
7596 __isl_take isl_multi_val *mv);
7597 __isl_give isl_multi_union_pw_aff *
7598 isl_multi_union_pw_aff_scale_multi_val(
7599 __isl_take isl_multi_union_pw_aff *mupa,
7600 __isl_take isl_multi_val *mv);
7601 __isl_give isl_union_pw_multi_aff *
7602 isl_union_pw_multi_aff_scale_multi_val(
7603 __isl_take isl_union_pw_multi_aff *upma,
7604 __isl_take isl_multi_val *mv);
7605 __isl_give isl_multi_aff *
7606 isl_multi_aff_scale_down_multi_val(
7607 __isl_take isl_multi_aff *ma,
7608 __isl_take isl_multi_val *mv);
7609 __isl_give isl_multi_pw_aff *
7610 isl_multi_pw_aff_scale_down_multi_val(
7611 __isl_take isl_multi_pw_aff *mpa,
7612 __isl_take isl_multi_val *mv);
7613 __isl_give isl_multi_union_pw_aff *
7614 isl_multi_union_pw_aff_scale_down_multi_val(
7615 __isl_take isl_multi_union_pw_aff *mupa,
7616 __isl_take isl_multi_val *mv);
7618 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7619 by the corresponding elements of C<mv>.
7621 #include <isl/aff.h>
7622 __isl_give isl_aff *isl_aff_mul(
7623 __isl_take isl_aff *aff1,
7624 __isl_take isl_aff *aff2);
7625 __isl_give isl_aff *isl_aff_div(
7626 __isl_take isl_aff *aff1,
7627 __isl_take isl_aff *aff2);
7628 __isl_give isl_pw_aff *isl_pw_aff_mul(
7629 __isl_take isl_pw_aff *pwaff1,
7630 __isl_take isl_pw_aff *pwaff2);
7631 __isl_give isl_pw_aff *isl_pw_aff_div(
7632 __isl_take isl_pw_aff *pa1,
7633 __isl_take isl_pw_aff *pa2);
7634 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7635 __isl_take isl_pw_aff *pa1,
7636 __isl_take isl_pw_aff *pa2);
7637 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7638 __isl_take isl_pw_aff *pa1,
7639 __isl_take isl_pw_aff *pa2);
7641 When multiplying two affine expressions, at least one of the two needs
7642 to be a constant. Similarly, when dividing an affine expression by another,
7643 the second expression needs to be a constant.
7644 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7645 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7648 #include <isl/polynomial.h>
7649 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7650 __isl_take isl_qpolynomial *qp1,
7651 __isl_take isl_qpolynomial *qp2);
7652 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7653 __isl_take isl_pw_qpolynomial *pwqp1,
7654 __isl_take isl_pw_qpolynomial *pwqp2);
7655 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7656 __isl_take isl_union_pw_qpolynomial *upwqp1,
7657 __isl_take isl_union_pw_qpolynomial *upwqp2);
7661 =head3 Lexicographic Optimization
7663 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7664 the following functions
7665 compute a set that contains the lexicographic minimum or maximum
7666 of the elements in C<set> (or C<bset>) for those values of the parameters
7667 that satisfy C<dom>.
7668 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7669 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7671 In other words, the union of the parameter values
7672 for which the result is non-empty and of C<*empty>
7675 #include <isl/set.h>
7676 __isl_give isl_set *isl_basic_set_partial_lexmin(
7677 __isl_take isl_basic_set *bset,
7678 __isl_take isl_basic_set *dom,
7679 __isl_give isl_set **empty);
7680 __isl_give isl_set *isl_basic_set_partial_lexmax(
7681 __isl_take isl_basic_set *bset,
7682 __isl_take isl_basic_set *dom,
7683 __isl_give isl_set **empty);
7684 __isl_give isl_set *isl_set_partial_lexmin(
7685 __isl_take isl_set *set, __isl_take isl_set *dom,
7686 __isl_give isl_set **empty);
7687 __isl_give isl_set *isl_set_partial_lexmax(
7688 __isl_take isl_set *set, __isl_take isl_set *dom,
7689 __isl_give isl_set **empty);
7691 Given a (basic) set C<set> (or C<bset>), the following functions simply
7692 return a set containing the lexicographic minimum or maximum
7693 of the elements in C<set> (or C<bset>).
7694 In case of union sets, the optimum is computed per space.
7696 #include <isl/set.h>
7697 __isl_give isl_set *isl_basic_set_lexmin(
7698 __isl_take isl_basic_set *bset);
7699 __isl_give isl_set *isl_basic_set_lexmax(
7700 __isl_take isl_basic_set *bset);
7701 __isl_give isl_set *isl_set_lexmin(
7702 __isl_take isl_set *set);
7703 __isl_give isl_set *isl_set_lexmax(
7704 __isl_take isl_set *set);
7705 __isl_give isl_union_set *isl_union_set_lexmin(
7706 __isl_take isl_union_set *uset);
7707 __isl_give isl_union_set *isl_union_set_lexmax(
7708 __isl_take isl_union_set *uset);
7710 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7711 the following functions
7712 compute a relation that maps each element of C<dom>
7713 to the single lexicographic minimum or maximum
7714 of the elements that are associated to that same
7715 element in C<map> (or C<bmap>).
7716 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7717 that contains the elements in C<dom> that do not map
7718 to any elements in C<map> (or C<bmap>).
7719 In other words, the union of the domain of the result and of C<*empty>
7722 #include <isl/map.h>
7723 __isl_give isl_map *isl_basic_map_partial_lexmax(
7724 __isl_take isl_basic_map *bmap,
7725 __isl_take isl_basic_set *dom,
7726 __isl_give isl_set **empty);
7727 __isl_give isl_map *isl_basic_map_partial_lexmin(
7728 __isl_take isl_basic_map *bmap,
7729 __isl_take isl_basic_set *dom,
7730 __isl_give isl_set **empty);
7731 __isl_give isl_map *isl_map_partial_lexmax(
7732 __isl_take isl_map *map, __isl_take isl_set *dom,
7733 __isl_give isl_set **empty);
7734 __isl_give isl_map *isl_map_partial_lexmin(
7735 __isl_take isl_map *map, __isl_take isl_set *dom,
7736 __isl_give isl_set **empty);
7738 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7739 return a map mapping each element in the domain of
7740 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7741 of all elements associated to that element.
7742 In case of union relations, the optimum is computed per space.
7744 #include <isl/map.h>
7745 __isl_give isl_map *isl_basic_map_lexmin(
7746 __isl_take isl_basic_map *bmap);
7747 __isl_give isl_map *isl_basic_map_lexmax(
7748 __isl_take isl_basic_map *bmap);
7749 __isl_give isl_map *isl_map_lexmin(
7750 __isl_take isl_map *map);
7751 __isl_give isl_map *isl_map_lexmax(
7752 __isl_take isl_map *map);
7753 __isl_give isl_union_map *isl_union_map_lexmin(
7754 __isl_take isl_union_map *umap);
7755 __isl_give isl_union_map *isl_union_map_lexmax(
7756 __isl_take isl_union_map *umap);
7758 The following functions return their result in the form of
7759 a piecewise multi-affine expression,
7760 but are otherwise equivalent to the corresponding functions
7761 returning a basic set or relation.
7763 #include <isl/set.h>
7764 __isl_give isl_pw_multi_aff *
7765 isl_basic_set_partial_lexmin_pw_multi_aff(
7766 __isl_take isl_basic_set *bset,
7767 __isl_take isl_basic_set *dom,
7768 __isl_give isl_set **empty);
7769 __isl_give isl_pw_multi_aff *
7770 isl_basic_set_partial_lexmax_pw_multi_aff(
7771 __isl_take isl_basic_set *bset,
7772 __isl_take isl_basic_set *dom,
7773 __isl_give isl_set **empty);
7774 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7775 __isl_take isl_set *set);
7776 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7777 __isl_take isl_set *set);
7779 #include <isl/map.h>
7780 __isl_give isl_pw_multi_aff *
7781 isl_basic_map_lexmin_pw_multi_aff(
7782 __isl_take isl_basic_map *bmap);
7783 __isl_give isl_pw_multi_aff *
7784 isl_basic_map_partial_lexmin_pw_multi_aff(
7785 __isl_take isl_basic_map *bmap,
7786 __isl_take isl_basic_set *dom,
7787 __isl_give isl_set **empty);
7788 __isl_give isl_pw_multi_aff *
7789 isl_basic_map_partial_lexmax_pw_multi_aff(
7790 __isl_take isl_basic_map *bmap,
7791 __isl_take isl_basic_set *dom,
7792 __isl_give isl_set **empty);
7793 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7794 __isl_take isl_map *map);
7795 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7796 __isl_take isl_map *map);
7798 The following functions return the lexicographic minimum or maximum
7799 on the shared domain of the inputs and the single defined function
7800 on those parts of the domain where only a single function is defined.
7802 #include <isl/aff.h>
7803 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7804 __isl_take isl_pw_multi_aff *pma1,
7805 __isl_take isl_pw_multi_aff *pma2);
7806 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7807 __isl_take isl_pw_multi_aff *pma1,
7808 __isl_take isl_pw_multi_aff *pma2);
7810 If the input to a lexicographic optimization problem has
7811 multiple constraints with the same coefficients for the optimized
7812 variables, then, by default, this symmetry is exploited by
7813 replacing those constraints by a single constraint with
7814 an abstract bound, which is in turn bounded by the corresponding terms
7815 in the original constraints.
7816 Without this optimization, the solver would typically consider
7817 all possible orderings of those original bounds, resulting in a needless
7818 decomposition of the domain.
7819 However, the optimization can also result in slowdowns since
7820 an extra parameter is introduced that may get used in additional
7822 The following option determines whether symmetry detection is applied
7823 during lexicographic optimization.
7825 #include <isl/options.h>
7826 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7828 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7832 See also \autoref{s:offline}.
7836 =head2 Ternary Operations
7838 #include <isl/aff.h>
7839 __isl_give isl_pw_aff *isl_pw_aff_cond(
7840 __isl_take isl_pw_aff *cond,
7841 __isl_take isl_pw_aff *pwaff_true,
7842 __isl_take isl_pw_aff *pwaff_false);
7844 The function C<isl_pw_aff_cond> performs a conditional operator
7845 and returns an expression that is equal to C<pwaff_true>
7846 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7847 where C<cond> is zero.
7851 Lists are defined over several element types, including
7852 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
7853 C<isl_union_pw_aff>,
7854 C<isl_union_pw_multi_aff>,
7855 C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
7857 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7858 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7859 Here we take lists of C<isl_set>s as an example.
7860 Lists can be created, copied, modified and freed using the following functions.
7862 #include <isl/set.h>
7863 __isl_give isl_set_list *isl_set_list_from_set(
7864 __isl_take isl_set *el);
7865 __isl_give isl_set_list *isl_set_list_alloc(
7866 isl_ctx *ctx, int n);
7867 __isl_give isl_set_list *isl_set_list_copy(
7868 __isl_keep isl_set_list *list);
7869 __isl_give isl_set_list *isl_set_list_insert(
7870 __isl_take isl_set_list *list, unsigned pos,
7871 __isl_take isl_set *el);
7872 __isl_give isl_set_list *isl_set_list_add(
7873 __isl_take isl_set_list *list,
7874 __isl_take isl_set *el);
7875 __isl_give isl_set_list *isl_set_list_drop(
7876 __isl_take isl_set_list *list,
7877 unsigned first, unsigned n);
7878 __isl_give isl_set_list *isl_set_list_swap(
7879 __isl_take isl_set_list *list,
7880 unsigned pos1, unsigned pos2);
7881 __isl_give isl_set_list *isl_set_list_reverse(
7882 __isl_take isl_set_list *list);
7883 __isl_give isl_set_list *isl_set_list_set_set(
7884 __isl_take isl_set_list *list, int index,
7885 __isl_take isl_set *set);
7886 __isl_give isl_set_list *isl_set_list_concat(
7887 __isl_take isl_set_list *list1,
7888 __isl_take isl_set_list *list2);
7889 __isl_give isl_set_list *isl_set_list_map(
7890 __isl_take isl_set_list *list,
7891 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7894 __isl_give isl_set_list *isl_set_list_sort(
7895 __isl_take isl_set_list *list,
7896 int (*cmp)(__isl_keep isl_set *a,
7897 __isl_keep isl_set *b, void *user),
7899 __isl_null isl_set_list *isl_set_list_free(
7900 __isl_take isl_set_list *list);
7902 C<isl_set_list_alloc> creates an empty list with an initial capacity
7903 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7904 add elements to a list, increasing its capacity as needed.
7905 C<isl_set_list_from_set> creates a list with a single element.
7906 C<isl_set_list_swap> swaps the elements at the specified locations.
7907 C<isl_set_list_reverse> reverses the elements in the list.
7909 Lists can be inspected using the following functions.
7911 #include <isl/set.h>
7912 int isl_set_list_size(__isl_keep isl_set_list *list);
7913 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7914 __isl_give isl_set *isl_set_list_get_at(
7915 __isl_keep isl_set_list *list, int index);
7916 __isl_give isl_set *isl_set_list_get_set(
7917 __isl_keep isl_set_list *list, int index);
7918 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7919 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7921 isl_stat isl_set_list_foreach_scc(
7922 __isl_keep isl_set_list *list,
7923 isl_bool (*follows)(__isl_keep isl_set *a,
7924 __isl_keep isl_set *b, void *user),
7926 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7929 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
7931 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
7932 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7933 strongly connected components of the graph with as vertices the elements
7934 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7935 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7936 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7938 Lists can be printed using
7940 #include <isl/set.h>
7941 __isl_give isl_printer *isl_printer_print_set_list(
7942 __isl_take isl_printer *p,
7943 __isl_keep isl_set_list *list);
7945 =head2 Associative arrays
7947 Associative arrays map isl objects of a specific type to isl objects
7948 of some (other) specific type. They are defined for several pairs
7949 of types, including (C<isl_map>, C<isl_basic_set>),
7950 (C<isl_id>, C<isl_ast_expr>),
7951 (C<isl_id>, C<isl_id>) and
7952 (C<isl_id>, C<isl_pw_aff>).
7953 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7956 Associative arrays can be created, copied and freed using
7957 the following functions.
7959 #include <isl/id_to_ast_expr.h>
7960 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7961 isl_ctx *ctx, int min_size);
7962 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7963 __isl_keep isl_id_to_ast_expr *id2expr);
7964 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7965 __isl_take isl_id_to_ast_expr *id2expr);
7967 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7968 to specify the expected size of the associative array.
7969 The associative array will be grown automatically as needed.
7971 Associative arrays can be inspected using the following functions.
7973 #include <isl/id_to_ast_expr.h>
7974 __isl_give isl_maybe_isl_ast_expr
7975 isl_id_to_ast_expr_try_get(
7976 __isl_keep isl_id_to_ast_expr *id2expr,
7977 __isl_keep isl_id *key);
7978 isl_bool isl_id_to_ast_expr_has(
7979 __isl_keep isl_id_to_ast_expr *id2expr,
7980 __isl_keep isl_id *key);
7981 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7982 __isl_keep isl_id_to_ast_expr *id2expr,
7983 __isl_take isl_id *key);
7984 isl_stat isl_id_to_ast_expr_foreach(
7985 __isl_keep isl_id_to_ast_expr *id2expr,
7986 isl_stat (*fn)(__isl_take isl_id *key,
7987 __isl_take isl_ast_expr *val, void *user),
7990 The function C<isl_id_to_ast_expr_try_get> returns a structure
7991 containing two elements, C<valid> and C<value>.
7992 If there is a value associated to the key, then C<valid>
7993 is set to C<isl_bool_true> and C<value> contains a copy of
7994 the associated value. Otherwise C<value> is C<NULL> and
7995 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7996 on whether some error has occurred or there simply is no associated value.
7997 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7998 in the structure and
7999 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
8001 Associative arrays can be modified using the following functions.
8003 #include <isl/id_to_ast_expr.h>
8004 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
8005 __isl_take isl_id_to_ast_expr *id2expr,
8006 __isl_take isl_id *key,
8007 __isl_take isl_ast_expr *val);
8008 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
8009 __isl_take isl_id_to_ast_expr *id2expr,
8010 __isl_take isl_id *key);
8012 Associative arrays can be printed using the following function.
8014 #include <isl/id_to_ast_expr.h>
8015 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
8016 __isl_take isl_printer *p,
8017 __isl_keep isl_id_to_ast_expr *id2expr);
8021 Vectors can be created, copied and freed using the following functions.
8023 #include <isl/vec.h>
8024 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
8026 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
8028 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
8029 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
8031 Note that the elements of a vector created by C<isl_vec_alloc>
8032 may have arbitrary values.
8033 A vector created by C<isl_vec_zero> has elements with value zero.
8034 The elements can be changed and inspected using the following functions.
8036 int isl_vec_size(__isl_keep isl_vec *vec);
8037 __isl_give isl_val *isl_vec_get_element_val(
8038 __isl_keep isl_vec *vec, int pos);
8039 __isl_give isl_vec *isl_vec_set_element_si(
8040 __isl_take isl_vec *vec, int pos, int v);
8041 __isl_give isl_vec *isl_vec_set_element_val(
8042 __isl_take isl_vec *vec, int pos,
8043 __isl_take isl_val *v);
8044 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
8046 __isl_give isl_vec *isl_vec_set_val(
8047 __isl_take isl_vec *vec, __isl_take isl_val *v);
8048 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
8049 __isl_keep isl_vec *vec2, int pos);
8051 C<isl_vec_get_element> will return a negative value if anything went wrong.
8052 In that case, the value of C<*v> is undefined.
8054 The following function can be used to concatenate two vectors.
8056 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
8057 __isl_take isl_vec *vec2);
8061 Matrices can be created, copied and freed using the following functions.
8063 #include <isl/mat.h>
8064 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
8065 unsigned n_row, unsigned n_col);
8066 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
8067 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
8069 Note that the elements of a newly created matrix may have arbitrary values.
8070 The elements can be changed and inspected using the following functions.
8072 int isl_mat_rows(__isl_keep isl_mat *mat);
8073 int isl_mat_cols(__isl_keep isl_mat *mat);
8074 __isl_give isl_val *isl_mat_get_element_val(
8075 __isl_keep isl_mat *mat, int row, int col);
8076 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
8077 int row, int col, int v);
8078 __isl_give isl_mat *isl_mat_set_element_val(
8079 __isl_take isl_mat *mat, int row, int col,
8080 __isl_take isl_val *v);
8082 The following function computes the rank of a matrix.
8083 The return value may be -1 if some error occurred.
8085 #include <isl/mat.h>
8086 int isl_mat_rank(__isl_keep isl_mat *mat);
8088 The following function can be used to compute the (right) inverse
8089 of a matrix, i.e., a matrix such that the product of the original
8090 and the inverse (in that order) is a multiple of the identity matrix.
8091 The input matrix is assumed to be of full row-rank.
8093 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
8095 The following function can be used to compute the (right) kernel
8096 (or null space) of a matrix, i.e., a matrix such that the product of
8097 the original and the kernel (in that order) is the zero matrix.
8099 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
8101 The following function computes a basis for the space spanned
8102 by the rows of a matrix.
8104 __isl_give isl_mat *isl_mat_row_basis(
8105 __isl_take isl_mat *mat);
8107 The following function computes rows that extend a basis of C<mat1>
8108 to a basis that also covers C<mat2>.
8110 __isl_give isl_mat *isl_mat_row_basis_extension(
8111 __isl_take isl_mat *mat1,
8112 __isl_take isl_mat *mat2);
8114 The following function checks whether there is no linear dependence
8115 among the combined rows of "mat1" and "mat2" that is not already present
8116 in "mat1" or "mat2" individually.
8117 If "mat1" and "mat2" have linearly independent rows by themselves,
8118 then this means that there is no linear dependence among all rows together.
8120 isl_bool isl_mat_has_linearly_independent_rows(
8121 __isl_keep isl_mat *mat1,
8122 __isl_keep isl_mat *mat2);
8124 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
8126 The following functions determine
8127 an upper or lower bound on a quasipolynomial over its domain.
8129 __isl_give isl_pw_qpolynomial_fold *
8130 isl_pw_qpolynomial_bound(
8131 __isl_take isl_pw_qpolynomial *pwqp,
8132 enum isl_fold type, int *tight);
8134 __isl_give isl_union_pw_qpolynomial_fold *
8135 isl_union_pw_qpolynomial_bound(
8136 __isl_take isl_union_pw_qpolynomial *upwqp,
8137 enum isl_fold type, int *tight);
8139 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
8140 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
8141 is the returned bound is known be tight, i.e., for each value
8142 of the parameters there is at least
8143 one element in the domain that reaches the bound.
8144 If the domain of C<pwqp> is not wrapping, then the bound is computed
8145 over all elements in that domain and the result has a purely parametric
8146 domain. If the domain of C<pwqp> is wrapping, then the bound is
8147 computed over the range of the wrapped relation. The domain of the
8148 wrapped relation becomes the domain of the result.
8150 =head2 Parametric Vertex Enumeration
8152 The parametric vertex enumeration described in this section
8153 is mainly intended to be used internally and by the C<barvinok>
8156 #include <isl/vertices.h>
8157 __isl_give isl_vertices *isl_basic_set_compute_vertices(
8158 __isl_keep isl_basic_set *bset);
8160 The function C<isl_basic_set_compute_vertices> performs the
8161 actual computation of the parametric vertices and the chamber
8162 decomposition and stores the result in an C<isl_vertices> object.
8163 This information can be queried by either iterating over all
8164 the vertices or iterating over all the chambers or cells
8165 and then iterating over all vertices that are active on the chamber.
8167 isl_stat isl_vertices_foreach_vertex(
8168 __isl_keep isl_vertices *vertices,
8169 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8170 void *user), void *user);
8172 isl_stat isl_vertices_foreach_cell(
8173 __isl_keep isl_vertices *vertices,
8174 isl_stat (*fn)(__isl_take isl_cell *cell,
8175 void *user), void *user);
8176 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
8177 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8178 void *user), void *user);
8180 Other operations that can be performed on an C<isl_vertices> object are
8183 int isl_vertices_get_n_vertices(
8184 __isl_keep isl_vertices *vertices);
8185 __isl_null isl_vertices *isl_vertices_free(
8186 __isl_take isl_vertices *vertices);
8188 Vertices can be inspected and destroyed using the following functions.
8190 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
8191 __isl_give isl_basic_set *isl_vertex_get_domain(
8192 __isl_keep isl_vertex *vertex);
8193 __isl_give isl_multi_aff *isl_vertex_get_expr(
8194 __isl_keep isl_vertex *vertex);
8195 __isl_null isl_vertex *isl_vertex_free(
8196 __isl_take isl_vertex *vertex);
8198 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
8199 describing the vertex in terms of the parameters,
8200 while C<isl_vertex_get_domain> returns the activity domain
8203 Chambers can be inspected and destroyed using the following functions.
8205 __isl_give isl_basic_set *isl_cell_get_domain(
8206 __isl_keep isl_cell *cell);
8207 __isl_null isl_cell *isl_cell_free(
8208 __isl_take isl_cell *cell);
8210 =head1 Polyhedral Compilation Library
8212 This section collects functionality in C<isl> that has been specifically
8213 designed for use during polyhedral compilation.
8215 =head2 Schedule Trees
8217 A schedule tree is a structured representation of a schedule,
8218 assigning a relative order to a set of domain elements.
8219 The relative order expressed by the schedule tree is
8220 defined recursively. In particular, the order between
8221 two domain elements is determined by the node that is closest
8222 to the root that refers to both elements and that orders them apart.
8223 Each node in the tree is of one of several types.
8224 The root node is always of type C<isl_schedule_node_domain>
8225 (or C<isl_schedule_node_extension>)
8226 and it describes the (extra) domain elements to which the schedule applies.
8227 The other types of nodes are as follows.
8231 =item C<isl_schedule_node_band>
8233 A band of schedule dimensions. Each schedule dimension is represented
8234 by a union piecewise quasi-affine expression. If this expression
8235 assigns a different value to two domain elements, while all previous
8236 schedule dimensions in the same band assign them the same value,
8237 then the two domain elements are ordered according to these two
8239 Each expression is required to be total in the domain elements
8240 that reach the band node.
8242 =item C<isl_schedule_node_expansion>
8244 An expansion node maps each of the domain elements that reach the node
8245 to one or more domain elements. The image of this mapping forms
8246 the set of domain elements that reach the child of the expansion node.
8247 The function that maps each of the expanded domain elements
8248 to the original domain element from which it was expanded
8249 is called the contraction.
8251 =item C<isl_schedule_node_filter>
8253 A filter node does not impose any ordering, but rather intersects
8254 the set of domain elements that the current subtree refers to
8255 with a given union set. The subtree of the filter node only
8256 refers to domain elements in the intersection.
8257 A filter node is typically only used as a child of a sequence or
8260 =item C<isl_schedule_node_leaf>
8262 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
8264 =item C<isl_schedule_node_mark>
8266 A mark node can be used to attach any kind of information to a subtree
8267 of the schedule tree.
8269 =item C<isl_schedule_node_sequence>
8271 A sequence node has one or more children, each of which is a filter node.
8272 The filters on these filter nodes form a partition of
8273 the domain elements that the current subtree refers to.
8274 If two domain elements appear in distinct filters then the sequence
8275 node orders them according to the child positions of the corresponding
8278 =item C<isl_schedule_node_set>
8280 A set node is similar to a sequence node, except that
8281 it expresses that domain elements appearing in distinct filters
8282 may have any order. The order of the children of a set node
8283 is therefore also immaterial.
8287 The following node types are only supported by the AST generator.
8291 =item C<isl_schedule_node_context>
8293 The context describes constraints on the parameters and
8294 the schedule dimensions of outer
8295 bands that the AST generator may assume to hold. It is also the only
8296 kind of node that may introduce additional parameters.
8297 The space of the context is that of the flat product of the outer
8298 band nodes. In particular, if there are no outer band nodes, then
8299 this space is the unnamed zero-dimensional space.
8300 Since a context node references the outer band nodes, any tree
8301 containing a context node is considered to be anchored.
8303 =item C<isl_schedule_node_extension>
8305 An extension node instructs the AST generator to add additional
8306 domain elements that need to be scheduled.
8307 The additional domain elements are described by the range of
8308 the extension map in terms of the outer schedule dimensions,
8309 i.e., the flat product of the outer band nodes.
8310 Note that domain elements are added whenever the AST generator
8311 reaches the extension node, meaning that there are still some
8312 active domain elements for which an AST needs to be generated.
8313 The conditions under which some domain elements are still active
8314 may however not be completely described by the outer AST nodes
8315 generated at that point.
8316 Since an extension node references the outer band nodes, any tree
8317 containing an extension node is considered to be anchored.
8319 An extension node may also appear as the root of a schedule tree,
8320 when it is intended to be inserted into another tree
8321 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8322 In this case, the domain of the extension node should
8323 correspond to the flat product of the outer band nodes
8324 in this other schedule tree at the point where the extension tree
8327 =item C<isl_schedule_node_guard>
8329 The guard describes constraints on the parameters and
8330 the schedule dimensions of outer
8331 bands that need to be enforced by the outer nodes
8332 in the generated AST.
8333 That is, the part of the AST that is generated from descendants
8334 of the guard node can assume that these constraints are satisfied.
8335 The space of the guard is that of the flat product of the outer
8336 band nodes. In particular, if there are no outer band nodes, then
8337 this space is the unnamed zero-dimensional space.
8338 Since a guard node references the outer band nodes, any tree
8339 containing a guard node is considered to be anchored.
8343 Except for the C<isl_schedule_node_context> nodes,
8344 none of the nodes may introduce any parameters that were not
8345 already present in the root domain node.
8347 A schedule tree is encapsulated in an C<isl_schedule> object.
8348 The simplest such objects, those with a tree consisting of single domain node,
8349 can be created using the following functions with either an empty
8350 domain or a given domain.
8352 #include <isl/schedule.h>
8353 __isl_give isl_schedule *isl_schedule_empty(
8354 __isl_take isl_space *space);
8355 __isl_give isl_schedule *isl_schedule_from_domain(
8356 __isl_take isl_union_set *domain);
8358 The function C<isl_schedule_constraints_compute_schedule> described
8359 in L</"Scheduling"> can also be used to construct schedules.
8361 C<isl_schedule> objects may be copied and freed using the following functions.
8363 #include <isl/schedule.h>
8364 __isl_give isl_schedule *isl_schedule_copy(
8365 __isl_keep isl_schedule *sched);
8366 __isl_null isl_schedule *isl_schedule_free(
8367 __isl_take isl_schedule *sched);
8369 The following functions checks whether two C<isl_schedule> objects
8370 are obviously the same.
8372 #include <isl/schedule.h>
8373 isl_bool isl_schedule_plain_is_equal(
8374 __isl_keep isl_schedule *schedule1,
8375 __isl_keep isl_schedule *schedule2);
8377 The domain of the schedule, i.e., the domain described by the root node,
8378 can be obtained using the following function.
8380 #include <isl/schedule.h>
8381 __isl_give isl_union_set *isl_schedule_get_domain(
8382 __isl_keep isl_schedule *schedule);
8384 An extra top-level band node (right underneath the domain node) can
8385 be introduced into the schedule using the following function.
8386 The schedule tree is assumed not to have any anchored nodes.
8388 #include <isl/schedule.h>
8389 __isl_give isl_schedule *
8390 isl_schedule_insert_partial_schedule(
8391 __isl_take isl_schedule *schedule,
8392 __isl_take isl_multi_union_pw_aff *partial);
8394 A top-level context node (right underneath the domain node) can
8395 be introduced into the schedule using the following function.
8397 #include <isl/schedule.h>
8398 __isl_give isl_schedule *isl_schedule_insert_context(
8399 __isl_take isl_schedule *schedule,
8400 __isl_take isl_set *context)
8402 A top-level guard node (right underneath the domain node) can
8403 be introduced into the schedule using the following function.
8405 #include <isl/schedule.h>
8406 __isl_give isl_schedule *isl_schedule_insert_guard(
8407 __isl_take isl_schedule *schedule,
8408 __isl_take isl_set *guard)
8410 A schedule that combines two schedules either in the given
8411 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8412 or an C<isl_schedule_node_set> node,
8413 can be created using the following functions.
8415 #include <isl/schedule.h>
8416 __isl_give isl_schedule *isl_schedule_sequence(
8417 __isl_take isl_schedule *schedule1,
8418 __isl_take isl_schedule *schedule2);
8419 __isl_give isl_schedule *isl_schedule_set(
8420 __isl_take isl_schedule *schedule1,
8421 __isl_take isl_schedule *schedule2);
8423 The domains of the two input schedules need to be disjoint.
8425 The following function can be used to restrict the domain
8426 of a schedule with a domain node as root to be a subset of the given union set.
8427 This operation may remove nodes in the tree that have become
8430 #include <isl/schedule.h>
8431 __isl_give isl_schedule *isl_schedule_intersect_domain(
8432 __isl_take isl_schedule *schedule,
8433 __isl_take isl_union_set *domain);
8435 The following function can be used to simplify the domain
8436 of a schedule with a domain node as root with respect to the given
8439 #include <isl/schedule.h>
8440 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8441 __isl_take isl_schedule *schedule,
8442 __isl_take isl_set *context);
8444 The following function resets the user pointers on all parameter
8445 and tuple identifiers referenced by the nodes of the given schedule.
8447 #include <isl/schedule.h>
8448 __isl_give isl_schedule *isl_schedule_reset_user(
8449 __isl_take isl_schedule *schedule);
8451 The following function aligns the parameters of all nodes
8452 in the given schedule to the given space.
8454 #include <isl/schedule.h>
8455 __isl_give isl_schedule *isl_schedule_align_params(
8456 __isl_take isl_schedule *schedule,
8457 __isl_take isl_space *space);
8459 The following function allows the user to plug in a given function
8460 in the iteration domains. The input schedule is not allowed to contain
8461 any expansion nodes.
8463 #include <isl/schedule.h>
8464 __isl_give isl_schedule *
8465 isl_schedule_pullback_union_pw_multi_aff(
8466 __isl_take isl_schedule *schedule,
8467 __isl_take isl_union_pw_multi_aff *upma);
8469 The following function can be used to plug in the schedule C<expansion>
8470 in the leaves of C<schedule>, where C<contraction> describes how
8471 the domain elements of C<expansion> map to the domain elements
8472 at the original leaves of C<schedule>.
8473 The resulting schedule will contain expansion nodes, unless
8474 C<contraction> is an identity function.
8476 #include <isl/schedule.h>
8477 __isl_give isl_schedule *isl_schedule_expand(
8478 __isl_take isl_schedule *schedule,
8479 __isl_take isl_union_pw_multi_aff *contraction,
8480 __isl_take isl_schedule *expansion);
8482 An C<isl_union_map> representation of the schedule can be obtained
8483 from an C<isl_schedule> using the following function.
8485 #include <isl/schedule.h>
8486 __isl_give isl_union_map *isl_schedule_get_map(
8487 __isl_keep isl_schedule *sched);
8489 The resulting relation encodes the same relative ordering as
8490 the schedule by mapping the domain elements to a common schedule space.
8491 If the schedule_separate_components option is set, then the order
8492 of the children of a set node is explicitly encoded in the result.
8493 If the tree contains any expansion nodes, then the relation
8494 is formulated in terms of the expanded domain elements.
8496 Schedules can be read from input using the following functions.
8498 #include <isl/schedule.h>
8499 __isl_give isl_schedule *isl_schedule_read_from_file(
8500 isl_ctx *ctx, FILE *input);
8501 __isl_give isl_schedule *isl_schedule_read_from_str(
8502 isl_ctx *ctx, const char *str);
8504 A representation of the schedule can be printed using
8506 #include <isl/schedule.h>
8507 __isl_give isl_printer *isl_printer_print_schedule(
8508 __isl_take isl_printer *p,
8509 __isl_keep isl_schedule *schedule);
8510 __isl_give char *isl_schedule_to_str(
8511 __isl_keep isl_schedule *schedule);
8513 C<isl_schedule_to_str> prints the schedule in flow format.
8515 The schedule tree can be traversed through the use of
8516 C<isl_schedule_node> objects that point to a particular
8517 position in the schedule tree. Whenever a C<isl_schedule_node>
8518 is used to modify a node in the schedule tree, the original schedule
8519 tree is left untouched and the modifications are performed to a copy
8520 of the tree. The returned C<isl_schedule_node> then points to
8521 this modified copy of the tree.
8523 The root of the schedule tree can be obtained using the following function.
8525 #include <isl/schedule.h>
8526 __isl_give isl_schedule_node *isl_schedule_get_root(
8527 __isl_keep isl_schedule *schedule);
8529 A pointer to a newly created schedule tree with a single domain
8530 node can be created using the following functions.
8532 #include <isl/schedule_node.h>
8533 __isl_give isl_schedule_node *
8534 isl_schedule_node_from_domain(
8535 __isl_take isl_union_set *domain);
8536 __isl_give isl_schedule_node *
8537 isl_schedule_node_from_extension(
8538 __isl_take isl_union_map *extension);
8540 C<isl_schedule_node_from_extension> creates a tree with an extension
8543 Schedule nodes can be copied and freed using the following functions.
8545 #include <isl/schedule_node.h>
8546 __isl_give isl_schedule_node *isl_schedule_node_copy(
8547 __isl_keep isl_schedule_node *node);
8548 __isl_null isl_schedule_node *isl_schedule_node_free(
8549 __isl_take isl_schedule_node *node);
8551 The following functions can be used to check if two schedule
8552 nodes point to the same position in the same schedule.
8554 #include <isl/schedule_node.h>
8555 isl_bool isl_schedule_node_is_equal(
8556 __isl_keep isl_schedule_node *node1,
8557 __isl_keep isl_schedule_node *node2);
8559 The following properties can be obtained from a schedule node.
8561 #include <isl/schedule_node.h>
8562 enum isl_schedule_node_type isl_schedule_node_get_type(
8563 __isl_keep isl_schedule_node *node);
8564 enum isl_schedule_node_type
8565 isl_schedule_node_get_parent_type(
8566 __isl_keep isl_schedule_node *node);
8567 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8568 __isl_keep isl_schedule_node *node);
8570 The function C<isl_schedule_node_get_type> returns the type of
8571 the node, while C<isl_schedule_node_get_parent_type> returns
8572 type of the parent of the node, which is required to exist.
8573 The function C<isl_schedule_node_get_schedule> returns a copy
8574 to the schedule to which the node belongs.
8576 The following functions can be used to move the schedule node
8577 to a different position in the tree or to check if such a position
8580 #include <isl/schedule_node.h>
8581 isl_bool isl_schedule_node_has_parent(
8582 __isl_keep isl_schedule_node *node);
8583 __isl_give isl_schedule_node *isl_schedule_node_parent(
8584 __isl_take isl_schedule_node *node);
8585 __isl_give isl_schedule_node *isl_schedule_node_root(
8586 __isl_take isl_schedule_node *node);
8587 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8588 __isl_take isl_schedule_node *node,
8590 int isl_schedule_node_n_children(
8591 __isl_keep isl_schedule_node *node);
8592 __isl_give isl_schedule_node *isl_schedule_node_child(
8593 __isl_take isl_schedule_node *node, int pos);
8594 isl_bool isl_schedule_node_has_children(
8595 __isl_keep isl_schedule_node *node);
8596 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8597 __isl_take isl_schedule_node *node);
8598 isl_bool isl_schedule_node_has_previous_sibling(
8599 __isl_keep isl_schedule_node *node);
8600 __isl_give isl_schedule_node *
8601 isl_schedule_node_previous_sibling(
8602 __isl_take isl_schedule_node *node);
8603 isl_bool isl_schedule_node_has_next_sibling(
8604 __isl_keep isl_schedule_node *node);
8605 __isl_give isl_schedule_node *
8606 isl_schedule_node_next_sibling(
8607 __isl_take isl_schedule_node *node);
8609 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8610 is the node itself, the ancestor of generation 1 is its parent and so on.
8612 It is also possible to query the number of ancestors of a node,
8613 the position of the current node
8614 within the children of its parent, the position of the subtree
8615 containing a node within the children of an ancestor
8616 or to obtain a copy of a given
8617 child without destroying the current node.
8618 Given two nodes that point to the same schedule, their closest
8619 shared ancestor can be obtained using
8620 C<isl_schedule_node_get_shared_ancestor>.
8622 #include <isl/schedule_node.h>
8623 int isl_schedule_node_get_tree_depth(
8624 __isl_keep isl_schedule_node *node);
8625 int isl_schedule_node_get_child_position(
8626 __isl_keep isl_schedule_node *node);
8627 int isl_schedule_node_get_ancestor_child_position(
8628 __isl_keep isl_schedule_node *node,
8629 __isl_keep isl_schedule_node *ancestor);
8630 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8631 __isl_keep isl_schedule_node *node, int pos);
8632 __isl_give isl_schedule_node *
8633 isl_schedule_node_get_shared_ancestor(
8634 __isl_keep isl_schedule_node *node1,
8635 __isl_keep isl_schedule_node *node2);
8637 All nodes in a schedule tree or
8638 all descendants of a specific node (including the node) can be visited
8639 in depth-first pre-order using the following functions.
8641 #include <isl/schedule.h>
8642 isl_stat isl_schedule_foreach_schedule_node_top_down(
8643 __isl_keep isl_schedule *sched,
8644 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8645 void *user), void *user);
8647 #include <isl/schedule_node.h>
8648 isl_stat isl_schedule_node_foreach_descendant_top_down(
8649 __isl_keep isl_schedule_node *node,
8650 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8651 void *user), void *user);
8653 The callback function is slightly different from the usual
8654 callbacks in that it not only indicates success (non-negative result)
8655 or failure (negative result), but also indicates whether the children
8656 of the given node should be visited. In particular, if the callback
8657 returns a positive value, then the children are visited, but if
8658 the callback returns zero, then the children are not visited.
8660 The following functions checks whether
8661 all descendants of a specific node (including the node itself)
8662 satisfy a user-specified test.
8664 #include <isl/schedule_node.h>
8665 isl_bool isl_schedule_node_every_descendant(
8666 __isl_keep isl_schedule_node *node,
8667 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8668 void *user), void *user)
8670 The ancestors of a node in a schedule tree can be visited from
8671 the root down to and including the parent of the node using
8672 the following function.
8674 #include <isl/schedule_node.h>
8675 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8676 __isl_keep isl_schedule_node *node,
8677 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8678 void *user), void *user);
8680 The following functions allows for a depth-first post-order
8681 traversal of the nodes in a schedule tree or
8682 of the descendants of a specific node (including the node
8683 itself), where the user callback is allowed to modify the
8686 #include <isl/schedule.h>
8687 __isl_give isl_schedule *
8688 isl_schedule_map_schedule_node_bottom_up(
8689 __isl_take isl_schedule *schedule,
8690 __isl_give isl_schedule_node *(*fn)(
8691 __isl_take isl_schedule_node *node,
8692 void *user), void *user);
8694 #include <isl/schedule_node.h>
8695 __isl_give isl_schedule_node *
8696 isl_schedule_node_map_descendant_bottom_up(
8697 __isl_take isl_schedule_node *node,
8698 __isl_give isl_schedule_node *(*fn)(
8699 __isl_take isl_schedule_node *node,
8700 void *user), void *user);
8702 The traversal continues from the node returned by the callback function.
8703 It is the responsibility of the user to ensure that this does not
8704 lead to an infinite loop. It is safest to always return a pointer
8705 to the same position (same ancestors and child positions) as the input node.
8707 The following function removes a node (along with its descendants)
8708 from a schedule tree and returns a pointer to the leaf at the
8709 same position in the updated tree.
8710 It is not allowed to remove the root of a schedule tree or
8711 a child of a set or sequence node.
8713 #include <isl/schedule_node.h>
8714 __isl_give isl_schedule_node *isl_schedule_node_cut(
8715 __isl_take isl_schedule_node *node);
8717 The following function removes a single node
8718 from a schedule tree and returns a pointer to the child
8719 of the node, now located at the position of the original node
8720 or to a leaf node at that position if there was no child.
8721 It is not allowed to remove the root of a schedule tree,
8722 a set or sequence node, a child of a set or sequence node or
8723 a band node with an anchored subtree.
8725 #include <isl/schedule_node.h>
8726 __isl_give isl_schedule_node *isl_schedule_node_delete(
8727 __isl_take isl_schedule_node *node);
8729 Most nodes in a schedule tree only contain local information.
8730 In some cases, however, a node may also refer to the schedule dimensions
8731 of its outer band nodes.
8732 This means that the position of the node within the tree should
8733 not be changed, or at least that no changes are performed to the
8734 outer band nodes. The following function can be used to test
8735 whether the subtree rooted at a given node contains any such nodes.
8737 #include <isl/schedule_node.h>
8738 isl_bool isl_schedule_node_is_subtree_anchored(
8739 __isl_keep isl_schedule_node *node);
8741 The following function resets the user pointers on all parameter
8742 and tuple identifiers referenced by the given schedule node.
8744 #include <isl/schedule_node.h>
8745 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8746 __isl_take isl_schedule_node *node);
8748 The following function aligns the parameters of the given schedule
8749 node to the given space.
8751 #include <isl/schedule_node.h>
8752 __isl_give isl_schedule_node *
8753 isl_schedule_node_align_params(
8754 __isl_take isl_schedule_node *node,
8755 __isl_take isl_space *space);
8757 Several node types have their own functions for querying
8758 (and in some cases setting) some node type specific properties.
8760 #include <isl/schedule_node.h>
8761 __isl_give isl_space *isl_schedule_node_band_get_space(
8762 __isl_keep isl_schedule_node *node);
8763 __isl_give isl_multi_union_pw_aff *
8764 isl_schedule_node_band_get_partial_schedule(
8765 __isl_keep isl_schedule_node *node);
8766 __isl_give isl_union_map *
8767 isl_schedule_node_band_get_partial_schedule_union_map(
8768 __isl_keep isl_schedule_node *node);
8769 unsigned isl_schedule_node_band_n_member(
8770 __isl_keep isl_schedule_node *node);
8771 isl_bool isl_schedule_node_band_member_get_coincident(
8772 __isl_keep isl_schedule_node *node, int pos);
8773 __isl_give isl_schedule_node *
8774 isl_schedule_node_band_member_set_coincident(
8775 __isl_take isl_schedule_node *node, int pos,
8777 isl_bool isl_schedule_node_band_get_permutable(
8778 __isl_keep isl_schedule_node *node);
8779 __isl_give isl_schedule_node *
8780 isl_schedule_node_band_set_permutable(
8781 __isl_take isl_schedule_node *node, int permutable);
8782 enum isl_ast_loop_type
8783 isl_schedule_node_band_member_get_ast_loop_type(
8784 __isl_keep isl_schedule_node *node, int pos);
8785 __isl_give isl_schedule_node *
8786 isl_schedule_node_band_member_set_ast_loop_type(
8787 __isl_take isl_schedule_node *node, int pos,
8788 enum isl_ast_loop_type type);
8789 __isl_give isl_union_set *
8790 enum isl_ast_loop_type
8791 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8792 __isl_keep isl_schedule_node *node, int pos);
8793 __isl_give isl_schedule_node *
8794 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8795 __isl_take isl_schedule_node *node, int pos,
8796 enum isl_ast_loop_type type);
8797 isl_schedule_node_band_get_ast_build_options(
8798 __isl_keep isl_schedule_node *node);
8799 __isl_give isl_schedule_node *
8800 isl_schedule_node_band_set_ast_build_options(
8801 __isl_take isl_schedule_node *node,
8802 __isl_take isl_union_set *options);
8803 __isl_give isl_set *
8804 isl_schedule_node_band_get_ast_isolate_option(
8805 __isl_keep isl_schedule_node *node);
8807 The function C<isl_schedule_node_band_get_space> returns the space
8808 of the partial schedule of the band.
8809 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8810 returns a representation of the partial schedule of the band node
8811 in the form of an C<isl_union_map>.
8812 The coincident and permutable properties are set by
8813 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8815 A scheduling dimension is considered to be ``coincident''
8816 if it satisfies the coincidence constraints within its band.
8817 That is, if the dependence distances of the coincidence
8818 constraints are all zero in that direction (for fixed
8819 iterations of outer bands).
8820 A band is marked permutable if it was produced using the Pluto-like scheduler.
8821 Note that the scheduler may have to resort to a Feautrier style scheduling
8822 step even if the default scheduler is used.
8823 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8824 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8825 For the meaning of these loop AST generation types and the difference
8826 between the regular loop AST generation type and the isolate
8827 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8828 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8829 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8830 may return C<isl_ast_loop_error> if an error occurs.
8831 The AST build options govern how an AST is generated for
8832 the individual schedule dimensions during AST generation.
8833 See L</"AST Generation Options (Schedule Tree)">.
8834 The isolate option for the given node can be extracted from these
8835 AST build options using the function
8836 C<isl_schedule_node_band_get_ast_isolate_option>.
8838 #include <isl/schedule_node.h>
8839 __isl_give isl_set *
8840 isl_schedule_node_context_get_context(
8841 __isl_keep isl_schedule_node *node);
8843 #include <isl/schedule_node.h>
8844 __isl_give isl_union_set *
8845 isl_schedule_node_domain_get_domain(
8846 __isl_keep isl_schedule_node *node);
8848 #include <isl/schedule_node.h>
8849 __isl_give isl_union_map *
8850 isl_schedule_node_expansion_get_expansion(
8851 __isl_keep isl_schedule_node *node);
8852 __isl_give isl_union_pw_multi_aff *
8853 isl_schedule_node_expansion_get_contraction(
8854 __isl_keep isl_schedule_node *node);
8856 #include <isl/schedule_node.h>
8857 __isl_give isl_union_map *
8858 isl_schedule_node_extension_get_extension(
8859 __isl_keep isl_schedule_node *node);
8861 #include <isl/schedule_node.h>
8862 __isl_give isl_union_set *
8863 isl_schedule_node_filter_get_filter(
8864 __isl_keep isl_schedule_node *node);
8866 #include <isl/schedule_node.h>
8867 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8868 __isl_keep isl_schedule_node *node);
8870 #include <isl/schedule_node.h>
8871 __isl_give isl_id *isl_schedule_node_mark_get_id(
8872 __isl_keep isl_schedule_node *node);
8874 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8875 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8876 partial schedules related to the node.
8878 #include <isl/schedule_node.h>
8879 __isl_give isl_multi_union_pw_aff *
8880 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8881 __isl_keep isl_schedule_node *node);
8882 __isl_give isl_union_pw_multi_aff *
8883 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8884 __isl_keep isl_schedule_node *node);
8885 __isl_give isl_union_map *
8886 isl_schedule_node_get_prefix_schedule_union_map(
8887 __isl_keep isl_schedule_node *node);
8888 __isl_give isl_union_map *
8889 isl_schedule_node_get_prefix_schedule_relation(
8890 __isl_keep isl_schedule_node *node);
8891 __isl_give isl_union_map *
8892 isl_schedule_node_get_subtree_schedule_union_map(
8893 __isl_keep isl_schedule_node *node);
8895 In particular, the functions
8896 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8897 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8898 and C<isl_schedule_node_get_prefix_schedule_union_map>
8899 return a relative ordering on the domain elements that reach the given
8900 node determined by its ancestors.
8901 The function C<isl_schedule_node_get_prefix_schedule_relation>
8902 additionally includes the domain constraints in the result.
8903 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8904 returns a representation of the partial schedule defined by the
8905 subtree rooted at the given node.
8906 If the tree contains any expansion nodes, then the subtree schedule
8907 is formulated in terms of the expanded domain elements.
8908 The tree passed to functions returning a prefix schedule
8909 may only contain extension nodes if these would not affect
8910 the result of these functions. That is, if one of the ancestors
8911 is an extension node, then all of the domain elements that were
8912 added by the extension node need to have been filtered out
8913 by filter nodes between the extension node and the input node.
8914 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8915 may not contain in extension nodes in the selected subtree.
8917 The expansion/contraction defined by an entire subtree, combining
8918 the expansions/contractions
8919 on the expansion nodes in the subtree, can be obtained using
8920 the following functions.
8922 #include <isl/schedule_node.h>
8923 __isl_give isl_union_map *
8924 isl_schedule_node_get_subtree_expansion(
8925 __isl_keep isl_schedule_node *node);
8926 __isl_give isl_union_pw_multi_aff *
8927 isl_schedule_node_get_subtree_contraction(
8928 __isl_keep isl_schedule_node *node);
8930 The total number of outer band members of given node, i.e.,
8931 the shared output dimension of the maps in the result
8932 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8933 using the following function.
8935 #include <isl/schedule_node.h>
8936 int isl_schedule_node_get_schedule_depth(
8937 __isl_keep isl_schedule_node *node);
8939 The following functions return the elements that reach the given node
8940 or the union of universes in the spaces that contain these elements.
8942 #include <isl/schedule_node.h>
8943 __isl_give isl_union_set *
8944 isl_schedule_node_get_domain(
8945 __isl_keep isl_schedule_node *node);
8946 __isl_give isl_union_set *
8947 isl_schedule_node_get_universe_domain(
8948 __isl_keep isl_schedule_node *node);
8950 The input tree of C<isl_schedule_node_get_domain>
8951 may only contain extension nodes if these would not affect
8952 the result of this function. That is, if one of the ancestors
8953 is an extension node, then all of the domain elements that were
8954 added by the extension node need to have been filtered out
8955 by filter nodes between the extension node and the input node.
8957 The following functions can be used to introduce additional nodes
8958 in the schedule tree. The new node is introduced at the point
8959 in the tree where the C<isl_schedule_node> points to and
8960 the results points to the new node.
8962 #include <isl/schedule_node.h>
8963 __isl_give isl_schedule_node *
8964 isl_schedule_node_insert_partial_schedule(
8965 __isl_take isl_schedule_node *node,
8966 __isl_take isl_multi_union_pw_aff *schedule);
8968 This function inserts a new band node with (the greatest integer
8969 part of) the given partial schedule.
8970 The subtree rooted at the given node is assumed not to have
8973 #include <isl/schedule_node.h>
8974 __isl_give isl_schedule_node *
8975 isl_schedule_node_insert_context(
8976 __isl_take isl_schedule_node *node,
8977 __isl_take isl_set *context);
8979 This function inserts a new context node with the given context constraints.
8981 #include <isl/schedule_node.h>
8982 __isl_give isl_schedule_node *
8983 isl_schedule_node_insert_filter(
8984 __isl_take isl_schedule_node *node,
8985 __isl_take isl_union_set *filter);
8987 This function inserts a new filter node with the given filter.
8988 If the original node already pointed to a filter node, then the
8989 two filter nodes are merged into one.
8991 #include <isl/schedule_node.h>
8992 __isl_give isl_schedule_node *
8993 isl_schedule_node_insert_guard(
8994 __isl_take isl_schedule_node *node,
8995 __isl_take isl_set *guard);
8997 This function inserts a new guard node with the given guard constraints.
8999 #include <isl/schedule_node.h>
9000 __isl_give isl_schedule_node *
9001 isl_schedule_node_insert_mark(
9002 __isl_take isl_schedule_node *node,
9003 __isl_take isl_id *mark);
9005 This function inserts a new mark node with the give mark identifier.
9007 #include <isl/schedule_node.h>
9008 __isl_give isl_schedule_node *
9009 isl_schedule_node_insert_sequence(
9010 __isl_take isl_schedule_node *node,
9011 __isl_take isl_union_set_list *filters);
9012 __isl_give isl_schedule_node *
9013 isl_schedule_node_insert_set(
9014 __isl_take isl_schedule_node *node,
9015 __isl_take isl_union_set_list *filters);
9017 These functions insert a new sequence or set node with the given
9018 filters as children.
9020 #include <isl/schedule_node.h>
9021 __isl_give isl_schedule_node *isl_schedule_node_group(
9022 __isl_take isl_schedule_node *node,
9023 __isl_take isl_id *group_id);
9025 This function introduces an expansion node in between the current
9026 node and its parent that expands instances of a space with tuple
9027 identifier C<group_id> to the original domain elements that reach
9028 the node. The group instances are identified by the prefix schedule
9029 of those domain elements. The ancestors of the node are adjusted
9030 to refer to the group instances instead of the original domain
9031 elements. The return value points to the same node in the updated
9032 schedule tree as the input node, i.e., to the child of the newly
9033 introduced expansion node. Grouping instances of different statements
9034 ensures that they will be treated as a single statement by the
9035 AST generator up to the point of the expansion node.
9037 The following function can be used to flatten a nested
9040 #include <isl/schedule_node.h>
9041 __isl_give isl_schedule_node *
9042 isl_schedule_node_sequence_splice_child(
9043 __isl_take isl_schedule_node *node, int pos);
9045 That is, given a sequence node C<node> that has another sequence node
9046 in its child at position C<pos> (in particular, the child of that filter
9047 node is a sequence node), attach the children of that other sequence
9048 node as children of C<node>, replacing the original child at position
9051 The partial schedule of a band node can be scaled (down) or reduced using
9052 the following functions.
9054 #include <isl/schedule_node.h>
9055 __isl_give isl_schedule_node *
9056 isl_schedule_node_band_scale(
9057 __isl_take isl_schedule_node *node,
9058 __isl_take isl_multi_val *mv);
9059 __isl_give isl_schedule_node *
9060 isl_schedule_node_band_scale_down(
9061 __isl_take isl_schedule_node *node,
9062 __isl_take isl_multi_val *mv);
9063 __isl_give isl_schedule_node *
9064 isl_schedule_node_band_mod(
9065 __isl_take isl_schedule_node *node,
9066 __isl_take isl_multi_val *mv);
9068 The spaces of the two arguments need to match.
9069 After scaling, the partial schedule is replaced by its greatest
9070 integer part to ensure that the schedule remains integral.
9072 The partial schedule of a band node can be shifted by an
9073 C<isl_multi_union_pw_aff> with a domain that is a superset
9074 of the domain of the partial schedule using
9075 the following function.
9077 #include <isl/schedule_node.h>
9078 __isl_give isl_schedule_node *
9079 isl_schedule_node_band_shift(
9080 __isl_take isl_schedule_node *node,
9081 __isl_take isl_multi_union_pw_aff *shift);
9083 A band node can be tiled using the following function.
9085 #include <isl/schedule_node.h>
9086 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
9087 __isl_take isl_schedule_node *node,
9088 __isl_take isl_multi_val *sizes);
9090 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
9092 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
9093 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
9095 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
9097 The C<isl_schedule_node_band_tile> function tiles
9098 the band using the given tile sizes inside its schedule.
9099 A new child band node is created to represent the point loops and it is
9100 inserted between the modified band and its children.
9101 The subtree rooted at the given node is assumed not to have
9103 The C<tile_scale_tile_loops> option specifies whether the tile
9104 loops iterators should be scaled by the tile sizes.
9105 If the C<tile_shift_point_loops> option is set, then the point loops
9106 are shifted to start at zero.
9108 A band node can be split into two nested band nodes
9109 using the following function.
9111 #include <isl/schedule_node.h>
9112 __isl_give isl_schedule_node *isl_schedule_node_band_split(
9113 __isl_take isl_schedule_node *node, int pos);
9115 The resulting outer band node contains the first C<pos> dimensions of
9116 the schedule of C<node> while the inner band contains the remaining dimensions.
9117 The schedules of the two band nodes live in anonymous spaces.
9118 The loop AST generation type options and the isolate option
9119 are split over the two band nodes.
9121 A band node can be moved down to the leaves of the subtree rooted
9122 at the band node using the following function.
9124 #include <isl/schedule_node.h>
9125 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
9126 __isl_take isl_schedule_node *node);
9128 The subtree rooted at the given node is assumed not to have
9130 The result points to the node in the resulting tree that is in the same
9131 position as the node pointed to by C<node> in the original tree.
9133 #include <isl/schedule_node.h>
9134 __isl_give isl_schedule_node *
9135 isl_schedule_node_order_before(
9136 __isl_take isl_schedule_node *node,
9137 __isl_take isl_union_set *filter);
9138 __isl_give isl_schedule_node *
9139 isl_schedule_node_order_after(
9140 __isl_take isl_schedule_node *node,
9141 __isl_take isl_union_set *filter);
9143 These functions split the domain elements that reach C<node>
9144 into those that satisfy C<filter> and those that do not and
9145 arranges for the elements that do satisfy the filter to be
9146 executed before (in case of C<isl_schedule_node_order_before>)
9147 or after (in case of C<isl_schedule_node_order_after>)
9148 those that do not. The order is imposed by
9149 a sequence node, possibly reusing the grandparent of C<node>
9150 on two copies of the subtree attached to the original C<node>.
9151 Both copies are simplified with respect to their filter.
9153 Return a pointer to the copy of the subtree that does not
9154 satisfy C<filter>. If there is no such copy (because all
9155 reaching domain elements satisfy the filter), then return
9156 the original pointer.
9158 #include <isl/schedule_node.h>
9159 __isl_give isl_schedule_node *
9160 isl_schedule_node_graft_before(
9161 __isl_take isl_schedule_node *node,
9162 __isl_take isl_schedule_node *graft);
9163 __isl_give isl_schedule_node *
9164 isl_schedule_node_graft_after(
9165 __isl_take isl_schedule_node *node,
9166 __isl_take isl_schedule_node *graft);
9168 This function inserts the C<graft> tree into the tree containing C<node>
9169 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
9170 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
9171 The root node of C<graft>
9172 should be an extension node where the domain of the extension
9173 is the flat product of all outer band nodes of C<node>.
9174 The root node may also be a domain node.
9175 The elements of the domain or the range of the extension may not
9176 intersect with the domain elements that reach "node".
9177 The schedule tree of C<graft> may not be anchored.
9179 The schedule tree of C<node> is modified to include an extension node
9180 corresponding to the root node of C<graft> as a child of the original
9181 parent of C<node>. The original node that C<node> points to and the
9182 child of the root node of C<graft> are attached to this extension node
9183 through a sequence, with appropriate filters and with the child
9184 of C<graft> appearing before or after the original C<node>.
9186 If C<node> already appears inside a sequence that is the child of
9187 an extension node and if the spaces of the new domain elements
9188 do not overlap with those of the original domain elements,
9189 then that extension node is extended with the new extension
9190 rather than introducing a new segment of extension and sequence nodes.
9192 Return a pointer to the same node in the modified tree that
9193 C<node> pointed to in the original tree.
9195 A representation of the schedule node can be printed using
9197 #include <isl/schedule_node.h>
9198 __isl_give isl_printer *isl_printer_print_schedule_node(
9199 __isl_take isl_printer *p,
9200 __isl_keep isl_schedule_node *node);
9201 __isl_give char *isl_schedule_node_to_str(
9202 __isl_keep isl_schedule_node *node);
9204 C<isl_schedule_node_to_str> prints the schedule node in block format.
9206 =head2 Dependence Analysis
9208 C<isl> contains specialized functionality for performing
9209 array dataflow analysis. That is, given a I<sink> access relation,
9210 a collection of possible I<source> accesses and
9211 a collection of I<kill> accesses,
9212 C<isl> can compute relations that describe
9213 for each iteration of the sink access, which iterations
9214 of which of the source access relations may have
9215 accessed the same data element before the given iteration
9216 of the sink access without any intermediate kill of that data element.
9217 The resulting dependence relations map source iterations
9218 to either the corresponding sink iterations or
9219 pairs of corresponding sink iterations and accessed data elements.
9220 To compute standard flow dependences, the sink should be
9221 a read, while the sources should be writes.
9222 If no kills are specified,
9223 then memory based dependence analysis is performed.
9224 If, on the other hand, all sources are also kills,
9225 then value based dependence analysis is performed.
9226 If any of the source accesses are marked as being I<must>
9227 accesses, then they are also treated as kills.
9228 Furthermore, the specification of must-sources results
9229 in the computation of must-dependences.
9230 Only dependences originating in a must access not coscheduled
9231 with any other access to the same element and without
9232 any may accesses between the must access and the sink access
9233 are considered to be must dependences.
9235 =head3 High-level Interface
9237 A high-level interface to dependence analysis is provided
9238 by the following function.
9240 #include <isl/flow.h>
9241 __isl_give isl_union_flow *
9242 isl_union_access_info_compute_flow(
9243 __isl_take isl_union_access_info *access);
9245 The input C<isl_union_access_info> object describes the sink
9246 access relations, the source access relations and a schedule,
9247 while the output C<isl_union_flow> object describes
9248 the resulting dependence relations and the subsets of the
9249 sink relations for which no source was found.
9251 An C<isl_union_access_info> is created, modified, copied and freed using
9252 the following functions.
9254 #include <isl/flow.h>
9255 __isl_give isl_union_access_info *
9256 isl_union_access_info_from_sink(
9257 __isl_take isl_union_map *sink);
9258 __isl_give isl_union_access_info *
9259 isl_union_access_info_set_kill(
9260 __isl_take isl_union_access_info *access,
9261 __isl_take isl_union_map *kill);
9262 __isl_give isl_union_access_info *
9263 isl_union_access_info_set_may_source(
9264 __isl_take isl_union_access_info *access,
9265 __isl_take isl_union_map *may_source);
9266 __isl_give isl_union_access_info *
9267 isl_union_access_info_set_must_source(
9268 __isl_take isl_union_access_info *access,
9269 __isl_take isl_union_map *must_source);
9270 __isl_give isl_union_access_info *
9271 isl_union_access_info_set_schedule(
9272 __isl_take isl_union_access_info *access,
9273 __isl_take isl_schedule *schedule);
9274 __isl_give isl_union_access_info *
9275 isl_union_access_info_set_schedule_map(
9276 __isl_take isl_union_access_info *access,
9277 __isl_take isl_union_map *schedule_map);
9278 __isl_give isl_union_access_info *
9279 isl_union_access_info_copy(
9280 __isl_keep isl_union_access_info *access);
9281 __isl_null isl_union_access_info *
9282 isl_union_access_info_free(
9283 __isl_take isl_union_access_info *access);
9285 The may sources set by C<isl_union_access_info_set_may_source>
9286 do not need to include the must sources set by
9287 C<isl_union_access_info_set_must_source> as a subset.
9288 The kills set by C<isl_union_access_info_set_kill> may overlap
9289 with the may-sources and/or must-sources.
9290 The user is free not to call one (or more) of these functions,
9291 in which case the corresponding set is kept to its empty default.
9292 Similarly, the default schedule initialized by
9293 C<isl_union_access_info_from_sink> is empty.
9294 The current schedule is determined by the last call to either
9295 C<isl_union_access_info_set_schedule> or
9296 C<isl_union_access_info_set_schedule_map>.
9297 The domain of the schedule corresponds to the domains of
9298 the access relations. In particular, the domains of the access
9299 relations are effectively intersected with the domain of the schedule
9300 and only the resulting accesses are considered by the dependence analysis.
9302 An C<isl_union_access_info> object can be read from input
9303 using the following function.
9305 #include <isl/flow.h>
9306 __isl_give isl_union_access_info *
9307 isl_union_access_info_read_from_file(isl_ctx *ctx,
9310 A representation of the information contained in an object
9311 of type C<isl_union_access_info> can be obtained using
9313 #include <isl/flow.h>
9314 __isl_give isl_printer *
9315 isl_printer_print_union_access_info(
9316 __isl_take isl_printer *p,
9317 __isl_keep isl_union_access_info *access);
9318 __isl_give char *isl_union_access_info_to_str(
9319 __isl_keep isl_union_access_info *access);
9321 C<isl_union_access_info_to_str> prints the information in flow format.
9323 The output of C<isl_union_access_info_compute_flow> can be examined,
9324 copied, and freed using the following functions.
9326 #include <isl/flow.h>
9327 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9328 __isl_keep isl_union_flow *flow);
9329 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9330 __isl_keep isl_union_flow *flow);
9331 __isl_give isl_union_map *
9332 isl_union_flow_get_full_must_dependence(
9333 __isl_keep isl_union_flow *flow);
9334 __isl_give isl_union_map *
9335 isl_union_flow_get_full_may_dependence(
9336 __isl_keep isl_union_flow *flow);
9337 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9338 __isl_keep isl_union_flow *flow);
9339 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9340 __isl_keep isl_union_flow *flow);
9341 __isl_give isl_union_flow *isl_union_flow_copy(
9342 __isl_keep isl_union_flow *flow);
9343 __isl_null isl_union_flow *isl_union_flow_free(
9344 __isl_take isl_union_flow *flow);
9346 The relation returned by C<isl_union_flow_get_must_dependence>
9347 relates domain elements of must sources to domain elements of the sink.
9348 The relation returned by C<isl_union_flow_get_may_dependence>
9349 relates domain elements of must or may sources to domain elements of the sink
9350 and includes the previous relation as a subset.
9351 The relation returned by C<isl_union_flow_get_full_must_dependence>
9352 relates domain elements of must sources to pairs of domain elements of the sink
9353 and accessed data elements.
9354 The relation returned by C<isl_union_flow_get_full_may_dependence>
9355 relates domain elements of must or may sources to pairs of
9356 domain elements of the sink and accessed data elements.
9357 This relation includes the previous relation as a subset.
9358 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9359 of the sink relation for which no dependences have been found.
9360 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9361 of the sink relation for which no definite dependences have been found.
9362 That is, it contains those sink access that do not contribute to any
9363 of the elements in the relation returned
9364 by C<isl_union_flow_get_must_dependence>.
9366 A representation of the information contained in an object
9367 of type C<isl_union_flow> can be obtained using
9369 #include <isl/flow.h>
9370 __isl_give isl_printer *isl_printer_print_union_flow(
9371 __isl_take isl_printer *p,
9372 __isl_keep isl_union_flow *flow);
9373 __isl_give char *isl_union_flow_to_str(
9374 __isl_keep isl_union_flow *flow);
9376 C<isl_union_flow_to_str> prints the information in flow format.
9378 =head3 Low-level Interface
9380 A lower-level interface is provided by the following functions.
9382 #include <isl/flow.h>
9384 typedef int (*isl_access_level_before)(void *first, void *second);
9386 __isl_give isl_access_info *isl_access_info_alloc(
9387 __isl_take isl_map *sink,
9388 void *sink_user, isl_access_level_before fn,
9390 __isl_give isl_access_info *isl_access_info_add_source(
9391 __isl_take isl_access_info *acc,
9392 __isl_take isl_map *source, int must,
9394 __isl_null isl_access_info *isl_access_info_free(
9395 __isl_take isl_access_info *acc);
9397 __isl_give isl_flow *isl_access_info_compute_flow(
9398 __isl_take isl_access_info *acc);
9400 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9401 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9402 void *dep_user, void *user),
9404 __isl_give isl_map *isl_flow_get_no_source(
9405 __isl_keep isl_flow *deps, int must);
9406 __isl_null isl_flow *isl_flow_free(
9407 __isl_take isl_flow *deps);
9409 The function C<isl_access_info_compute_flow> performs the actual
9410 dependence analysis. The other functions are used to construct
9411 the input for this function or to read off the output.
9413 The input is collected in an C<isl_access_info>, which can
9414 be created through a call to C<isl_access_info_alloc>.
9415 The arguments to this functions are the sink access relation
9416 C<sink>, a token C<sink_user> used to identify the sink
9417 access to the user, a callback function for specifying the
9418 relative order of source and sink accesses, and the number
9419 of source access relations that will be added.
9421 The callback function has type C<int (*)(void *first, void *second)>.
9422 The function is called with two user supplied tokens identifying
9423 either a source or the sink and it should return the shared nesting
9424 level and the relative order of the two accesses.
9425 In particular, let I<n> be the number of loops shared by
9426 the two accesses. If C<first> precedes C<second> textually,
9427 then the function should return I<2 * n + 1>; otherwise,
9428 it should return I<2 * n>.
9429 The low-level interface assumes that no sources are coscheduled.
9430 If the information returned by the callback does not allow
9431 the relative order to be determined, then one of the sources
9432 is arbitrarily taken to be executed after the other(s).
9434 The sources can be added to the C<isl_access_info> object by performing
9435 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9436 C<must> indicates whether the source is a I<must> access
9437 or a I<may> access. Note that a multi-valued access relation
9438 should only be marked I<must> if every iteration in the domain
9439 of the relation accesses I<all> elements in its image.
9440 The C<source_user> token is again used to identify
9441 the source access. The range of the source access relation
9442 C<source> should have the same dimension as the range
9443 of the sink access relation.
9444 The C<isl_access_info_free> function should usually not be
9445 called explicitly, because it is already called implicitly by
9446 C<isl_access_info_compute_flow>.
9448 The result of the dependence analysis is collected in an
9449 C<isl_flow>. There may be elements of
9450 the sink access for which no preceding source access could be
9451 found or for which all preceding sources are I<may> accesses.
9452 The relations containing these elements can be obtained through
9453 calls to C<isl_flow_get_no_source>, the first with C<must> set
9454 and the second with C<must> unset.
9455 In the case of standard flow dependence analysis,
9456 with the sink a read and the sources I<must> writes,
9457 the first relation corresponds to the reads from uninitialized
9458 array elements and the second relation is empty.
9459 The actual flow dependences can be extracted using
9460 C<isl_flow_foreach>. This function will call the user-specified
9461 callback function C<fn> for each B<non-empty> dependence between
9462 a source and the sink. The callback function is called
9463 with four arguments, the actual flow dependence relation
9464 mapping source iterations to sink iterations, a boolean that
9465 indicates whether it is a I<must> or I<may> dependence, a token
9466 identifying the source and an additional C<void *> with value
9467 equal to the third argument of the C<isl_flow_foreach> call.
9468 A dependence is marked I<must> if it originates from a I<must>
9469 source and if it is not followed by any I<may> sources.
9471 After finishing with an C<isl_flow>, the user should call
9472 C<isl_flow_free> to free all associated memory.
9474 =head3 Interaction with the Low-level Interface
9476 During the dependence analysis, we frequently need to perform
9477 the following operation. Given a relation between sink iterations
9478 and potential source iterations from a particular source domain,
9479 what is the last potential source iteration corresponding to each
9480 sink iteration. It can sometimes be convenient to adjust
9481 the set of potential source iterations before or after each such operation.
9482 The prototypical example is fuzzy array dataflow analysis,
9483 where we need to analyze if, based on data-dependent constraints,
9484 the sink iteration can ever be executed without one or more of
9485 the corresponding potential source iterations being executed.
9486 If so, we can introduce extra parameters and select an unknown
9487 but fixed source iteration from the potential source iterations.
9488 To be able to perform such manipulations, C<isl> provides the following
9491 #include <isl/flow.h>
9493 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9494 __isl_keep isl_map *source_map,
9495 __isl_keep isl_set *sink, void *source_user,
9497 __isl_give isl_access_info *isl_access_info_set_restrict(
9498 __isl_take isl_access_info *acc,
9499 isl_access_restrict fn, void *user);
9501 The function C<isl_access_info_set_restrict> should be called
9502 before calling C<isl_access_info_compute_flow> and registers a callback function
9503 that will be called any time C<isl> is about to compute the last
9504 potential source. The first argument is the (reverse) proto-dependence,
9505 mapping sink iterations to potential source iterations.
9506 The second argument represents the sink iterations for which
9507 we want to compute the last source iteration.
9508 The third argument is the token corresponding to the source
9509 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9510 The callback is expected to return a restriction on either the input or
9511 the output of the operation computing the last potential source.
9512 If the input needs to be restricted then restrictions are needed
9513 for both the source and the sink iterations. The sink iterations
9514 and the potential source iterations will be intersected with these sets.
9515 If the output needs to be restricted then only a restriction on the source
9516 iterations is required.
9517 If any error occurs, the callback should return C<NULL>.
9518 An C<isl_restriction> object can be created, freed and inspected
9519 using the following functions.
9521 #include <isl/flow.h>
9523 __isl_give isl_restriction *isl_restriction_input(
9524 __isl_take isl_set *source_restr,
9525 __isl_take isl_set *sink_restr);
9526 __isl_give isl_restriction *isl_restriction_output(
9527 __isl_take isl_set *source_restr);
9528 __isl_give isl_restriction *isl_restriction_none(
9529 __isl_take isl_map *source_map);
9530 __isl_give isl_restriction *isl_restriction_empty(
9531 __isl_take isl_map *source_map);
9532 __isl_null isl_restriction *isl_restriction_free(
9533 __isl_take isl_restriction *restr);
9535 C<isl_restriction_none> and C<isl_restriction_empty> are special
9536 cases of C<isl_restriction_input>. C<isl_restriction_none>
9537 is essentially equivalent to
9539 isl_restriction_input(isl_set_universe(
9540 isl_space_range(isl_map_get_space(source_map))),
9542 isl_space_domain(isl_map_get_space(source_map))));
9544 whereas C<isl_restriction_empty> is essentially equivalent to
9546 isl_restriction_input(isl_set_empty(
9547 isl_space_range(isl_map_get_space(source_map))),
9549 isl_space_domain(isl_map_get_space(source_map))));
9553 #include <isl/schedule.h>
9554 __isl_give isl_schedule *
9555 isl_schedule_constraints_compute_schedule(
9556 __isl_take isl_schedule_constraints *sc);
9558 The function C<isl_schedule_constraints_compute_schedule> can be
9559 used to compute a schedule that satisfies the given schedule constraints.
9560 These schedule constraints include the iteration domain for which
9561 a schedule should be computed and dependences between pairs of
9562 iterations. In particular, these dependences include
9563 I<validity> dependences and I<proximity> dependences.
9564 By default, the algorithm used to construct the schedule is similar
9565 to that of C<Pluto>.
9566 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9568 The generated schedule respects all validity dependences.
9569 That is, all dependence distances over these dependences in the
9570 scheduled space are lexicographically positive.
9572 The default algorithm tries to ensure that the dependence distances
9573 over coincidence constraints are zero and to minimize the
9574 dependence distances over proximity dependences.
9575 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9576 for groups of domains where the dependence distances over validity
9577 dependences have only non-negative values.
9578 Note that when minimizing the maximal dependence distance
9579 over proximity dependences, a single affine expression in the parameters
9580 is constructed that bounds all dependence distances. If no such expression
9581 exists, then the algorithm will fail and resort to an alternative
9582 scheduling algorithm. In particular, this means that adding proximity
9583 dependences may eliminate valid solutions. A typical example where this
9584 phenomenon may occur is when some subset of the proximity dependences
9585 has no restriction on some parameter, forcing the coefficient of that
9586 parameter to be zero, while some other subset forces the dependence
9587 distance to depend on that parameter, requiring the same coefficient
9589 When using Feautrier's algorithm, the coincidence and proximity constraints
9590 are only taken into account during the extension to a
9591 full-dimensional schedule.
9593 An C<isl_schedule_constraints> object can be constructed
9594 and manipulated using the following functions.
9596 #include <isl/schedule.h>
9597 __isl_give isl_schedule_constraints *
9598 isl_schedule_constraints_copy(
9599 __isl_keep isl_schedule_constraints *sc);
9600 __isl_give isl_schedule_constraints *
9601 isl_schedule_constraints_on_domain(
9602 __isl_take isl_union_set *domain);
9603 __isl_give isl_schedule_constraints *
9604 isl_schedule_constraints_set_context(
9605 __isl_take isl_schedule_constraints *sc,
9606 __isl_take isl_set *context);
9607 __isl_give isl_schedule_constraints *
9608 isl_schedule_constraints_set_validity(
9609 __isl_take isl_schedule_constraints *sc,
9610 __isl_take isl_union_map *validity);
9611 __isl_give isl_schedule_constraints *
9612 isl_schedule_constraints_set_coincidence(
9613 __isl_take isl_schedule_constraints *sc,
9614 __isl_take isl_union_map *coincidence);
9615 __isl_give isl_schedule_constraints *
9616 isl_schedule_constraints_set_proximity(
9617 __isl_take isl_schedule_constraints *sc,
9618 __isl_take isl_union_map *proximity);
9619 __isl_give isl_schedule_constraints *
9620 isl_schedule_constraints_set_conditional_validity(
9621 __isl_take isl_schedule_constraints *sc,
9622 __isl_take isl_union_map *condition,
9623 __isl_take isl_union_map *validity);
9624 __isl_give isl_schedule_constraints *
9625 isl_schedule_constraints_apply(
9626 __isl_take isl_schedule_constraints *sc,
9627 __isl_take isl_union_map *umap);
9628 __isl_null isl_schedule_constraints *
9629 isl_schedule_constraints_free(
9630 __isl_take isl_schedule_constraints *sc);
9632 The initial C<isl_schedule_constraints> object created by
9633 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9634 That is, it has an empty set of dependences.
9635 The function C<isl_schedule_constraints_set_context> allows the user
9636 to specify additional constraints on the parameters that may
9637 be assumed to hold during the construction of the schedule.
9638 The function C<isl_schedule_constraints_set_validity> replaces the
9639 validity dependences, mapping domain elements I<i> to domain
9640 elements that should be scheduled after I<i>.
9641 The function C<isl_schedule_constraints_set_coincidence> replaces the
9642 coincidence dependences, mapping domain elements I<i> to domain
9643 elements that should be scheduled together with I<I>, if possible.
9644 The function C<isl_schedule_constraints_set_proximity> replaces the
9645 proximity dependences, mapping domain elements I<i> to domain
9646 elements that should be scheduled either before I<I>
9647 or as early as possible after I<i>.
9649 The function C<isl_schedule_constraints_set_conditional_validity>
9650 replaces the conditional validity constraints.
9651 A conditional validity constraint is only imposed when any of the corresponding
9652 conditions is satisfied, i.e., when any of them is non-zero.
9653 That is, the scheduler ensures that within each band if the dependence
9654 distances over the condition constraints are not all zero
9655 then all corresponding conditional validity constraints are respected.
9656 A conditional validity constraint corresponds to a condition
9657 if the two are adjacent, i.e., if the domain of one relation intersect
9658 the range of the other relation.
9659 The typical use case of conditional validity constraints is
9660 to allow order constraints between live ranges to be violated
9661 as long as the live ranges themselves are local to the band.
9662 To allow more fine-grained control over which conditions correspond
9663 to which conditional validity constraints, the domains and ranges
9664 of these relations may include I<tags>. That is, the domains and
9665 ranges of those relation may themselves be wrapped relations
9666 where the iteration domain appears in the domain of those wrapped relations
9667 and the range of the wrapped relations can be arbitrarily chosen
9668 by the user. Conditions and conditional validity constraints are only
9669 considered adjacent to each other if the entire wrapped relation matches.
9670 In particular, a relation with a tag will never be considered adjacent
9671 to a relation without a tag.
9673 The function C<isl_schedule_constraints_apply> takes
9674 schedule constraints that are defined on some set of domain elements
9675 and transforms them to schedule constraints on the elements
9676 to which these domain elements are mapped by the given transformation.
9678 An C<isl_schedule_constraints> object can be inspected
9679 using the following functions.
9681 #include <isl/schedule.h>
9682 __isl_give isl_union_set *
9683 isl_schedule_constraints_get_domain(
9684 __isl_keep isl_schedule_constraints *sc);
9685 __isl_give isl_set *isl_schedule_constraints_get_context(
9686 __isl_keep isl_schedule_constraints *sc);
9687 __isl_give isl_union_map *
9688 isl_schedule_constraints_get_validity(
9689 __isl_keep isl_schedule_constraints *sc);
9690 __isl_give isl_union_map *
9691 isl_schedule_constraints_get_coincidence(
9692 __isl_keep isl_schedule_constraints *sc);
9693 __isl_give isl_union_map *
9694 isl_schedule_constraints_get_proximity(
9695 __isl_keep isl_schedule_constraints *sc);
9696 __isl_give isl_union_map *
9697 isl_schedule_constraints_get_conditional_validity(
9698 __isl_keep isl_schedule_constraints *sc);
9699 __isl_give isl_union_map *
9700 isl_schedule_constraints_get_conditional_validity_condition(
9701 __isl_keep isl_schedule_constraints *sc);
9703 An C<isl_schedule_constraints> object can be read from input
9704 using the following functions.
9706 #include <isl/schedule.h>
9707 __isl_give isl_schedule_constraints *
9708 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9710 __isl_give isl_schedule_constraints *
9711 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9714 The contents of an C<isl_schedule_constraints> object can be printed
9715 using the following functions.
9717 #include <isl/schedule.h>
9718 __isl_give isl_printer *
9719 isl_printer_print_schedule_constraints(
9720 __isl_take isl_printer *p,
9721 __isl_keep isl_schedule_constraints *sc);
9722 __isl_give char *isl_schedule_constraints_to_str(
9723 __isl_keep isl_schedule_constraints *sc);
9725 The following function computes a schedule directly from
9726 an iteration domain and validity and proximity dependences
9727 and is implemented in terms of the functions described above.
9728 The use of C<isl_union_set_compute_schedule> is discouraged.
9730 #include <isl/schedule.h>
9731 __isl_give isl_schedule *isl_union_set_compute_schedule(
9732 __isl_take isl_union_set *domain,
9733 __isl_take isl_union_map *validity,
9734 __isl_take isl_union_map *proximity);
9736 The generated schedule represents a schedule tree.
9737 For more information on schedule trees, see
9738 L</"Schedule Trees">.
9742 #include <isl/schedule.h>
9743 isl_stat isl_options_set_schedule_max_coefficient(
9744 isl_ctx *ctx, int val);
9745 int isl_options_get_schedule_max_coefficient(
9747 isl_stat isl_options_set_schedule_max_constant_term(
9748 isl_ctx *ctx, int val);
9749 int isl_options_get_schedule_max_constant_term(
9751 isl_stat isl_options_set_schedule_serialize_sccs(
9752 isl_ctx *ctx, int val);
9753 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9754 isl_stat isl_options_set_schedule_whole_component(
9755 isl_ctx *ctx, int val);
9756 int isl_options_get_schedule_whole_component(
9758 isl_stat isl_options_set_schedule_maximize_band_depth(
9759 isl_ctx *ctx, int val);
9760 int isl_options_get_schedule_maximize_band_depth(
9762 isl_stat isl_options_set_schedule_maximize_coincidence(
9763 isl_ctx *ctx, int val);
9764 int isl_options_get_schedule_maximize_coincidence(
9766 isl_stat isl_options_set_schedule_outer_coincidence(
9767 isl_ctx *ctx, int val);
9768 int isl_options_get_schedule_outer_coincidence(
9770 isl_stat isl_options_set_schedule_split_scaled(
9771 isl_ctx *ctx, int val);
9772 int isl_options_get_schedule_split_scaled(
9774 isl_stat isl_options_set_schedule_treat_coalescing(
9775 isl_ctx *ctx, int val);
9776 int isl_options_get_schedule_treat_coalescing(
9778 isl_stat isl_options_set_schedule_algorithm(
9779 isl_ctx *ctx, int val);
9780 int isl_options_get_schedule_algorithm(
9782 isl_stat isl_options_set_schedule_carry_self_first(
9783 isl_ctx *ctx, int val);
9784 int isl_options_get_schedule_carry_self_first(
9786 isl_stat isl_options_set_schedule_separate_components(
9787 isl_ctx *ctx, int val);
9788 int isl_options_get_schedule_separate_components(
9793 =item * schedule_max_coefficient
9795 This option enforces that the coefficients for variable and parameter
9796 dimensions in the calculated schedule are not larger than the specified value.
9797 This option can significantly increase the speed of the scheduling calculation
9798 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9799 this option does not introduce bounds on the variable or parameter
9801 This option has no effect on the Feautrier style scheduler.
9803 =item * schedule_max_constant_term
9805 This option enforces that the constant coefficients in the calculated schedule
9806 are not larger than the maximal constant term. This option can significantly
9807 increase the speed of the scheduling calculation and may also prevent fusing of
9808 unrelated dimensions. A value of -1 means that this option does not introduce
9809 bounds on the constant coefficients.
9811 =item * schedule_serialize_sccs
9813 If this option is set, then all strongly connected components
9814 in the dependence graph are serialized as soon as they are detected.
9815 This means in particular that instances of statements will only
9816 appear in the same band node if these statements belong
9817 to the same strongly connected component at the point where
9818 the band node is constructed.
9820 =item * schedule_whole_component
9822 If this option is set, then entire (weakly) connected
9823 components in the dependence graph are scheduled together
9825 Otherwise, each strongly connected component within
9826 such a weakly connected component is first scheduled separately
9827 and then combined with other strongly connected components.
9828 This option has no effect if C<schedule_serialize_sccs> is set.
9830 =item * schedule_maximize_band_depth
9832 If this option is set, then the scheduler tries to maximize
9833 the width of the bands. Wider bands give more possibilities for tiling.
9834 In particular, if the C<schedule_whole_component> option is set,
9835 then bands are split if this might result in wider bands.
9836 Otherwise, the effect of this option is to only allow
9837 strongly connected components to be combined if this does
9838 not reduce the width of the bands.
9839 Note that if the C<schedule_serialize_sccs> options is set, then
9840 the C<schedule_maximize_band_depth> option therefore has no effect.
9842 =item * schedule_maximize_coincidence
9844 This option is only effective if the C<schedule_whole_component>
9845 option is turned off.
9846 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9847 strongly connected components are only combined with each other
9848 if this does not reduce the number of coincident band members.
9850 =item * schedule_outer_coincidence
9852 If this option is set, then we try to construct schedules
9853 where the outermost scheduling dimension in each band
9854 satisfies the coincidence constraints.
9856 =item * schedule_algorithm
9858 Selects the scheduling algorithm to be used.
9859 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9860 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9862 =item * schedule_split_scaled
9864 If this option is set, then we try to construct schedules in which the
9865 constant term is split off from the linear part if the linear parts of
9866 the scheduling rows for all nodes in the graph have a common non-trivial
9868 The constant term is then dropped and the linear
9870 This option is only effective when the Feautrier style scheduler is
9871 being used, either as the main scheduler or as a fallback for the
9872 Pluto-like scheduler.
9874 =item * schedule_treat_coalescing
9876 If this option is set, then the scheduler will try and avoid
9877 producing schedules that perform loop coalescing.
9878 In particular, for the Pluto-like scheduler, this option places
9879 bounds on the schedule coefficients based on the sizes of the instance sets.
9880 For the Feautrier style scheduler, this option detects potentially
9881 coalescing schedules and then tries to adjust the schedule to avoid
9884 =item * schedule_carry_self_first
9886 If this option is set, then the Feautrier style scheduler
9887 (when used as a fallback for the Pluto-like scheduler) will
9888 first try to only carry self-dependences.
9890 =item * schedule_separate_components
9892 If this option is set then the function C<isl_schedule_get_map>
9893 will treat set nodes in the same way as sequence nodes.
9897 =head2 AST Generation
9899 This section describes the C<isl> functionality for generating
9900 ASTs that visit all the elements
9901 in a domain in an order specified by a schedule tree or
9903 In case the schedule given as a C<isl_union_map>, an AST is generated
9904 that visits all the elements in the domain of the C<isl_union_map>
9905 according to the lexicographic order of the corresponding image
9906 element(s). If the range of the C<isl_union_map> consists of
9907 elements in more than one space, then each of these spaces is handled
9908 separately in an arbitrary order.
9909 It should be noted that the schedule tree or the image elements
9910 in a schedule map only specify the I<order>
9911 in which the corresponding domain elements should be visited.
9912 No direct relation between the partial schedule values
9913 or the image elements on the one hand and the loop iterators
9914 in the generated AST on the other hand should be assumed.
9916 Each AST is generated within a build. The initial build
9917 simply specifies the constraints on the parameters (if any)
9918 and can be created, inspected, copied and freed using the following functions.
9920 #include <isl/ast_build.h>
9921 __isl_give isl_ast_build *isl_ast_build_alloc(
9923 __isl_give isl_ast_build *isl_ast_build_from_context(
9924 __isl_take isl_set *set);
9925 __isl_give isl_ast_build *isl_ast_build_copy(
9926 __isl_keep isl_ast_build *build);
9927 __isl_null isl_ast_build *isl_ast_build_free(
9928 __isl_take isl_ast_build *build);
9930 The C<set> argument is usually a parameter set with zero or more parameters.
9931 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9932 this set is required to be a parameter set.
9933 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9934 specify any parameter constraints.
9935 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9936 and L</"Fine-grained Control over AST Generation">.
9937 Finally, the AST itself can be constructed using one of the following
9940 #include <isl/ast_build.h>
9941 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9942 __isl_keep isl_ast_build *build,
9943 __isl_take isl_schedule *schedule);
9944 __isl_give isl_ast_node *
9945 isl_ast_build_node_from_schedule_map(
9946 __isl_keep isl_ast_build *build,
9947 __isl_take isl_union_map *schedule);
9949 =head3 Inspecting the AST
9951 The basic properties of an AST node can be obtained as follows.
9953 #include <isl/ast.h>
9954 enum isl_ast_node_type isl_ast_node_get_type(
9955 __isl_keep isl_ast_node *node);
9957 The type of an AST node is one of
9958 C<isl_ast_node_for>,
9960 C<isl_ast_node_block>,
9961 C<isl_ast_node_mark> or
9962 C<isl_ast_node_user>.
9963 An C<isl_ast_node_for> represents a for node.
9964 An C<isl_ast_node_if> represents an if node.
9965 An C<isl_ast_node_block> represents a compound node.
9966 An C<isl_ast_node_mark> introduces a mark in the AST.
9967 An C<isl_ast_node_user> represents an expression statement.
9968 An expression statement typically corresponds to a domain element, i.e.,
9969 one of the elements that is visited by the AST.
9971 Each type of node has its own additional properties.
9973 #include <isl/ast.h>
9974 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9975 __isl_keep isl_ast_node *node);
9976 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9977 __isl_keep isl_ast_node *node);
9978 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9979 __isl_keep isl_ast_node *node);
9980 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9981 __isl_keep isl_ast_node *node);
9982 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9983 __isl_keep isl_ast_node *node);
9984 isl_bool isl_ast_node_for_is_degenerate(
9985 __isl_keep isl_ast_node *node);
9987 An C<isl_ast_for> is considered degenerate if it is known to execute
9990 #include <isl/ast.h>
9991 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9992 __isl_keep isl_ast_node *node);
9993 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9994 __isl_keep isl_ast_node *node);
9995 isl_bool isl_ast_node_if_has_else(
9996 __isl_keep isl_ast_node *node);
9997 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9998 __isl_keep isl_ast_node *node);
10000 __isl_give isl_ast_node_list *
10001 isl_ast_node_block_get_children(
10002 __isl_keep isl_ast_node *node);
10004 __isl_give isl_id *isl_ast_node_mark_get_id(
10005 __isl_keep isl_ast_node *node);
10006 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
10007 __isl_keep isl_ast_node *node);
10009 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
10010 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
10012 #include <isl/ast.h>
10013 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
10014 __isl_keep isl_ast_node *node);
10016 All descendants of a specific node in the AST (including the node itself)
10018 in depth-first pre-order using the following function.
10020 #include <isl/ast.h>
10021 isl_stat isl_ast_node_foreach_descendant_top_down(
10022 __isl_keep isl_ast_node *node,
10023 isl_bool (*fn)(__isl_keep isl_ast_node *node,
10024 void *user), void *user);
10026 The callback function should return C<isl_bool_true> if the children
10027 of the given node should be visited and C<isl_bool_false> if they should not.
10028 It should return C<isl_bool_error> in case of failure, in which case
10029 the entire traversal is aborted.
10031 Each of the returned C<isl_ast_expr>s can in turn be inspected using
10032 the following functions.
10034 #include <isl/ast.h>
10035 enum isl_ast_expr_type isl_ast_expr_get_type(
10036 __isl_keep isl_ast_expr *expr);
10038 The type of an AST expression is one of
10039 C<isl_ast_expr_op>,
10040 C<isl_ast_expr_id> or
10041 C<isl_ast_expr_int>.
10042 An C<isl_ast_expr_op> represents the result of an operation.
10043 An C<isl_ast_expr_id> represents an identifier.
10044 An C<isl_ast_expr_int> represents an integer value.
10046 Each type of expression has its own additional properties.
10048 #include <isl/ast.h>
10049 enum isl_ast_op_type isl_ast_expr_get_op_type(
10050 __isl_keep isl_ast_expr *expr);
10051 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
10052 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
10053 __isl_keep isl_ast_expr *expr, int pos);
10054 isl_stat isl_ast_expr_foreach_ast_op_type(
10055 __isl_keep isl_ast_expr *expr,
10056 isl_stat (*fn)(enum isl_ast_op_type type,
10057 void *user), void *user);
10058 isl_stat isl_ast_node_foreach_ast_op_type(
10059 __isl_keep isl_ast_node *node,
10060 isl_stat (*fn)(enum isl_ast_op_type type,
10061 void *user), void *user);
10063 C<isl_ast_expr_get_op_type> returns the type of the operation
10064 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
10065 arguments. C<isl_ast_expr_get_op_arg> returns the specified
10067 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
10068 C<isl_ast_op_type> that appears in C<expr>.
10069 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
10070 C<isl_ast_op_type> that appears in C<node>.
10071 The operation type is one of the following.
10075 =item C<isl_ast_op_and>
10077 Logical I<and> of two arguments.
10078 Both arguments can be evaluated.
10080 =item C<isl_ast_op_and_then>
10082 Logical I<and> of two arguments.
10083 The second argument can only be evaluated if the first evaluates to true.
10085 =item C<isl_ast_op_or>
10087 Logical I<or> of two arguments.
10088 Both arguments can be evaluated.
10090 =item C<isl_ast_op_or_else>
10092 Logical I<or> of two arguments.
10093 The second argument can only be evaluated if the first evaluates to false.
10095 =item C<isl_ast_op_max>
10097 Maximum of two or more arguments.
10099 =item C<isl_ast_op_min>
10101 Minimum of two or more arguments.
10103 =item C<isl_ast_op_minus>
10107 =item C<isl_ast_op_add>
10109 Sum of two arguments.
10111 =item C<isl_ast_op_sub>
10113 Difference of two arguments.
10115 =item C<isl_ast_op_mul>
10117 Product of two arguments.
10119 =item C<isl_ast_op_div>
10121 Exact division. That is, the result is known to be an integer.
10123 =item C<isl_ast_op_fdiv_q>
10125 Result of integer division, rounded towards negative
10127 The divisor is known to be positive.
10129 =item C<isl_ast_op_pdiv_q>
10131 Result of integer division, where dividend is known to be non-negative.
10132 The divisor is known to be positive.
10134 =item C<isl_ast_op_pdiv_r>
10136 Remainder of integer division, where dividend is known to be non-negative.
10137 The divisor is known to be positive.
10139 =item C<isl_ast_op_zdiv_r>
10141 Equal to zero iff the remainder on integer division is zero.
10142 The divisor is known to be positive.
10144 =item C<isl_ast_op_cond>
10146 Conditional operator defined on three arguments.
10147 If the first argument evaluates to true, then the result
10148 is equal to the second argument. Otherwise, the result
10149 is equal to the third argument.
10150 The second and third argument may only be evaluated if
10151 the first argument evaluates to true and false, respectively.
10152 Corresponds to C<a ? b : c> in C.
10154 =item C<isl_ast_op_select>
10156 Conditional operator defined on three arguments.
10157 If the first argument evaluates to true, then the result
10158 is equal to the second argument. Otherwise, the result
10159 is equal to the third argument.
10160 The second and third argument may be evaluated independently
10161 of the value of the first argument.
10162 Corresponds to C<a * b + (1 - a) * c> in C.
10164 =item C<isl_ast_op_eq>
10168 =item C<isl_ast_op_le>
10170 Less than or equal relation.
10172 =item C<isl_ast_op_lt>
10174 Less than relation.
10176 =item C<isl_ast_op_ge>
10178 Greater than or equal relation.
10180 =item C<isl_ast_op_gt>
10182 Greater than relation.
10184 =item C<isl_ast_op_call>
10187 The number of arguments of the C<isl_ast_expr> is one more than
10188 the number of arguments in the function call, the first argument
10189 representing the function being called.
10191 =item C<isl_ast_op_access>
10194 The number of arguments of the C<isl_ast_expr> is one more than
10195 the number of index expressions in the array access, the first argument
10196 representing the array being accessed.
10198 =item C<isl_ast_op_member>
10201 This operation has two arguments, a structure and the name of
10202 the member of the structure being accessed.
10206 #include <isl/ast.h>
10207 __isl_give isl_id *isl_ast_expr_get_id(
10208 __isl_keep isl_ast_expr *expr);
10210 Return the identifier represented by the AST expression.
10212 #include <isl/ast.h>
10213 __isl_give isl_val *isl_ast_expr_get_val(
10214 __isl_keep isl_ast_expr *expr);
10216 Return the integer represented by the AST expression.
10218 =head3 Properties of ASTs
10220 #include <isl/ast.h>
10221 isl_bool isl_ast_expr_is_equal(
10222 __isl_keep isl_ast_expr *expr1,
10223 __isl_keep isl_ast_expr *expr2);
10225 Check if two C<isl_ast_expr>s are equal to each other.
10227 =head3 Manipulating and printing the AST
10229 AST nodes can be copied and freed using the following functions.
10231 #include <isl/ast.h>
10232 __isl_give isl_ast_node *isl_ast_node_copy(
10233 __isl_keep isl_ast_node *node);
10234 __isl_null isl_ast_node *isl_ast_node_free(
10235 __isl_take isl_ast_node *node);
10237 AST expressions can be copied and freed using the following functions.
10239 #include <isl/ast.h>
10240 __isl_give isl_ast_expr *isl_ast_expr_copy(
10241 __isl_keep isl_ast_expr *expr);
10242 __isl_null isl_ast_expr *isl_ast_expr_free(
10243 __isl_take isl_ast_expr *expr);
10245 New AST expressions can be created either directly or within
10246 the context of an C<isl_ast_build>.
10248 #include <isl/ast.h>
10249 __isl_give isl_ast_expr *isl_ast_expr_from_val(
10250 __isl_take isl_val *v);
10251 __isl_give isl_ast_expr *isl_ast_expr_from_id(
10252 __isl_take isl_id *id);
10253 __isl_give isl_ast_expr *isl_ast_expr_neg(
10254 __isl_take isl_ast_expr *expr);
10255 __isl_give isl_ast_expr *isl_ast_expr_address_of(
10256 __isl_take isl_ast_expr *expr);
10257 __isl_give isl_ast_expr *isl_ast_expr_add(
10258 __isl_take isl_ast_expr *expr1,
10259 __isl_take isl_ast_expr *expr2);
10260 __isl_give isl_ast_expr *isl_ast_expr_sub(
10261 __isl_take isl_ast_expr *expr1,
10262 __isl_take isl_ast_expr *expr2);
10263 __isl_give isl_ast_expr *isl_ast_expr_mul(
10264 __isl_take isl_ast_expr *expr1,
10265 __isl_take isl_ast_expr *expr2);
10266 __isl_give isl_ast_expr *isl_ast_expr_div(
10267 __isl_take isl_ast_expr *expr1,
10268 __isl_take isl_ast_expr *expr2);
10269 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
10270 __isl_take isl_ast_expr *expr1,
10271 __isl_take isl_ast_expr *expr2);
10272 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
10273 __isl_take isl_ast_expr *expr1,
10274 __isl_take isl_ast_expr *expr2);
10275 __isl_give isl_ast_expr *isl_ast_expr_and(
10276 __isl_take isl_ast_expr *expr1,
10277 __isl_take isl_ast_expr *expr2)
10278 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10279 __isl_take isl_ast_expr *expr1,
10280 __isl_take isl_ast_expr *expr2)
10281 __isl_give isl_ast_expr *isl_ast_expr_or(
10282 __isl_take isl_ast_expr *expr1,
10283 __isl_take isl_ast_expr *expr2)
10284 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10285 __isl_take isl_ast_expr *expr1,
10286 __isl_take isl_ast_expr *expr2)
10287 __isl_give isl_ast_expr *isl_ast_expr_eq(
10288 __isl_take isl_ast_expr *expr1,
10289 __isl_take isl_ast_expr *expr2);
10290 __isl_give isl_ast_expr *isl_ast_expr_le(
10291 __isl_take isl_ast_expr *expr1,
10292 __isl_take isl_ast_expr *expr2);
10293 __isl_give isl_ast_expr *isl_ast_expr_lt(
10294 __isl_take isl_ast_expr *expr1,
10295 __isl_take isl_ast_expr *expr2);
10296 __isl_give isl_ast_expr *isl_ast_expr_ge(
10297 __isl_take isl_ast_expr *expr1,
10298 __isl_take isl_ast_expr *expr2);
10299 __isl_give isl_ast_expr *isl_ast_expr_gt(
10300 __isl_take isl_ast_expr *expr1,
10301 __isl_take isl_ast_expr *expr2);
10302 __isl_give isl_ast_expr *isl_ast_expr_access(
10303 __isl_take isl_ast_expr *array,
10304 __isl_take isl_ast_expr_list *indices);
10305 __isl_give isl_ast_expr *isl_ast_expr_call(
10306 __isl_take isl_ast_expr *function,
10307 __isl_take isl_ast_expr_list *arguments);
10309 The function C<isl_ast_expr_address_of> can be applied to an
10310 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10311 to represent the address of the C<isl_ast_expr_access>.
10312 The second argument of the functions C<isl_ast_expr_pdiv_q> and
10313 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
10315 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10316 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10318 #include <isl/ast_build.h>
10319 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10320 __isl_keep isl_ast_build *build,
10321 __isl_take isl_set *set);
10322 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10323 __isl_keep isl_ast_build *build,
10324 __isl_take isl_pw_aff *pa);
10325 __isl_give isl_ast_expr *
10326 isl_ast_build_access_from_pw_multi_aff(
10327 __isl_keep isl_ast_build *build,
10328 __isl_take isl_pw_multi_aff *pma);
10329 __isl_give isl_ast_expr *
10330 isl_ast_build_access_from_multi_pw_aff(
10331 __isl_keep isl_ast_build *build,
10332 __isl_take isl_multi_pw_aff *mpa);
10333 __isl_give isl_ast_expr *
10334 isl_ast_build_call_from_pw_multi_aff(
10335 __isl_keep isl_ast_build *build,
10336 __isl_take isl_pw_multi_aff *pma);
10337 __isl_give isl_ast_expr *
10338 isl_ast_build_call_from_multi_pw_aff(
10339 __isl_keep isl_ast_build *build,
10340 __isl_take isl_multi_pw_aff *mpa);
10343 the domains of C<pa>, C<mpa> and C<pma> should correspond
10344 to the schedule space of C<build>.
10345 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10346 the function being called.
10347 If the accessed space is a nested relation, then it is taken
10348 to represent an access of the member specified by the range
10349 of this nested relation of the structure specified by the domain
10350 of the nested relation.
10352 The following functions can be used to modify an C<isl_ast_expr>.
10354 #include <isl/ast.h>
10355 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10356 __isl_take isl_ast_expr *expr, int pos,
10357 __isl_take isl_ast_expr *arg);
10359 Replace the argument of C<expr> at position C<pos> by C<arg>.
10361 #include <isl/ast.h>
10362 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10363 __isl_take isl_ast_expr *expr,
10364 __isl_take isl_id_to_ast_expr *id2expr);
10366 The function C<isl_ast_expr_substitute_ids> replaces the
10367 subexpressions of C<expr> of type C<isl_ast_expr_id>
10368 by the corresponding expression in C<id2expr>, if there is any.
10371 User specified data can be attached to an C<isl_ast_node> and obtained
10372 from the same C<isl_ast_node> using the following functions.
10374 #include <isl/ast.h>
10375 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10376 __isl_take isl_ast_node *node,
10377 __isl_take isl_id *annotation);
10378 __isl_give isl_id *isl_ast_node_get_annotation(
10379 __isl_keep isl_ast_node *node);
10381 Basic printing can be performed using the following functions.
10383 #include <isl/ast.h>
10384 __isl_give isl_printer *isl_printer_print_ast_expr(
10385 __isl_take isl_printer *p,
10386 __isl_keep isl_ast_expr *expr);
10387 __isl_give isl_printer *isl_printer_print_ast_node(
10388 __isl_take isl_printer *p,
10389 __isl_keep isl_ast_node *node);
10390 __isl_give char *isl_ast_expr_to_str(
10391 __isl_keep isl_ast_expr *expr);
10392 __isl_give char *isl_ast_node_to_str(
10393 __isl_keep isl_ast_node *node);
10394 __isl_give char *isl_ast_expr_to_C_str(
10395 __isl_keep isl_ast_expr *expr);
10396 __isl_give char *isl_ast_node_to_C_str(
10397 __isl_keep isl_ast_node *node);
10399 The functions C<isl_ast_expr_to_C_str> and
10400 C<isl_ast_node_to_C_str> are convenience functions
10401 that return a string representation of the input in C format.
10403 More advanced printing can be performed using the following functions.
10405 #include <isl/ast.h>
10406 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10407 __isl_take isl_printer *p,
10408 enum isl_ast_op_type type,
10409 __isl_keep const char *name);
10410 isl_stat isl_options_set_ast_print_macro_once(
10411 isl_ctx *ctx, int val);
10412 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10413 __isl_give isl_printer *isl_ast_op_type_print_macro(
10414 enum isl_ast_op_type type,
10415 __isl_take isl_printer *p);
10416 __isl_give isl_printer *isl_ast_expr_print_macros(
10417 __isl_keep isl_ast_expr *expr,
10418 __isl_take isl_printer *p);
10419 __isl_give isl_printer *isl_ast_node_print_macros(
10420 __isl_keep isl_ast_node *node,
10421 __isl_take isl_printer *p);
10422 __isl_give isl_printer *isl_ast_node_print(
10423 __isl_keep isl_ast_node *node,
10424 __isl_take isl_printer *p,
10425 __isl_take isl_ast_print_options *options);
10426 __isl_give isl_printer *isl_ast_node_for_print(
10427 __isl_keep isl_ast_node *node,
10428 __isl_take isl_printer *p,
10429 __isl_take isl_ast_print_options *options);
10430 __isl_give isl_printer *isl_ast_node_if_print(
10431 __isl_keep isl_ast_node *node,
10432 __isl_take isl_printer *p,
10433 __isl_take isl_ast_print_options *options);
10435 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10436 C<isl> may print out an AST that makes use of macros such
10437 as C<floord>, C<min> and C<max>.
10438 The names of these macros may be modified by a call
10439 to C<isl_ast_op_type_set_print_name>. The user-specified
10440 names are associated to the printer object.
10441 C<isl_ast_op_type_print_macro> prints out the macro
10442 corresponding to a specific C<isl_ast_op_type>.
10443 If the print-macro-once option is set, then a given macro definition
10444 is only printed once to any given printer object.
10445 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10446 for subexpressions where these macros would be used and prints
10447 out the required macro definitions.
10448 Essentially, C<isl_ast_expr_print_macros> calls
10449 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10450 as function argument.
10451 C<isl_ast_node_print_macros> does the same
10452 for expressions in its C<isl_ast_node> argument.
10453 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10454 C<isl_ast_node_if_print> print an C<isl_ast_node>
10455 in C<ISL_FORMAT_C>, but allow for some extra control
10456 through an C<isl_ast_print_options> object.
10457 This object can be created using the following functions.
10459 #include <isl/ast.h>
10460 __isl_give isl_ast_print_options *
10461 isl_ast_print_options_alloc(isl_ctx *ctx);
10462 __isl_give isl_ast_print_options *
10463 isl_ast_print_options_copy(
10464 __isl_keep isl_ast_print_options *options);
10465 __isl_null isl_ast_print_options *
10466 isl_ast_print_options_free(
10467 __isl_take isl_ast_print_options *options);
10469 __isl_give isl_ast_print_options *
10470 isl_ast_print_options_set_print_user(
10471 __isl_take isl_ast_print_options *options,
10472 __isl_give isl_printer *(*print_user)(
10473 __isl_take isl_printer *p,
10474 __isl_take isl_ast_print_options *options,
10475 __isl_keep isl_ast_node *node, void *user),
10477 __isl_give isl_ast_print_options *
10478 isl_ast_print_options_set_print_for(
10479 __isl_take isl_ast_print_options *options,
10480 __isl_give isl_printer *(*print_for)(
10481 __isl_take isl_printer *p,
10482 __isl_take isl_ast_print_options *options,
10483 __isl_keep isl_ast_node *node, void *user),
10486 The callback set by C<isl_ast_print_options_set_print_user>
10487 is called whenever a node of type C<isl_ast_node_user> needs to
10489 The callback set by C<isl_ast_print_options_set_print_for>
10490 is called whenever a node of type C<isl_ast_node_for> needs to
10492 Note that C<isl_ast_node_for_print> will I<not> call the
10493 callback set by C<isl_ast_print_options_set_print_for> on the node
10494 on which C<isl_ast_node_for_print> is called, but only on nested
10495 nodes of type C<isl_ast_node_for>. It is therefore safe to
10496 call C<isl_ast_node_for_print> from within the callback set by
10497 C<isl_ast_print_options_set_print_for>.
10499 The following option determines the type to be used for iterators
10500 while printing the AST.
10502 isl_stat isl_options_set_ast_iterator_type(
10503 isl_ctx *ctx, const char *val);
10504 const char *isl_options_get_ast_iterator_type(
10507 The AST printer only prints body nodes as blocks if these
10508 blocks cannot be safely omitted.
10509 For example, a C<for> node with one body node will not be
10510 surrounded with braces in C<ISL_FORMAT_C>.
10511 A block will always be printed by setting the following option.
10513 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10515 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10519 #include <isl/ast_build.h>
10520 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10521 isl_ctx *ctx, int val);
10522 int isl_options_get_ast_build_atomic_upper_bound(
10524 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10526 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10527 isl_stat isl_options_set_ast_build_detect_min_max(
10528 isl_ctx *ctx, int val);
10529 int isl_options_get_ast_build_detect_min_max(
10531 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10532 isl_ctx *ctx, int val);
10533 int isl_options_get_ast_build_exploit_nested_bounds(
10535 isl_stat isl_options_set_ast_build_group_coscheduled(
10536 isl_ctx *ctx, int val);
10537 int isl_options_get_ast_build_group_coscheduled(
10539 isl_stat isl_options_set_ast_build_separation_bounds(
10540 isl_ctx *ctx, int val);
10541 int isl_options_get_ast_build_separation_bounds(
10543 isl_stat isl_options_set_ast_build_scale_strides(
10544 isl_ctx *ctx, int val);
10545 int isl_options_get_ast_build_scale_strides(
10547 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10549 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10550 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10552 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10556 =item * ast_build_atomic_upper_bound
10558 Generate loop upper bounds that consist of the current loop iterator,
10559 an operator and an expression not involving the iterator.
10560 If this option is not set, then the current loop iterator may appear
10561 several times in the upper bound.
10562 For example, when this option is turned off, AST generation
10565 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10569 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10572 When the option is turned on, the following AST is generated
10574 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10577 =item * ast_build_prefer_pdiv
10579 If this option is turned off, then the AST generation will
10580 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10581 operators, but no C<isl_ast_op_pdiv_q> or
10582 C<isl_ast_op_pdiv_r> operators.
10583 If this option is turned on, then C<isl> will try to convert
10584 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10585 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10587 =item * ast_build_detect_min_max
10589 If this option is turned on, then C<isl> will try and detect
10590 min or max-expressions when building AST expressions from
10591 piecewise affine expressions.
10593 =item * ast_build_exploit_nested_bounds
10595 Simplify conditions based on bounds of nested for loops.
10596 In particular, remove conditions that are implied by the fact
10597 that one or more nested loops have at least one iteration,
10598 meaning that the upper bound is at least as large as the lower bound.
10599 For example, when this option is turned off, AST generation
10602 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10608 for (int c0 = 0; c0 <= N; c0 += 1)
10609 for (int c1 = 0; c1 <= M; c1 += 1)
10612 When the option is turned on, the following AST is generated
10614 for (int c0 = 0; c0 <= N; c0 += 1)
10615 for (int c1 = 0; c1 <= M; c1 += 1)
10618 =item * ast_build_group_coscheduled
10620 If two domain elements are assigned the same schedule point, then
10621 they may be executed in any order and they may even appear in different
10622 loops. If this options is set, then the AST generator will make
10623 sure that coscheduled domain elements do not appear in separate parts
10624 of the AST. This is useful in case of nested AST generation
10625 if the outer AST generation is given only part of a schedule
10626 and the inner AST generation should handle the domains that are
10627 coscheduled by this initial part of the schedule together.
10628 For example if an AST is generated for a schedule
10630 { A[i] -> [0]; B[i] -> [0] }
10632 then the C<isl_ast_build_set_create_leaf> callback described
10633 below may get called twice, once for each domain.
10634 Setting this option ensures that the callback is only called once
10635 on both domains together.
10637 =item * ast_build_separation_bounds
10639 This option specifies which bounds to use during separation.
10640 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10641 then all (possibly implicit) bounds on the current dimension will
10642 be used during separation.
10643 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10644 then only those bounds that are explicitly available will
10645 be used during separation.
10647 =item * ast_build_scale_strides
10649 This option specifies whether the AST generator is allowed
10650 to scale down iterators of strided loops.
10652 =item * ast_build_allow_else
10654 This option specifies whether the AST generator is allowed
10655 to construct if statements with else branches.
10657 =item * ast_build_allow_or
10659 This option specifies whether the AST generator is allowed
10660 to construct if conditions with disjunctions.
10664 =head3 AST Generation Options (Schedule Tree)
10666 In case of AST construction from a schedule tree, the options
10667 that control how an AST is created from the individual schedule
10668 dimensions are stored in the band nodes of the tree
10669 (see L</"Schedule Trees">).
10671 In particular, a schedule dimension can be handled in four
10672 different ways, atomic, separate, unroll or the default.
10673 This loop AST generation type can be set using
10674 C<isl_schedule_node_band_member_set_ast_loop_type>.
10676 the first three can be selected by including a one-dimensional
10677 element with as value the position of the schedule dimension
10678 within the band and as name one of C<atomic>, C<separate>
10679 or C<unroll> in the options
10680 set by C<isl_schedule_node_band_set_ast_build_options>.
10681 Only one of these three may be specified for
10682 any given schedule dimension within a band node.
10683 If none of these is specified, then the default
10684 is used. The meaning of the options is as follows.
10690 When this option is specified, the AST generator will make
10691 sure that a given domains space only appears in a single
10692 loop at the specified level.
10694 For example, for the schedule tree
10696 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10698 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10699 options: "{ atomic[x] }"
10701 the following AST will be generated
10703 for (int c0 = 0; c0 <= 10; c0 += 1) {
10710 On the other hand, for the schedule tree
10712 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10714 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10715 options: "{ separate[x] }"
10717 the following AST will be generated
10721 for (int c0 = 1; c0 <= 9; c0 += 1) {
10728 If neither C<atomic> nor C<separate> is specified, then the AST generator
10729 may produce either of these two results or some intermediate form.
10733 When this option is specified, the AST generator will
10734 split the domain of the specified schedule dimension
10735 into pieces with a fixed set of statements for which
10736 instances need to be executed by the iterations in
10737 the schedule domain part. This option tends to avoid
10738 the generation of guards inside the corresponding loops.
10739 See also the C<atomic> option.
10743 When this option is specified, the AST generator will
10744 I<completely> unroll the corresponding schedule dimension.
10745 It is the responsibility of the user to ensure that such
10746 unrolling is possible.
10747 To obtain a partial unrolling, the user should apply an additional
10748 strip-mining to the schedule and fully unroll the inner schedule
10753 The C<isolate> option is a bit more involved. It allows the user
10754 to isolate a range of schedule dimension values from smaller and
10755 greater values. Additionally, the user may specify a different
10756 atomic/separate/unroll choice for the isolated part and the remaining
10757 parts. The typical use case of the C<isolate> option is to isolate
10758 full tiles from partial tiles.
10759 The part that needs to be isolated may depend on outer schedule dimensions.
10760 The option therefore needs to be able to reference those outer schedule
10761 dimensions. In particular, the space of the C<isolate> option is that
10762 of a wrapped map with as domain the flat product of all outer band nodes
10763 and as range the space of the current band node.
10764 The atomic/separate/unroll choice for the isolated part is determined
10765 by an option that lives in an unnamed wrapped space with as domain
10766 a zero-dimensional C<isolate> space and as range the regular
10767 C<atomic>, C<separate> or C<unroll> space.
10768 This option may also be set directly using
10769 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10770 The atomic/separate/unroll choice for the remaining part is determined
10771 by the regular C<atomic>, C<separate> or C<unroll> option.
10772 Since the C<isolate> option references outer schedule dimensions,
10773 its use in a band node causes any tree containing the node
10774 to be considered anchored.
10776 As an example, consider the isolation of full tiles from partial tiles
10777 in a tiling of a triangular domain. The original schedule is as follows.
10779 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10781 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10782 { A[i,j] -> [floor(j/10)] }, \
10783 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10787 for (int c0 = 0; c0 <= 10; c0 += 1)
10788 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10789 for (int c2 = 10 * c0;
10790 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10791 for (int c3 = 10 * c1;
10792 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10795 Isolating the full tiles, we have the following input
10797 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10799 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10800 { A[i,j] -> [floor(j/10)] }, \
10801 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10802 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10803 10a+9+10b+9 <= 100 }"
10808 for (int c0 = 0; c0 <= 8; c0 += 1) {
10809 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10810 for (int c2 = 10 * c0;
10811 c2 <= 10 * c0 + 9; c2 += 1)
10812 for (int c3 = 10 * c1;
10813 c3 <= 10 * c1 + 9; c3 += 1)
10815 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10816 for (int c2 = 10 * c0;
10817 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10818 for (int c3 = 10 * c1;
10819 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10822 for (int c0 = 9; c0 <= 10; c0 += 1)
10823 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10824 for (int c2 = 10 * c0;
10825 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10826 for (int c3 = 10 * c1;
10827 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10831 We may then additionally unroll the innermost loop of the isolated part
10833 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10835 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10836 { A[i,j] -> [floor(j/10)] }, \
10837 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10838 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10839 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10844 for (int c0 = 0; c0 <= 8; c0 += 1) {
10845 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10846 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10848 A(c2, 10 * c1 + 1);
10849 A(c2, 10 * c1 + 2);
10850 A(c2, 10 * c1 + 3);
10851 A(c2, 10 * c1 + 4);
10852 A(c2, 10 * c1 + 5);
10853 A(c2, 10 * c1 + 6);
10854 A(c2, 10 * c1 + 7);
10855 A(c2, 10 * c1 + 8);
10856 A(c2, 10 * c1 + 9);
10858 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10859 for (int c2 = 10 * c0;
10860 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10861 for (int c3 = 10 * c1;
10862 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10865 for (int c0 = 9; c0 <= 10; c0 += 1)
10866 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10867 for (int c2 = 10 * c0;
10868 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10869 for (int c3 = 10 * c1;
10870 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10875 =head3 AST Generation Options (Schedule Map)
10877 In case of AST construction using
10878 C<isl_ast_build_node_from_schedule_map>, the options
10879 that control how an AST is created from the individual schedule
10880 dimensions are stored in the C<isl_ast_build>.
10881 They can be set using the following function.
10883 #include <isl/ast_build.h>
10884 __isl_give isl_ast_build *
10885 isl_ast_build_set_options(
10886 __isl_take isl_ast_build *build,
10887 __isl_take isl_union_map *options);
10889 The options are encoded in an C<isl_union_map>.
10890 The domain of this union relation refers to the schedule domain,
10891 i.e., the range of the schedule passed
10892 to C<isl_ast_build_node_from_schedule_map>.
10893 In the case of nested AST generation (see L</"Nested AST Generation">),
10894 the domain of C<options> should refer to the extra piece of the schedule.
10895 That is, it should be equal to the range of the wrapped relation in the
10896 range of the schedule.
10897 The range of the options can consist of elements in one or more spaces,
10898 the names of which determine the effect of the option.
10899 The values of the range typically also refer to the schedule dimension
10900 to which the option applies, with value C<0> representing
10901 the outermost schedule dimension. In case of nested AST generation
10902 (see L</"Nested AST Generation">), these values refer to the position
10903 of the schedule dimension within the innermost AST generation.
10904 The constraints on the domain elements of
10905 the option should only refer to this dimension and earlier dimensions.
10906 We consider the following spaces.
10910 =item C<separation_class>
10912 B<This option has been deprecated. Use the isolate option on
10913 schedule trees instead.>
10915 This space is a wrapped relation between two one dimensional spaces.
10916 The input space represents the schedule dimension to which the option
10917 applies and the output space represents the separation class.
10918 While constructing a loop corresponding to the specified schedule
10919 dimension(s), the AST generator will try to generate separate loops
10920 for domain elements that are assigned different classes.
10921 If only some of the elements are assigned a class, then those elements
10922 that are not assigned any class will be treated as belonging to a class
10923 that is separate from the explicitly assigned classes.
10924 The typical use case for this option is to separate full tiles from
10926 The other options, described below, are applied after the separation
10929 As an example, consider the separation into full and partial tiles
10930 of a tiling of a triangular domain.
10931 Take, for example, the domain
10933 { A[i,j] : 0 <= i,j and i + j <= 100 }
10935 and a tiling into tiles of 10 by 10. The input to the AST generator
10936 is then the schedule
10938 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10941 Without any options, the following AST is generated
10943 for (int c0 = 0; c0 <= 10; c0 += 1)
10944 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10945 for (int c2 = 10 * c0;
10946 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10948 for (int c3 = 10 * c1;
10949 c3 <= min(10 * c1 + 9, -c2 + 100);
10953 Separation into full and partial tiles can be obtained by assigning
10954 a class, say C<0>, to the full tiles. The full tiles are represented by those
10955 values of the first and second schedule dimensions for which there are
10956 values of the third and fourth dimensions to cover an entire tile.
10957 That is, we need to specify the following option
10959 { [a,b,c,d] -> separation_class[[0]->[0]] :
10960 exists b': 0 <= 10a,10b' and
10961 10a+9+10b'+9 <= 100;
10962 [a,b,c,d] -> separation_class[[1]->[0]] :
10963 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10965 which simplifies to
10967 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10968 a >= 0 and b >= 0 and b <= 8 - a;
10969 [a, b, c, d] -> separation_class[[0] -> [0]] :
10970 a >= 0 and a <= 8 }
10972 With this option, the generated AST is as follows
10975 for (int c0 = 0; c0 <= 8; c0 += 1) {
10976 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10977 for (int c2 = 10 * c0;
10978 c2 <= 10 * c0 + 9; c2 += 1)
10979 for (int c3 = 10 * c1;
10980 c3 <= 10 * c1 + 9; c3 += 1)
10982 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10983 for (int c2 = 10 * c0;
10984 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10986 for (int c3 = 10 * c1;
10987 c3 <= min(-c2 + 100, 10 * c1 + 9);
10991 for (int c0 = 9; c0 <= 10; c0 += 1)
10992 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10993 for (int c2 = 10 * c0;
10994 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10996 for (int c3 = 10 * c1;
10997 c3 <= min(10 * c1 + 9, -c2 + 100);
11004 This is a single-dimensional space representing the schedule dimension(s)
11005 to which ``separation'' should be applied. Separation tries to split
11006 a loop into several pieces if this can avoid the generation of guards
11008 See also the C<atomic> option.
11012 This is a single-dimensional space representing the schedule dimension(s)
11013 for which the domains should be considered ``atomic''. That is, the
11014 AST generator will make sure that any given domain space will only appear
11015 in a single loop at the specified level.
11017 Consider the following schedule
11019 { a[i] -> [i] : 0 <= i < 10;
11020 b[i] -> [i+1] : 0 <= i < 10 }
11022 If the following option is specified
11024 { [i] -> separate[x] }
11026 then the following AST will be generated
11030 for (int c0 = 1; c0 <= 9; c0 += 1) {
11037 If, on the other hand, the following option is specified
11039 { [i] -> atomic[x] }
11041 then the following AST will be generated
11043 for (int c0 = 0; c0 <= 10; c0 += 1) {
11050 If neither C<atomic> nor C<separate> is specified, then the AST generator
11051 may produce either of these two results or some intermediate form.
11055 This is a single-dimensional space representing the schedule dimension(s)
11056 that should be I<completely> unrolled.
11057 To obtain a partial unrolling, the user should apply an additional
11058 strip-mining to the schedule and fully unroll the inner loop.
11062 =head3 Fine-grained Control over AST Generation
11064 Besides specifying the constraints on the parameters,
11065 an C<isl_ast_build> object can be used to control
11066 various aspects of the AST generation process.
11067 In case of AST construction using
11068 C<isl_ast_build_node_from_schedule_map>,
11069 the most prominent way of control is through ``options'',
11070 as explained above.
11072 Additional control is available through the following functions.
11074 #include <isl/ast_build.h>
11075 __isl_give isl_ast_build *
11076 isl_ast_build_set_iterators(
11077 __isl_take isl_ast_build *build,
11078 __isl_take isl_id_list *iterators);
11080 The function C<isl_ast_build_set_iterators> allows the user to
11081 specify a list of iterator C<isl_id>s to be used as iterators.
11082 If the input schedule is injective, then
11083 the number of elements in this list should be as large as the dimension
11084 of the schedule space, but no direct correspondence should be assumed
11085 between dimensions and elements.
11086 If the input schedule is not injective, then an additional number
11087 of C<isl_id>s equal to the largest dimension of the input domains
11089 If the number of provided C<isl_id>s is insufficient, then additional
11090 names are automatically generated.
11092 #include <isl/ast_build.h>
11093 __isl_give isl_ast_build *
11094 isl_ast_build_set_create_leaf(
11095 __isl_take isl_ast_build *build,
11096 __isl_give isl_ast_node *(*fn)(
11097 __isl_take isl_ast_build *build,
11098 void *user), void *user);
11101 C<isl_ast_build_set_create_leaf> function allows for the
11102 specification of a callback that should be called whenever the AST
11103 generator arrives at an element of the schedule domain.
11104 The callback should return an AST node that should be inserted
11105 at the corresponding position of the AST. The default action (when
11106 the callback is not set) is to continue generating parts of the AST to scan
11107 all the domain elements associated to the schedule domain element
11108 and to insert user nodes, ``calling'' the domain element, for each of them.
11109 The C<build> argument contains the current state of the C<isl_ast_build>.
11110 To ease nested AST generation (see L</"Nested AST Generation">),
11111 all control information that is
11112 specific to the current AST generation such as the options and
11113 the callbacks has been removed from this C<isl_ast_build>.
11114 The callback would typically return the result of a nested
11115 AST generation or a
11116 user defined node created using the following function.
11118 #include <isl/ast.h>
11119 __isl_give isl_ast_node *isl_ast_node_alloc_user(
11120 __isl_take isl_ast_expr *expr);
11122 #include <isl/ast_build.h>
11123 __isl_give isl_ast_build *
11124 isl_ast_build_set_at_each_domain(
11125 __isl_take isl_ast_build *build,
11126 __isl_give isl_ast_node *(*fn)(
11127 __isl_take isl_ast_node *node,
11128 __isl_keep isl_ast_build *build,
11129 void *user), void *user);
11130 __isl_give isl_ast_build *
11131 isl_ast_build_set_before_each_for(
11132 __isl_take isl_ast_build *build,
11133 __isl_give isl_id *(*fn)(
11134 __isl_keep isl_ast_build *build,
11135 void *user), void *user);
11136 __isl_give isl_ast_build *
11137 isl_ast_build_set_after_each_for(
11138 __isl_take isl_ast_build *build,
11139 __isl_give isl_ast_node *(*fn)(
11140 __isl_take isl_ast_node *node,
11141 __isl_keep isl_ast_build *build,
11142 void *user), void *user);
11143 __isl_give isl_ast_build *
11144 isl_ast_build_set_before_each_mark(
11145 __isl_take isl_ast_build *build,
11146 isl_stat (*fn)(__isl_keep isl_id *mark,
11147 __isl_keep isl_ast_build *build,
11148 void *user), void *user);
11149 __isl_give isl_ast_build *
11150 isl_ast_build_set_after_each_mark(
11151 __isl_take isl_ast_build *build,
11152 __isl_give isl_ast_node *(*fn)(
11153 __isl_take isl_ast_node *node,
11154 __isl_keep isl_ast_build *build,
11155 void *user), void *user);
11157 The callback set by C<isl_ast_build_set_at_each_domain> will
11158 be called for each domain AST node.
11159 The callbacks set by C<isl_ast_build_set_before_each_for>
11160 and C<isl_ast_build_set_after_each_for> will be called
11161 for each for AST node. The first will be called in depth-first
11162 pre-order, while the second will be called in depth-first post-order.
11163 Since C<isl_ast_build_set_before_each_for> is called before the for
11164 node is actually constructed, it is only passed an C<isl_ast_build>.
11165 The returned C<isl_id> will be added as an annotation (using
11166 C<isl_ast_node_set_annotation>) to the constructed for node.
11167 In particular, if the user has also specified an C<after_each_for>
11168 callback, then the annotation can be retrieved from the node passed to
11169 that callback using C<isl_ast_node_get_annotation>.
11170 The callbacks set by C<isl_ast_build_set_before_each_mark>
11171 and C<isl_ast_build_set_after_each_mark> will be called for each
11172 mark AST node that is created, i.e., for each mark schedule node
11173 in the input schedule tree. The first will be called in depth-first
11174 pre-order, while the second will be called in depth-first post-order.
11175 Since the callback set by C<isl_ast_build_set_before_each_mark>
11176 is called before the mark AST node is actually constructed, it is passed
11177 the identifier of the mark node.
11178 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
11179 The given C<isl_ast_build> can be used to create new
11180 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
11181 or C<isl_ast_build_call_from_pw_multi_aff>.
11183 =head3 Nested AST Generation
11185 C<isl> allows the user to create an AST within the context
11186 of another AST. These nested ASTs are created using the
11187 same C<isl_ast_build_node_from_schedule_map> function that is used to create
11188 the outer AST. The C<build> argument should be an C<isl_ast_build>
11189 passed to a callback set by
11190 C<isl_ast_build_set_create_leaf>.
11191 The space of the range of the C<schedule> argument should refer
11192 to this build. In particular, the space should be a wrapped
11193 relation and the domain of this wrapped relation should be the
11194 same as that of the range of the schedule returned by
11195 C<isl_ast_build_get_schedule> below.
11196 In practice, the new schedule is typically
11197 created by calling C<isl_union_map_range_product> on the old schedule
11198 and some extra piece of the schedule.
11199 The space of the schedule domain is also available from
11200 the C<isl_ast_build>.
11202 #include <isl/ast_build.h>
11203 __isl_give isl_union_map *isl_ast_build_get_schedule(
11204 __isl_keep isl_ast_build *build);
11205 __isl_give isl_space *isl_ast_build_get_schedule_space(
11206 __isl_keep isl_ast_build *build);
11207 __isl_give isl_ast_build *isl_ast_build_restrict(
11208 __isl_take isl_ast_build *build,
11209 __isl_take isl_set *set);
11211 The C<isl_ast_build_get_schedule> function returns a (partial)
11212 schedule for the domains elements for which part of the AST still needs to
11213 be generated in the current build.
11214 In particular, the domain elements are mapped to those iterations of the loops
11215 enclosing the current point of the AST generation inside which
11216 the domain elements are executed.
11217 No direct correspondence between
11218 the input schedule and this schedule should be assumed.
11219 The space obtained from C<isl_ast_build_get_schedule_space> can be used
11220 to create a set for C<isl_ast_build_restrict> to intersect
11221 with the current build. In particular, the set passed to
11222 C<isl_ast_build_restrict> can have additional parameters.
11223 The ids of the set dimensions in the space returned by
11224 C<isl_ast_build_get_schedule_space> correspond to the
11225 iterators of the already generated loops.
11226 The user should not rely on the ids of the output dimensions
11227 of the relations in the union relation returned by
11228 C<isl_ast_build_get_schedule> having any particular value.
11230 =head1 Applications
11232 Although C<isl> is mainly meant to be used as a library,
11233 it also contains some basic applications that use some
11234 of the functionality of C<isl>.
11235 For applications that take one or more polytopes or polyhedra
11236 as input, this input may be specified in either the L<isl format>
11237 or the L<PolyLib format>.
11239 =head2 C<isl_polyhedron_sample>
11241 C<isl_polyhedron_sample> takes a polyhedron as input and prints
11242 an integer element of the polyhedron, if there is any.
11243 The first column in the output is the denominator and is always
11244 equal to 1. If the polyhedron contains no integer points,
11245 then a vector of length zero is printed.
11249 C<isl_pip> takes the same input as the C<example> program
11250 from the C<piplib> distribution, i.e., a set of constraints
11251 on the parameters, a line containing only -1 and finally a set
11252 of constraints on a parametric polyhedron.
11253 The coefficients of the parameters appear in the last columns
11254 (but before the final constant column).
11255 The output is the lexicographic minimum of the parametric polyhedron.
11256 As C<isl> currently does not have its own output format, the output
11257 is just a dump of the internal state.
11259 =head2 C<isl_polyhedron_minimize>
11261 C<isl_polyhedron_minimize> computes the minimum of some linear
11262 or affine objective function over the integer points in a polyhedron.
11263 If an affine objective function
11264 is given, then the constant should appear in the last column.
11266 =head2 C<isl_polytope_scan>
11268 Given a polytope, C<isl_polytope_scan> prints
11269 all integer points in the polytope.
11273 Given an C<isl_union_access_info> object as input,
11274 C<isl_flow> prints out the corresponding dependences,
11275 as computed by C<isl_union_access_info_compute_flow>.
11277 =head2 C<isl_codegen>
11279 Given either a schedule tree or a sequence consisting of
11280 a schedule map, a context set and an options relation,
11281 C<isl_codegen> prints out an AST that scans the domain elements
11282 of the schedule in the order of their image(s) taking into account
11283 the constraints in the context set.
11285 =head2 C<isl_schedule>
11287 Given an C<isl_schedule_constraints> object as input,
11288 C<isl_schedule> prints out a schedule that satisfies the given