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 The identifiers or names of the individual dimensions of spaces
1216 may be set or read off using the following functions on spaces
1217 or objects that live in spaces.
1218 These functions are mostly useful to obtain the identifiers, positions
1219 or names of the parameters. Identifiers of individual dimensions are
1220 essentially only useful for printing. They are ignored by all other
1221 operations and may not be preserved across those operations.
1223 #include <isl/space.h>
1224 __isl_give isl_space *isl_space_set_dim_id(
1225 __isl_take isl_space *space,
1226 enum isl_dim_type type, unsigned pos,
1227 __isl_take isl_id *id);
1228 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1229 enum isl_dim_type type, unsigned pos);
1230 __isl_give isl_id *isl_space_get_dim_id(
1231 __isl_keep isl_space *space,
1232 enum isl_dim_type type, unsigned pos);
1233 __isl_give isl_space *isl_space_set_dim_name(
1234 __isl_take isl_space *space,
1235 enum isl_dim_type type, unsigned pos,
1236 __isl_keep const char *name);
1237 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1238 enum isl_dim_type type, unsigned pos);
1239 __isl_keep const char *isl_space_get_dim_name(
1240 __isl_keep isl_space *space,
1241 enum isl_dim_type type, unsigned pos);
1243 #include <isl/local_space.h>
1244 __isl_give isl_local_space *isl_local_space_set_dim_id(
1245 __isl_take isl_local_space *ls,
1246 enum isl_dim_type type, unsigned pos,
1247 __isl_take isl_id *id);
1248 isl_bool isl_local_space_has_dim_id(
1249 __isl_keep isl_local_space *ls,
1250 enum isl_dim_type type, unsigned pos);
1251 __isl_give isl_id *isl_local_space_get_dim_id(
1252 __isl_keep isl_local_space *ls,
1253 enum isl_dim_type type, unsigned pos);
1254 __isl_give isl_local_space *isl_local_space_set_dim_name(
1255 __isl_take isl_local_space *ls,
1256 enum isl_dim_type type, unsigned pos, const char *s);
1257 isl_bool isl_local_space_has_dim_name(
1258 __isl_keep isl_local_space *ls,
1259 enum isl_dim_type type, unsigned pos)
1260 const char *isl_local_space_get_dim_name(
1261 __isl_keep isl_local_space *ls,
1262 enum isl_dim_type type, unsigned pos);
1264 #include <isl/constraint.h>
1265 const char *isl_constraint_get_dim_name(
1266 __isl_keep isl_constraint *constraint,
1267 enum isl_dim_type type, unsigned pos);
1269 #include <isl/set.h>
1270 __isl_give isl_id *isl_basic_set_get_dim_id(
1271 __isl_keep isl_basic_set *bset,
1272 enum isl_dim_type type, unsigned pos);
1273 __isl_give isl_set *isl_set_set_dim_id(
1274 __isl_take isl_set *set, enum isl_dim_type type,
1275 unsigned pos, __isl_take isl_id *id);
1276 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1277 enum isl_dim_type type, unsigned pos);
1278 __isl_give isl_id *isl_set_get_dim_id(
1279 __isl_keep isl_set *set, enum isl_dim_type type,
1281 const char *isl_basic_set_get_dim_name(
1282 __isl_keep isl_basic_set *bset,
1283 enum isl_dim_type type, unsigned pos);
1284 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1285 enum isl_dim_type type, unsigned pos);
1286 const char *isl_set_get_dim_name(
1287 __isl_keep isl_set *set,
1288 enum isl_dim_type type, unsigned pos);
1290 #include <isl/map.h>
1291 __isl_give isl_map *isl_map_set_dim_id(
1292 __isl_take isl_map *map, enum isl_dim_type type,
1293 unsigned pos, __isl_take isl_id *id);
1294 isl_bool isl_basic_map_has_dim_id(
1295 __isl_keep isl_basic_map *bmap,
1296 enum isl_dim_type type, unsigned pos);
1297 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1298 enum isl_dim_type type, unsigned pos);
1299 __isl_give isl_id *isl_map_get_dim_id(
1300 __isl_keep isl_map *map, enum isl_dim_type type,
1302 __isl_give isl_id *isl_union_map_get_dim_id(
1303 __isl_keep isl_union_map *umap,
1304 enum isl_dim_type type, unsigned pos);
1305 const char *isl_basic_map_get_dim_name(
1306 __isl_keep isl_basic_map *bmap,
1307 enum isl_dim_type type, unsigned pos);
1308 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1309 enum isl_dim_type type, unsigned pos);
1310 const char *isl_map_get_dim_name(
1311 __isl_keep isl_map *map,
1312 enum isl_dim_type type, unsigned pos);
1314 #include <isl/val.h>
1315 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1316 __isl_take isl_multi_val *mv,
1317 enum isl_dim_type type, unsigned pos,
1318 __isl_take isl_id *id);
1319 __isl_give isl_id *isl_multi_val_get_dim_id(
1320 __isl_keep isl_multi_val *mv,
1321 enum isl_dim_type type, unsigned pos);
1322 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1323 __isl_take isl_multi_val *mv,
1324 enum isl_dim_type type, unsigned pos, const char *s);
1326 #include <isl/aff.h>
1327 __isl_give isl_aff *isl_aff_set_dim_id(
1328 __isl_take isl_aff *aff, enum isl_dim_type type,
1329 unsigned pos, __isl_take isl_id *id);
1330 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1331 __isl_take isl_multi_aff *maff,
1332 enum isl_dim_type type, unsigned pos,
1333 __isl_take isl_id *id);
1334 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1335 __isl_take isl_pw_aff *pma,
1336 enum isl_dim_type type, unsigned pos,
1337 __isl_take isl_id *id);
1338 __isl_give isl_multi_pw_aff *
1339 isl_multi_pw_aff_set_dim_id(
1340 __isl_take isl_multi_pw_aff *mpa,
1341 enum isl_dim_type type, unsigned pos,
1342 __isl_take isl_id *id);
1343 __isl_give isl_multi_union_pw_aff *
1344 isl_multi_union_pw_aff_set_dim_id(
1345 __isl_take isl_multi_union_pw_aff *mupa,
1346 enum isl_dim_type type, unsigned pos,
1347 __isl_take isl_id *id);
1348 __isl_give isl_id *isl_multi_aff_get_dim_id(
1349 __isl_keep isl_multi_aff *ma,
1350 enum isl_dim_type type, unsigned pos);
1351 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1352 enum isl_dim_type type, unsigned pos);
1353 __isl_give isl_id *isl_pw_aff_get_dim_id(
1354 __isl_keep isl_pw_aff *pa,
1355 enum isl_dim_type type, unsigned pos);
1356 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1357 __isl_keep isl_pw_multi_aff *pma,
1358 enum isl_dim_type type, unsigned pos);
1359 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1360 __isl_keep isl_multi_pw_aff *mpa,
1361 enum isl_dim_type type, unsigned pos);
1362 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1363 __isl_keep isl_multi_union_pw_aff *mupa,
1364 enum isl_dim_type type, unsigned pos);
1365 __isl_give isl_aff *isl_aff_set_dim_name(
1366 __isl_take isl_aff *aff, enum isl_dim_type type,
1367 unsigned pos, const char *s);
1368 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1369 __isl_take isl_multi_aff *maff,
1370 enum isl_dim_type type, unsigned pos, const char *s);
1371 __isl_give isl_multi_pw_aff *
1372 isl_multi_pw_aff_set_dim_name(
1373 __isl_take isl_multi_pw_aff *mpa,
1374 enum isl_dim_type type, unsigned pos, const char *s);
1375 __isl_give isl_union_pw_aff *
1376 isl_union_pw_aff_set_dim_name(
1377 __isl_take isl_union_pw_aff *upa,
1378 enum isl_dim_type type, unsigned pos,
1380 __isl_give isl_union_pw_multi_aff *
1381 isl_union_pw_multi_aff_set_dim_name(
1382 __isl_take isl_union_pw_multi_aff *upma,
1383 enum isl_dim_type type, unsigned pos,
1385 __isl_give isl_multi_union_pw_aff *
1386 isl_multi_union_pw_aff_set_dim_name(
1387 __isl_take isl_multi_union_pw_aff *mupa,
1388 enum isl_dim_type type, unsigned pos,
1389 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1390 enum isl_dim_type type, unsigned pos);
1391 const char *isl_pw_aff_get_dim_name(
1392 __isl_keep isl_pw_aff *pa,
1393 enum isl_dim_type type, unsigned pos);
1394 const char *isl_pw_multi_aff_get_dim_name(
1395 __isl_keep isl_pw_multi_aff *pma,
1396 enum isl_dim_type type, unsigned pos);
1398 #include <isl/polynomial.h>
1399 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1400 __isl_take isl_qpolynomial *qp,
1401 enum isl_dim_type type, unsigned pos,
1403 __isl_give isl_pw_qpolynomial *
1404 isl_pw_qpolynomial_set_dim_name(
1405 __isl_take isl_pw_qpolynomial *pwqp,
1406 enum isl_dim_type type, unsigned pos,
1408 __isl_give isl_pw_qpolynomial_fold *
1409 isl_pw_qpolynomial_fold_set_dim_name(
1410 __isl_take isl_pw_qpolynomial_fold *pwf,
1411 enum isl_dim_type type, unsigned pos,
1413 __isl_give isl_union_pw_qpolynomial *
1414 isl_union_pw_qpolynomial_set_dim_name(
1415 __isl_take isl_union_pw_qpolynomial *upwqp,
1416 enum isl_dim_type type, unsigned pos,
1418 __isl_give isl_union_pw_qpolynomial_fold *
1419 isl_union_pw_qpolynomial_fold_set_dim_name(
1420 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1421 enum isl_dim_type type, unsigned pos,
1424 Note that C<isl_space_get_name> returns a pointer to some internal
1425 data structure, so the result can only be used while the
1426 corresponding C<isl_space> is alive.
1427 Also note that every function that operates on two sets or relations
1428 requires that both arguments have the same parameters. This also
1429 means that if one of the arguments has named parameters, then the
1430 other needs to have named parameters too and the names need to match.
1431 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1432 arguments may have different parameters (as long as they are named),
1433 in which case the result will have as parameters the union of the parameters of
1436 Given the identifier or name of a dimension (typically a parameter),
1437 its position can be obtained from the following functions.
1439 #include <isl/space.h>
1440 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1441 enum isl_dim_type type, __isl_keep isl_id *id);
1442 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1443 enum isl_dim_type type, const char *name);
1445 #include <isl/local_space.h>
1446 int isl_local_space_find_dim_by_name(
1447 __isl_keep isl_local_space *ls,
1448 enum isl_dim_type type, const char *name);
1450 #include <isl/val.h>
1451 int isl_multi_val_find_dim_by_id(
1452 __isl_keep isl_multi_val *mv,
1453 enum isl_dim_type type, __isl_keep isl_id *id);
1454 int isl_multi_val_find_dim_by_name(
1455 __isl_keep isl_multi_val *mv,
1456 enum isl_dim_type type, const char *name);
1458 #include <isl/set.h>
1459 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1460 enum isl_dim_type type, __isl_keep isl_id *id);
1461 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1462 enum isl_dim_type type, const char *name);
1464 #include <isl/map.h>
1465 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1466 enum isl_dim_type type, __isl_keep isl_id *id);
1467 int isl_basic_map_find_dim_by_name(
1468 __isl_keep isl_basic_map *bmap,
1469 enum isl_dim_type type, const char *name);
1470 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1471 enum isl_dim_type type, const char *name);
1472 int isl_union_map_find_dim_by_name(
1473 __isl_keep isl_union_map *umap,
1474 enum isl_dim_type type, const char *name);
1476 #include <isl/aff.h>
1477 int isl_multi_aff_find_dim_by_id(
1478 __isl_keep isl_multi_aff *ma,
1479 enum isl_dim_type type, __isl_keep isl_id *id);
1480 int isl_multi_pw_aff_find_dim_by_id(
1481 __isl_keep isl_multi_pw_aff *mpa,
1482 enum isl_dim_type type, __isl_keep isl_id *id);
1483 int isl_multi_union_pw_aff_find_dim_by_id(
1484 __isl_keep isl_union_multi_pw_aff *mupa,
1485 enum isl_dim_type type, __isl_keep isl_id *id);
1486 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1487 enum isl_dim_type type, const char *name);
1488 int isl_multi_aff_find_dim_by_name(
1489 __isl_keep isl_multi_aff *ma,
1490 enum isl_dim_type type, const char *name);
1491 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1492 enum isl_dim_type type, const char *name);
1493 int isl_multi_pw_aff_find_dim_by_name(
1494 __isl_keep isl_multi_pw_aff *mpa,
1495 enum isl_dim_type type, const char *name);
1496 int isl_pw_multi_aff_find_dim_by_name(
1497 __isl_keep isl_pw_multi_aff *pma,
1498 enum isl_dim_type type, const char *name);
1499 int isl_union_pw_aff_find_dim_by_name(
1500 __isl_keep isl_union_pw_aff *upa,
1501 enum isl_dim_type type, const char *name);
1502 int isl_union_pw_multi_aff_find_dim_by_name(
1503 __isl_keep isl_union_pw_multi_aff *upma,
1504 enum isl_dim_type type, const char *name);
1505 int isl_multi_union_pw_aff_find_dim_by_name(
1506 __isl_keep isl_multi_union_pw_aff *mupa,
1507 enum isl_dim_type type, const char *name);
1509 #include <isl/polynomial.h>
1510 int isl_pw_qpolynomial_find_dim_by_name(
1511 __isl_keep isl_pw_qpolynomial *pwqp,
1512 enum isl_dim_type type, const char *name);
1513 int isl_pw_qpolynomial_fold_find_dim_by_name(
1514 __isl_keep isl_pw_qpolynomial_fold *pwf,
1515 enum isl_dim_type type, const char *name);
1516 int isl_union_pw_qpolynomial_find_dim_by_name(
1517 __isl_keep isl_union_pw_qpolynomial *upwqp,
1518 enum isl_dim_type type, const char *name);
1519 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1520 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1521 enum isl_dim_type type, const char *name);
1523 The identifiers or names of entire spaces may be set or read off
1524 using the following functions.
1526 #include <isl/space.h>
1527 __isl_give isl_space *isl_space_set_tuple_id(
1528 __isl_take isl_space *space,
1529 enum isl_dim_type type, __isl_take isl_id *id);
1530 __isl_give isl_space *isl_space_reset_tuple_id(
1531 __isl_take isl_space *space, enum isl_dim_type type);
1532 isl_bool isl_space_has_tuple_id(
1533 __isl_keep isl_space *space,
1534 enum isl_dim_type type);
1535 __isl_give isl_id *isl_space_get_tuple_id(
1536 __isl_keep isl_space *space, enum isl_dim_type type);
1537 __isl_give isl_space *isl_space_set_tuple_name(
1538 __isl_take isl_space *space,
1539 enum isl_dim_type type, const char *s);
1540 isl_bool isl_space_has_tuple_name(
1541 __isl_keep isl_space *space,
1542 enum isl_dim_type type);
1543 __isl_keep const char *isl_space_get_tuple_name(
1544 __isl_keep isl_space *space,
1545 enum isl_dim_type type);
1547 #include <isl/local_space.h>
1548 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1549 __isl_take isl_local_space *ls,
1550 enum isl_dim_type type, __isl_take isl_id *id);
1552 #include <isl/set.h>
1553 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1554 __isl_take isl_basic_set *bset,
1555 __isl_take isl_id *id);
1556 __isl_give isl_set *isl_set_set_tuple_id(
1557 __isl_take isl_set *set, __isl_take isl_id *id);
1558 __isl_give isl_set *isl_set_reset_tuple_id(
1559 __isl_take isl_set *set);
1560 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1561 __isl_give isl_id *isl_set_get_tuple_id(
1562 __isl_keep isl_set *set);
1563 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1564 __isl_take isl_basic_set *set, const char *s);
1565 __isl_give isl_set *isl_set_set_tuple_name(
1566 __isl_take isl_set *set, const char *s);
1567 const char *isl_basic_set_get_tuple_name(
1568 __isl_keep isl_basic_set *bset);
1569 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1570 const char *isl_set_get_tuple_name(
1571 __isl_keep isl_set *set);
1573 #include <isl/map.h>
1574 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1575 __isl_take isl_basic_map *bmap,
1576 enum isl_dim_type type, __isl_take isl_id *id);
1577 __isl_give isl_map *isl_map_set_tuple_id(
1578 __isl_take isl_map *map, enum isl_dim_type type,
1579 __isl_take isl_id *id);
1580 __isl_give isl_map *isl_map_reset_tuple_id(
1581 __isl_take isl_map *map, enum isl_dim_type type);
1582 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1583 enum isl_dim_type type);
1584 __isl_give isl_id *isl_map_get_tuple_id(
1585 __isl_keep isl_map *map, enum isl_dim_type type);
1586 __isl_give isl_map *isl_map_set_tuple_name(
1587 __isl_take isl_map *map,
1588 enum isl_dim_type type, const char *s);
1589 const char *isl_basic_map_get_tuple_name(
1590 __isl_keep isl_basic_map *bmap,
1591 enum isl_dim_type type);
1592 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1593 __isl_take isl_basic_map *bmap,
1594 enum isl_dim_type type, const char *s);
1595 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1596 enum isl_dim_type type);
1597 const char *isl_map_get_tuple_name(
1598 __isl_keep isl_map *map,
1599 enum isl_dim_type type);
1601 #include <isl/val.h>
1602 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1603 __isl_take isl_multi_val *mv,
1604 enum isl_dim_type type, __isl_take isl_id *id);
1605 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1606 __isl_take isl_multi_val *mv,
1607 enum isl_dim_type type);
1608 isl_bool isl_multi_val_has_tuple_id(
1609 __isl_keep isl_multi_val *mv,
1610 enum isl_dim_type type);
1611 __isl_give isl_id *isl_multi_val_get_tuple_id(
1612 __isl_keep isl_multi_val *mv,
1613 enum isl_dim_type type);
1614 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1615 __isl_take isl_multi_val *mv,
1616 enum isl_dim_type type, const char *s);
1617 const char *isl_multi_val_get_tuple_name(
1618 __isl_keep isl_multi_val *mv,
1619 enum isl_dim_type type);
1621 #include <isl/aff.h>
1622 __isl_give isl_aff *isl_aff_set_tuple_id(
1623 __isl_take isl_aff *aff,
1624 enum isl_dim_type type, __isl_take isl_id *id);
1625 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1626 __isl_take isl_multi_aff *maff,
1627 enum isl_dim_type type, __isl_take isl_id *id);
1628 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1629 __isl_take isl_pw_aff *pwaff,
1630 enum isl_dim_type type, __isl_take isl_id *id);
1631 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1632 __isl_take isl_pw_multi_aff *pma,
1633 enum isl_dim_type type, __isl_take isl_id *id);
1634 __isl_give isl_multi_union_pw_aff *
1635 isl_multi_union_pw_aff_set_tuple_id(
1636 __isl_take isl_multi_union_pw_aff *mupa,
1637 enum isl_dim_type type, __isl_take isl_id *id);
1638 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1639 __isl_take isl_multi_aff *ma,
1640 enum isl_dim_type type);
1641 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1642 __isl_take isl_pw_aff *pa,
1643 enum isl_dim_type type);
1644 __isl_give isl_multi_pw_aff *
1645 isl_multi_pw_aff_reset_tuple_id(
1646 __isl_take isl_multi_pw_aff *mpa,
1647 enum isl_dim_type type);
1648 __isl_give isl_pw_multi_aff *
1649 isl_pw_multi_aff_reset_tuple_id(
1650 __isl_take isl_pw_multi_aff *pma,
1651 enum isl_dim_type type);
1652 __isl_give isl_multi_union_pw_aff *
1653 isl_multi_union_pw_aff_reset_tuple_id(
1654 __isl_take isl_multi_union_pw_aff *mupa,
1655 enum isl_dim_type type);
1656 isl_bool isl_multi_aff_has_tuple_id(
1657 __isl_keep isl_multi_aff *ma,
1658 enum isl_dim_type type);
1659 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1660 __isl_keep isl_multi_aff *ma,
1661 enum isl_dim_type type);
1662 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1663 enum isl_dim_type type);
1664 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1665 __isl_keep isl_pw_aff *pa,
1666 enum isl_dim_type type);
1667 isl_bool isl_pw_multi_aff_has_tuple_id(
1668 __isl_keep isl_pw_multi_aff *pma,
1669 enum isl_dim_type type);
1670 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1671 __isl_keep isl_pw_multi_aff *pma,
1672 enum isl_dim_type type);
1673 isl_bool isl_multi_pw_aff_has_tuple_id(
1674 __isl_keep isl_multi_pw_aff *mpa,
1675 enum isl_dim_type type);
1676 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1677 __isl_keep isl_multi_pw_aff *mpa,
1678 enum isl_dim_type type);
1679 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1680 __isl_keep isl_multi_union_pw_aff *mupa,
1681 enum isl_dim_type type);
1682 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1683 __isl_keep isl_multi_union_pw_aff *mupa,
1684 enum isl_dim_type type);
1685 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1686 __isl_take isl_multi_aff *maff,
1687 enum isl_dim_type type, const char *s);
1688 __isl_give isl_multi_pw_aff *
1689 isl_multi_pw_aff_set_tuple_name(
1690 __isl_take isl_multi_pw_aff *mpa,
1691 enum isl_dim_type type, const char *s);
1692 __isl_give isl_multi_union_pw_aff *
1693 isl_multi_union_pw_aff_set_tuple_name(
1694 __isl_take isl_multi_union_pw_aff *mupa,
1695 enum isl_dim_type type, const char *s);
1696 const char *isl_multi_aff_get_tuple_name(
1697 __isl_keep isl_multi_aff *multi,
1698 enum isl_dim_type type);
1699 isl_bool isl_pw_multi_aff_has_tuple_name(
1700 __isl_keep isl_pw_multi_aff *pma,
1701 enum isl_dim_type type);
1702 const char *isl_pw_multi_aff_get_tuple_name(
1703 __isl_keep isl_pw_multi_aff *pma,
1704 enum isl_dim_type type);
1705 const char *isl_multi_union_pw_aff_get_tuple_name(
1706 __isl_keep isl_multi_union_pw_aff *mupa,
1707 enum isl_dim_type type);
1709 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1710 or C<isl_dim_set>. As with C<isl_space_get_name>,
1711 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1713 Binary operations require the corresponding spaces of their arguments
1714 to have the same name.
1716 To keep the names of all parameters and tuples, but reset the user pointers
1717 of all the corresponding identifiers, use the following function.
1719 #include <isl/space.h>
1720 __isl_give isl_space *isl_space_reset_user(
1721 __isl_take isl_space *space);
1723 #include <isl/set.h>
1724 __isl_give isl_set *isl_set_reset_user(
1725 __isl_take isl_set *set);
1727 #include <isl/map.h>
1728 __isl_give isl_map *isl_map_reset_user(
1729 __isl_take isl_map *map);
1731 #include <isl/union_set.h>
1732 __isl_give isl_union_set *isl_union_set_reset_user(
1733 __isl_take isl_union_set *uset);
1735 #include <isl/union_map.h>
1736 __isl_give isl_union_map *isl_union_map_reset_user(
1737 __isl_take isl_union_map *umap);
1739 #include <isl/val.h>
1740 __isl_give isl_multi_val *isl_multi_val_reset_user(
1741 __isl_take isl_multi_val *mv);
1743 #include <isl/aff.h>
1744 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1745 __isl_take isl_multi_aff *ma);
1746 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1747 __isl_take isl_pw_aff *pa);
1748 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1749 __isl_take isl_multi_pw_aff *mpa);
1750 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1751 __isl_take isl_pw_multi_aff *pma);
1752 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1753 __isl_take isl_union_pw_aff *upa);
1754 __isl_give isl_multi_union_pw_aff *
1755 isl_multi_union_pw_aff_reset_user(
1756 __isl_take isl_multi_union_pw_aff *mupa);
1757 __isl_give isl_union_pw_multi_aff *
1758 isl_union_pw_multi_aff_reset_user(
1759 __isl_take isl_union_pw_multi_aff *upma);
1761 #include <isl/polynomial.h>
1762 __isl_give isl_pw_qpolynomial *
1763 isl_pw_qpolynomial_reset_user(
1764 __isl_take isl_pw_qpolynomial *pwqp);
1765 __isl_give isl_union_pw_qpolynomial *
1766 isl_union_pw_qpolynomial_reset_user(
1767 __isl_take isl_union_pw_qpolynomial *upwqp);
1768 __isl_give isl_pw_qpolynomial_fold *
1769 isl_pw_qpolynomial_fold_reset_user(
1770 __isl_take isl_pw_qpolynomial_fold *pwf);
1771 __isl_give isl_union_pw_qpolynomial_fold *
1772 isl_union_pw_qpolynomial_fold_reset_user(
1773 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1775 Spaces can be nested. In particular, the domain of a set or
1776 the domain or range of a relation can be a nested relation.
1777 This process is also called I<wrapping>.
1778 The functions for detecting, constructing and deconstructing
1779 such nested spaces can be found in the wrapping properties
1780 of L</"Unary Properties">, the wrapping operations
1781 of L</"Unary Operations"> and the Cartesian product operations
1782 of L</"Basic Operations">.
1784 Spaces can be created from other spaces
1785 using the functions described in L</"Unary Operations">
1786 and L</"Binary Operations">.
1790 A local space is essentially a space with
1791 zero or more existentially quantified variables.
1792 The local space of various objects can be obtained
1793 using the following functions.
1795 #include <isl/constraint.h>
1796 __isl_give isl_local_space *isl_constraint_get_local_space(
1797 __isl_keep isl_constraint *constraint);
1799 #include <isl/set.h>
1800 __isl_give isl_local_space *isl_basic_set_get_local_space(
1801 __isl_keep isl_basic_set *bset);
1803 #include <isl/map.h>
1804 __isl_give isl_local_space *isl_basic_map_get_local_space(
1805 __isl_keep isl_basic_map *bmap);
1807 #include <isl/aff.h>
1808 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1809 __isl_keep isl_aff *aff);
1810 __isl_give isl_local_space *isl_aff_get_local_space(
1811 __isl_keep isl_aff *aff);
1813 A new local space can be created from a space using
1815 #include <isl/local_space.h>
1816 __isl_give isl_local_space *isl_local_space_from_space(
1817 __isl_take isl_space *space);
1819 They can be inspected, modified, copied and freed using the following functions.
1821 #include <isl/local_space.h>
1822 isl_bool isl_local_space_is_params(
1823 __isl_keep isl_local_space *ls);
1824 isl_bool isl_local_space_is_set(
1825 __isl_keep isl_local_space *ls);
1826 __isl_give isl_space *isl_local_space_get_space(
1827 __isl_keep isl_local_space *ls);
1828 __isl_give isl_aff *isl_local_space_get_div(
1829 __isl_keep isl_local_space *ls, int pos);
1830 __isl_give isl_local_space *isl_local_space_copy(
1831 __isl_keep isl_local_space *ls);
1832 __isl_null isl_local_space *isl_local_space_free(
1833 __isl_take isl_local_space *ls);
1835 Note that C<isl_local_space_get_div> can only be used on local spaces
1838 Two local spaces can be compared using
1840 isl_bool isl_local_space_is_equal(
1841 __isl_keep isl_local_space *ls1,
1842 __isl_keep isl_local_space *ls2);
1844 Local spaces can be created from other local spaces
1845 using the functions described in L</"Unary Operations">
1846 and L</"Binary Operations">.
1848 =head2 Creating New Sets and Relations
1850 C<isl> has functions for creating some standard sets and relations.
1854 =item * Empty sets and relations
1856 __isl_give isl_basic_set *isl_basic_set_empty(
1857 __isl_take isl_space *space);
1858 __isl_give isl_basic_map *isl_basic_map_empty(
1859 __isl_take isl_space *space);
1860 __isl_give isl_set *isl_set_empty(
1861 __isl_take isl_space *space);
1862 __isl_give isl_map *isl_map_empty(
1863 __isl_take isl_space *space);
1864 __isl_give isl_union_set *isl_union_set_empty(
1865 __isl_take isl_space *space);
1866 __isl_give isl_union_map *isl_union_map_empty(
1867 __isl_take isl_space *space);
1869 For C<isl_union_set>s and C<isl_union_map>s, the space
1870 is only used to specify the parameters.
1872 =item * Universe sets and relations
1874 __isl_give isl_basic_set *isl_basic_set_universe(
1875 __isl_take isl_space *space);
1876 __isl_give isl_basic_map *isl_basic_map_universe(
1877 __isl_take isl_space *space);
1878 __isl_give isl_set *isl_set_universe(
1879 __isl_take isl_space *space);
1880 __isl_give isl_map *isl_map_universe(
1881 __isl_take isl_space *space);
1882 __isl_give isl_union_set *isl_union_set_universe(
1883 __isl_take isl_union_set *uset);
1884 __isl_give isl_union_map *isl_union_map_universe(
1885 __isl_take isl_union_map *umap);
1887 The sets and relations constructed by the functions above
1888 contain all integer values, while those constructed by the
1889 functions below only contain non-negative values.
1891 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1892 __isl_take isl_space *space);
1893 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1894 __isl_take isl_space *space);
1895 __isl_give isl_set *isl_set_nat_universe(
1896 __isl_take isl_space *space);
1897 __isl_give isl_map *isl_map_nat_universe(
1898 __isl_take isl_space *space);
1900 =item * Identity relations
1902 __isl_give isl_basic_map *isl_basic_map_identity(
1903 __isl_take isl_space *space);
1904 __isl_give isl_map *isl_map_identity(
1905 __isl_take isl_space *space);
1907 The number of input and output dimensions in C<space> needs
1910 =item * Lexicographic order
1912 __isl_give isl_map *isl_map_lex_lt(
1913 __isl_take isl_space *set_space);
1914 __isl_give isl_map *isl_map_lex_le(
1915 __isl_take isl_space *set_space);
1916 __isl_give isl_map *isl_map_lex_gt(
1917 __isl_take isl_space *set_space);
1918 __isl_give isl_map *isl_map_lex_ge(
1919 __isl_take isl_space *set_space);
1920 __isl_give isl_map *isl_map_lex_lt_first(
1921 __isl_take isl_space *space, unsigned n);
1922 __isl_give isl_map *isl_map_lex_le_first(
1923 __isl_take isl_space *space, unsigned n);
1924 __isl_give isl_map *isl_map_lex_gt_first(
1925 __isl_take isl_space *space, unsigned n);
1926 __isl_give isl_map *isl_map_lex_ge_first(
1927 __isl_take isl_space *space, unsigned n);
1929 The first four functions take a space for a B<set>
1930 and return relations that express that the elements in the domain
1931 are lexicographically less
1932 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1933 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1934 than the elements in the range.
1935 The last four functions take a space for a map
1936 and return relations that express that the first C<n> dimensions
1937 in the domain are lexicographically less
1938 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1939 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1940 than the first C<n> dimensions in the range.
1944 A basic set or relation can be converted to a set or relation
1945 using the following functions.
1947 __isl_give isl_set *isl_set_from_basic_set(
1948 __isl_take isl_basic_set *bset);
1949 __isl_give isl_map *isl_map_from_basic_map(
1950 __isl_take isl_basic_map *bmap);
1952 Sets and relations can be converted to union sets and relations
1953 using the following functions.
1955 __isl_give isl_union_set *isl_union_set_from_basic_set(
1956 __isl_take isl_basic_set *bset);
1957 __isl_give isl_union_map *isl_union_map_from_basic_map(
1958 __isl_take isl_basic_map *bmap);
1959 __isl_give isl_union_set *isl_union_set_from_set(
1960 __isl_take isl_set *set);
1961 __isl_give isl_union_map *isl_union_map_from_map(
1962 __isl_take isl_map *map);
1964 The inverse conversions below can only be used if the input
1965 union set or relation is known to contain elements in exactly one
1968 __isl_give isl_set *isl_set_from_union_set(
1969 __isl_take isl_union_set *uset);
1970 __isl_give isl_map *isl_map_from_union_map(
1971 __isl_take isl_union_map *umap);
1973 Sets and relations can be copied and freed again using the following
1976 __isl_give isl_basic_set *isl_basic_set_copy(
1977 __isl_keep isl_basic_set *bset);
1978 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1979 __isl_give isl_union_set *isl_union_set_copy(
1980 __isl_keep isl_union_set *uset);
1981 __isl_give isl_basic_map *isl_basic_map_copy(
1982 __isl_keep isl_basic_map *bmap);
1983 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1984 __isl_give isl_union_map *isl_union_map_copy(
1985 __isl_keep isl_union_map *umap);
1986 __isl_null isl_basic_set *isl_basic_set_free(
1987 __isl_take isl_basic_set *bset);
1988 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1989 __isl_null isl_union_set *isl_union_set_free(
1990 __isl_take isl_union_set *uset);
1991 __isl_null isl_basic_map *isl_basic_map_free(
1992 __isl_take isl_basic_map *bmap);
1993 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1994 __isl_null isl_union_map *isl_union_map_free(
1995 __isl_take isl_union_map *umap);
1997 Other sets and relations can be constructed by starting
1998 from a universe set or relation, adding equality and/or
1999 inequality constraints and then projecting out the
2000 existentially quantified variables, if any.
2001 Constraints can be constructed, manipulated and
2002 added to (or removed from) (basic) sets and relations
2003 using the following functions.
2005 #include <isl/constraint.h>
2006 __isl_give isl_constraint *isl_constraint_alloc_equality(
2007 __isl_take isl_local_space *ls);
2008 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2009 __isl_take isl_local_space *ls);
2010 __isl_give isl_constraint *isl_constraint_set_constant_si(
2011 __isl_take isl_constraint *constraint, int v);
2012 __isl_give isl_constraint *isl_constraint_set_constant_val(
2013 __isl_take isl_constraint *constraint,
2014 __isl_take isl_val *v);
2015 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2016 __isl_take isl_constraint *constraint,
2017 enum isl_dim_type type, int pos, int v);
2018 __isl_give isl_constraint *
2019 isl_constraint_set_coefficient_val(
2020 __isl_take isl_constraint *constraint,
2021 enum isl_dim_type type, int pos,
2022 __isl_take isl_val *v);
2023 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2024 __isl_take isl_basic_map *bmap,
2025 __isl_take isl_constraint *constraint);
2026 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2027 __isl_take isl_basic_set *bset,
2028 __isl_take isl_constraint *constraint);
2029 __isl_give isl_map *isl_map_add_constraint(
2030 __isl_take isl_map *map,
2031 __isl_take isl_constraint *constraint);
2032 __isl_give isl_set *isl_set_add_constraint(
2033 __isl_take isl_set *set,
2034 __isl_take isl_constraint *constraint);
2036 For example, to create a set containing the even integers
2037 between 10 and 42, you would use the following code.
2040 isl_local_space *ls;
2042 isl_basic_set *bset;
2044 space = isl_space_set_alloc(ctx, 0, 2);
2045 bset = isl_basic_set_universe(isl_space_copy(space));
2046 ls = isl_local_space_from_space(space);
2048 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2049 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2050 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2051 bset = isl_basic_set_add_constraint(bset, c);
2053 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2054 c = isl_constraint_set_constant_si(c, -10);
2055 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2056 bset = isl_basic_set_add_constraint(bset, c);
2058 c = isl_constraint_alloc_inequality(ls);
2059 c = isl_constraint_set_constant_si(c, 42);
2060 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2061 bset = isl_basic_set_add_constraint(bset, c);
2063 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2067 isl_basic_set *bset;
2068 bset = isl_basic_set_read_from_str(ctx,
2069 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2071 A basic set or relation can also be constructed from two matrices
2072 describing the equalities and the inequalities.
2074 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2075 __isl_take isl_space *space,
2076 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2077 enum isl_dim_type c1,
2078 enum isl_dim_type c2, enum isl_dim_type c3,
2079 enum isl_dim_type c4);
2080 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2081 __isl_take isl_space *space,
2082 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2083 enum isl_dim_type c1,
2084 enum isl_dim_type c2, enum isl_dim_type c3,
2085 enum isl_dim_type c4, enum isl_dim_type c5);
2087 The C<isl_dim_type> arguments indicate the order in which
2088 different kinds of variables appear in the input matrices
2089 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2090 C<isl_dim_set> and C<isl_dim_div> for sets and
2091 of C<isl_dim_cst>, C<isl_dim_param>,
2092 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2094 A (basic or union) set or relation can also be constructed from a
2095 (union) (piecewise) (multiple) affine expression
2096 or a list of affine expressions
2097 (See L</"Functions">), provided these affine expressions do not
2100 #include <isl/set.h>
2101 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2102 __isl_take isl_multi_aff *ma);
2103 __isl_give isl_set *isl_set_from_multi_aff(
2104 __isl_take isl_multi_aff *ma);
2106 #include <isl/map.h>
2107 __isl_give isl_basic_map *isl_basic_map_from_aff(
2108 __isl_take isl_aff *aff);
2109 __isl_give isl_map *isl_map_from_aff(
2110 __isl_take isl_aff *aff);
2111 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2112 __isl_take isl_space *domain_space,
2113 __isl_take isl_aff_list *list);
2114 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2115 __isl_take isl_multi_aff *maff)
2116 __isl_give isl_map *isl_map_from_multi_aff(
2117 __isl_take isl_multi_aff *maff)
2119 #include <isl/aff.h>
2120 __isl_give isl_set *isl_set_from_pw_aff(
2121 __isl_take isl_pw_aff *pwaff);
2122 __isl_give isl_map *isl_map_from_pw_aff(
2123 __isl_take isl_pw_aff *pwaff);
2124 __isl_give isl_set *isl_set_from_pw_multi_aff(
2125 __isl_take isl_pw_multi_aff *pma);
2126 __isl_give isl_map *isl_map_from_pw_multi_aff(
2127 __isl_take isl_pw_multi_aff *pma);
2128 __isl_give isl_set *isl_set_from_multi_pw_aff(
2129 __isl_take isl_multi_pw_aff *mpa);
2130 __isl_give isl_map *isl_map_from_multi_pw_aff(
2131 __isl_take isl_multi_pw_aff *mpa);
2132 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2133 __isl_take isl_union_pw_aff *upa);
2134 __isl_give isl_union_map *
2135 isl_union_map_from_union_pw_multi_aff(
2136 __isl_take isl_union_pw_multi_aff *upma);
2137 __isl_give isl_union_map *
2138 isl_union_map_from_multi_union_pw_aff(
2139 __isl_take isl_multi_union_pw_aff *mupa);
2141 The C<domain_space> argument describes the domain of the resulting
2142 basic relation. It is required because the C<list> may consist
2143 of zero affine expressions.
2144 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2145 is not allowed to be zero-dimensional. The domain of the result
2146 is the shared domain of the union piecewise affine elements.
2148 =head2 Inspecting Sets and Relations
2150 Usually, the user should not have to care about the actual constraints
2151 of the sets and maps, but should instead apply the abstract operations
2152 explained in the following sections.
2153 Occasionally, however, it may be required to inspect the individual
2154 coefficients of the constraints. This section explains how to do so.
2155 In these cases, it may also be useful to have C<isl> compute
2156 an explicit representation of the existentially quantified variables.
2158 __isl_give isl_set *isl_set_compute_divs(
2159 __isl_take isl_set *set);
2160 __isl_give isl_map *isl_map_compute_divs(
2161 __isl_take isl_map *map);
2162 __isl_give isl_union_set *isl_union_set_compute_divs(
2163 __isl_take isl_union_set *uset);
2164 __isl_give isl_union_map *isl_union_map_compute_divs(
2165 __isl_take isl_union_map *umap);
2167 This explicit representation defines the existentially quantified
2168 variables as integer divisions of the other variables, possibly
2169 including earlier existentially quantified variables.
2170 An explicitly represented existentially quantified variable therefore
2171 has a unique value when the values of the other variables are known.
2173 Alternatively, the existentially quantified variables can be removed
2174 using the following functions, which compute an overapproximation.
2176 #include <isl/set.h>
2177 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2178 __isl_take isl_basic_set *bset);
2179 __isl_give isl_set *isl_set_remove_divs(
2180 __isl_take isl_set *set);
2182 #include <isl/map.h>
2183 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2184 __isl_take isl_basic_map *bmap);
2185 __isl_give isl_map *isl_map_remove_divs(
2186 __isl_take isl_map *map);
2188 #include <isl/union_set.h>
2189 __isl_give isl_union_set *isl_union_set_remove_divs(
2190 __isl_take isl_union_set *bset);
2192 #include <isl/union_map.h>
2193 __isl_give isl_union_map *isl_union_map_remove_divs(
2194 __isl_take isl_union_map *bmap);
2196 It is also possible to only remove those divs that are defined
2197 in terms of a given range of dimensions or only those for which
2198 no explicit representation is known.
2200 __isl_give isl_basic_set *
2201 isl_basic_set_remove_divs_involving_dims(
2202 __isl_take isl_basic_set *bset,
2203 enum isl_dim_type type,
2204 unsigned first, unsigned n);
2205 __isl_give isl_basic_map *
2206 isl_basic_map_remove_divs_involving_dims(
2207 __isl_take isl_basic_map *bmap,
2208 enum isl_dim_type type,
2209 unsigned first, unsigned n);
2210 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2211 __isl_take isl_set *set, enum isl_dim_type type,
2212 unsigned first, unsigned n);
2213 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2214 __isl_take isl_map *map, enum isl_dim_type type,
2215 unsigned first, unsigned n);
2217 __isl_give isl_basic_set *
2218 isl_basic_set_remove_unknown_divs(
2219 __isl_take isl_basic_set *bset);
2220 __isl_give isl_set *isl_set_remove_unknown_divs(
2221 __isl_take isl_set *set);
2222 __isl_give isl_map *isl_map_remove_unknown_divs(
2223 __isl_take isl_map *map);
2225 To iterate over all the sets or maps in a union set or map, use
2227 #include <isl/union_set.h>
2228 isl_stat isl_union_set_foreach_set(
2229 __isl_keep isl_union_set *uset,
2230 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2233 #include <isl/union_map.h>
2234 isl_stat isl_union_map_foreach_map(
2235 __isl_keep isl_union_map *umap,
2236 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2238 isl_bool isl_union_map_every_map(
2239 __isl_keep isl_union_map *umap,
2240 isl_bool (*test)(__isl_keep isl_map *map,
2244 These functions call the callback function once for each
2245 (pair of) space(s) for which there are elements in the input.
2246 The argument to the callback contains all elements in the input
2247 with that (pair of) space(s).
2248 The C<isl_union_map_every_map> variant check whether each
2249 call to the callback returns true and stops checking as soon as one
2250 of these calls returns false.
2252 The number of sets or maps in a union set or map can be obtained
2255 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2256 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2258 To extract the set or map in a given space from a union, use
2260 __isl_give isl_set *isl_union_set_extract_set(
2261 __isl_keep isl_union_set *uset,
2262 __isl_take isl_space *space);
2263 __isl_give isl_map *isl_union_map_extract_map(
2264 __isl_keep isl_union_map *umap,
2265 __isl_take isl_space *space);
2267 To iterate over all the basic sets or maps in a set or map, use
2269 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2270 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2273 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2274 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2278 The callback function C<fn> should return C<isl_stat_ok> if successful and
2279 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2280 occurs, the above functions will return C<isl_stat_error>.
2282 It should be noted that C<isl> does not guarantee that
2283 the basic sets or maps passed to C<fn> are disjoint.
2284 If this is required, then the user should call one of
2285 the following functions first.
2287 __isl_give isl_set *isl_set_make_disjoint(
2288 __isl_take isl_set *set);
2289 __isl_give isl_map *isl_map_make_disjoint(
2290 __isl_take isl_map *map);
2292 The number of basic sets in a set can be obtained
2293 or the number of basic maps in a map can be obtained
2296 #include <isl/set.h>
2297 int isl_set_n_basic_set(__isl_keep isl_set *set);
2299 #include <isl/map.h>
2300 int isl_map_n_basic_map(__isl_keep isl_map *map);
2302 It is also possible to obtain a list of (basic) sets from a set
2303 or union set, a list of basic maps from a map and a list of maps from a union
2306 #include <isl/set.h>
2307 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2308 __isl_keep isl_set *set);
2310 #include <isl/union_set.h>
2311 __isl_give isl_basic_set_list *
2312 isl_union_set_get_basic_set_list(
2313 __isl_keep isl_union_set *uset);
2314 __isl_give isl_set_list *isl_union_set_get_set_list(
2315 __isl_keep isl_union_set *uset);
2317 #include <isl/map.h>
2318 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2319 __isl_keep isl_map *map);
2321 #include <isl/union_map.h>
2322 __isl_give isl_map_list *isl_union_map_get_map_list(
2323 __isl_keep isl_union_map *umap);
2325 The returned list can be manipulated using the functions in L<"Lists">.
2327 To iterate over the constraints of a basic set or map, use
2329 #include <isl/constraint.h>
2331 int isl_basic_set_n_constraint(
2332 __isl_keep isl_basic_set *bset);
2333 isl_stat isl_basic_set_foreach_constraint(
2334 __isl_keep isl_basic_set *bset,
2335 isl_stat (*fn)(__isl_take isl_constraint *c,
2338 int isl_basic_map_n_constraint(
2339 __isl_keep isl_basic_map *bmap);
2340 isl_stat isl_basic_map_foreach_constraint(
2341 __isl_keep isl_basic_map *bmap,
2342 isl_stat (*fn)(__isl_take isl_constraint *c,
2345 __isl_null isl_constraint *isl_constraint_free(
2346 __isl_take isl_constraint *c);
2348 Again, the callback function C<fn> should return C<isl_stat_ok>
2350 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2351 occurs, the above functions will return C<isl_stat_error>.
2352 The constraint C<c> represents either an equality or an inequality.
2353 Use the following function to find out whether a constraint
2354 represents an equality. If not, it represents an inequality.
2356 isl_bool isl_constraint_is_equality(
2357 __isl_keep isl_constraint *constraint);
2359 It is also possible to obtain a list of constraints from a basic
2362 #include <isl/constraint.h>
2363 __isl_give isl_constraint_list *
2364 isl_basic_map_get_constraint_list(
2365 __isl_keep isl_basic_map *bmap);
2366 __isl_give isl_constraint_list *
2367 isl_basic_set_get_constraint_list(
2368 __isl_keep isl_basic_set *bset);
2370 These functions require that all existentially quantified variables
2371 have an explicit representation.
2372 The returned list can be manipulated using the functions in L<"Lists">.
2374 The coefficients of the constraints can be inspected using
2375 the following functions.
2377 isl_bool isl_constraint_is_lower_bound(
2378 __isl_keep isl_constraint *constraint,
2379 enum isl_dim_type type, unsigned pos);
2380 isl_bool isl_constraint_is_upper_bound(
2381 __isl_keep isl_constraint *constraint,
2382 enum isl_dim_type type, unsigned pos);
2383 __isl_give isl_val *isl_constraint_get_constant_val(
2384 __isl_keep isl_constraint *constraint);
2385 __isl_give isl_val *isl_constraint_get_coefficient_val(
2386 __isl_keep isl_constraint *constraint,
2387 enum isl_dim_type type, int pos);
2389 The explicit representations of the existentially quantified
2390 variables can be inspected using the following function.
2391 Note that the user is only allowed to use this function
2392 if the inspected set or map is the result of a call
2393 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2394 The existentially quantified variable is equal to the floor
2395 of the returned affine expression. The affine expression
2396 itself can be inspected using the functions in
2399 __isl_give isl_aff *isl_constraint_get_div(
2400 __isl_keep isl_constraint *constraint, int pos);
2402 To obtain the constraints of a basic set or map in matrix
2403 form, use the following functions.
2405 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2406 __isl_keep isl_basic_set *bset,
2407 enum isl_dim_type c1, enum isl_dim_type c2,
2408 enum isl_dim_type c3, enum isl_dim_type c4);
2409 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2410 __isl_keep isl_basic_set *bset,
2411 enum isl_dim_type c1, enum isl_dim_type c2,
2412 enum isl_dim_type c3, enum isl_dim_type c4);
2413 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2414 __isl_keep isl_basic_map *bmap,
2415 enum isl_dim_type c1,
2416 enum isl_dim_type c2, enum isl_dim_type c3,
2417 enum isl_dim_type c4, enum isl_dim_type c5);
2418 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2419 __isl_keep isl_basic_map *bmap,
2420 enum isl_dim_type c1,
2421 enum isl_dim_type c2, enum isl_dim_type c3,
2422 enum isl_dim_type c4, enum isl_dim_type c5);
2424 The C<isl_dim_type> arguments dictate the order in which
2425 different kinds of variables appear in the resulting matrix.
2426 For set inputs, they should be a permutation of
2427 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2428 For map inputs, they should be a permutation of
2429 C<isl_dim_cst>, C<isl_dim_param>,
2430 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2434 Points are elements of a set. They can be used to construct
2435 simple sets (boxes) or they can be used to represent the
2436 individual elements of a set.
2437 The zero point (the origin) can be created using
2439 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2441 The coordinates of a point can be inspected, set and changed
2444 __isl_give isl_val *isl_point_get_coordinate_val(
2445 __isl_keep isl_point *pnt,
2446 enum isl_dim_type type, int pos);
2447 __isl_give isl_point *isl_point_set_coordinate_val(
2448 __isl_take isl_point *pnt,
2449 enum isl_dim_type type, int pos,
2450 __isl_take isl_val *v);
2452 __isl_give isl_point *isl_point_add_ui(
2453 __isl_take isl_point *pnt,
2454 enum isl_dim_type type, int pos, unsigned val);
2455 __isl_give isl_point *isl_point_sub_ui(
2456 __isl_take isl_point *pnt,
2457 enum isl_dim_type type, int pos, unsigned val);
2459 Points can be copied or freed using
2461 __isl_give isl_point *isl_point_copy(
2462 __isl_keep isl_point *pnt);
2463 __isl_null isl_point *isl_point_free(
2464 __isl_take isl_point *pnt);
2466 A singleton set can be created from a point using
2468 __isl_give isl_basic_set *isl_basic_set_from_point(
2469 __isl_take isl_point *pnt);
2470 __isl_give isl_set *isl_set_from_point(
2471 __isl_take isl_point *pnt);
2472 __isl_give isl_union_set *isl_union_set_from_point(
2473 __isl_take isl_point *pnt);
2475 and a box can be created from two opposite extremal points using
2477 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2478 __isl_take isl_point *pnt1,
2479 __isl_take isl_point *pnt2);
2480 __isl_give isl_set *isl_set_box_from_points(
2481 __isl_take isl_point *pnt1,
2482 __isl_take isl_point *pnt2);
2484 All elements of a B<bounded> (union) set can be enumerated using
2485 the following functions.
2487 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2488 isl_stat (*fn)(__isl_take isl_point *pnt,
2491 isl_stat isl_union_set_foreach_point(
2492 __isl_keep isl_union_set *uset,
2493 isl_stat (*fn)(__isl_take isl_point *pnt,
2497 The function C<fn> is called for each integer point in
2498 C<set> with as second argument the last argument of
2499 the C<isl_set_foreach_point> call. The function C<fn>
2500 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2501 In the latter case, C<isl_set_foreach_point> will stop
2502 enumerating and return C<isl_stat_error> as well.
2503 If the enumeration is performed successfully and to completion,
2504 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2506 To obtain a single point of a (basic or union) set, use
2508 __isl_give isl_point *isl_basic_set_sample_point(
2509 __isl_take isl_basic_set *bset);
2510 __isl_give isl_point *isl_set_sample_point(
2511 __isl_take isl_set *set);
2512 __isl_give isl_point *isl_union_set_sample_point(
2513 __isl_take isl_union_set *uset);
2515 If C<set> does not contain any (integer) points, then the
2516 resulting point will be ``void'', a property that can be
2519 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2523 Besides sets and relation, C<isl> also supports various types of functions.
2524 Each of these types is derived from the value type (see L</"Values">)
2525 or from one of two primitive function types
2526 through the application of zero or more type constructors.
2527 We first describe the primitive type and then we describe
2528 the types derived from these primitive types.
2530 =head3 Primitive Functions
2532 C<isl> support two primitive function types, quasi-affine
2533 expressions and quasipolynomials.
2534 A quasi-affine expression is defined either over a parameter
2535 space or over a set and is composed of integer constants,
2536 parameters and set variables, addition, subtraction and
2537 integer division by an integer constant.
2538 For example, the quasi-affine expression
2540 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2542 maps C<x> to C<2*floor((4 n + x)/9>.
2543 A quasipolynomial is a polynomial expression in quasi-affine
2544 expression. That is, it additionally allows for multiplication.
2545 Note, though, that it is not allowed to construct an integer
2546 division of an expression involving multiplications.
2547 Here is an example of a quasipolynomial that is not
2548 quasi-affine expression
2550 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2552 Note that the external representations of quasi-affine expressions
2553 and quasipolynomials are different. Quasi-affine expressions
2554 use a notation with square brackets just like binary relations,
2555 while quasipolynomials do not. This might change at some point.
2557 If a primitive function is defined over a parameter space,
2558 then the space of the function itself is that of a set.
2559 If it is defined over a set, then the space of the function
2560 is that of a relation. In both cases, the set space (or
2561 the output space) is single-dimensional, anonymous and unstructured.
2562 To create functions with multiple dimensions or with other kinds
2563 of set or output spaces, use multiple expressions
2564 (see L</"Multiple Expressions">).
2568 =item * Quasi-affine Expressions
2570 Besides the expressions described above, a quasi-affine
2571 expression can also be set to NaN. Such expressions
2572 typically represent a failure to represent a result
2573 as a quasi-affine expression.
2575 The zero quasi affine expression or the quasi affine expression
2576 that is equal to a given value, parameter or
2577 a specified dimension on a given domain can be created using
2579 #include <isl/aff.h>
2580 __isl_give isl_aff *isl_aff_zero_on_domain(
2581 __isl_take isl_local_space *ls);
2582 __isl_give isl_aff *isl_aff_val_on_domain(
2583 __isl_take isl_local_space *ls,
2584 __isl_take isl_val *val);
2585 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2586 __isl_take isl_space *space,
2587 __isl_take isl_id *id);
2588 __isl_give isl_aff *isl_aff_var_on_domain(
2589 __isl_take isl_local_space *ls,
2590 enum isl_dim_type type, unsigned pos);
2591 __isl_give isl_aff *isl_aff_nan_on_domain(
2592 __isl_take isl_local_space *ls);
2594 The space passed to C<isl_aff_param_on_domain_space_id>
2595 is required to have a parameter with the given identifier.
2597 Quasi affine expressions can be copied and freed using
2599 #include <isl/aff.h>
2600 __isl_give isl_aff *isl_aff_copy(
2601 __isl_keep isl_aff *aff);
2602 __isl_null isl_aff *isl_aff_free(
2603 __isl_take isl_aff *aff);
2605 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2606 using the following function. The constraint is required to have
2607 a non-zero coefficient for the specified dimension.
2609 #include <isl/constraint.h>
2610 __isl_give isl_aff *isl_constraint_get_bound(
2611 __isl_keep isl_constraint *constraint,
2612 enum isl_dim_type type, int pos);
2614 The entire affine expression of the constraint can also be extracted
2615 using the following function.
2617 #include <isl/constraint.h>
2618 __isl_give isl_aff *isl_constraint_get_aff(
2619 __isl_keep isl_constraint *constraint);
2621 Conversely, an equality constraint equating
2622 the affine expression to zero or an inequality constraint enforcing
2623 the affine expression to be non-negative, can be constructed using
2625 __isl_give isl_constraint *isl_equality_from_aff(
2626 __isl_take isl_aff *aff);
2627 __isl_give isl_constraint *isl_inequality_from_aff(
2628 __isl_take isl_aff *aff);
2630 The coefficients and the integer divisions of an affine expression
2631 can be inspected using the following functions.
2633 #include <isl/aff.h>
2634 __isl_give isl_val *isl_aff_get_constant_val(
2635 __isl_keep isl_aff *aff);
2636 __isl_give isl_val *isl_aff_get_coefficient_val(
2637 __isl_keep isl_aff *aff,
2638 enum isl_dim_type type, int pos);
2639 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2640 enum isl_dim_type type, int pos);
2641 __isl_give isl_val *isl_aff_get_denominator_val(
2642 __isl_keep isl_aff *aff);
2643 __isl_give isl_aff *isl_aff_get_div(
2644 __isl_keep isl_aff *aff, int pos);
2646 They can be modified using the following functions.
2648 #include <isl/aff.h>
2649 __isl_give isl_aff *isl_aff_set_constant_si(
2650 __isl_take isl_aff *aff, int v);
2651 __isl_give isl_aff *isl_aff_set_constant_val(
2652 __isl_take isl_aff *aff, __isl_take isl_val *v);
2653 __isl_give isl_aff *isl_aff_set_coefficient_si(
2654 __isl_take isl_aff *aff,
2655 enum isl_dim_type type, int pos, int v);
2656 __isl_give isl_aff *isl_aff_set_coefficient_val(
2657 __isl_take isl_aff *aff,
2658 enum isl_dim_type type, int pos,
2659 __isl_take isl_val *v);
2661 __isl_give isl_aff *isl_aff_add_constant_si(
2662 __isl_take isl_aff *aff, int v);
2663 __isl_give isl_aff *isl_aff_add_constant_val(
2664 __isl_take isl_aff *aff, __isl_take isl_val *v);
2665 __isl_give isl_aff *isl_aff_add_constant_num_si(
2666 __isl_take isl_aff *aff, int v);
2667 __isl_give isl_aff *isl_aff_add_coefficient_si(
2668 __isl_take isl_aff *aff,
2669 enum isl_dim_type type, int pos, int v);
2670 __isl_give isl_aff *isl_aff_add_coefficient_val(
2671 __isl_take isl_aff *aff,
2672 enum isl_dim_type type, int pos,
2673 __isl_take isl_val *v);
2675 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2676 set the I<numerator> of the constant or coefficient, while
2677 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2678 the constant or coefficient as a whole.
2679 The C<add_constant> and C<add_coefficient> functions add an integer
2680 or rational value to
2681 the possibly rational constant or coefficient.
2682 The C<add_constant_num> functions add an integer value to
2685 =item * Quasipolynomials
2687 Some simple quasipolynomials can be created using the following functions.
2689 #include <isl/polynomial.h>
2690 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2691 __isl_take isl_space *domain);
2692 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2693 __isl_take isl_space *domain);
2694 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2695 __isl_take isl_space *domain);
2696 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2697 __isl_take isl_space *domain);
2698 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2699 __isl_take isl_space *domain);
2700 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2701 __isl_take isl_space *domain,
2702 __isl_take isl_val *val);
2703 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2704 __isl_take isl_space *domain,
2705 enum isl_dim_type type, unsigned pos);
2706 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2707 __isl_take isl_aff *aff);
2709 Recall that the space in which a quasipolynomial lives is a map space
2710 with a one-dimensional range. The C<domain> argument in some of
2711 the functions above corresponds to the domain of this map space.
2713 Quasipolynomials can be copied and freed again using the following
2716 #include <isl/polynomial.h>
2717 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2718 __isl_keep isl_qpolynomial *qp);
2719 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2720 __isl_take isl_qpolynomial *qp);
2722 The constant term of a quasipolynomial can be extracted using
2724 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2725 __isl_keep isl_qpolynomial *qp);
2727 To iterate over all terms in a quasipolynomial,
2730 isl_stat isl_qpolynomial_foreach_term(
2731 __isl_keep isl_qpolynomial *qp,
2732 isl_stat (*fn)(__isl_take isl_term *term,
2733 void *user), void *user);
2735 The terms themselves can be inspected and freed using
2738 unsigned isl_term_dim(__isl_keep isl_term *term,
2739 enum isl_dim_type type);
2740 __isl_give isl_val *isl_term_get_coefficient_val(
2741 __isl_keep isl_term *term);
2742 int isl_term_get_exp(__isl_keep isl_term *term,
2743 enum isl_dim_type type, unsigned pos);
2744 __isl_give isl_aff *isl_term_get_div(
2745 __isl_keep isl_term *term, unsigned pos);
2746 __isl_null isl_term *isl_term_free(
2747 __isl_take isl_term *term);
2749 Each term is a product of parameters, set variables and
2750 integer divisions. The function C<isl_term_get_exp>
2751 returns the exponent of a given dimensions in the given term.
2757 A reduction represents a maximum or a minimum of its
2759 The only reduction type defined by C<isl> is
2760 C<isl_qpolynomial_fold>.
2762 There are currently no functions to directly create such
2763 objects, but they do appear in the piecewise quasipolynomial
2764 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2766 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2768 Reductions can be copied and freed using
2769 the following functions.
2771 #include <isl/polynomial.h>
2772 __isl_give isl_qpolynomial_fold *
2773 isl_qpolynomial_fold_copy(
2774 __isl_keep isl_qpolynomial_fold *fold);
2775 __isl_null isl_qpolynomial_fold *
2776 isl_qpolynomial_fold_free(
2777 __isl_take isl_qpolynomial_fold *fold);
2779 To iterate over all quasipolynomials in a reduction, use
2781 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2782 __isl_keep isl_qpolynomial_fold *fold,
2783 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2784 void *user), void *user);
2786 =head3 Multiple Expressions
2788 A multiple expression represents a sequence of zero or
2789 more base expressions, all defined on the same domain space.
2790 The domain space of the multiple expression is the same
2791 as that of the base expressions, but the range space
2792 can be any space. In case the base expressions have
2793 a set space, the corresponding multiple expression
2794 also has a set space.
2795 Objects of the value type do not have an associated space.
2796 The space of a multiple value is therefore always a set space.
2797 Similarly, the space of a multiple union piecewise
2798 affine expression is always a set space.
2799 If the base expressions are not total, then
2800 a corresponding zero-dimensional multiple expression may
2801 have an explicit domain that keeps track of the domain
2802 outside of any base expressions.
2804 The multiple expression types defined by C<isl>
2805 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2806 C<isl_multi_union_pw_aff>.
2808 A multiple expression with the value zero for
2809 each output (or set) dimension can be created
2810 using the following functions.
2812 #include <isl/val.h>
2813 __isl_give isl_multi_val *isl_multi_val_zero(
2814 __isl_take isl_space *space);
2816 #include <isl/aff.h>
2817 __isl_give isl_multi_aff *isl_multi_aff_zero(
2818 __isl_take isl_space *space);
2819 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2820 __isl_take isl_space *space);
2821 __isl_give isl_multi_union_pw_aff *
2822 isl_multi_union_pw_aff_zero(
2823 __isl_take isl_space *space);
2825 Since there is no canonical way of representing a zero
2826 value of type C<isl_union_pw_aff>, the space passed
2827 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2829 An identity function can be created using the following
2830 functions. The space needs to be that of a relation
2831 with the same number of input and output dimensions.
2833 #include <isl/aff.h>
2834 __isl_give isl_multi_aff *isl_multi_aff_identity(
2835 __isl_take isl_space *space);
2836 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2837 __isl_take isl_space *space);
2839 A function that performs a projection on a universe
2840 relation or set can be created using the following functions.
2841 See also the corresponding
2842 projection operations in L</"Unary Operations">.
2844 #include <isl/aff.h>
2845 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2846 __isl_take isl_space *space);
2847 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2848 __isl_take isl_space *space);
2849 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2850 __isl_take isl_space *space,
2851 enum isl_dim_type type,
2852 unsigned first, unsigned n);
2854 A multiple expression can be created from a single
2855 base expression using the following functions.
2856 The space of the created multiple expression is the same
2857 as that of the base expression, except for
2858 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2859 lives in a parameter space and the output lives
2860 in a single-dimensional set space.
2862 #include <isl/aff.h>
2863 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2864 __isl_take isl_aff *aff);
2865 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2866 __isl_take isl_pw_aff *pa);
2867 __isl_give isl_multi_union_pw_aff *
2868 isl_multi_union_pw_aff_from_union_pw_aff(
2869 __isl_take isl_union_pw_aff *upa);
2871 A multiple expression can be created from a list
2872 of base expression in a specified space.
2873 The domain of this space needs to be the same
2874 as the domains of the base expressions in the list.
2875 If the base expressions have a set space (or no associated space),
2876 then this space also needs to be a set space.
2878 #include <isl/val.h>
2879 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2880 __isl_take isl_space *space,
2881 __isl_take isl_val_list *list);
2883 #include <isl/aff.h>
2884 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2885 __isl_take isl_space *space,
2886 __isl_take isl_aff_list *list);
2887 __isl_give isl_multi_pw_aff *
2888 isl_multi_pw_aff_from_pw_aff_list(
2889 __isl_take isl_space *space,
2890 __isl_take isl_pw_aff_list *list);
2891 __isl_give isl_multi_union_pw_aff *
2892 isl_multi_union_pw_aff_from_union_pw_aff_list(
2893 __isl_take isl_space *space,
2894 __isl_take isl_union_pw_aff_list *list);
2896 As a convenience, a multiple piecewise expression can
2897 also be created from a multiple expression.
2898 Each piecewise expression in the result has a single
2901 #include <isl/aff.h>
2902 __isl_give isl_multi_pw_aff *
2903 isl_multi_pw_aff_from_multi_aff(
2904 __isl_take isl_multi_aff *ma);
2906 Similarly, a multiple union expression can be
2907 created from a multiple expression.
2909 #include <isl/aff.h>
2910 __isl_give isl_multi_union_pw_aff *
2911 isl_multi_union_pw_aff_from_multi_aff(
2912 __isl_take isl_multi_aff *ma);
2913 __isl_give isl_multi_union_pw_aff *
2914 isl_multi_union_pw_aff_from_multi_pw_aff(
2915 __isl_take isl_multi_pw_aff *mpa);
2917 A multiple quasi-affine expression can be created from
2918 a multiple value with a given domain space using the following
2921 #include <isl/aff.h>
2922 __isl_give isl_multi_aff *
2923 isl_multi_aff_multi_val_on_space(
2924 __isl_take isl_space *space,
2925 __isl_take isl_multi_val *mv);
2928 a multiple union piecewise affine expression can be created from
2929 a multiple value with a given domain or
2930 a (piecewise) multiple affine expression with a given domain
2931 using the following functions.
2933 #include <isl/aff.h>
2934 __isl_give isl_multi_union_pw_aff *
2935 isl_multi_union_pw_aff_multi_val_on_domain(
2936 __isl_take isl_union_set *domain,
2937 __isl_take isl_multi_val *mv);
2938 __isl_give isl_multi_union_pw_aff *
2939 isl_multi_union_pw_aff_multi_aff_on_domain(
2940 __isl_take isl_union_set *domain,
2941 __isl_take isl_multi_aff *ma);
2942 __isl_give isl_multi_union_pw_aff *
2943 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2944 __isl_take isl_union_set *domain,
2945 __isl_take isl_pw_multi_aff *pma);
2947 Multiple expressions can be copied and freed using
2948 the following functions.
2950 #include <isl/val.h>
2951 __isl_give isl_multi_val *isl_multi_val_copy(
2952 __isl_keep isl_multi_val *mv);
2953 __isl_null isl_multi_val *isl_multi_val_free(
2954 __isl_take isl_multi_val *mv);
2956 #include <isl/aff.h>
2957 __isl_give isl_multi_aff *isl_multi_aff_copy(
2958 __isl_keep isl_multi_aff *maff);
2959 __isl_null isl_multi_aff *isl_multi_aff_free(
2960 __isl_take isl_multi_aff *maff);
2961 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2962 __isl_keep isl_multi_pw_aff *mpa);
2963 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2964 __isl_take isl_multi_pw_aff *mpa);
2965 __isl_give isl_multi_union_pw_aff *
2966 isl_multi_union_pw_aff_copy(
2967 __isl_keep isl_multi_union_pw_aff *mupa);
2968 __isl_null isl_multi_union_pw_aff *
2969 isl_multi_union_pw_aff_free(
2970 __isl_take isl_multi_union_pw_aff *mupa);
2972 The base expression at a given position of a multiple
2973 expression can be extracted using the following functions.
2975 #include <isl/val.h>
2976 __isl_give isl_val *isl_multi_val_get_val(
2977 __isl_keep isl_multi_val *mv, int pos);
2979 #include <isl/aff.h>
2980 __isl_give isl_aff *isl_multi_aff_get_aff(
2981 __isl_keep isl_multi_aff *multi, int pos);
2982 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2983 __isl_keep isl_multi_pw_aff *mpa, int pos);
2984 __isl_give isl_union_pw_aff *
2985 isl_multi_union_pw_aff_get_union_pw_aff(
2986 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2988 It can be replaced using the following functions.
2990 #include <isl/val.h>
2991 __isl_give isl_multi_val *isl_multi_val_set_val(
2992 __isl_take isl_multi_val *mv, int pos,
2993 __isl_take isl_val *val);
2995 #include <isl/aff.h>
2996 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2997 __isl_take isl_multi_aff *multi, int pos,
2998 __isl_take isl_aff *aff);
2999 __isl_give isl_multi_union_pw_aff *
3000 isl_multi_union_pw_aff_set_union_pw_aff(
3001 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3002 __isl_take isl_union_pw_aff *upa);
3004 As a convenience, a sequence of base expressions that have
3005 their domains in a given space can be extracted from a sequence
3006 of union expressions using the following function.
3008 #include <isl/aff.h>
3009 __isl_give isl_multi_pw_aff *
3010 isl_multi_union_pw_aff_extract_multi_pw_aff(
3011 __isl_keep isl_multi_union_pw_aff *mupa,
3012 __isl_take isl_space *space);
3014 Note that there is a difference between C<isl_multi_union_pw_aff>
3015 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3016 of unions of piecewise expressions, while the second is a union
3017 of piecewise sequences. In particular, multiple affine expressions
3018 in an C<isl_union_pw_multi_aff> may live in different spaces,
3019 while there is only a single multiple expression in
3020 an C<isl_multi_union_pw_aff>, which can therefore only live
3021 in a single space. This means that not every
3022 C<isl_union_pw_multi_aff> can be converted to
3023 an C<isl_multi_union_pw_aff>. Conversely, the elements
3024 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3025 while each multiple expression inside an C<isl_union_pw_multi_aff>
3026 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3027 of dimension greater than one may therefore not be exact.
3028 The following functions can
3029 be used to perform these conversions when they are possible.
3031 #include <isl/aff.h>
3032 __isl_give isl_multi_union_pw_aff *
3033 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3034 __isl_take isl_union_pw_multi_aff *upma);
3035 __isl_give isl_union_pw_multi_aff *
3036 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3037 __isl_take isl_multi_union_pw_aff *mupa);
3039 =head3 Piecewise Expressions
3041 A piecewise expression is an expression that is described
3042 using zero or more base expression defined over the same
3043 number of cells in the domain space of the base expressions.
3044 All base expressions are defined over the same
3045 domain space and the cells are disjoint.
3046 The space of a piecewise expression is the same as
3047 that of the base expressions.
3048 If the union of the cells is a strict subset of the domain
3049 space, then the value of the piecewise expression outside
3050 this union is different for types derived from quasi-affine
3051 expressions and those derived from quasipolynomials.
3052 Piecewise expressions derived from quasi-affine expressions
3053 are considered to be undefined outside the union of their cells.
3054 Piecewise expressions derived from quasipolynomials
3055 are considered to be zero outside the union of their cells.
3057 Piecewise quasipolynomials are mainly used by the C<barvinok>
3058 library for representing the number of elements in a parametric set or map.
3059 For example, the piecewise quasipolynomial
3061 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3063 represents the number of points in the map
3065 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3067 The piecewise expression types defined by C<isl>
3068 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3069 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3071 A piecewise expression with no cells can be created using
3072 the following functions.
3074 #include <isl/aff.h>
3075 __isl_give isl_pw_aff *isl_pw_aff_empty(
3076 __isl_take isl_space *space);
3077 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3078 __isl_take isl_space *space);
3080 A piecewise expression with a single universe cell can be
3081 created using the following functions.
3083 #include <isl/aff.h>
3084 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3085 __isl_take isl_aff *aff);
3086 __isl_give isl_pw_multi_aff *
3087 isl_pw_multi_aff_from_multi_aff(
3088 __isl_take isl_multi_aff *ma);
3090 #include <isl/polynomial.h>
3091 __isl_give isl_pw_qpolynomial *
3092 isl_pw_qpolynomial_from_qpolynomial(
3093 __isl_take isl_qpolynomial *qp);
3095 A piecewise expression with a single specified cell can be
3096 created using the following functions.
3098 #include <isl/aff.h>
3099 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3100 __isl_take isl_set *set, __isl_take isl_aff *aff);
3101 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3102 __isl_take isl_set *set,
3103 __isl_take isl_multi_aff *maff);
3105 #include <isl/polynomial.h>
3106 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3107 __isl_take isl_set *set,
3108 __isl_take isl_qpolynomial *qp);
3110 The following convenience functions first create a base expression and
3111 then create a piecewise expression over a universe domain.
3113 #include <isl/aff.h>
3114 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3115 __isl_take isl_local_space *ls);
3116 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3117 __isl_take isl_local_space *ls,
3118 enum isl_dim_type type, unsigned pos);
3119 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3120 __isl_take isl_local_space *ls);
3121 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3122 __isl_take isl_space *space);
3123 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3124 __isl_take isl_space *space);
3125 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3126 __isl_take isl_space *space);
3127 __isl_give isl_pw_multi_aff *
3128 isl_pw_multi_aff_project_out_map(
3129 __isl_take isl_space *space,
3130 enum isl_dim_type type,
3131 unsigned first, unsigned n);
3133 #include <isl/polynomial.h>
3134 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3135 __isl_take isl_space *space);
3137 The following convenience functions first create a base expression and
3138 then create a piecewise expression over a given domain.
3140 #include <isl/aff.h>
3141 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3142 __isl_take isl_set *domain,
3143 __isl_take isl_val *v);
3144 __isl_give isl_pw_multi_aff *
3145 isl_pw_multi_aff_multi_val_on_domain(
3146 __isl_take isl_set *domain,
3147 __isl_take isl_multi_val *mv);
3149 As a convenience, a piecewise multiple expression can
3150 also be created from a piecewise expression.
3151 Each multiple expression in the result is derived
3152 from the corresponding base expression.
3154 #include <isl/aff.h>
3155 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3156 __isl_take isl_pw_aff *pa);
3158 Similarly, a piecewise quasipolynomial can be
3159 created from a piecewise quasi-affine expression using
3160 the following function.
3162 #include <isl/polynomial.h>
3163 __isl_give isl_pw_qpolynomial *
3164 isl_pw_qpolynomial_from_pw_aff(
3165 __isl_take isl_pw_aff *pwaff);
3167 Piecewise expressions can be copied and freed using the following functions.
3169 #include <isl/aff.h>
3170 __isl_give isl_pw_aff *isl_pw_aff_copy(
3171 __isl_keep isl_pw_aff *pwaff);
3172 __isl_null isl_pw_aff *isl_pw_aff_free(
3173 __isl_take isl_pw_aff *pwaff);
3174 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3175 __isl_keep isl_pw_multi_aff *pma);
3176 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3177 __isl_take isl_pw_multi_aff *pma);
3179 #include <isl/polynomial.h>
3180 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3181 __isl_keep isl_pw_qpolynomial *pwqp);
3182 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3183 __isl_take isl_pw_qpolynomial *pwqp);
3184 __isl_give isl_pw_qpolynomial_fold *
3185 isl_pw_qpolynomial_fold_copy(
3186 __isl_keep isl_pw_qpolynomial_fold *pwf);
3187 __isl_null isl_pw_qpolynomial_fold *
3188 isl_pw_qpolynomial_fold_free(
3189 __isl_take isl_pw_qpolynomial_fold *pwf);
3191 To iterate over the different cells of a piecewise expression,
3192 use the following functions.
3194 #include <isl/aff.h>
3195 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3196 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3197 isl_stat isl_pw_aff_foreach_piece(
3198 __isl_keep isl_pw_aff *pwaff,
3199 isl_stat (*fn)(__isl_take isl_set *set,
3200 __isl_take isl_aff *aff,
3201 void *user), void *user);
3202 int isl_pw_multi_aff_n_piece(
3203 __isl_keep isl_pw_multi_aff *pma);
3204 isl_stat isl_pw_multi_aff_foreach_piece(
3205 __isl_keep isl_pw_multi_aff *pma,
3206 isl_stat (*fn)(__isl_take isl_set *set,
3207 __isl_take isl_multi_aff *maff,
3208 void *user), void *user);
3210 #include <isl/polynomial.h>
3211 int isl_pw_qpolynomial_n_piece(
3212 __isl_keep isl_pw_qpolynomial *pwqp);
3213 isl_stat isl_pw_qpolynomial_foreach_piece(
3214 __isl_keep isl_pw_qpolynomial *pwqp,
3215 isl_stat (*fn)(__isl_take isl_set *set,
3216 __isl_take isl_qpolynomial *qp,
3217 void *user), void *user);
3218 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3219 __isl_keep isl_pw_qpolynomial *pwqp,
3220 isl_stat (*fn)(__isl_take isl_set *set,
3221 __isl_take isl_qpolynomial *qp,
3222 void *user), void *user);
3223 int isl_pw_qpolynomial_fold_n_piece(
3224 __isl_keep isl_pw_qpolynomial_fold *pwf);
3225 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3226 __isl_keep isl_pw_qpolynomial_fold *pwf,
3227 isl_stat (*fn)(__isl_take isl_set *set,
3228 __isl_take isl_qpolynomial_fold *fold,
3229 void *user), void *user);
3230 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3231 __isl_keep isl_pw_qpolynomial_fold *pwf,
3232 isl_stat (*fn)(__isl_take isl_set *set,
3233 __isl_take isl_qpolynomial_fold *fold,
3234 void *user), void *user);
3236 As usual, the function C<fn> should return C<isl_stat_ok> on success
3237 and C<isl_stat_error> on failure. The difference between
3238 C<isl_pw_qpolynomial_foreach_piece> and
3239 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3240 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3241 compute unique representations for all existentially quantified
3242 variables and then turn these existentially quantified variables
3243 into extra set variables, adapting the associated quasipolynomial
3244 accordingly. This means that the C<set> passed to C<fn>
3245 will not have any existentially quantified variables, but that
3246 the dimensions of the sets may be different for different
3247 invocations of C<fn>.
3248 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3249 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3251 A piecewise expression consisting of the expressions at a given
3252 position of a piecewise multiple expression can be extracted
3253 using the following function.
3255 #include <isl/aff.h>
3256 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3257 __isl_keep isl_pw_multi_aff *pma, int pos);
3259 These expressions can be replaced using the following function.
3261 #include <isl/aff.h>
3262 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3263 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3264 __isl_take isl_pw_aff *pa);
3266 Note that there is a difference between C<isl_multi_pw_aff> and
3267 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3268 affine expressions, while the second is a piecewise sequence
3269 of affine expressions. In particular, each of the piecewise
3270 affine expressions in an C<isl_multi_pw_aff> may have a different
3271 domain, while all multiple expressions associated to a cell
3272 in an C<isl_pw_multi_aff> have the same domain.
3273 It is possible to convert between the two, but when converting
3274 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3275 of the result is the intersection of the domains of the input.
3276 The reverse conversion is exact.
3278 #include <isl/aff.h>
3279 __isl_give isl_pw_multi_aff *
3280 isl_pw_multi_aff_from_multi_pw_aff(
3281 __isl_take isl_multi_pw_aff *mpa);
3282 __isl_give isl_multi_pw_aff *
3283 isl_multi_pw_aff_from_pw_multi_aff(
3284 __isl_take isl_pw_multi_aff *pma);
3286 =head3 Union Expressions
3288 A union expression collects base expressions defined
3289 over different domains. The space of a union expression
3290 is that of the shared parameter space.
3292 The union expression types defined by C<isl>
3293 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3294 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3296 C<isl_union_pw_aff>,
3297 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3298 there can be at most one base expression for a given domain space.
3300 C<isl_union_pw_multi_aff>,
3301 there can be multiple such expressions for a given domain space,
3302 but the domains of these expressions need to be disjoint.
3304 An empty union expression can be created using the following functions.
3306 #include <isl/aff.h>
3307 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3308 __isl_take isl_space *space);
3309 __isl_give isl_union_pw_multi_aff *
3310 isl_union_pw_multi_aff_empty(
3311 __isl_take isl_space *space);
3313 #include <isl/polynomial.h>
3314 __isl_give isl_union_pw_qpolynomial *
3315 isl_union_pw_qpolynomial_zero(
3316 __isl_take isl_space *space);
3318 A union expression containing a single base expression
3319 can be created using the following functions.
3321 #include <isl/aff.h>
3322 __isl_give isl_union_pw_aff *
3323 isl_union_pw_aff_from_pw_aff(
3324 __isl_take isl_pw_aff *pa);
3325 __isl_give isl_union_pw_multi_aff *
3326 isl_union_pw_multi_aff_from_aff(
3327 __isl_take isl_aff *aff);
3328 __isl_give isl_union_pw_multi_aff *
3329 isl_union_pw_multi_aff_from_pw_multi_aff(
3330 __isl_take isl_pw_multi_aff *pma);
3332 #include <isl/polynomial.h>
3333 __isl_give isl_union_pw_qpolynomial *
3334 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3335 __isl_take isl_pw_qpolynomial *pwqp);
3337 The following functions create a base expression on each
3338 of the sets in the union set and collect the results.
3340 #include <isl/aff.h>
3341 __isl_give isl_union_pw_multi_aff *
3342 isl_union_pw_multi_aff_from_union_pw_aff(
3343 __isl_take isl_union_pw_aff *upa);
3344 __isl_give isl_union_pw_aff *
3345 isl_union_pw_multi_aff_get_union_pw_aff(
3346 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3347 __isl_give isl_union_pw_aff *
3348 isl_union_pw_aff_val_on_domain(
3349 __isl_take isl_union_set *domain,
3350 __isl_take isl_val *v);
3351 __isl_give isl_union_pw_multi_aff *
3352 isl_union_pw_multi_aff_multi_val_on_domain(
3353 __isl_take isl_union_set *domain,
3354 __isl_take isl_multi_val *mv);
3355 __isl_give isl_union_pw_aff *
3356 isl_union_pw_aff_param_on_domain_id(
3357 __isl_take isl_union_set *domain,
3358 __isl_take isl_id *id);
3360 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3361 is the identifier of a parameter that may or may not already
3362 be present in C<domain>.
3364 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3366 expression on a given domain can be created using the following
3369 #include <isl/aff.h>
3370 __isl_give isl_union_pw_aff *
3371 isl_union_pw_aff_aff_on_domain(
3372 __isl_take isl_union_set *domain,
3373 __isl_take isl_aff *aff);
3374 __isl_give isl_union_pw_aff *
3375 isl_union_pw_aff_pw_aff_on_domain(
3376 __isl_take isl_union_set *domain,
3377 __isl_take isl_pw_aff *pa);
3379 A base expression can be added to a union expression using
3380 the following functions.
3382 #include <isl/aff.h>
3383 __isl_give isl_union_pw_aff *
3384 isl_union_pw_aff_add_pw_aff(
3385 __isl_take isl_union_pw_aff *upa,
3386 __isl_take isl_pw_aff *pa);
3387 __isl_give isl_union_pw_multi_aff *
3388 isl_union_pw_multi_aff_add_pw_multi_aff(
3389 __isl_take isl_union_pw_multi_aff *upma,
3390 __isl_take isl_pw_multi_aff *pma);
3392 #include <isl/polynomial.h>
3393 __isl_give isl_union_pw_qpolynomial *
3394 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3395 __isl_take isl_union_pw_qpolynomial *upwqp,
3396 __isl_take isl_pw_qpolynomial *pwqp);
3398 Union expressions can be copied and freed using
3399 the following functions.
3401 #include <isl/aff.h>
3402 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3403 __isl_keep isl_union_pw_aff *upa);
3404 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3405 __isl_take isl_union_pw_aff *upa);
3406 __isl_give isl_union_pw_multi_aff *
3407 isl_union_pw_multi_aff_copy(
3408 __isl_keep isl_union_pw_multi_aff *upma);
3409 __isl_null isl_union_pw_multi_aff *
3410 isl_union_pw_multi_aff_free(
3411 __isl_take isl_union_pw_multi_aff *upma);
3413 #include <isl/polynomial.h>
3414 __isl_give isl_union_pw_qpolynomial *
3415 isl_union_pw_qpolynomial_copy(
3416 __isl_keep isl_union_pw_qpolynomial *upwqp);
3417 __isl_null isl_union_pw_qpolynomial *
3418 isl_union_pw_qpolynomial_free(
3419 __isl_take isl_union_pw_qpolynomial *upwqp);
3420 __isl_give isl_union_pw_qpolynomial_fold *
3421 isl_union_pw_qpolynomial_fold_copy(
3422 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3423 __isl_null isl_union_pw_qpolynomial_fold *
3424 isl_union_pw_qpolynomial_fold_free(
3425 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3427 To iterate over the base expressions in a union expression,
3428 use the following functions.
3430 #include <isl/aff.h>
3431 int isl_union_pw_aff_n_pw_aff(
3432 __isl_keep isl_union_pw_aff *upa);
3433 isl_stat isl_union_pw_aff_foreach_pw_aff(
3434 __isl_keep isl_union_pw_aff *upa,
3435 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3436 void *user), void *user);
3437 int isl_union_pw_multi_aff_n_pw_multi_aff(
3438 __isl_keep isl_union_pw_multi_aff *upma);
3439 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3440 __isl_keep isl_union_pw_multi_aff *upma,
3441 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3442 void *user), void *user);
3444 #include <isl/polynomial.h>
3445 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3446 __isl_keep isl_union_pw_qpolynomial *upwqp);
3447 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3448 __isl_keep isl_union_pw_qpolynomial *upwqp,
3449 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3450 void *user), void *user);
3451 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3452 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3453 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3454 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3455 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3456 void *user), void *user);
3458 To extract the base expression in a given space from a union, use
3459 the following functions.
3461 #include <isl/aff.h>
3462 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3463 __isl_keep isl_union_pw_aff *upa,
3464 __isl_take isl_space *space);
3465 __isl_give isl_pw_multi_aff *
3466 isl_union_pw_multi_aff_extract_pw_multi_aff(
3467 __isl_keep isl_union_pw_multi_aff *upma,
3468 __isl_take isl_space *space);
3470 #include <isl/polynomial.h>
3471 __isl_give isl_pw_qpolynomial *
3472 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3473 __isl_keep isl_union_pw_qpolynomial *upwqp,
3474 __isl_take isl_space *space);
3476 It is also possible to obtain a list of the base expressions using
3477 the following functions.
3479 #include <isl/aff.h>
3480 __isl_give isl_pw_aff_list *
3481 isl_union_pw_aff_get_pw_aff_list(
3482 __isl_keep isl_union_pw_aff *upa);
3483 __isl_give isl_pw_multi_aff_list *
3484 isl_union_pw_multi_aff_get_pw_multi_aff_list(
3485 __isl_keep isl_union_pw_multi_aff *upma);
3487 #include <isl/polynomial.h>
3488 __isl_give isl_pw_qpolynomial_list *
3489 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
3490 __isl_keep isl_union_pw_qpolynomial *upwqp);
3491 __isl_give isl_pw_qpolynomial_fold_list *
3492 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
3493 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3495 The returned list can be manipulated using the functions in L<"Lists">.
3497 =head2 Input and Output
3499 For set and relation,
3500 C<isl> supports its own input/output format, which is similar
3501 to the C<Omega> format, but also supports the C<PolyLib> format
3503 For other object types, typically only an C<isl> format is supported.
3505 =head3 C<isl> format
3507 The C<isl> format is similar to that of C<Omega>, but has a different
3508 syntax for describing the parameters and allows for the definition
3509 of an existentially quantified variable as the integer division
3510 of an affine expression.
3511 For example, the set of integers C<i> between C<0> and C<n>
3512 such that C<i % 10 <= 6> can be described as
3514 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3517 A set or relation can have several disjuncts, separated
3518 by the keyword C<or>. Each disjunct is either a conjunction
3519 of constraints or a projection (C<exists>) of a conjunction
3520 of constraints. The constraints are separated by the keyword
3523 =head3 C<PolyLib> format
3525 If the represented set is a union, then the first line
3526 contains a single number representing the number of disjuncts.
3527 Otherwise, a line containing the number C<1> is optional.
3529 Each disjunct is represented by a matrix of constraints.
3530 The first line contains two numbers representing
3531 the number of rows and columns,
3532 where the number of rows is equal to the number of constraints
3533 and the number of columns is equal to two plus the number of variables.
3534 The following lines contain the actual rows of the constraint matrix.
3535 In each row, the first column indicates whether the constraint
3536 is an equality (C<0>) or inequality (C<1>). The final column
3537 corresponds to the constant term.
3539 If the set is parametric, then the coefficients of the parameters
3540 appear in the last columns before the constant column.
3541 The coefficients of any existentially quantified variables appear
3542 between those of the set variables and those of the parameters.
3544 =head3 Extended C<PolyLib> format
3546 The extended C<PolyLib> format is nearly identical to the
3547 C<PolyLib> format. The only difference is that the line
3548 containing the number of rows and columns of a constraint matrix
3549 also contains four additional numbers:
3550 the number of output dimensions, the number of input dimensions,
3551 the number of local dimensions (i.e., the number of existentially
3552 quantified variables) and the number of parameters.
3553 For sets, the number of ``output'' dimensions is equal
3554 to the number of set dimensions, while the number of ``input''
3559 Objects can be read from input using the following functions.
3561 #include <isl/val.h>
3562 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3564 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3565 isl_ctx *ctx, const char *str);
3567 #include <isl/set.h>
3568 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3569 isl_ctx *ctx, FILE *input);
3570 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3571 isl_ctx *ctx, const char *str);
3572 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3574 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3577 #include <isl/map.h>
3578 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3579 isl_ctx *ctx, FILE *input);
3580 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3581 isl_ctx *ctx, const char *str);
3582 __isl_give isl_map *isl_map_read_from_file(
3583 isl_ctx *ctx, FILE *input);
3584 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3587 #include <isl/union_set.h>
3588 __isl_give isl_union_set *isl_union_set_read_from_file(
3589 isl_ctx *ctx, FILE *input);
3590 __isl_give isl_union_set *isl_union_set_read_from_str(
3591 isl_ctx *ctx, const char *str);
3593 #include <isl/union_map.h>
3594 __isl_give isl_union_map *isl_union_map_read_from_file(
3595 isl_ctx *ctx, FILE *input);
3596 __isl_give isl_union_map *isl_union_map_read_from_str(
3597 isl_ctx *ctx, const char *str);
3599 #include <isl/aff.h>
3600 __isl_give isl_aff *isl_aff_read_from_str(
3601 isl_ctx *ctx, const char *str);
3602 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3603 isl_ctx *ctx, const char *str);
3604 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3605 isl_ctx *ctx, const char *str);
3606 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3607 isl_ctx *ctx, const char *str);
3608 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3609 isl_ctx *ctx, const char *str);
3610 __isl_give isl_union_pw_aff *
3611 isl_union_pw_aff_read_from_str(
3612 isl_ctx *ctx, const char *str);
3613 __isl_give isl_union_pw_multi_aff *
3614 isl_union_pw_multi_aff_read_from_str(
3615 isl_ctx *ctx, const char *str);
3616 __isl_give isl_multi_union_pw_aff *
3617 isl_multi_union_pw_aff_read_from_str(
3618 isl_ctx *ctx, const char *str);
3620 #include <isl/polynomial.h>
3621 __isl_give isl_union_pw_qpolynomial *
3622 isl_union_pw_qpolynomial_read_from_str(
3623 isl_ctx *ctx, const char *str);
3625 For sets and relations,
3626 the input format is autodetected and may be either the C<PolyLib> format
3627 or the C<isl> format.
3631 Before anything can be printed, an C<isl_printer> needs to
3634 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3636 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3637 __isl_null isl_printer *isl_printer_free(
3638 __isl_take isl_printer *printer);
3640 C<isl_printer_to_file> prints to the given file, while
3641 C<isl_printer_to_str> prints to a string that can be extracted
3642 using the following function.
3644 #include <isl/printer.h>
3645 __isl_give char *isl_printer_get_str(
3646 __isl_keep isl_printer *printer);
3648 The printer can be inspected using the following functions.
3650 FILE *isl_printer_get_file(
3651 __isl_keep isl_printer *printer);
3652 int isl_printer_get_output_format(
3653 __isl_keep isl_printer *p);
3654 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3656 The behavior of the printer can be modified in various ways
3658 __isl_give isl_printer *isl_printer_set_output_format(
3659 __isl_take isl_printer *p, int output_format);
3660 __isl_give isl_printer *isl_printer_set_indent(
3661 __isl_take isl_printer *p, int indent);
3662 __isl_give isl_printer *isl_printer_set_indent_prefix(
3663 __isl_take isl_printer *p, const char *prefix);
3664 __isl_give isl_printer *isl_printer_indent(
3665 __isl_take isl_printer *p, int indent);
3666 __isl_give isl_printer *isl_printer_set_prefix(
3667 __isl_take isl_printer *p, const char *prefix);
3668 __isl_give isl_printer *isl_printer_set_suffix(
3669 __isl_take isl_printer *p, const char *suffix);
3670 __isl_give isl_printer *isl_printer_set_yaml_style(
3671 __isl_take isl_printer *p, int yaml_style);
3673 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3674 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3675 and defaults to C<ISL_FORMAT_ISL>.
3676 Each line in the output is prefixed by C<indent_prefix>,
3677 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3678 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3679 In the C<PolyLib> format output,
3680 the coefficients of the existentially quantified variables
3681 appear between those of the set variables and those
3683 The function C<isl_printer_indent> increases the indentation
3684 by the specified amount (which may be negative).
3685 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3686 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3689 To actually print something, use
3691 #include <isl/printer.h>
3692 __isl_give isl_printer *isl_printer_print_double(
3693 __isl_take isl_printer *p, double d);
3695 #include <isl/val.h>
3696 __isl_give isl_printer *isl_printer_print_val(
3697 __isl_take isl_printer *p, __isl_keep isl_val *v);
3699 #include <isl/set.h>
3700 __isl_give isl_printer *isl_printer_print_basic_set(
3701 __isl_take isl_printer *printer,
3702 __isl_keep isl_basic_set *bset);
3703 __isl_give isl_printer *isl_printer_print_set(
3704 __isl_take isl_printer *printer,
3705 __isl_keep isl_set *set);
3707 #include <isl/map.h>
3708 __isl_give isl_printer *isl_printer_print_basic_map(
3709 __isl_take isl_printer *printer,
3710 __isl_keep isl_basic_map *bmap);
3711 __isl_give isl_printer *isl_printer_print_map(
3712 __isl_take isl_printer *printer,
3713 __isl_keep isl_map *map);
3715 #include <isl/union_set.h>
3716 __isl_give isl_printer *isl_printer_print_union_set(
3717 __isl_take isl_printer *p,
3718 __isl_keep isl_union_set *uset);
3720 #include <isl/union_map.h>
3721 __isl_give isl_printer *isl_printer_print_union_map(
3722 __isl_take isl_printer *p,
3723 __isl_keep isl_union_map *umap);
3725 #include <isl/val.h>
3726 __isl_give isl_printer *isl_printer_print_multi_val(
3727 __isl_take isl_printer *p,
3728 __isl_keep isl_multi_val *mv);
3730 #include <isl/aff.h>
3731 __isl_give isl_printer *isl_printer_print_aff(
3732 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3733 __isl_give isl_printer *isl_printer_print_multi_aff(
3734 __isl_take isl_printer *p,
3735 __isl_keep isl_multi_aff *maff);
3736 __isl_give isl_printer *isl_printer_print_pw_aff(
3737 __isl_take isl_printer *p,
3738 __isl_keep isl_pw_aff *pwaff);
3739 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3740 __isl_take isl_printer *p,
3741 __isl_keep isl_pw_multi_aff *pma);
3742 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3743 __isl_take isl_printer *p,
3744 __isl_keep isl_multi_pw_aff *mpa);
3745 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3746 __isl_take isl_printer *p,
3747 __isl_keep isl_union_pw_aff *upa);
3748 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3749 __isl_take isl_printer *p,
3750 __isl_keep isl_union_pw_multi_aff *upma);
3751 __isl_give isl_printer *
3752 isl_printer_print_multi_union_pw_aff(
3753 __isl_take isl_printer *p,
3754 __isl_keep isl_multi_union_pw_aff *mupa);
3756 #include <isl/polynomial.h>
3757 __isl_give isl_printer *isl_printer_print_qpolynomial(
3758 __isl_take isl_printer *p,
3759 __isl_keep isl_qpolynomial *qp);
3760 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3761 __isl_take isl_printer *p,
3762 __isl_keep isl_pw_qpolynomial *pwqp);
3763 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3764 __isl_take isl_printer *p,
3765 __isl_keep isl_union_pw_qpolynomial *upwqp);
3767 __isl_give isl_printer *
3768 isl_printer_print_pw_qpolynomial_fold(
3769 __isl_take isl_printer *p,
3770 __isl_keep isl_pw_qpolynomial_fold *pwf);
3771 __isl_give isl_printer *
3772 isl_printer_print_union_pw_qpolynomial_fold(
3773 __isl_take isl_printer *p,
3774 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3776 For C<isl_printer_print_qpolynomial>,
3777 C<isl_printer_print_pw_qpolynomial> and
3778 C<isl_printer_print_pw_qpolynomial_fold>,
3779 the output format of the printer
3780 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3781 For C<isl_printer_print_union_pw_qpolynomial> and
3782 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3784 In case of printing in C<ISL_FORMAT_C>, the user may want
3785 to set the names of all dimensions first.
3787 C<isl> also provides limited support for printing YAML documents,
3788 just enough for the internal use for printing such documents.
3790 #include <isl/printer.h>
3791 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3792 __isl_take isl_printer *p);
3793 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3794 __isl_take isl_printer *p);
3795 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3796 __isl_take isl_printer *p);
3797 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3798 __isl_take isl_printer *p);
3799 __isl_give isl_printer *isl_printer_yaml_next(
3800 __isl_take isl_printer *p);
3802 A document is started by a call to either
3803 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3804 Anything printed to the printer after such a call belong to the
3805 first key of the mapping or the first element in the sequence.
3806 The function C<isl_printer_yaml_next> moves to the value if
3807 we are currently printing a mapping key, the next key if we
3808 are printing a value or the next element if we are printing
3809 an element in a sequence.
3810 Nested mappings and sequences are initiated by the same
3811 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3812 Each call to these functions needs to have a corresponding call to
3813 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3815 When called on a file printer, the following function flushes
3816 the file. When called on a string printer, the buffer is cleared.
3818 __isl_give isl_printer *isl_printer_flush(
3819 __isl_take isl_printer *p);
3821 The following functions allow the user to attach
3822 notes to a printer in order to keep track of additional state.
3824 #include <isl/printer.h>
3825 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3826 __isl_keep isl_id *id);
3827 __isl_give isl_id *isl_printer_get_note(
3828 __isl_keep isl_printer *p, __isl_take isl_id *id);
3829 __isl_give isl_printer *isl_printer_set_note(
3830 __isl_take isl_printer *p,
3831 __isl_take isl_id *id, __isl_take isl_id *note);
3833 C<isl_printer_set_note> associates the given note to the given
3834 identifier in the printer.
3835 C<isl_printer_get_note> retrieves a note associated to an
3837 C<isl_printer_has_note> checks if there is such a note.
3838 C<isl_printer_get_note> fails if the requested note does not exist.
3840 Alternatively, a string representation can be obtained
3841 directly using the following functions, which always print
3845 __isl_give char *isl_id_to_str(
3846 __isl_keep isl_id *id);
3848 #include <isl/space.h>
3849 __isl_give char *isl_space_to_str(
3850 __isl_keep isl_space *space);
3852 #include <isl/val.h>
3853 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3854 __isl_give char *isl_multi_val_to_str(
3855 __isl_keep isl_multi_val *mv);
3857 #include <isl/set.h>
3858 __isl_give char *isl_basic_set_to_str(
3859 __isl_keep isl_basic_set *bset);
3860 __isl_give char *isl_set_to_str(
3861 __isl_keep isl_set *set);
3863 #include <isl/union_set.h>
3864 __isl_give char *isl_union_set_to_str(
3865 __isl_keep isl_union_set *uset);
3867 #include <isl/map.h>
3868 __isl_give char *isl_basic_map_to_str(
3869 __isl_keep isl_basic_map *bmap);
3870 __isl_give char *isl_map_to_str(
3871 __isl_keep isl_map *map);
3873 #include <isl/union_map.h>
3874 __isl_give char *isl_union_map_to_str(
3875 __isl_keep isl_union_map *umap);
3877 #include <isl/aff.h>
3878 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3879 __isl_give char *isl_pw_aff_to_str(
3880 __isl_keep isl_pw_aff *pa);
3881 __isl_give char *isl_multi_aff_to_str(
3882 __isl_keep isl_multi_aff *ma);
3883 __isl_give char *isl_pw_multi_aff_to_str(
3884 __isl_keep isl_pw_multi_aff *pma);
3885 __isl_give char *isl_multi_pw_aff_to_str(
3886 __isl_keep isl_multi_pw_aff *mpa);
3887 __isl_give char *isl_union_pw_aff_to_str(
3888 __isl_keep isl_union_pw_aff *upa);
3889 __isl_give char *isl_union_pw_multi_aff_to_str(
3890 __isl_keep isl_union_pw_multi_aff *upma);
3891 __isl_give char *isl_multi_union_pw_aff_to_str(
3892 __isl_keep isl_multi_union_pw_aff *mupa);
3894 #include <isl/point.h>
3895 __isl_give char *isl_point_to_str(
3896 __isl_keep isl_point *pnt);
3898 #include <isl/polynomial.h>
3899 __isl_give char *isl_pw_qpolynomial_to_str(
3900 __isl_keep isl_pw_qpolynomial *pwqp);
3901 __isl_give char *isl_union_pw_qpolynomial_to_str(
3902 __isl_keep isl_union_pw_qpolynomial *upwqp);
3906 =head3 Unary Properties
3912 The following functions test whether the given set or relation
3913 contains any integer points. The ``plain'' variants do not perform
3914 any computations, but simply check if the given set or relation
3915 is already known to be empty.
3917 #include <isl/set.h>
3918 isl_bool isl_basic_set_plain_is_empty(
3919 __isl_keep isl_basic_set *bset);
3920 isl_bool isl_basic_set_is_empty(
3921 __isl_keep isl_basic_set *bset);
3922 isl_bool isl_set_plain_is_empty(
3923 __isl_keep isl_set *set);
3924 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3926 #include <isl/union_set.h>
3927 isl_bool isl_union_set_is_empty(
3928 __isl_keep isl_union_set *uset);
3930 #include <isl/map.h>
3931 isl_bool isl_basic_map_plain_is_empty(
3932 __isl_keep isl_basic_map *bmap);
3933 isl_bool isl_basic_map_is_empty(
3934 __isl_keep isl_basic_map *bmap);
3935 isl_bool isl_map_plain_is_empty(
3936 __isl_keep isl_map *map);
3937 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3939 #include <isl/union_map.h>
3940 isl_bool isl_union_map_plain_is_empty(
3941 __isl_keep isl_union_map *umap);
3942 isl_bool isl_union_map_is_empty(
3943 __isl_keep isl_union_map *umap);
3945 =item * Universality
3947 isl_bool isl_basic_set_plain_is_universe(
3948 __isl_keep isl_basic_set *bset);
3949 isl_bool isl_basic_set_is_universe(
3950 __isl_keep isl_basic_set *bset);
3951 isl_bool isl_basic_map_plain_is_universe(
3952 __isl_keep isl_basic_map *bmap);
3953 isl_bool isl_basic_map_is_universe(
3954 __isl_keep isl_basic_map *bmap);
3955 isl_bool isl_set_plain_is_universe(
3956 __isl_keep isl_set *set);
3957 isl_bool isl_map_plain_is_universe(
3958 __isl_keep isl_map *map);
3960 =item * Single-valuedness
3962 #include <isl/set.h>
3963 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3965 #include <isl/map.h>
3966 isl_bool isl_basic_map_is_single_valued(
3967 __isl_keep isl_basic_map *bmap);
3968 isl_bool isl_map_plain_is_single_valued(
3969 __isl_keep isl_map *map);
3970 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3972 #include <isl/union_map.h>
3973 isl_bool isl_union_map_is_single_valued(
3974 __isl_keep isl_union_map *umap);
3978 isl_bool isl_map_plain_is_injective(
3979 __isl_keep isl_map *map);
3980 isl_bool isl_map_is_injective(
3981 __isl_keep isl_map *map);
3982 isl_bool isl_union_map_plain_is_injective(
3983 __isl_keep isl_union_map *umap);
3984 isl_bool isl_union_map_is_injective(
3985 __isl_keep isl_union_map *umap);
3989 isl_bool isl_map_is_bijective(
3990 __isl_keep isl_map *map);
3991 isl_bool isl_union_map_is_bijective(
3992 __isl_keep isl_union_map *umap);
3996 The following functions test whether the given relation
3997 only maps elements to themselves.
3999 #include <isl/map.h>
4000 isl_bool isl_map_is_identity(
4001 __isl_keep isl_map *map);
4003 #include <isl/union_map.h>
4004 isl_bool isl_union_map_is_identity(
4005 __isl_keep isl_union_map *umap);
4009 __isl_give isl_val *
4010 isl_basic_map_plain_get_val_if_fixed(
4011 __isl_keep isl_basic_map *bmap,
4012 enum isl_dim_type type, unsigned pos);
4013 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4014 __isl_keep isl_set *set,
4015 enum isl_dim_type type, unsigned pos);
4016 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4017 __isl_keep isl_map *map,
4018 enum isl_dim_type type, unsigned pos);
4020 If the set or relation obviously lies on a hyperplane where the given dimension
4021 has a fixed value, then return that value.
4022 Otherwise return NaN.
4026 isl_stat isl_set_dim_residue_class_val(
4027 __isl_keep isl_set *set,
4028 int pos, __isl_give isl_val **modulo,
4029 __isl_give isl_val **residue);
4031 Check if the values of the given set dimension are equal to a fixed
4032 value modulo some integer value. If so, assign the modulo to C<*modulo>
4033 and the fixed value to C<*residue>. If the given dimension attains only
4034 a single value, then assign C<0> to C<*modulo> and the fixed value to
4036 If the dimension does not attain only a single value and if no modulo
4037 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4039 #include <isl/set.h>
4040 __isl_give isl_stride_info *isl_set_get_stride_info(
4041 __isl_keep isl_set *set, int pos);
4042 __isl_give isl_val *isl_set_get_stride(
4043 __isl_keep isl_set *set, int pos);
4045 #include <isl/map.h>
4046 __isl_give isl_stride_info *
4047 isl_map_get_range_stride_info(
4048 __isl_keep isl_map *map, int pos);
4050 Check if the values of the given set dimension are equal to
4051 some affine expression of the other dimensions (the offset)
4052 modulo some integer stride or
4053 check if the values of the given output dimensions are equal to
4054 some affine expression of the input dimensions (the offset)
4055 modulo some integer stride.
4056 If no more specific information can be found, then the stride
4057 is taken to be one and the offset is taken to be the zero expression.
4058 The function C<isl_set_get_stride> performs the same
4059 computation as C<isl_set_get_stride_info> but only returns the stride.
4060 For the other functions,
4061 the stride and offset can be extracted from the returned object
4062 using the following functions.
4064 #include <isl/stride_info.h>
4065 __isl_give isl_val *isl_stride_info_get_stride(
4066 __isl_keep isl_stride_info *si);
4067 __isl_give isl_aff *isl_stride_info_get_offset(
4068 __isl_keep isl_stride_info *si);
4070 The stride info object can be copied and released using the following
4073 #include <isl/stride_info.h>
4074 __isl_give isl_stride_info *isl_stride_info_copy(
4075 __isl_keep isl_stride_info *si);
4076 __isl_null isl_stride_info *isl_stride_info_free(
4077 __isl_take isl_stride_info *si);
4081 To check whether the description of a set, relation or function depends
4082 on one or more given dimensions,
4083 the following functions can be used.
4085 #include <isl/constraint.h>
4086 isl_bool isl_constraint_involves_dims(
4087 __isl_keep isl_constraint *constraint,
4088 enum isl_dim_type type, unsigned first, unsigned n);
4090 #include <isl/set.h>
4091 isl_bool isl_basic_set_involves_dims(
4092 __isl_keep isl_basic_set *bset,
4093 enum isl_dim_type type, unsigned first, unsigned n);
4094 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4095 enum isl_dim_type type, unsigned first, unsigned n);
4097 #include <isl/map.h>
4098 isl_bool isl_basic_map_involves_dims(
4099 __isl_keep isl_basic_map *bmap,
4100 enum isl_dim_type type, unsigned first, unsigned n);
4101 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4102 enum isl_dim_type type, unsigned first, unsigned n);
4104 #include <isl/union_map.h>
4105 isl_bool isl_union_map_involves_dims(
4106 __isl_keep isl_union_map *umap,
4107 enum isl_dim_type type, unsigned first, unsigned n);
4109 #include <isl/aff.h>
4110 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4111 enum isl_dim_type type, unsigned first, unsigned n);
4112 isl_bool isl_pw_aff_involves_dims(
4113 __isl_keep isl_pw_aff *pwaff,
4114 enum isl_dim_type type, unsigned first, unsigned n);
4115 isl_bool isl_multi_aff_involves_dims(
4116 __isl_keep isl_multi_aff *ma,
4117 enum isl_dim_type type, unsigned first, unsigned n);
4118 isl_bool isl_pw_multi_aff_involves_dims(
4119 __isl_keep isl_pw_multi_aff *pma,
4120 enum isl_dim_type type, unsigned first, unsigned n);
4121 isl_bool isl_multi_pw_aff_involves_dims(
4122 __isl_keep isl_multi_pw_aff *mpa,
4123 enum isl_dim_type type, unsigned first, unsigned n);
4125 #include <isl/polynomial.h>
4126 isl_bool isl_qpolynomial_involves_dims(
4127 __isl_keep isl_qpolynomial *qp,
4128 enum isl_dim_type type, unsigned first, unsigned n);
4130 Similarly, the following functions can be used to check whether
4131 a given dimension is involved in any lower or upper bound.
4133 #include <isl/set.h>
4134 isl_bool isl_set_dim_has_any_lower_bound(
4135 __isl_keep isl_set *set,
4136 enum isl_dim_type type, unsigned pos);
4137 isl_bool isl_set_dim_has_any_upper_bound(
4138 __isl_keep isl_set *set,
4139 enum isl_dim_type type, unsigned pos);
4141 Note that these functions return true even if there is a bound on
4142 the dimension on only some of the basic sets of C<set>.
4143 To check if they have a bound for all of the basic sets in C<set>,
4144 use the following functions instead.
4146 #include <isl/set.h>
4147 isl_bool isl_set_dim_has_lower_bound(
4148 __isl_keep isl_set *set,
4149 enum isl_dim_type type, unsigned pos);
4150 isl_bool isl_set_dim_has_upper_bound(
4151 __isl_keep isl_set *set,
4152 enum isl_dim_type type, unsigned pos);
4156 To check whether a set is a parameter domain, use this function:
4158 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4159 isl_bool isl_union_set_is_params(
4160 __isl_keep isl_union_set *uset);
4164 The following functions check whether the space of the given
4165 (basic) set or relation domain and/or range is a wrapped relation.
4167 #include <isl/space.h>
4168 isl_bool isl_space_is_wrapping(
4169 __isl_keep isl_space *space);
4170 isl_bool isl_space_domain_is_wrapping(
4171 __isl_keep isl_space *space);
4172 isl_bool isl_space_range_is_wrapping(
4173 __isl_keep isl_space *space);
4174 isl_bool isl_space_is_product(
4175 __isl_keep isl_space *space);
4177 #include <isl/set.h>
4178 isl_bool isl_basic_set_is_wrapping(
4179 __isl_keep isl_basic_set *bset);
4180 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4182 #include <isl/map.h>
4183 isl_bool isl_map_domain_is_wrapping(
4184 __isl_keep isl_map *map);
4185 isl_bool isl_map_range_is_wrapping(
4186 __isl_keep isl_map *map);
4187 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4189 #include <isl/val.h>
4190 isl_bool isl_multi_val_range_is_wrapping(
4191 __isl_keep isl_multi_val *mv);
4193 #include <isl/aff.h>
4194 isl_bool isl_multi_aff_range_is_wrapping(
4195 __isl_keep isl_multi_aff *ma);
4196 isl_bool isl_multi_pw_aff_range_is_wrapping(
4197 __isl_keep isl_multi_pw_aff *mpa);
4198 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4199 __isl_keep isl_multi_union_pw_aff *mupa);
4201 The input to C<isl_space_is_wrapping> should
4202 be the space of a set, while that of
4203 C<isl_space_domain_is_wrapping> and
4204 C<isl_space_range_is_wrapping> should be the space of a relation.
4205 The input to C<isl_space_is_product> can be either the space
4206 of a set or that of a binary relation.
4207 In case the input is the space of a binary relation, it checks
4208 whether both domain and range are wrapping.
4210 =item * Internal Product
4212 isl_bool isl_basic_map_can_zip(
4213 __isl_keep isl_basic_map *bmap);
4214 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4216 Check whether the product of domain and range of the given relation
4218 i.e., whether both domain and range are nested relations.
4222 #include <isl/space.h>
4223 isl_bool isl_space_can_curry(
4224 __isl_keep isl_space *space);
4226 #include <isl/map.h>
4227 isl_bool isl_basic_map_can_curry(
4228 __isl_keep isl_basic_map *bmap);
4229 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4231 Check whether the domain of the (basic) relation is a wrapped relation.
4233 #include <isl/space.h>
4234 __isl_give isl_space *isl_space_uncurry(
4235 __isl_take isl_space *space);
4237 #include <isl/map.h>
4238 isl_bool isl_basic_map_can_uncurry(
4239 __isl_keep isl_basic_map *bmap);
4240 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4242 Check whether the range of the (basic) relation is a wrapped relation.
4244 #include <isl/space.h>
4245 isl_bool isl_space_can_range_curry(
4246 __isl_keep isl_space *space);
4248 #include <isl/map.h>
4249 isl_bool isl_map_can_range_curry(
4250 __isl_keep isl_map *map);
4252 Check whether the domain of the relation wrapped in the range of
4253 the input is itself a wrapped relation.
4255 =item * Special Values
4257 #include <isl/aff.h>
4258 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4259 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4260 isl_bool isl_multi_pw_aff_is_cst(
4261 __isl_keep isl_multi_pw_aff *mpa);
4263 Check whether the given expression is a constant.
4265 #include <isl/val.h>
4266 isl_bool isl_multi_val_involves_nan(
4267 __isl_keep isl_multi_val *mv);
4269 #include <isl/aff.h>
4270 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4271 isl_bool isl_multi_aff_involves_nan(
4272 __isl_keep isl_multi_aff *ma);
4273 isl_bool isl_pw_aff_involves_nan(
4274 __isl_keep isl_pw_aff *pa);
4275 isl_bool isl_pw_multi_aff_involves_nan(
4276 __isl_keep isl_pw_multi_aff *pma);
4277 isl_bool isl_multi_pw_aff_involves_nan(
4278 __isl_keep isl_multi_pw_aff *mpa);
4279 isl_bool isl_union_pw_aff_involves_nan(
4280 __isl_keep isl_union_pw_aff *upa);
4281 isl_bool isl_union_pw_multi_aff_involves_nan(
4282 __isl_keep isl_union_pw_multi_aff *upma);
4283 isl_bool isl_multi_union_pw_aff_involves_nan(
4284 __isl_keep isl_multi_union_pw_aff *mupa);
4286 #include <isl/polynomial.h>
4287 isl_bool isl_qpolynomial_is_nan(
4288 __isl_keep isl_qpolynomial *qp);
4289 isl_bool isl_qpolynomial_fold_is_nan(
4290 __isl_keep isl_qpolynomial_fold *fold);
4291 isl_bool isl_pw_qpolynomial_involves_nan(
4292 __isl_keep isl_pw_qpolynomial *pwqp);
4293 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4294 __isl_keep isl_pw_qpolynomial_fold *pwf);
4295 isl_bool isl_union_pw_qpolynomial_involves_nan(
4296 __isl_keep isl_union_pw_qpolynomial *upwqp);
4297 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4298 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4300 Check whether the given expression is equal to or involves NaN.
4302 #include <isl/aff.h>
4303 isl_bool isl_aff_plain_is_zero(
4304 __isl_keep isl_aff *aff);
4306 Check whether the affine expression is obviously zero.
4310 =head3 Binary Properties
4316 The following functions check whether two objects
4317 represent the same set, relation or function.
4318 The C<plain> variants only return true if the objects
4319 are obviously the same. That is, they may return false
4320 even if the objects are the same, but they will never
4321 return true if the objects are not the same.
4323 #include <isl/set.h>
4324 isl_bool isl_basic_set_plain_is_equal(
4325 __isl_keep isl_basic_set *bset1,
4326 __isl_keep isl_basic_set *bset2);
4327 isl_bool isl_basic_set_is_equal(
4328 __isl_keep isl_basic_set *bset1,
4329 __isl_keep isl_basic_set *bset2);
4330 isl_bool isl_set_plain_is_equal(
4331 __isl_keep isl_set *set1,
4332 __isl_keep isl_set *set2);
4333 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4334 __isl_keep isl_set *set2);
4336 #include <isl/map.h>
4337 isl_bool isl_basic_map_is_equal(
4338 __isl_keep isl_basic_map *bmap1,
4339 __isl_keep isl_basic_map *bmap2);
4340 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4341 __isl_keep isl_map *map2);
4342 isl_bool isl_map_plain_is_equal(
4343 __isl_keep isl_map *map1,
4344 __isl_keep isl_map *map2);
4346 #include <isl/union_set.h>
4347 isl_bool isl_union_set_is_equal(
4348 __isl_keep isl_union_set *uset1,
4349 __isl_keep isl_union_set *uset2);
4351 #include <isl/union_map.h>
4352 isl_bool isl_union_map_is_equal(
4353 __isl_keep isl_union_map *umap1,
4354 __isl_keep isl_union_map *umap2);
4356 #include <isl/val.h>
4357 isl_bool isl_multi_val_plain_is_equal(
4358 __isl_keep isl_multi_val *mv1,
4359 __isl_keep isl_multi_val *mv2);
4361 #include <isl/aff.h>
4362 isl_bool isl_aff_plain_is_equal(
4363 __isl_keep isl_aff *aff1,
4364 __isl_keep isl_aff *aff2);
4365 isl_bool isl_multi_aff_plain_is_equal(
4366 __isl_keep isl_multi_aff *maff1,
4367 __isl_keep isl_multi_aff *maff2);
4368 isl_bool isl_pw_aff_plain_is_equal(
4369 __isl_keep isl_pw_aff *pwaff1,
4370 __isl_keep isl_pw_aff *pwaff2);
4371 isl_bool isl_pw_aff_is_equal(
4372 __isl_keep isl_pw_aff *pa1,
4373 __isl_keep isl_pw_aff *pa2);
4374 isl_bool isl_pw_multi_aff_plain_is_equal(
4375 __isl_keep isl_pw_multi_aff *pma1,
4376 __isl_keep isl_pw_multi_aff *pma2);
4377 isl_bool isl_pw_multi_aff_is_equal(
4378 __isl_keep isl_pw_multi_aff *pma1,
4379 __isl_keep isl_pw_multi_aff *pma2);
4380 isl_bool isl_multi_pw_aff_plain_is_equal(
4381 __isl_keep isl_multi_pw_aff *mpa1,
4382 __isl_keep isl_multi_pw_aff *mpa2);
4383 isl_bool isl_multi_pw_aff_is_equal(
4384 __isl_keep isl_multi_pw_aff *mpa1,
4385 __isl_keep isl_multi_pw_aff *mpa2);
4386 isl_bool isl_union_pw_aff_plain_is_equal(
4387 __isl_keep isl_union_pw_aff *upa1,
4388 __isl_keep isl_union_pw_aff *upa2);
4389 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4390 __isl_keep isl_union_pw_multi_aff *upma1,
4391 __isl_keep isl_union_pw_multi_aff *upma2);
4392 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4393 __isl_keep isl_multi_union_pw_aff *mupa1,
4394 __isl_keep isl_multi_union_pw_aff *mupa2);
4396 #include <isl/polynomial.h>
4397 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4398 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4399 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4400 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4401 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4402 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4404 =item * Disjointness
4406 #include <isl/set.h>
4407 isl_bool isl_basic_set_is_disjoint(
4408 __isl_keep isl_basic_set *bset1,
4409 __isl_keep isl_basic_set *bset2);
4410 isl_bool isl_set_plain_is_disjoint(
4411 __isl_keep isl_set *set1,
4412 __isl_keep isl_set *set2);
4413 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4414 __isl_keep isl_set *set2);
4416 #include <isl/map.h>
4417 isl_bool isl_basic_map_is_disjoint(
4418 __isl_keep isl_basic_map *bmap1,
4419 __isl_keep isl_basic_map *bmap2);
4420 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4421 __isl_keep isl_map *map2);
4423 #include <isl/union_set.h>
4424 isl_bool isl_union_set_is_disjoint(
4425 __isl_keep isl_union_set *uset1,
4426 __isl_keep isl_union_set *uset2);
4428 #include <isl/union_map.h>
4429 isl_bool isl_union_map_is_disjoint(
4430 __isl_keep isl_union_map *umap1,
4431 __isl_keep isl_union_map *umap2);
4435 isl_bool isl_basic_set_is_subset(
4436 __isl_keep isl_basic_set *bset1,
4437 __isl_keep isl_basic_set *bset2);
4438 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4439 __isl_keep isl_set *set2);
4440 isl_bool isl_set_is_strict_subset(
4441 __isl_keep isl_set *set1,
4442 __isl_keep isl_set *set2);
4443 isl_bool isl_union_set_is_subset(
4444 __isl_keep isl_union_set *uset1,
4445 __isl_keep isl_union_set *uset2);
4446 isl_bool isl_union_set_is_strict_subset(
4447 __isl_keep isl_union_set *uset1,
4448 __isl_keep isl_union_set *uset2);
4449 isl_bool isl_basic_map_is_subset(
4450 __isl_keep isl_basic_map *bmap1,
4451 __isl_keep isl_basic_map *bmap2);
4452 isl_bool isl_basic_map_is_strict_subset(
4453 __isl_keep isl_basic_map *bmap1,
4454 __isl_keep isl_basic_map *bmap2);
4455 isl_bool isl_map_is_subset(
4456 __isl_keep isl_map *map1,
4457 __isl_keep isl_map *map2);
4458 isl_bool isl_map_is_strict_subset(
4459 __isl_keep isl_map *map1,
4460 __isl_keep isl_map *map2);
4461 isl_bool isl_union_map_is_subset(
4462 __isl_keep isl_union_map *umap1,
4463 __isl_keep isl_union_map *umap2);
4464 isl_bool isl_union_map_is_strict_subset(
4465 __isl_keep isl_union_map *umap1,
4466 __isl_keep isl_union_map *umap2);
4468 Check whether the first argument is a (strict) subset of the
4473 Every comparison function returns a negative value if the first
4474 argument is considered smaller than the second, a positive value
4475 if the first argument is considered greater and zero if the two
4476 constraints are considered the same by the comparison criterion.
4478 #include <isl/constraint.h>
4479 int isl_constraint_plain_cmp(
4480 __isl_keep isl_constraint *c1,
4481 __isl_keep isl_constraint *c2);
4483 This function is useful for sorting C<isl_constraint>s.
4484 The order depends on the internal representation of the inputs.
4485 The order is fixed over different calls to the function (assuming
4486 the internal representation of the inputs has not changed), but may
4487 change over different versions of C<isl>.
4489 #include <isl/constraint.h>
4490 int isl_constraint_cmp_last_non_zero(
4491 __isl_keep isl_constraint *c1,
4492 __isl_keep isl_constraint *c2);
4494 This function can be used to sort constraints that live in the same
4495 local space. Constraints that involve ``earlier'' dimensions or
4496 that have a smaller coefficient for the shared latest dimension
4497 are considered smaller than other constraints.
4498 This function only defines a B<partial> order.
4500 #include <isl/set.h>
4501 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4502 __isl_keep isl_set *set2);
4504 This function is useful for sorting C<isl_set>s.
4505 The order depends on the internal representation of the inputs.
4506 The order is fixed over different calls to the function (assuming
4507 the internal representation of the inputs has not changed), but may
4508 change over different versions of C<isl>.
4510 #include <isl/aff.h>
4511 int isl_multi_aff_plain_cmp(
4512 __isl_keep isl_multi_aff *ma1,
4513 __isl_keep isl_multi_aff *ma2);
4514 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4515 __isl_keep isl_pw_aff *pa2);
4517 The functions C<isl_multi_aff_plain_cmp> and
4518 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4519 C<isl_pw_aff>s. The order is not strictly defined.
4520 The current order sorts expressions that only involve
4521 earlier dimensions before those that involve later dimensions.
4525 =head2 Unary Operations
4531 __isl_give isl_set *isl_set_complement(
4532 __isl_take isl_set *set);
4533 __isl_give isl_map *isl_map_complement(
4534 __isl_take isl_map *map);
4538 #include <isl/space.h>
4539 __isl_give isl_space *isl_space_reverse(
4540 __isl_take isl_space *space);
4542 #include <isl/map.h>
4543 __isl_give isl_basic_map *isl_basic_map_reverse(
4544 __isl_take isl_basic_map *bmap);
4545 __isl_give isl_map *isl_map_reverse(
4546 __isl_take isl_map *map);
4548 #include <isl/union_map.h>
4549 __isl_give isl_union_map *isl_union_map_reverse(
4550 __isl_take isl_union_map *umap);
4554 #include <isl/space.h>
4555 __isl_give isl_space *isl_space_domain(
4556 __isl_take isl_space *space);
4557 __isl_give isl_space *isl_space_range(
4558 __isl_take isl_space *space);
4559 __isl_give isl_space *isl_space_params(
4560 __isl_take isl_space *space);
4562 #include <isl/local_space.h>
4563 __isl_give isl_local_space *isl_local_space_domain(
4564 __isl_take isl_local_space *ls);
4565 __isl_give isl_local_space *isl_local_space_range(
4566 __isl_take isl_local_space *ls);
4568 #include <isl/set.h>
4569 __isl_give isl_basic_set *isl_basic_set_project_out(
4570 __isl_take isl_basic_set *bset,
4571 enum isl_dim_type type, unsigned first, unsigned n);
4572 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4573 enum isl_dim_type type, unsigned first, unsigned n);
4574 __isl_give isl_map *isl_set_project_onto_map(
4575 __isl_take isl_set *set,
4576 enum isl_dim_type type, unsigned first,
4578 __isl_give isl_basic_set *isl_basic_set_params(
4579 __isl_take isl_basic_set *bset);
4580 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4582 The function C<isl_set_project_onto_map> returns a relation
4583 that projects the input set onto the given set dimensions.
4585 #include <isl/map.h>
4586 __isl_give isl_basic_map *isl_basic_map_project_out(
4587 __isl_take isl_basic_map *bmap,
4588 enum isl_dim_type type, unsigned first, unsigned n);
4589 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4590 enum isl_dim_type type, unsigned first, unsigned n);
4591 __isl_give isl_basic_set *isl_basic_map_domain(
4592 __isl_take isl_basic_map *bmap);
4593 __isl_give isl_basic_set *isl_basic_map_range(
4594 __isl_take isl_basic_map *bmap);
4595 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4596 __isl_give isl_set *isl_map_domain(
4597 __isl_take isl_map *bmap);
4598 __isl_give isl_set *isl_map_range(
4599 __isl_take isl_map *map);
4601 #include <isl/union_set.h>
4602 __isl_give isl_union_set *isl_union_set_project_out(
4603 __isl_take isl_union_set *uset,
4604 enum isl_dim_type type,
4605 unsigned first, unsigned n);
4606 __isl_give isl_set *isl_union_set_params(
4607 __isl_take isl_union_set *uset);
4609 The function C<isl_union_set_project_out> can only project out
4612 #include <isl/union_map.h>
4613 __isl_give isl_union_map *isl_union_map_project_out(
4614 __isl_take isl_union_map *umap,
4615 enum isl_dim_type type, unsigned first, unsigned n);
4616 __isl_give isl_union_map *
4617 isl_union_map_project_out_all_params(
4618 __isl_take isl_union_map *umap);
4619 __isl_give isl_set *isl_union_map_params(
4620 __isl_take isl_union_map *umap);
4621 __isl_give isl_union_set *isl_union_map_domain(
4622 __isl_take isl_union_map *umap);
4623 __isl_give isl_union_set *isl_union_map_range(
4624 __isl_take isl_union_map *umap);
4626 The function C<isl_union_map_project_out> can only project out
4629 #include <isl/aff.h>
4630 __isl_give isl_aff *isl_aff_project_domain_on_params(
4631 __isl_take isl_aff *aff);
4632 __isl_give isl_multi_aff *
4633 isl_multi_aff_project_domain_on_params(
4634 __isl_take isl_multi_aff *ma);
4635 __isl_give isl_pw_aff *
4636 isl_pw_aff_project_domain_on_params(
4637 __isl_take isl_pw_aff *pa);
4638 __isl_give isl_multi_pw_aff *
4639 isl_multi_pw_aff_project_domain_on_params(
4640 __isl_take isl_multi_pw_aff *mpa);
4641 __isl_give isl_pw_multi_aff *
4642 isl_pw_multi_aff_project_domain_on_params(
4643 __isl_take isl_pw_multi_aff *pma);
4644 __isl_give isl_set *isl_pw_aff_domain(
4645 __isl_take isl_pw_aff *pwaff);
4646 __isl_give isl_set *isl_pw_multi_aff_domain(
4647 __isl_take isl_pw_multi_aff *pma);
4648 __isl_give isl_set *isl_multi_pw_aff_domain(
4649 __isl_take isl_multi_pw_aff *mpa);
4650 __isl_give isl_union_set *isl_union_pw_aff_domain(
4651 __isl_take isl_union_pw_aff *upa);
4652 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4653 __isl_take isl_union_pw_multi_aff *upma);
4654 __isl_give isl_union_set *
4655 isl_multi_union_pw_aff_domain(
4656 __isl_take isl_multi_union_pw_aff *mupa);
4657 __isl_give isl_set *isl_pw_aff_params(
4658 __isl_take isl_pw_aff *pwa);
4660 If no explicit domain was set on a zero-dimensional input to
4661 C<isl_multi_union_pw_aff_domain>, then this function will
4662 return a parameter set.
4664 #include <isl/polynomial.h>
4665 __isl_give isl_qpolynomial *
4666 isl_qpolynomial_project_domain_on_params(
4667 __isl_take isl_qpolynomial *qp);
4668 __isl_give isl_pw_qpolynomial *
4669 isl_pw_qpolynomial_project_domain_on_params(
4670 __isl_take isl_pw_qpolynomial *pwqp);
4671 __isl_give isl_pw_qpolynomial_fold *
4672 isl_pw_qpolynomial_fold_project_domain_on_params(
4673 __isl_take isl_pw_qpolynomial_fold *pwf);
4674 __isl_give isl_set *isl_pw_qpolynomial_domain(
4675 __isl_take isl_pw_qpolynomial *pwqp);
4676 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4677 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4678 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4679 __isl_take isl_union_pw_qpolynomial *upwqp);
4681 #include <isl/space.h>
4682 __isl_give isl_space *isl_space_domain_map(
4683 __isl_take isl_space *space);
4684 __isl_give isl_space *isl_space_range_map(
4685 __isl_take isl_space *space);
4687 #include <isl/map.h>
4688 __isl_give isl_map *isl_set_wrapped_domain_map(
4689 __isl_take isl_set *set);
4690 __isl_give isl_basic_map *isl_basic_map_domain_map(
4691 __isl_take isl_basic_map *bmap);
4692 __isl_give isl_basic_map *isl_basic_map_range_map(
4693 __isl_take isl_basic_map *bmap);
4694 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4695 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4697 #include <isl/union_map.h>
4698 __isl_give isl_union_map *isl_union_map_domain_map(
4699 __isl_take isl_union_map *umap);
4700 __isl_give isl_union_pw_multi_aff *
4701 isl_union_map_domain_map_union_pw_multi_aff(
4702 __isl_take isl_union_map *umap);
4703 __isl_give isl_union_map *isl_union_map_range_map(
4704 __isl_take isl_union_map *umap);
4705 __isl_give isl_union_map *
4706 isl_union_set_wrapped_domain_map(
4707 __isl_take isl_union_set *uset);
4709 The functions above construct a (basic, regular or union) relation
4710 that maps (a wrapped version of) the input relation to its domain or range.
4711 C<isl_set_wrapped_domain_map> maps the input set to the domain
4712 of its wrapped relation.
4716 __isl_give isl_basic_set *isl_basic_set_eliminate(
4717 __isl_take isl_basic_set *bset,
4718 enum isl_dim_type type,
4719 unsigned first, unsigned n);
4720 __isl_give isl_set *isl_set_eliminate(
4721 __isl_take isl_set *set, enum isl_dim_type type,
4722 unsigned first, unsigned n);
4723 __isl_give isl_basic_map *isl_basic_map_eliminate(
4724 __isl_take isl_basic_map *bmap,
4725 enum isl_dim_type type,
4726 unsigned first, unsigned n);
4727 __isl_give isl_map *isl_map_eliminate(
4728 __isl_take isl_map *map, enum isl_dim_type type,
4729 unsigned first, unsigned n);
4731 Eliminate the coefficients for the given dimensions from the constraints,
4732 without removing the dimensions.
4734 =item * Constructing a set from a parameter domain
4736 A zero-dimensional (local) space or (basic) set can be constructed
4737 on a given parameter domain using the following functions.
4739 #include <isl/space.h>
4740 __isl_give isl_space *isl_space_set_from_params(
4741 __isl_take isl_space *space);
4743 #include <isl/local_space.h>
4744 __isl_give isl_local_space *
4745 isl_local_space_set_from_params(
4746 __isl_take isl_local_space *ls);
4748 #include <isl/set.h>
4749 __isl_give isl_basic_set *isl_basic_set_from_params(
4750 __isl_take isl_basic_set *bset);
4751 __isl_give isl_set *isl_set_from_params(
4752 __isl_take isl_set *set);
4754 =item * Constructing a relation from one or two sets
4756 Create a relation with the given set(s) as domain and/or range.
4757 If only the domain or the range is specified, then
4758 the range or domain of the created relation is a zero-dimensional
4759 flat anonymous space.
4761 #include <isl/space.h>
4762 __isl_give isl_space *isl_space_from_domain(
4763 __isl_take isl_space *space);
4764 __isl_give isl_space *isl_space_from_range(
4765 __isl_take isl_space *space);
4766 __isl_give isl_space *isl_space_map_from_set(
4767 __isl_take isl_space *space);
4768 __isl_give isl_space *isl_space_map_from_domain_and_range(
4769 __isl_take isl_space *domain,
4770 __isl_take isl_space *range);
4772 #include <isl/local_space.h>
4773 __isl_give isl_local_space *isl_local_space_from_domain(
4774 __isl_take isl_local_space *ls);
4776 #include <isl/map.h>
4777 __isl_give isl_map *isl_map_from_domain(
4778 __isl_take isl_set *set);
4779 __isl_give isl_map *isl_map_from_range(
4780 __isl_take isl_set *set);
4782 #include <isl/union_map.h>
4783 __isl_give isl_union_map *isl_union_map_from_domain(
4784 __isl_take isl_union_set *uset);
4785 __isl_give isl_union_map *isl_union_map_from_range(
4786 __isl_take isl_union_set *uset);
4787 __isl_give isl_union_map *
4788 isl_union_map_from_domain_and_range(
4789 __isl_take isl_union_set *domain,
4790 __isl_take isl_union_set *range);
4792 #include <isl/val.h>
4793 __isl_give isl_multi_val *isl_multi_val_from_range(
4794 __isl_take isl_multi_val *mv);
4796 #include <isl/aff.h>
4797 __isl_give isl_aff *isl_aff_from_range(
4798 __isl_take isl_aff *aff);
4799 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4800 __isl_take isl_multi_aff *ma);
4801 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4802 __isl_take isl_pw_aff *pwa);
4803 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4804 __isl_take isl_multi_pw_aff *mpa);
4805 __isl_give isl_multi_union_pw_aff *
4806 isl_multi_union_pw_aff_from_range(
4807 __isl_take isl_multi_union_pw_aff *mupa);
4808 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4809 __isl_take isl_set *set);
4810 __isl_give isl_union_pw_multi_aff *
4811 isl_union_pw_multi_aff_from_domain(
4812 __isl_take isl_union_set *uset);
4814 #include <isl/polynomial.h>
4815 __isl_give isl_pw_qpolynomial *
4816 isl_pw_qpolynomial_from_range(
4817 __isl_take isl_pw_qpolynomial *pwqp);
4818 __isl_give isl_pw_qpolynomial_fold *
4819 isl_pw_qpolynomial_fold_from_range(
4820 __isl_take isl_pw_qpolynomial_fold *pwf);
4824 #include <isl/set.h>
4825 __isl_give isl_basic_set *isl_basic_set_fix_si(
4826 __isl_take isl_basic_set *bset,
4827 enum isl_dim_type type, unsigned pos, int value);
4828 __isl_give isl_basic_set *isl_basic_set_fix_val(
4829 __isl_take isl_basic_set *bset,
4830 enum isl_dim_type type, unsigned pos,
4831 __isl_take isl_val *v);
4832 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4833 enum isl_dim_type type, unsigned pos, int value);
4834 __isl_give isl_set *isl_set_fix_val(
4835 __isl_take isl_set *set,
4836 enum isl_dim_type type, unsigned pos,
4837 __isl_take isl_val *v);
4839 #include <isl/map.h>
4840 __isl_give isl_basic_map *isl_basic_map_fix_si(
4841 __isl_take isl_basic_map *bmap,
4842 enum isl_dim_type type, unsigned pos, int value);
4843 __isl_give isl_basic_map *isl_basic_map_fix_val(
4844 __isl_take isl_basic_map *bmap,
4845 enum isl_dim_type type, unsigned pos,
4846 __isl_take isl_val *v);
4847 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4848 enum isl_dim_type type, unsigned pos, int value);
4849 __isl_give isl_map *isl_map_fix_val(
4850 __isl_take isl_map *map,
4851 enum isl_dim_type type, unsigned pos,
4852 __isl_take isl_val *v);
4854 #include <isl/aff.h>
4855 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4856 __isl_take isl_pw_multi_aff *pma,
4857 enum isl_dim_type type, unsigned pos, int value);
4859 #include <isl/polynomial.h>
4860 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4861 __isl_take isl_pw_qpolynomial *pwqp,
4862 enum isl_dim_type type, unsigned n,
4863 __isl_take isl_val *v);
4864 __isl_give isl_pw_qpolynomial_fold *
4865 isl_pw_qpolynomial_fold_fix_val(
4866 __isl_take isl_pw_qpolynomial_fold *pwf,
4867 enum isl_dim_type type, unsigned n,
4868 __isl_take isl_val *v);
4870 Intersect the set, relation or function domain
4871 with the hyperplane where the given
4872 dimension has the fixed given value.
4874 #include <isl/set.h>
4875 __isl_give isl_basic_set *
4876 isl_basic_set_lower_bound_val(
4877 __isl_take isl_basic_set *bset,
4878 enum isl_dim_type type, unsigned pos,
4879 __isl_take isl_val *value);
4880 __isl_give isl_basic_set *
4881 isl_basic_set_upper_bound_val(
4882 __isl_take isl_basic_set *bset,
4883 enum isl_dim_type type, unsigned pos,
4884 __isl_take isl_val *value);
4885 __isl_give isl_set *isl_set_lower_bound_si(
4886 __isl_take isl_set *set,
4887 enum isl_dim_type type, unsigned pos, int value);
4888 __isl_give isl_set *isl_set_lower_bound_val(
4889 __isl_take isl_set *set,
4890 enum isl_dim_type type, unsigned pos,
4891 __isl_take isl_val *value);
4892 __isl_give isl_set *isl_set_upper_bound_si(
4893 __isl_take isl_set *set,
4894 enum isl_dim_type type, unsigned pos, int value);
4895 __isl_give isl_set *isl_set_upper_bound_val(
4896 __isl_take isl_set *set,
4897 enum isl_dim_type type, unsigned pos,
4898 __isl_take isl_val *value);
4900 #include <isl/map.h>
4901 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4902 __isl_take isl_basic_map *bmap,
4903 enum isl_dim_type type, unsigned pos, int value);
4904 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4905 __isl_take isl_basic_map *bmap,
4906 enum isl_dim_type type, unsigned pos, int value);
4907 __isl_give isl_map *isl_map_lower_bound_si(
4908 __isl_take isl_map *map,
4909 enum isl_dim_type type, unsigned pos, int value);
4910 __isl_give isl_map *isl_map_upper_bound_si(
4911 __isl_take isl_map *map,
4912 enum isl_dim_type type, unsigned pos, int value);
4914 Intersect the set or relation with the half-space where the given
4915 dimension has a value bounded by the fixed given integer value.
4917 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4918 enum isl_dim_type type1, int pos1,
4919 enum isl_dim_type type2, int pos2);
4920 __isl_give isl_basic_map *isl_basic_map_equate(
4921 __isl_take isl_basic_map *bmap,
4922 enum isl_dim_type type1, int pos1,
4923 enum isl_dim_type type2, int pos2);
4924 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4925 enum isl_dim_type type1, int pos1,
4926 enum isl_dim_type type2, int pos2);
4928 Intersect the set or relation with the hyperplane where the given
4929 dimensions are equal to each other.
4931 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4932 enum isl_dim_type type1, int pos1,
4933 enum isl_dim_type type2, int pos2);
4935 Intersect the relation with the hyperplane where the given
4936 dimensions have opposite values.
4938 __isl_give isl_map *isl_map_order_le(
4939 __isl_take isl_map *map,
4940 enum isl_dim_type type1, int pos1,
4941 enum isl_dim_type type2, int pos2);
4942 __isl_give isl_basic_map *isl_basic_map_order_ge(
4943 __isl_take isl_basic_map *bmap,
4944 enum isl_dim_type type1, int pos1,
4945 enum isl_dim_type type2, int pos2);
4946 __isl_give isl_map *isl_map_order_ge(
4947 __isl_take isl_map *map,
4948 enum isl_dim_type type1, int pos1,
4949 enum isl_dim_type type2, int pos2);
4950 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4951 enum isl_dim_type type1, int pos1,
4952 enum isl_dim_type type2, int pos2);
4953 __isl_give isl_basic_map *isl_basic_map_order_gt(
4954 __isl_take isl_basic_map *bmap,
4955 enum isl_dim_type type1, int pos1,
4956 enum isl_dim_type type2, int pos2);
4957 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4958 enum isl_dim_type type1, int pos1,
4959 enum isl_dim_type type2, int pos2);
4961 Intersect the relation with the half-space where the given
4962 dimensions satisfy the given ordering.
4964 #include <isl/union_set.h>
4965 __isl_give isl_union_map *isl_union_map_remove_map_if(
4966 __isl_take isl_union_map *umap,
4967 isl_bool (*fn)(__isl_keep isl_map *map,
4968 void *user), void *user);
4970 This function calls the callback function once for each
4971 pair of spaces for which there are elements in the input.
4972 If the callback returns C<isl_bool_true>, then all those elements
4973 are removed from the result. The only remaining elements in the output
4974 are then those for which the callback returns C<isl_bool_false>.
4978 #include <isl/aff.h>
4979 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4980 __isl_take isl_aff *aff);
4981 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4982 __isl_take isl_aff *aff);
4983 __isl_give isl_set *isl_pw_aff_pos_set(
4984 __isl_take isl_pw_aff *pa);
4985 __isl_give isl_set *isl_pw_aff_nonneg_set(
4986 __isl_take isl_pw_aff *pwaff);
4987 __isl_give isl_set *isl_pw_aff_zero_set(
4988 __isl_take isl_pw_aff *pwaff);
4989 __isl_give isl_set *isl_pw_aff_non_zero_set(
4990 __isl_take isl_pw_aff *pwaff);
4991 __isl_give isl_union_set *
4992 isl_union_pw_aff_zero_union_set(
4993 __isl_take isl_union_pw_aff *upa);
4994 __isl_give isl_union_set *
4995 isl_multi_union_pw_aff_zero_union_set(
4996 __isl_take isl_multi_union_pw_aff *mupa);
4998 The function C<isl_aff_neg_basic_set> returns a basic set
4999 containing those elements in the domain space
5000 of C<aff> where C<aff> is negative.
5001 The function C<isl_pw_aff_nonneg_set> returns a set
5002 containing those elements in the domain
5003 of C<pwaff> where C<pwaff> is non-negative.
5004 The function C<isl_multi_union_pw_aff_zero_union_set>
5005 returns a union set containing those elements
5006 in the domains of its elements where they are all zero.
5010 __isl_give isl_map *isl_set_identity(
5011 __isl_take isl_set *set);
5012 __isl_give isl_union_map *isl_union_set_identity(
5013 __isl_take isl_union_set *uset);
5014 __isl_give isl_union_pw_multi_aff *
5015 isl_union_set_identity_union_pw_multi_aff(
5016 __isl_take isl_union_set *uset);
5018 Construct an identity relation on the given (union) set.
5020 =item * Function Extraction
5022 A piecewise quasi affine expression that is equal to 1 on a set
5023 and 0 outside the set can be created using the following function.
5025 #include <isl/aff.h>
5026 __isl_give isl_pw_aff *isl_set_indicator_function(
5027 __isl_take isl_set *set);
5029 A piecewise multiple quasi affine expression can be extracted
5030 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
5031 and the C<isl_map> is single-valued.
5032 In case of a conversion from an C<isl_union_map>
5033 to an C<isl_union_pw_multi_aff>, these properties need to hold
5034 in each domain space.
5035 A conversion to a C<isl_multi_union_pw_aff> additionally
5036 requires that the input is non-empty and involves only a single
5039 #include <isl/aff.h>
5040 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
5041 __isl_take isl_set *set);
5042 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
5043 __isl_take isl_map *map);
5045 __isl_give isl_union_pw_multi_aff *
5046 isl_union_pw_multi_aff_from_union_set(
5047 __isl_take isl_union_set *uset);
5048 __isl_give isl_union_pw_multi_aff *
5049 isl_union_pw_multi_aff_from_union_map(
5050 __isl_take isl_union_map *umap);
5052 __isl_give isl_multi_union_pw_aff *
5053 isl_multi_union_pw_aff_from_union_map(
5054 __isl_take isl_union_map *umap);
5058 __isl_give isl_basic_set *isl_basic_map_deltas(
5059 __isl_take isl_basic_map *bmap);
5060 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
5061 __isl_give isl_union_set *isl_union_map_deltas(
5062 __isl_take isl_union_map *umap);
5064 These functions return a (basic) set containing the differences
5065 between image elements and corresponding domain elements in the input.
5067 __isl_give isl_basic_map *isl_basic_map_deltas_map(
5068 __isl_take isl_basic_map *bmap);
5069 __isl_give isl_map *isl_map_deltas_map(
5070 __isl_take isl_map *map);
5071 __isl_give isl_union_map *isl_union_map_deltas_map(
5072 __isl_take isl_union_map *umap);
5074 The functions above construct a (basic, regular or union) relation
5075 that maps (a wrapped version of) the input relation to its delta set.
5079 Simplify the representation of a set, relation or functions by trying
5080 to combine pairs of basic sets or relations into a single
5081 basic set or relation.
5083 #include <isl/set.h>
5084 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
5086 #include <isl/map.h>
5087 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5089 #include <isl/union_set.h>
5090 __isl_give isl_union_set *isl_union_set_coalesce(
5091 __isl_take isl_union_set *uset);
5093 #include <isl/union_map.h>
5094 __isl_give isl_union_map *isl_union_map_coalesce(
5095 __isl_take isl_union_map *umap);
5097 #include <isl/aff.h>
5098 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5099 __isl_take isl_pw_aff *pwqp);
5100 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5101 __isl_take isl_pw_multi_aff *pma);
5102 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5103 __isl_take isl_multi_pw_aff *mpa);
5104 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5105 __isl_take isl_union_pw_aff *upa);
5106 __isl_give isl_union_pw_multi_aff *
5107 isl_union_pw_multi_aff_coalesce(
5108 __isl_take isl_union_pw_multi_aff *upma);
5109 __isl_give isl_multi_union_pw_aff *
5110 isl_multi_union_pw_aff_coalesce(
5111 __isl_take isl_multi_union_pw_aff *aff);
5113 #include <isl/polynomial.h>
5114 __isl_give isl_pw_qpolynomial_fold *
5115 isl_pw_qpolynomial_fold_coalesce(
5116 __isl_take isl_pw_qpolynomial_fold *pwf);
5117 __isl_give isl_union_pw_qpolynomial *
5118 isl_union_pw_qpolynomial_coalesce(
5119 __isl_take isl_union_pw_qpolynomial *upwqp);
5120 __isl_give isl_union_pw_qpolynomial_fold *
5121 isl_union_pw_qpolynomial_fold_coalesce(
5122 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5124 One of the methods for combining pairs of basic sets or relations
5125 can result in coefficients that are much larger than those that appear
5126 in the constraints of the input. By default, the coefficients are
5127 not allowed to grow larger, but this can be changed by unsetting
5128 the following option.
5130 isl_stat isl_options_set_coalesce_bounded_wrapping(
5131 isl_ctx *ctx, int val);
5132 int isl_options_get_coalesce_bounded_wrapping(
5135 One of the other methods tries to combine pairs of basic sets
5136 with different local variables, treating them as existentially
5137 quantified variables even if they have known (but different)
5138 integer division expressions. The result may then also have
5139 existentially quantified variables. Turning on the following
5140 option prevents this from happening.
5142 isl_stat isl_options_set_coalesce_preserve_locals(
5143 isl_ctx *ctx, int val);
5144 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
5146 =item * Detecting equalities
5148 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5149 __isl_take isl_basic_set *bset);
5150 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5151 __isl_take isl_basic_map *bmap);
5152 __isl_give isl_set *isl_set_detect_equalities(
5153 __isl_take isl_set *set);
5154 __isl_give isl_map *isl_map_detect_equalities(
5155 __isl_take isl_map *map);
5156 __isl_give isl_union_set *isl_union_set_detect_equalities(
5157 __isl_take isl_union_set *uset);
5158 __isl_give isl_union_map *isl_union_map_detect_equalities(
5159 __isl_take isl_union_map *umap);
5161 Simplify the representation of a set or relation by detecting implicit
5164 =item * Removing redundant constraints
5166 #include <isl/set.h>
5167 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5168 __isl_take isl_basic_set *bset);
5169 __isl_give isl_set *isl_set_remove_redundancies(
5170 __isl_take isl_set *set);
5172 #include <isl/union_set.h>
5173 __isl_give isl_union_set *
5174 isl_union_set_remove_redundancies(
5175 __isl_take isl_union_set *uset);
5177 #include <isl/map.h>
5178 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5179 __isl_take isl_basic_map *bmap);
5180 __isl_give isl_map *isl_map_remove_redundancies(
5181 __isl_take isl_map *map);
5183 #include <isl/union_map.h>
5184 __isl_give isl_union_map *
5185 isl_union_map_remove_redundancies(
5186 __isl_take isl_union_map *umap);
5190 __isl_give isl_basic_set *isl_set_convex_hull(
5191 __isl_take isl_set *set);
5192 __isl_give isl_basic_map *isl_map_convex_hull(
5193 __isl_take isl_map *map);
5195 If the input set or relation has any existentially quantified
5196 variables, then the result of these operations is currently undefined.
5200 #include <isl/set.h>
5201 __isl_give isl_basic_set *
5202 isl_set_unshifted_simple_hull(
5203 __isl_take isl_set *set);
5204 __isl_give isl_basic_set *isl_set_simple_hull(
5205 __isl_take isl_set *set);
5206 __isl_give isl_basic_set *
5207 isl_set_plain_unshifted_simple_hull(
5208 __isl_take isl_set *set);
5209 __isl_give isl_basic_set *
5210 isl_set_unshifted_simple_hull_from_set_list(
5211 __isl_take isl_set *set,
5212 __isl_take isl_set_list *list);
5214 #include <isl/map.h>
5215 __isl_give isl_basic_map *
5216 isl_map_unshifted_simple_hull(
5217 __isl_take isl_map *map);
5218 __isl_give isl_basic_map *isl_map_simple_hull(
5219 __isl_take isl_map *map);
5220 __isl_give isl_basic_map *
5221 isl_map_plain_unshifted_simple_hull(
5222 __isl_take isl_map *map);
5223 __isl_give isl_basic_map *
5224 isl_map_unshifted_simple_hull_from_map_list(
5225 __isl_take isl_map *map,
5226 __isl_take isl_map_list *list);
5228 #include <isl/union_map.h>
5229 __isl_give isl_union_map *isl_union_map_simple_hull(
5230 __isl_take isl_union_map *umap);
5232 These functions compute a single basic set or relation
5233 that contains the whole input set or relation.
5234 In particular, the output is described by translates
5235 of the constraints describing the basic sets or relations in the input.
5236 In case of C<isl_set_unshifted_simple_hull>, only the original
5237 constraints are used, without any translation.
5238 In case of C<isl_set_plain_unshifted_simple_hull> and
5239 C<isl_map_plain_unshifted_simple_hull>, the result is described
5240 by original constraints that are obviously satisfied
5241 by the entire input set or relation.
5242 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5243 C<isl_map_unshifted_simple_hull_from_map_list>, the
5244 constraints are taken from the elements of the second argument.
5248 (See \autoref{s:simple hull}.)
5254 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5255 __isl_take isl_basic_set *bset);
5256 __isl_give isl_basic_set *isl_set_affine_hull(
5257 __isl_take isl_set *set);
5258 __isl_give isl_union_set *isl_union_set_affine_hull(
5259 __isl_take isl_union_set *uset);
5260 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5261 __isl_take isl_basic_map *bmap);
5262 __isl_give isl_basic_map *isl_map_affine_hull(
5263 __isl_take isl_map *map);
5264 __isl_give isl_union_map *isl_union_map_affine_hull(
5265 __isl_take isl_union_map *umap);
5267 In case of union sets and relations, the affine hull is computed
5270 =item * Polyhedral hull
5272 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5273 __isl_take isl_set *set);
5274 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5275 __isl_take isl_map *map);
5276 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5277 __isl_take isl_union_set *uset);
5278 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5279 __isl_take isl_union_map *umap);
5281 These functions compute a single basic set or relation
5282 not involving any existentially quantified variables
5283 that contains the whole input set or relation.
5284 In case of union sets and relations, the polyhedral hull is computed
5289 #include <isl/map.h>
5290 __isl_give isl_fixed_box *
5291 isl_map_get_range_simple_fixed_box_hull(
5292 __isl_keep isl_map *map);
5294 This function tries to approximate the range of the map by a box of fixed size.
5295 The box is described in terms of an offset living in the same space as
5296 the input map and a size living in the range space. For any element
5297 in the input map, the range value is greater than or equal to
5298 the offset applied to the domain value and the difference with
5299 this offset is strictly smaller than the size.
5300 If no fixed-size approximation of the range can be found,
5301 an I<invalid> box is returned, i.e., one for which
5302 C<isl_fixed_box_is_valid> below returns false.
5304 The validity, the offset and the size of the box can be obtained using
5305 the following functions.
5307 #include <isl/fixed_box.h>
5308 isl_bool isl_fixed_box_is_valid(
5309 __isl_keep isl_fixed_box *box);
5310 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
5311 __isl_keep isl_fixed_box *box);
5312 __isl_give isl_multi_val *isl_fixed_box_get_size(
5313 __isl_keep isl_fixed_box *box);
5315 The box can be copied and freed using the following functions.
5317 #include <isl/fixed_box.h>
5318 __isl_give isl_fixed_box *isl_fixed_box_copy(
5319 __isl_keep isl_fixed_box *box);
5320 __isl_null isl_fixed_box *isl_fixed_box_free(
5321 __isl_take isl_fixed_box *box);
5323 =item * Other approximations
5325 #include <isl/set.h>
5326 __isl_give isl_basic_set *
5327 isl_basic_set_drop_constraints_involving_dims(
5328 __isl_take isl_basic_set *bset,
5329 enum isl_dim_type type,
5330 unsigned first, unsigned n);
5331 __isl_give isl_basic_set *
5332 isl_basic_set_drop_constraints_not_involving_dims(
5333 __isl_take isl_basic_set *bset,
5334 enum isl_dim_type type,
5335 unsigned first, unsigned n);
5336 __isl_give isl_set *
5337 isl_set_drop_constraints_involving_dims(
5338 __isl_take isl_set *set,
5339 enum isl_dim_type type,
5340 unsigned first, unsigned n);
5341 __isl_give isl_set *
5342 isl_set_drop_constraints_not_involving_dims(
5343 __isl_take isl_set *set,
5344 enum isl_dim_type type,
5345 unsigned first, unsigned n);
5347 #include <isl/map.h>
5348 __isl_give isl_basic_map *
5349 isl_basic_map_drop_constraints_involving_dims(
5350 __isl_take isl_basic_map *bmap,
5351 enum isl_dim_type type,
5352 unsigned first, unsigned n);
5353 __isl_give isl_basic_map *
5354 isl_basic_map_drop_constraints_not_involving_dims(
5355 __isl_take isl_basic_map *bmap,
5356 enum isl_dim_type type,
5357 unsigned first, unsigned n);
5358 __isl_give isl_map *
5359 isl_map_drop_constraints_involving_dims(
5360 __isl_take isl_map *map,
5361 enum isl_dim_type type,
5362 unsigned first, unsigned n);
5363 __isl_give isl_map *
5364 isl_map_drop_constraints_not_involving_dims(
5365 __isl_take isl_map *map,
5366 enum isl_dim_type type,
5367 unsigned first, unsigned n);
5369 These functions drop any constraints (not) involving the specified dimensions.
5370 Note that the result depends on the representation of the input.
5372 #include <isl/polynomial.h>
5373 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5374 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5375 __isl_give isl_union_pw_qpolynomial *
5376 isl_union_pw_qpolynomial_to_polynomial(
5377 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5379 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5380 the polynomial will be an overapproximation. If C<sign> is negative,
5381 it will be an underapproximation. If C<sign> is zero, the approximation
5382 will lie somewhere in between.
5386 __isl_give isl_basic_set *isl_basic_set_sample(
5387 __isl_take isl_basic_set *bset);
5388 __isl_give isl_basic_set *isl_set_sample(
5389 __isl_take isl_set *set);
5390 __isl_give isl_basic_map *isl_basic_map_sample(
5391 __isl_take isl_basic_map *bmap);
5392 __isl_give isl_basic_map *isl_map_sample(
5393 __isl_take isl_map *map);
5395 If the input (basic) set or relation is non-empty, then return
5396 a singleton subset of the input. Otherwise, return an empty set.
5398 =item * Optimization
5400 #include <isl/ilp.h>
5401 __isl_give isl_val *isl_basic_set_max_val(
5402 __isl_keep isl_basic_set *bset,
5403 __isl_keep isl_aff *obj);
5404 __isl_give isl_val *isl_set_min_val(
5405 __isl_keep isl_set *set,
5406 __isl_keep isl_aff *obj);
5407 __isl_give isl_val *isl_set_max_val(
5408 __isl_keep isl_set *set,
5409 __isl_keep isl_aff *obj);
5410 __isl_give isl_multi_val *
5411 isl_union_set_min_multi_union_pw_aff(
5412 __isl_keep isl_union_set *uset,
5413 __isl_keep isl_multi_union_pw_aff *obj);
5415 Compute the minimum or maximum of the integer affine expression C<obj>
5416 over the points in C<set>.
5417 The result is C<NULL> in case of an error, the optimal value in case
5418 there is one, negative infinity or infinity if the problem is unbounded and
5419 NaN if the problem is empty.
5421 #include <isl/ilp.h>
5422 __isl_give isl_val *isl_union_pw_aff_min_val(
5423 __isl_take isl_union_pw_aff *upa);
5424 __isl_give isl_val *isl_union_pw_aff_max_val(
5425 __isl_take isl_union_pw_aff *upa);
5426 __isl_give isl_multi_val *
5427 isl_multi_union_pw_aff_min_multi_val(
5428 __isl_take isl_multi_union_pw_aff *mupa);
5429 __isl_give isl_multi_val *
5430 isl_multi_union_pw_aff_max_multi_val(
5431 __isl_take isl_multi_union_pw_aff *mupa);
5433 Compute the minimum or maximum of the integer affine expression
5434 over its definition domain.
5435 The result is C<NULL> in case of an error, the optimal value in case
5436 there is one, negative infinity or infinity if the problem is unbounded and
5437 NaN if the problem is empty.
5439 #include <isl/ilp.h>
5440 __isl_give isl_val *isl_basic_set_dim_max_val(
5441 __isl_take isl_basic_set *bset, int pos);
5443 Return the maximal value attained by the given set dimension,
5444 independently of the parameter values and of any other dimensions.
5445 The result is C<NULL> in case of an error, the optimal value in case
5446 there is one, infinity if the problem is unbounded and
5447 NaN if the input is empty.
5449 =item * Parametric optimization
5451 __isl_give isl_pw_aff *isl_set_dim_min(
5452 __isl_take isl_set *set, int pos);
5453 __isl_give isl_pw_aff *isl_set_dim_max(
5454 __isl_take isl_set *set, int pos);
5455 __isl_give isl_pw_aff *isl_map_dim_min(
5456 __isl_take isl_map *map, int pos);
5457 __isl_give isl_pw_aff *isl_map_dim_max(
5458 __isl_take isl_map *map, int pos);
5460 Compute the minimum or maximum of the given set or output dimension
5461 as a function of the parameters (and input dimensions), but independently
5462 of the other set or output dimensions.
5463 For lexicographic optimization, see L<"Lexicographic Optimization">.
5467 The following functions compute either the set of (rational) coefficient
5468 values of valid constraints for the given set or the set of (rational)
5469 values satisfying the constraints with coefficients from the given set.
5470 Internally, these two sets of functions perform essentially the
5471 same operations, except that the set of coefficients is assumed to
5472 be a cone, while the set of values may be any polyhedron.
5473 The current implementation is based on the Farkas lemma and
5474 Fourier-Motzkin elimination, but this may change or be made optional
5475 in future. In particular, future implementations may use different
5476 dualization algorithms or skip the elimination step.
5478 #include <isl/set.h>
5479 __isl_give isl_basic_set *isl_basic_set_coefficients(
5480 __isl_take isl_basic_set *bset);
5481 __isl_give isl_basic_set_list *
5482 isl_basic_set_list_coefficients(
5483 __isl_take isl_basic_set_list *list);
5484 __isl_give isl_basic_set *isl_set_coefficients(
5485 __isl_take isl_set *set);
5486 __isl_give isl_union_set *isl_union_set_coefficients(
5487 __isl_take isl_union_set *bset);
5488 __isl_give isl_basic_set *isl_basic_set_solutions(
5489 __isl_take isl_basic_set *bset);
5490 __isl_give isl_basic_set *isl_set_solutions(
5491 __isl_take isl_set *set);
5492 __isl_give isl_union_set *isl_union_set_solutions(
5493 __isl_take isl_union_set *bset);
5497 __isl_give isl_map *isl_map_fixed_power_val(
5498 __isl_take isl_map *map,
5499 __isl_take isl_val *exp);
5500 __isl_give isl_union_map *
5501 isl_union_map_fixed_power_val(
5502 __isl_take isl_union_map *umap,
5503 __isl_take isl_val *exp);
5505 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5506 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5507 of C<map> is computed.
5509 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5511 __isl_give isl_union_map *isl_union_map_power(
5512 __isl_take isl_union_map *umap, int *exact);
5514 Compute a parametric representation for all positive powers I<k> of C<map>.
5515 The result maps I<k> to a nested relation corresponding to the
5516 I<k>th power of C<map>.
5517 The result may be an overapproximation. If the result is known to be exact,
5518 then C<*exact> is set to C<1>.
5520 =item * Transitive closure
5522 __isl_give isl_map *isl_map_transitive_closure(
5523 __isl_take isl_map *map, int *exact);
5524 __isl_give isl_union_map *isl_union_map_transitive_closure(
5525 __isl_take isl_union_map *umap, int *exact);
5527 Compute the transitive closure of C<map>.
5528 The result may be an overapproximation. If the result is known to be exact,
5529 then C<*exact> is set to C<1>.
5531 =item * Reaching path lengths
5533 __isl_give isl_map *isl_map_reaching_path_lengths(
5534 __isl_take isl_map *map, int *exact);
5536 Compute a relation that maps each element in the range of C<map>
5537 to the lengths of all paths composed of edges in C<map> that
5538 end up in the given element.
5539 The result may be an overapproximation. If the result is known to be exact,
5540 then C<*exact> is set to C<1>.
5541 To compute the I<maximal> path length, the resulting relation
5542 should be postprocessed by C<isl_map_lexmax>.
5543 In particular, if the input relation is a dependence relation
5544 (mapping sources to sinks), then the maximal path length corresponds
5545 to the free schedule.
5546 Note, however, that C<isl_map_lexmax> expects the maximum to be
5547 finite, so if the path lengths are unbounded (possibly due to
5548 the overapproximation), then you will get an error message.
5552 #include <isl/space.h>
5553 __isl_give isl_space *isl_space_wrap(
5554 __isl_take isl_space *space);
5555 __isl_give isl_space *isl_space_unwrap(
5556 __isl_take isl_space *space);
5558 #include <isl/local_space.h>
5559 __isl_give isl_local_space *isl_local_space_wrap(
5560 __isl_take isl_local_space *ls);
5562 #include <isl/set.h>
5563 __isl_give isl_basic_map *isl_basic_set_unwrap(
5564 __isl_take isl_basic_set *bset);
5565 __isl_give isl_map *isl_set_unwrap(
5566 __isl_take isl_set *set);
5568 #include <isl/map.h>
5569 __isl_give isl_basic_set *isl_basic_map_wrap(
5570 __isl_take isl_basic_map *bmap);
5571 __isl_give isl_set *isl_map_wrap(
5572 __isl_take isl_map *map);
5574 #include <isl/union_set.h>
5575 __isl_give isl_union_map *isl_union_set_unwrap(
5576 __isl_take isl_union_set *uset);
5578 #include <isl/union_map.h>
5579 __isl_give isl_union_set *isl_union_map_wrap(
5580 __isl_take isl_union_map *umap);
5582 The input to C<isl_space_unwrap> should
5583 be the space of a set, while that of
5584 C<isl_space_wrap> should be the space of a relation.
5585 Conversely, the output of C<isl_space_unwrap> is the space
5586 of a relation, while that of C<isl_space_wrap> is the space of a set.
5590 Remove any internal structure of domain (and range) of the given
5591 set or relation. If there is any such internal structure in the input,
5592 then the name of the space is also removed.
5594 #include <isl/space.h>
5595 __isl_give isl_space *isl_space_flatten_domain(
5596 __isl_take isl_space *space);
5597 __isl_give isl_space *isl_space_flatten_range(
5598 __isl_take isl_space *space);
5600 #include <isl/local_space.h>
5601 __isl_give isl_local_space *
5602 isl_local_space_flatten_domain(
5603 __isl_take isl_local_space *ls);
5604 __isl_give isl_local_space *
5605 isl_local_space_flatten_range(
5606 __isl_take isl_local_space *ls);
5608 #include <isl/set.h>
5609 __isl_give isl_basic_set *isl_basic_set_flatten(
5610 __isl_take isl_basic_set *bset);
5611 __isl_give isl_set *isl_set_flatten(
5612 __isl_take isl_set *set);
5614 #include <isl/map.h>
5615 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5616 __isl_take isl_basic_map *bmap);
5617 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5618 __isl_take isl_basic_map *bmap);
5619 __isl_give isl_map *isl_map_flatten_range(
5620 __isl_take isl_map *map);
5621 __isl_give isl_map *isl_map_flatten_domain(
5622 __isl_take isl_map *map);
5623 __isl_give isl_basic_map *isl_basic_map_flatten(
5624 __isl_take isl_basic_map *bmap);
5625 __isl_give isl_map *isl_map_flatten(
5626 __isl_take isl_map *map);
5628 #include <isl/val.h>
5629 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5630 __isl_take isl_multi_val *mv);
5632 #include <isl/aff.h>
5633 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5634 __isl_take isl_multi_aff *ma);
5635 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5636 __isl_take isl_multi_aff *ma);
5637 __isl_give isl_multi_pw_aff *
5638 isl_multi_pw_aff_flatten_range(
5639 __isl_take isl_multi_pw_aff *mpa);
5640 __isl_give isl_multi_union_pw_aff *
5641 isl_multi_union_pw_aff_flatten_range(
5642 __isl_take isl_multi_union_pw_aff *mupa);
5644 #include <isl/map.h>
5645 __isl_give isl_map *isl_set_flatten_map(
5646 __isl_take isl_set *set);
5648 The function above constructs a relation
5649 that maps the input set to a flattened version of the set.
5653 Lift the input set to a space with extra dimensions corresponding
5654 to the existentially quantified variables in the input.
5655 In particular, the result lives in a wrapped map where the domain
5656 is the original space and the range corresponds to the original
5657 existentially quantified variables.
5659 #include <isl/set.h>
5660 __isl_give isl_basic_set *isl_basic_set_lift(
5661 __isl_take isl_basic_set *bset);
5662 __isl_give isl_set *isl_set_lift(
5663 __isl_take isl_set *set);
5664 __isl_give isl_union_set *isl_union_set_lift(
5665 __isl_take isl_union_set *uset);
5667 Given a local space that contains the existentially quantified
5668 variables of a set, a basic relation that, when applied to
5669 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5670 can be constructed using the following function.
5672 #include <isl/local_space.h>
5673 __isl_give isl_basic_map *isl_local_space_lifting(
5674 __isl_take isl_local_space *ls);
5676 #include <isl/aff.h>
5677 __isl_give isl_multi_aff *isl_multi_aff_lift(
5678 __isl_take isl_multi_aff *maff,
5679 __isl_give isl_local_space **ls);
5681 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5682 then it is assigned the local space that lies at the basis of
5683 the lifting applied.
5685 =item * Internal Product
5687 #include <isl/space.h>
5688 __isl_give isl_space *isl_space_zip(
5689 __isl_take isl_space *space);
5691 #include <isl/map.h>
5692 __isl_give isl_basic_map *isl_basic_map_zip(
5693 __isl_take isl_basic_map *bmap);
5694 __isl_give isl_map *isl_map_zip(
5695 __isl_take isl_map *map);
5697 #include <isl/union_map.h>
5698 __isl_give isl_union_map *isl_union_map_zip(
5699 __isl_take isl_union_map *umap);
5701 Given a relation with nested relations for domain and range,
5702 interchange the range of the domain with the domain of the range.
5706 #include <isl/space.h>
5707 __isl_give isl_space *isl_space_curry(
5708 __isl_take isl_space *space);
5709 __isl_give isl_space *isl_space_uncurry(
5710 __isl_take isl_space *space);
5712 #include <isl/map.h>
5713 __isl_give isl_basic_map *isl_basic_map_curry(
5714 __isl_take isl_basic_map *bmap);
5715 __isl_give isl_basic_map *isl_basic_map_uncurry(
5716 __isl_take isl_basic_map *bmap);
5717 __isl_give isl_map *isl_map_curry(
5718 __isl_take isl_map *map);
5719 __isl_give isl_map *isl_map_uncurry(
5720 __isl_take isl_map *map);
5722 #include <isl/union_map.h>
5723 __isl_give isl_union_map *isl_union_map_curry(
5724 __isl_take isl_union_map *umap);
5725 __isl_give isl_union_map *isl_union_map_uncurry(
5726 __isl_take isl_union_map *umap);
5728 Given a relation with a nested relation for domain,
5729 the C<curry> functions
5730 move the range of the nested relation out of the domain
5731 and use it as the domain of a nested relation in the range,
5732 with the original range as range of this nested relation.
5733 The C<uncurry> functions perform the inverse operation.
5735 #include <isl/space.h>
5736 __isl_give isl_space *isl_space_range_curry(
5737 __isl_take isl_space *space);
5739 #include <isl/map.h>
5740 __isl_give isl_map *isl_map_range_curry(
5741 __isl_take isl_map *map);
5743 #include <isl/union_map.h>
5744 __isl_give isl_union_map *isl_union_map_range_curry(
5745 __isl_take isl_union_map *umap);
5747 These functions apply the currying to the relation that
5748 is nested inside the range of the input.
5750 =item * Aligning parameters
5752 Change the order of the parameters of the given set, relation
5754 such that the first parameters match those of C<model>.
5755 This may involve the introduction of extra parameters.
5756 All parameters need to be named.
5758 #include <isl/space.h>
5759 __isl_give isl_space *isl_space_align_params(
5760 __isl_take isl_space *space1,
5761 __isl_take isl_space *space2)
5763 #include <isl/set.h>
5764 __isl_give isl_basic_set *isl_basic_set_align_params(
5765 __isl_take isl_basic_set *bset,
5766 __isl_take isl_space *model);
5767 __isl_give isl_set *isl_set_align_params(
5768 __isl_take isl_set *set,
5769 __isl_take isl_space *model);
5771 #include <isl/map.h>
5772 __isl_give isl_basic_map *isl_basic_map_align_params(
5773 __isl_take isl_basic_map *bmap,
5774 __isl_take isl_space *model);
5775 __isl_give isl_map *isl_map_align_params(
5776 __isl_take isl_map *map,
5777 __isl_take isl_space *model);
5779 #include <isl/val.h>
5780 __isl_give isl_multi_val *isl_multi_val_align_params(
5781 __isl_take isl_multi_val *mv,
5782 __isl_take isl_space *model);
5784 #include <isl/aff.h>
5785 __isl_give isl_aff *isl_aff_align_params(
5786 __isl_take isl_aff *aff,
5787 __isl_take isl_space *model);
5788 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5789 __isl_take isl_multi_aff *multi,
5790 __isl_take isl_space *model);
5791 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5792 __isl_take isl_pw_aff *pwaff,
5793 __isl_take isl_space *model);
5794 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5795 __isl_take isl_pw_multi_aff *pma,
5796 __isl_take isl_space *model);
5797 __isl_give isl_union_pw_aff *
5798 isl_union_pw_aff_align_params(
5799 __isl_take isl_union_pw_aff *upa,
5800 __isl_take isl_space *model);
5801 __isl_give isl_union_pw_multi_aff *
5802 isl_union_pw_multi_aff_align_params(
5803 __isl_take isl_union_pw_multi_aff *upma,
5804 __isl_take isl_space *model);
5805 __isl_give isl_multi_union_pw_aff *
5806 isl_multi_union_pw_aff_align_params(
5807 __isl_take isl_multi_union_pw_aff *mupa,
5808 __isl_take isl_space *model);
5810 #include <isl/polynomial.h>
5811 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5812 __isl_take isl_qpolynomial *qp,
5813 __isl_take isl_space *model);
5815 =item * Drop unused parameters
5817 Drop parameters that are not referenced by the isl object.
5818 All parameters need to be named.
5820 #include <isl/set.h>
5821 __isl_give isl_basic_set *
5822 isl_basic_set_drop_unused_params(
5823 __isl_take isl_basic_set *bset);
5824 __isl_give isl_set *isl_set_drop_unused_params(
5825 __isl_take isl_set *set);
5827 #include <isl/map.h>
5828 __isl_give isl_basic_map *
5829 isl_basic_map_drop_unused_params(
5830 __isl_take isl_basic_map *bmap);
5831 __isl_give isl_map *isl_map_drop_unused_params(
5832 __isl_take isl_map *map);
5834 #include <isl/aff.h>
5835 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
5836 __isl_take isl_pw_aff *pa);
5837 __isl_give isl_pw_multi_aff *
5838 isl_pw_multi_aff_drop_unused_params(
5839 __isl_take isl_pw_multi_aff *pma);
5841 #include <isl/polynomial.h>
5842 __isl_give isl_pw_qpolynomial *
5843 isl_pw_qpolynomial_drop_unused_params(
5844 __isl_take isl_pw_qpolynomial *pwqp);
5845 __isl_give isl_pw_qpolynomial_fold *
5846 isl_pw_qpolynomial_fold_drop_unused_params(
5847 __isl_take isl_pw_qpolynomial_fold *pwf);
5849 =item * Unary Arithmetic Operations
5851 #include <isl/set.h>
5852 __isl_give isl_set *isl_set_neg(
5853 __isl_take isl_set *set);
5854 #include <isl/map.h>
5855 __isl_give isl_map *isl_map_neg(
5856 __isl_take isl_map *map);
5858 C<isl_set_neg> constructs a set containing the opposites of
5859 the elements in its argument.
5860 The domain of the result of C<isl_map_neg> is the same
5861 as the domain of its argument. The corresponding range
5862 elements are the opposites of the corresponding range
5863 elements in the argument.
5865 #include <isl/val.h>
5866 __isl_give isl_multi_val *isl_multi_val_neg(
5867 __isl_take isl_multi_val *mv);
5869 #include <isl/aff.h>
5870 __isl_give isl_aff *isl_aff_neg(
5871 __isl_take isl_aff *aff);
5872 __isl_give isl_multi_aff *isl_multi_aff_neg(
5873 __isl_take isl_multi_aff *ma);
5874 __isl_give isl_pw_aff *isl_pw_aff_neg(
5875 __isl_take isl_pw_aff *pwaff);
5876 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5877 __isl_take isl_pw_multi_aff *pma);
5878 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5879 __isl_take isl_multi_pw_aff *mpa);
5880 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5881 __isl_take isl_union_pw_aff *upa);
5882 __isl_give isl_union_pw_multi_aff *
5883 isl_union_pw_multi_aff_neg(
5884 __isl_take isl_union_pw_multi_aff *upma);
5885 __isl_give isl_multi_union_pw_aff *
5886 isl_multi_union_pw_aff_neg(
5887 __isl_take isl_multi_union_pw_aff *mupa);
5888 __isl_give isl_aff *isl_aff_ceil(
5889 __isl_take isl_aff *aff);
5890 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5891 __isl_take isl_pw_aff *pwaff);
5892 __isl_give isl_aff *isl_aff_floor(
5893 __isl_take isl_aff *aff);
5894 __isl_give isl_multi_aff *isl_multi_aff_floor(
5895 __isl_take isl_multi_aff *ma);
5896 __isl_give isl_pw_aff *isl_pw_aff_floor(
5897 __isl_take isl_pw_aff *pwaff);
5898 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5899 __isl_take isl_union_pw_aff *upa);
5900 __isl_give isl_multi_union_pw_aff *
5901 isl_multi_union_pw_aff_floor(
5902 __isl_take isl_multi_union_pw_aff *mupa);
5904 #include <isl/aff.h>
5905 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5906 __isl_take isl_pw_aff_list *list);
5907 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5908 __isl_take isl_pw_aff_list *list);
5910 #include <isl/polynomial.h>
5911 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5912 __isl_take isl_qpolynomial *qp);
5913 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5914 __isl_take isl_pw_qpolynomial *pwqp);
5915 __isl_give isl_union_pw_qpolynomial *
5916 isl_union_pw_qpolynomial_neg(
5917 __isl_take isl_union_pw_qpolynomial *upwqp);
5918 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5919 __isl_take isl_qpolynomial *qp,
5921 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5922 __isl_take isl_pw_qpolynomial *pwqp,
5927 The following functions evaluate a function in a point.
5929 #include <isl/aff.h>
5930 __isl_give isl_val *isl_aff_eval(
5931 __isl_take isl_aff *aff,
5932 __isl_take isl_point *pnt);
5933 __isl_give isl_val *isl_pw_aff_eval(
5934 __isl_take isl_pw_aff *pa,
5935 __isl_take isl_point *pnt);
5937 #include <isl/polynomial.h>
5938 __isl_give isl_val *isl_pw_qpolynomial_eval(
5939 __isl_take isl_pw_qpolynomial *pwqp,
5940 __isl_take isl_point *pnt);
5941 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5942 __isl_take isl_pw_qpolynomial_fold *pwf,
5943 __isl_take isl_point *pnt);
5944 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5945 __isl_take isl_union_pw_qpolynomial *upwqp,
5946 __isl_take isl_point *pnt);
5947 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5948 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5949 __isl_take isl_point *pnt);
5951 These functions return NaN when evaluated at a void point.
5952 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
5953 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
5954 when the function is evaluated outside its explicit domain.
5956 =item * Dimension manipulation
5958 It is usually not advisable to directly change the (input or output)
5959 space of a set or a relation as this removes the name and the internal
5960 structure of the space. However, the functions below can be useful
5961 to add new parameters, assuming
5962 C<isl_set_align_params> and C<isl_map_align_params>
5965 #include <isl/space.h>
5966 __isl_give isl_space *isl_space_add_dims(
5967 __isl_take isl_space *space,
5968 enum isl_dim_type type, unsigned n);
5969 __isl_give isl_space *isl_space_insert_dims(
5970 __isl_take isl_space *space,
5971 enum isl_dim_type type, unsigned pos, unsigned n);
5972 __isl_give isl_space *isl_space_drop_dims(
5973 __isl_take isl_space *space,
5974 enum isl_dim_type type, unsigned first, unsigned n);
5975 __isl_give isl_space *isl_space_move_dims(
5976 __isl_take isl_space *space,
5977 enum isl_dim_type dst_type, unsigned dst_pos,
5978 enum isl_dim_type src_type, unsigned src_pos,
5981 #include <isl/local_space.h>
5982 __isl_give isl_local_space *isl_local_space_add_dims(
5983 __isl_take isl_local_space *ls,
5984 enum isl_dim_type type, unsigned n);
5985 __isl_give isl_local_space *isl_local_space_insert_dims(
5986 __isl_take isl_local_space *ls,
5987 enum isl_dim_type type, unsigned first, unsigned n);
5988 __isl_give isl_local_space *isl_local_space_drop_dims(
5989 __isl_take isl_local_space *ls,
5990 enum isl_dim_type type, unsigned first, unsigned n);
5992 #include <isl/set.h>
5993 __isl_give isl_basic_set *isl_basic_set_add_dims(
5994 __isl_take isl_basic_set *bset,
5995 enum isl_dim_type type, unsigned n);
5996 __isl_give isl_set *isl_set_add_dims(
5997 __isl_take isl_set *set,
5998 enum isl_dim_type type, unsigned n);
5999 __isl_give isl_basic_set *isl_basic_set_insert_dims(
6000 __isl_take isl_basic_set *bset,
6001 enum isl_dim_type type, unsigned pos,
6003 __isl_give isl_set *isl_set_insert_dims(
6004 __isl_take isl_set *set,
6005 enum isl_dim_type type, unsigned pos, unsigned n);
6006 __isl_give isl_basic_set *isl_basic_set_move_dims(
6007 __isl_take isl_basic_set *bset,
6008 enum isl_dim_type dst_type, unsigned dst_pos,
6009 enum isl_dim_type src_type, unsigned src_pos,
6011 __isl_give isl_set *isl_set_move_dims(
6012 __isl_take isl_set *set,
6013 enum isl_dim_type dst_type, unsigned dst_pos,
6014 enum isl_dim_type src_type, unsigned src_pos,
6017 #include <isl/map.h>
6018 __isl_give isl_basic_map *isl_basic_map_add_dims(
6019 __isl_take isl_basic_map *bmap,
6020 enum isl_dim_type type, unsigned n);
6021 __isl_give isl_map *isl_map_add_dims(
6022 __isl_take isl_map *map,
6023 enum isl_dim_type type, unsigned n);
6024 __isl_give isl_basic_map *isl_basic_map_insert_dims(
6025 __isl_take isl_basic_map *bmap,
6026 enum isl_dim_type type, unsigned pos,
6028 __isl_give isl_map *isl_map_insert_dims(
6029 __isl_take isl_map *map,
6030 enum isl_dim_type type, unsigned pos, unsigned n);
6031 __isl_give isl_basic_map *isl_basic_map_move_dims(
6032 __isl_take isl_basic_map *bmap,
6033 enum isl_dim_type dst_type, unsigned dst_pos,
6034 enum isl_dim_type src_type, unsigned src_pos,
6036 __isl_give isl_map *isl_map_move_dims(
6037 __isl_take isl_map *map,
6038 enum isl_dim_type dst_type, unsigned dst_pos,
6039 enum isl_dim_type src_type, unsigned src_pos,
6042 #include <isl/val.h>
6043 __isl_give isl_multi_val *isl_multi_val_insert_dims(
6044 __isl_take isl_multi_val *mv,
6045 enum isl_dim_type type, unsigned first, unsigned n);
6046 __isl_give isl_multi_val *isl_multi_val_add_dims(
6047 __isl_take isl_multi_val *mv,
6048 enum isl_dim_type type, unsigned n);
6049 __isl_give isl_multi_val *isl_multi_val_drop_dims(
6050 __isl_take isl_multi_val *mv,
6051 enum isl_dim_type type, unsigned first, unsigned n);
6053 #include <isl/aff.h>
6054 __isl_give isl_aff *isl_aff_insert_dims(
6055 __isl_take isl_aff *aff,
6056 enum isl_dim_type type, unsigned first, unsigned n);
6057 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
6058 __isl_take isl_multi_aff *ma,
6059 enum isl_dim_type type, unsigned first, unsigned n);
6060 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
6061 __isl_take isl_pw_aff *pwaff,
6062 enum isl_dim_type type, unsigned first, unsigned n);
6063 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
6064 __isl_take isl_multi_pw_aff *mpa,
6065 enum isl_dim_type type, unsigned first, unsigned n);
6066 __isl_give isl_aff *isl_aff_add_dims(
6067 __isl_take isl_aff *aff,
6068 enum isl_dim_type type, unsigned n);
6069 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
6070 __isl_take isl_multi_aff *ma,
6071 enum isl_dim_type type, unsigned n);
6072 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
6073 __isl_take isl_pw_aff *pwaff,
6074 enum isl_dim_type type, unsigned n);
6075 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
6076 __isl_take isl_multi_pw_aff *mpa,
6077 enum isl_dim_type type, unsigned n);
6078 __isl_give isl_aff *isl_aff_drop_dims(
6079 __isl_take isl_aff *aff,
6080 enum isl_dim_type type, unsigned first, unsigned n);
6081 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
6082 __isl_take isl_multi_aff *maff,
6083 enum isl_dim_type type, unsigned first, unsigned n);
6084 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
6085 __isl_take isl_pw_aff *pwaff,
6086 enum isl_dim_type type, unsigned first, unsigned n);
6087 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
6088 __isl_take isl_pw_multi_aff *pma,
6089 enum isl_dim_type type, unsigned first, unsigned n);
6090 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
6091 __isl_take isl_union_pw_aff *upa,
6092 enum isl_dim_type type, unsigned first, unsigned n);
6093 __isl_give isl_union_pw_multi_aff *
6094 isl_union_pw_multi_aff_drop_dims(
6095 __isl_take isl_union_pw_multi_aff *upma,
6096 enum isl_dim_type type,
6097 unsigned first, unsigned n);
6098 __isl_give isl_multi_union_pw_aff *
6099 isl_multi_union_pw_aff_drop_dims(
6100 __isl_take isl_multi_union_pw_aff *mupa,
6101 enum isl_dim_type type, unsigned first,
6103 __isl_give isl_aff *isl_aff_move_dims(
6104 __isl_take isl_aff *aff,
6105 enum isl_dim_type dst_type, unsigned dst_pos,
6106 enum isl_dim_type src_type, unsigned src_pos,
6108 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
6109 __isl_take isl_multi_aff *ma,
6110 enum isl_dim_type dst_type, unsigned dst_pos,
6111 enum isl_dim_type src_type, unsigned src_pos,
6113 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
6114 __isl_take isl_pw_aff *pa,
6115 enum isl_dim_type dst_type, unsigned dst_pos,
6116 enum isl_dim_type src_type, unsigned src_pos,
6118 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
6119 __isl_take isl_multi_pw_aff *pma,
6120 enum isl_dim_type dst_type, unsigned dst_pos,
6121 enum isl_dim_type src_type, unsigned src_pos,
6124 #include <isl/polynomial.h>
6125 __isl_give isl_union_pw_qpolynomial *
6126 isl_union_pw_qpolynomial_drop_dims(
6127 __isl_take isl_union_pw_qpolynomial *upwqp,
6128 enum isl_dim_type type,
6129 unsigned first, unsigned n);
6130 __isl_give isl_union_pw_qpolynomial_fold *
6131 isl_union_pw_qpolynomial_fold_drop_dims(
6132 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6133 enum isl_dim_type type,
6134 unsigned first, unsigned n);
6136 The operations on union expressions can only manipulate parameters.
6140 =head2 Binary Operations
6142 The two arguments of a binary operation not only need to live
6143 in the same C<isl_ctx>, they currently also need to have
6144 the same (number of) parameters.
6146 =head3 Basic Operations
6150 =item * Intersection
6152 #include <isl/local_space.h>
6153 __isl_give isl_local_space *isl_local_space_intersect(
6154 __isl_take isl_local_space *ls1,
6155 __isl_take isl_local_space *ls2);
6157 #include <isl/set.h>
6158 __isl_give isl_basic_set *isl_basic_set_intersect_params(
6159 __isl_take isl_basic_set *bset1,
6160 __isl_take isl_basic_set *bset2);
6161 __isl_give isl_basic_set *isl_basic_set_intersect(
6162 __isl_take isl_basic_set *bset1,
6163 __isl_take isl_basic_set *bset2);
6164 __isl_give isl_basic_set *isl_basic_set_list_intersect(
6165 __isl_take struct isl_basic_set_list *list);
6166 __isl_give isl_set *isl_set_intersect_params(
6167 __isl_take isl_set *set,
6168 __isl_take isl_set *params);
6169 __isl_give isl_set *isl_set_intersect(
6170 __isl_take isl_set *set1,
6171 __isl_take isl_set *set2);
6173 #include <isl/map.h>
6174 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
6175 __isl_take isl_basic_map *bmap,
6176 __isl_take isl_basic_set *bset);
6177 __isl_give isl_basic_map *isl_basic_map_intersect_range(
6178 __isl_take isl_basic_map *bmap,
6179 __isl_take isl_basic_set *bset);
6180 __isl_give isl_basic_map *isl_basic_map_intersect(
6181 __isl_take isl_basic_map *bmap1,
6182 __isl_take isl_basic_map *bmap2);
6183 __isl_give isl_basic_map *isl_basic_map_list_intersect(
6184 __isl_take isl_basic_map_list *list);
6185 __isl_give isl_map *isl_map_intersect_params(
6186 __isl_take isl_map *map,
6187 __isl_take isl_set *params);
6188 __isl_give isl_map *isl_map_intersect_domain(
6189 __isl_take isl_map *map,
6190 __isl_take isl_set *set);
6191 __isl_give isl_map *isl_map_intersect_range(
6192 __isl_take isl_map *map,
6193 __isl_take isl_set *set);
6194 __isl_give isl_map *isl_map_intersect(
6195 __isl_take isl_map *map1,
6196 __isl_take isl_map *map2);
6197 __isl_give isl_map *
6198 isl_map_intersect_domain_factor_range(
6199 __isl_take isl_map *map,
6200 __isl_take isl_map *factor);
6201 __isl_give isl_map *
6202 isl_map_intersect_range_factor_range(
6203 __isl_take isl_map *map,
6204 __isl_take isl_map *factor);
6206 #include <isl/union_set.h>
6207 __isl_give isl_union_set *isl_union_set_intersect_params(
6208 __isl_take isl_union_set *uset,
6209 __isl_take isl_set *set);
6210 __isl_give isl_union_set *isl_union_set_intersect(
6211 __isl_take isl_union_set *uset1,
6212 __isl_take isl_union_set *uset2);
6214 #include <isl/union_map.h>
6215 __isl_give isl_union_map *isl_union_map_intersect_params(
6216 __isl_take isl_union_map *umap,
6217 __isl_take isl_set *set);
6218 __isl_give isl_union_map *isl_union_map_intersect_domain(
6219 __isl_take isl_union_map *umap,
6220 __isl_take isl_union_set *uset);
6221 __isl_give isl_union_map *isl_union_map_intersect_range(
6222 __isl_take isl_union_map *umap,
6223 __isl_take isl_union_set *uset);
6224 __isl_give isl_union_map *isl_union_map_intersect(
6225 __isl_take isl_union_map *umap1,
6226 __isl_take isl_union_map *umap2);
6227 __isl_give isl_union_map *
6228 isl_union_map_intersect_range_factor_range(
6229 __isl_take isl_union_map *umap,
6230 __isl_take isl_union_map *factor);
6232 #include <isl/aff.h>
6233 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6234 __isl_take isl_pw_aff *pa,
6235 __isl_take isl_set *set);
6236 __isl_give isl_multi_pw_aff *
6237 isl_multi_pw_aff_intersect_domain(
6238 __isl_take isl_multi_pw_aff *mpa,
6239 __isl_take isl_set *domain);
6240 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6241 __isl_take isl_pw_multi_aff *pma,
6242 __isl_take isl_set *set);
6243 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6244 __isl_take isl_union_pw_aff *upa,
6245 __isl_take isl_union_set *uset);
6246 __isl_give isl_union_pw_multi_aff *
6247 isl_union_pw_multi_aff_intersect_domain(
6248 __isl_take isl_union_pw_multi_aff *upma,
6249 __isl_take isl_union_set *uset);
6250 __isl_give isl_multi_union_pw_aff *
6251 isl_multi_union_pw_aff_intersect_domain(
6252 __isl_take isl_multi_union_pw_aff *mupa,
6253 __isl_take isl_union_set *uset);
6254 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6255 __isl_take isl_pw_aff *pa,
6256 __isl_take isl_set *set);
6257 __isl_give isl_multi_pw_aff *
6258 isl_multi_pw_aff_intersect_params(
6259 __isl_take isl_multi_pw_aff *mpa,
6260 __isl_take isl_set *set);
6261 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6262 __isl_take isl_pw_multi_aff *pma,
6263 __isl_take isl_set *set);
6264 __isl_give isl_union_pw_aff *
6265 isl_union_pw_aff_intersect_params(
6266 __isl_take isl_union_pw_aff *upa,
6267 __isl_give isl_union_pw_multi_aff *
6268 isl_union_pw_multi_aff_intersect_params(
6269 __isl_take isl_union_pw_multi_aff *upma,
6270 __isl_take isl_set *set);
6271 __isl_give isl_multi_union_pw_aff *
6272 isl_multi_union_pw_aff_intersect_params(
6273 __isl_take isl_multi_union_pw_aff *mupa,
6274 __isl_take isl_set *params);
6275 isl_multi_union_pw_aff_intersect_range(
6276 __isl_take isl_multi_union_pw_aff *mupa,
6277 __isl_take isl_set *set);
6279 #include <isl/polynomial.h>
6280 __isl_give isl_pw_qpolynomial *
6281 isl_pw_qpolynomial_intersect_domain(
6282 __isl_take isl_pw_qpolynomial *pwpq,
6283 __isl_take isl_set *set);
6284 __isl_give isl_union_pw_qpolynomial *
6285 isl_union_pw_qpolynomial_intersect_domain(
6286 __isl_take isl_union_pw_qpolynomial *upwpq,
6287 __isl_take isl_union_set *uset);
6288 __isl_give isl_union_pw_qpolynomial_fold *
6289 isl_union_pw_qpolynomial_fold_intersect_domain(
6290 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6291 __isl_take isl_union_set *uset);
6292 __isl_give isl_pw_qpolynomial *
6293 isl_pw_qpolynomial_intersect_params(
6294 __isl_take isl_pw_qpolynomial *pwpq,
6295 __isl_take isl_set *set);
6296 __isl_give isl_pw_qpolynomial_fold *
6297 isl_pw_qpolynomial_fold_intersect_params(
6298 __isl_take isl_pw_qpolynomial_fold *pwf,
6299 __isl_take isl_set *set);
6300 __isl_give isl_union_pw_qpolynomial *
6301 isl_union_pw_qpolynomial_intersect_params(
6302 __isl_take isl_union_pw_qpolynomial *upwpq,
6303 __isl_take isl_set *set);
6304 __isl_give isl_union_pw_qpolynomial_fold *
6305 isl_union_pw_qpolynomial_fold_intersect_params(
6306 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6307 __isl_take isl_set *set);
6309 The second argument to the C<_params> functions needs to be
6310 a parametric (basic) set. For the other functions, a parametric set
6311 for either argument is only allowed if the other argument is
6312 a parametric set as well.
6313 The list passed to C<isl_basic_set_list_intersect> needs to have
6314 at least one element and all elements need to live in the same space.
6315 The function C<isl_multi_union_pw_aff_intersect_range>
6316 restricts the input function to those shared domain elements
6317 that map to the specified range.
6321 #include <isl/set.h>
6322 __isl_give isl_set *isl_basic_set_union(
6323 __isl_take isl_basic_set *bset1,
6324 __isl_take isl_basic_set *bset2);
6325 __isl_give isl_set *isl_set_union(
6326 __isl_take isl_set *set1,
6327 __isl_take isl_set *set2);
6328 __isl_give isl_set *isl_set_list_union(
6329 __isl_take isl_set_list *list);
6331 #include <isl/map.h>
6332 __isl_give isl_map *isl_basic_map_union(
6333 __isl_take isl_basic_map *bmap1,
6334 __isl_take isl_basic_map *bmap2);
6335 __isl_give isl_map *isl_map_union(
6336 __isl_take isl_map *map1,
6337 __isl_take isl_map *map2);
6339 #include <isl/union_set.h>
6340 __isl_give isl_union_set *isl_union_set_union(
6341 __isl_take isl_union_set *uset1,
6342 __isl_take isl_union_set *uset2);
6343 __isl_give isl_union_set *isl_union_set_list_union(
6344 __isl_take isl_union_set_list *list);
6346 #include <isl/union_map.h>
6347 __isl_give isl_union_map *isl_union_map_union(
6348 __isl_take isl_union_map *umap1,
6349 __isl_take isl_union_map *umap2);
6351 The list passed to C<isl_set_list_union> needs to have
6352 at least one element and all elements need to live in the same space.
6354 =item * Set difference
6356 #include <isl/set.h>
6357 __isl_give isl_set *isl_set_subtract(
6358 __isl_take isl_set *set1,
6359 __isl_take isl_set *set2);
6361 #include <isl/map.h>
6362 __isl_give isl_map *isl_map_subtract(
6363 __isl_take isl_map *map1,
6364 __isl_take isl_map *map2);
6365 __isl_give isl_map *isl_map_subtract_domain(
6366 __isl_take isl_map *map,
6367 __isl_take isl_set *dom);
6368 __isl_give isl_map *isl_map_subtract_range(
6369 __isl_take isl_map *map,
6370 __isl_take isl_set *dom);
6372 #include <isl/union_set.h>
6373 __isl_give isl_union_set *isl_union_set_subtract(
6374 __isl_take isl_union_set *uset1,
6375 __isl_take isl_union_set *uset2);
6377 #include <isl/union_map.h>
6378 __isl_give isl_union_map *isl_union_map_subtract(
6379 __isl_take isl_union_map *umap1,
6380 __isl_take isl_union_map *umap2);
6381 __isl_give isl_union_map *isl_union_map_subtract_domain(
6382 __isl_take isl_union_map *umap,
6383 __isl_take isl_union_set *dom);
6384 __isl_give isl_union_map *isl_union_map_subtract_range(
6385 __isl_take isl_union_map *umap,
6386 __isl_take isl_union_set *dom);
6388 #include <isl/aff.h>
6389 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6390 __isl_take isl_pw_aff *pa,
6391 __isl_take isl_set *set);
6392 __isl_give isl_pw_multi_aff *
6393 isl_pw_multi_aff_subtract_domain(
6394 __isl_take isl_pw_multi_aff *pma,
6395 __isl_take isl_set *set);
6396 __isl_give isl_union_pw_aff *
6397 isl_union_pw_aff_subtract_domain(
6398 __isl_take isl_union_pw_aff *upa,
6399 __isl_take isl_union_set *uset);
6400 __isl_give isl_union_pw_multi_aff *
6401 isl_union_pw_multi_aff_subtract_domain(
6402 __isl_take isl_union_pw_multi_aff *upma,
6403 __isl_take isl_set *set);
6405 #include <isl/polynomial.h>
6406 __isl_give isl_pw_qpolynomial *
6407 isl_pw_qpolynomial_subtract_domain(
6408 __isl_take isl_pw_qpolynomial *pwpq,
6409 __isl_take isl_set *set);
6410 __isl_give isl_pw_qpolynomial_fold *
6411 isl_pw_qpolynomial_fold_subtract_domain(
6412 __isl_take isl_pw_qpolynomial_fold *pwf,
6413 __isl_take isl_set *set);
6414 __isl_give isl_union_pw_qpolynomial *
6415 isl_union_pw_qpolynomial_subtract_domain(
6416 __isl_take isl_union_pw_qpolynomial *upwpq,
6417 __isl_take isl_union_set *uset);
6418 __isl_give isl_union_pw_qpolynomial_fold *
6419 isl_union_pw_qpolynomial_fold_subtract_domain(
6420 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6421 __isl_take isl_union_set *uset);
6425 #include <isl/space.h>
6426 __isl_give isl_space *isl_space_join(
6427 __isl_take isl_space *left,
6428 __isl_take isl_space *right);
6430 #include <isl/map.h>
6431 __isl_give isl_basic_set *isl_basic_set_apply(
6432 __isl_take isl_basic_set *bset,
6433 __isl_take isl_basic_map *bmap);
6434 __isl_give isl_set *isl_set_apply(
6435 __isl_take isl_set *set,
6436 __isl_take isl_map *map);
6437 __isl_give isl_union_set *isl_union_set_apply(
6438 __isl_take isl_union_set *uset,
6439 __isl_take isl_union_map *umap);
6440 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6441 __isl_take isl_basic_map *bmap1,
6442 __isl_take isl_basic_map *bmap2);
6443 __isl_give isl_basic_map *isl_basic_map_apply_range(
6444 __isl_take isl_basic_map *bmap1,
6445 __isl_take isl_basic_map *bmap2);
6446 __isl_give isl_map *isl_map_apply_domain(
6447 __isl_take isl_map *map1,
6448 __isl_take isl_map *map2);
6449 __isl_give isl_map *isl_map_apply_range(
6450 __isl_take isl_map *map1,
6451 __isl_take isl_map *map2);
6453 #include <isl/union_map.h>
6454 __isl_give isl_union_map *isl_union_map_apply_domain(
6455 __isl_take isl_union_map *umap1,
6456 __isl_take isl_union_map *umap2);
6457 __isl_give isl_union_map *isl_union_map_apply_range(
6458 __isl_take isl_union_map *umap1,
6459 __isl_take isl_union_map *umap2);
6461 #include <isl/aff.h>
6462 __isl_give isl_union_pw_aff *
6463 isl_multi_union_pw_aff_apply_aff(
6464 __isl_take isl_multi_union_pw_aff *mupa,
6465 __isl_take isl_aff *aff);
6466 __isl_give isl_union_pw_aff *
6467 isl_multi_union_pw_aff_apply_pw_aff(
6468 __isl_take isl_multi_union_pw_aff *mupa,
6469 __isl_take isl_pw_aff *pa);
6470 __isl_give isl_multi_union_pw_aff *
6471 isl_multi_union_pw_aff_apply_multi_aff(
6472 __isl_take isl_multi_union_pw_aff *mupa,
6473 __isl_take isl_multi_aff *ma);
6474 __isl_give isl_multi_union_pw_aff *
6475 isl_multi_union_pw_aff_apply_pw_multi_aff(
6476 __isl_take isl_multi_union_pw_aff *mupa,
6477 __isl_take isl_pw_multi_aff *pma);
6479 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6480 over the shared domain of the elements of the input. The dimension is
6481 required to be greater than zero.
6482 The C<isl_multi_union_pw_aff> argument of
6483 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6484 but only if the range of the C<isl_multi_aff> argument
6485 is also zero-dimensional.
6486 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6488 #include <isl/polynomial.h>
6489 __isl_give isl_pw_qpolynomial_fold *
6490 isl_set_apply_pw_qpolynomial_fold(
6491 __isl_take isl_set *set,
6492 __isl_take isl_pw_qpolynomial_fold *pwf,
6494 __isl_give isl_pw_qpolynomial_fold *
6495 isl_map_apply_pw_qpolynomial_fold(
6496 __isl_take isl_map *map,
6497 __isl_take isl_pw_qpolynomial_fold *pwf,
6499 __isl_give isl_union_pw_qpolynomial_fold *
6500 isl_union_set_apply_union_pw_qpolynomial_fold(
6501 __isl_take isl_union_set *uset,
6502 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6504 __isl_give isl_union_pw_qpolynomial_fold *
6505 isl_union_map_apply_union_pw_qpolynomial_fold(
6506 __isl_take isl_union_map *umap,
6507 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6510 The functions taking a map
6511 compose the given map with the given piecewise quasipolynomial reduction.
6512 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6513 over all elements in the intersection of the range of the map
6514 and the domain of the piecewise quasipolynomial reduction
6515 as a function of an element in the domain of the map.
6516 The functions taking a set compute a bound over all elements in the
6517 intersection of the set and the domain of the
6518 piecewise quasipolynomial reduction.
6522 #include <isl/set.h>
6523 __isl_give isl_basic_set *
6524 isl_basic_set_preimage_multi_aff(
6525 __isl_take isl_basic_set *bset,
6526 __isl_take isl_multi_aff *ma);
6527 __isl_give isl_set *isl_set_preimage_multi_aff(
6528 __isl_take isl_set *set,
6529 __isl_take isl_multi_aff *ma);
6530 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6531 __isl_take isl_set *set,
6532 __isl_take isl_pw_multi_aff *pma);
6533 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6534 __isl_take isl_set *set,
6535 __isl_take isl_multi_pw_aff *mpa);
6537 #include <isl/union_set.h>
6538 __isl_give isl_union_set *
6539 isl_union_set_preimage_multi_aff(
6540 __isl_take isl_union_set *uset,
6541 __isl_take isl_multi_aff *ma);
6542 __isl_give isl_union_set *
6543 isl_union_set_preimage_pw_multi_aff(
6544 __isl_take isl_union_set *uset,
6545 __isl_take isl_pw_multi_aff *pma);
6546 __isl_give isl_union_set *
6547 isl_union_set_preimage_union_pw_multi_aff(
6548 __isl_take isl_union_set *uset,
6549 __isl_take isl_union_pw_multi_aff *upma);
6551 #include <isl/map.h>
6552 __isl_give isl_basic_map *
6553 isl_basic_map_preimage_domain_multi_aff(
6554 __isl_take isl_basic_map *bmap,
6555 __isl_take isl_multi_aff *ma);
6556 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6557 __isl_take isl_map *map,
6558 __isl_take isl_multi_aff *ma);
6559 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6560 __isl_take isl_map *map,
6561 __isl_take isl_multi_aff *ma);
6562 __isl_give isl_map *
6563 isl_map_preimage_domain_pw_multi_aff(
6564 __isl_take isl_map *map,
6565 __isl_take isl_pw_multi_aff *pma);
6566 __isl_give isl_map *
6567 isl_map_preimage_range_pw_multi_aff(
6568 __isl_take isl_map *map,
6569 __isl_take isl_pw_multi_aff *pma);
6570 __isl_give isl_map *
6571 isl_map_preimage_domain_multi_pw_aff(
6572 __isl_take isl_map *map,
6573 __isl_take isl_multi_pw_aff *mpa);
6574 __isl_give isl_basic_map *
6575 isl_basic_map_preimage_range_multi_aff(
6576 __isl_take isl_basic_map *bmap,
6577 __isl_take isl_multi_aff *ma);
6579 #include <isl/union_map.h>
6580 __isl_give isl_union_map *
6581 isl_union_map_preimage_domain_multi_aff(
6582 __isl_take isl_union_map *umap,
6583 __isl_take isl_multi_aff *ma);
6584 __isl_give isl_union_map *
6585 isl_union_map_preimage_range_multi_aff(
6586 __isl_take isl_union_map *umap,
6587 __isl_take isl_multi_aff *ma);
6588 __isl_give isl_union_map *
6589 isl_union_map_preimage_domain_pw_multi_aff(
6590 __isl_take isl_union_map *umap,
6591 __isl_take isl_pw_multi_aff *pma);
6592 __isl_give isl_union_map *
6593 isl_union_map_preimage_range_pw_multi_aff(
6594 __isl_take isl_union_map *umap,
6595 __isl_take isl_pw_multi_aff *pma);
6596 __isl_give isl_union_map *
6597 isl_union_map_preimage_domain_union_pw_multi_aff(
6598 __isl_take isl_union_map *umap,
6599 __isl_take isl_union_pw_multi_aff *upma);
6600 __isl_give isl_union_map *
6601 isl_union_map_preimage_range_union_pw_multi_aff(
6602 __isl_take isl_union_map *umap,
6603 __isl_take isl_union_pw_multi_aff *upma);
6605 These functions compute the preimage of the given set or map domain/range under
6606 the given function. In other words, the expression is plugged
6607 into the set description or into the domain/range of the map.
6611 #include <isl/aff.h>
6612 __isl_give isl_aff *isl_aff_pullback_aff(
6613 __isl_take isl_aff *aff1,
6614 __isl_take isl_aff *aff2);
6615 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6616 __isl_take isl_aff *aff,
6617 __isl_take isl_multi_aff *ma);
6618 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6619 __isl_take isl_pw_aff *pa,
6620 __isl_take isl_multi_aff *ma);
6621 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6622 __isl_take isl_pw_aff *pa,
6623 __isl_take isl_pw_multi_aff *pma);
6624 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6625 __isl_take isl_pw_aff *pa,
6626 __isl_take isl_multi_pw_aff *mpa);
6627 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6628 __isl_take isl_multi_aff *ma1,
6629 __isl_take isl_multi_aff *ma2);
6630 __isl_give isl_pw_multi_aff *
6631 isl_pw_multi_aff_pullback_multi_aff(
6632 __isl_take isl_pw_multi_aff *pma,
6633 __isl_take isl_multi_aff *ma);
6634 __isl_give isl_multi_pw_aff *
6635 isl_multi_pw_aff_pullback_multi_aff(
6636 __isl_take isl_multi_pw_aff *mpa,
6637 __isl_take isl_multi_aff *ma);
6638 __isl_give isl_pw_multi_aff *
6639 isl_pw_multi_aff_pullback_pw_multi_aff(
6640 __isl_take isl_pw_multi_aff *pma1,
6641 __isl_take isl_pw_multi_aff *pma2);
6642 __isl_give isl_multi_pw_aff *
6643 isl_multi_pw_aff_pullback_pw_multi_aff(
6644 __isl_take isl_multi_pw_aff *mpa,
6645 __isl_take isl_pw_multi_aff *pma);
6646 __isl_give isl_multi_pw_aff *
6647 isl_multi_pw_aff_pullback_multi_pw_aff(
6648 __isl_take isl_multi_pw_aff *mpa1,
6649 __isl_take isl_multi_pw_aff *mpa2);
6650 __isl_give isl_union_pw_aff *
6651 isl_union_pw_aff_pullback_union_pw_multi_aff(
6652 __isl_take isl_union_pw_aff *upa,
6653 __isl_take isl_union_pw_multi_aff *upma);
6654 __isl_give isl_union_pw_multi_aff *
6655 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6656 __isl_take isl_union_pw_multi_aff *upma1,
6657 __isl_take isl_union_pw_multi_aff *upma2);
6658 __isl_give isl_multi_union_pw_aff *
6659 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6660 __isl_take isl_multi_union_pw_aff *mupa,
6661 __isl_take isl_union_pw_multi_aff *upma);
6663 These functions precompose the first expression by the second function.
6664 In other words, the second function is plugged
6665 into the first expression.
6669 #include <isl/aff.h>
6670 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6671 __isl_take isl_aff *aff1,
6672 __isl_take isl_aff *aff2);
6673 __isl_give isl_set *isl_aff_eq_set(
6674 __isl_take isl_aff *aff1,
6675 __isl_take isl_aff *aff2);
6676 __isl_give isl_set *isl_aff_ne_set(
6677 __isl_take isl_aff *aff1,
6678 __isl_take isl_aff *aff2);
6679 __isl_give isl_basic_set *isl_aff_le_basic_set(
6680 __isl_take isl_aff *aff1,
6681 __isl_take isl_aff *aff2);
6682 __isl_give isl_set *isl_aff_le_set(
6683 __isl_take isl_aff *aff1,
6684 __isl_take isl_aff *aff2);
6685 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6686 __isl_take isl_aff *aff1,
6687 __isl_take isl_aff *aff2);
6688 __isl_give isl_set *isl_aff_lt_set(
6689 __isl_take isl_aff *aff1,
6690 __isl_take isl_aff *aff2);
6691 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6692 __isl_take isl_aff *aff1,
6693 __isl_take isl_aff *aff2);
6694 __isl_give isl_set *isl_aff_ge_set(
6695 __isl_take isl_aff *aff1,
6696 __isl_take isl_aff *aff2);
6697 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6698 __isl_take isl_aff *aff1,
6699 __isl_take isl_aff *aff2);
6700 __isl_give isl_set *isl_aff_gt_set(
6701 __isl_take isl_aff *aff1,
6702 __isl_take isl_aff *aff2);
6703 __isl_give isl_set *isl_pw_aff_eq_set(
6704 __isl_take isl_pw_aff *pwaff1,
6705 __isl_take isl_pw_aff *pwaff2);
6706 __isl_give isl_set *isl_pw_aff_ne_set(
6707 __isl_take isl_pw_aff *pwaff1,
6708 __isl_take isl_pw_aff *pwaff2);
6709 __isl_give isl_set *isl_pw_aff_le_set(
6710 __isl_take isl_pw_aff *pwaff1,
6711 __isl_take isl_pw_aff *pwaff2);
6712 __isl_give isl_set *isl_pw_aff_lt_set(
6713 __isl_take isl_pw_aff *pwaff1,
6714 __isl_take isl_pw_aff *pwaff2);
6715 __isl_give isl_set *isl_pw_aff_ge_set(
6716 __isl_take isl_pw_aff *pwaff1,
6717 __isl_take isl_pw_aff *pwaff2);
6718 __isl_give isl_set *isl_pw_aff_gt_set(
6719 __isl_take isl_pw_aff *pwaff1,
6720 __isl_take isl_pw_aff *pwaff2);
6722 __isl_give isl_set *isl_multi_aff_lex_le_set(
6723 __isl_take isl_multi_aff *ma1,
6724 __isl_take isl_multi_aff *ma2);
6725 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6726 __isl_take isl_multi_aff *ma1,
6727 __isl_take isl_multi_aff *ma2);
6728 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6729 __isl_take isl_multi_aff *ma1,
6730 __isl_take isl_multi_aff *ma2);
6731 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6732 __isl_take isl_multi_aff *ma1,
6733 __isl_take isl_multi_aff *ma2);
6735 __isl_give isl_set *isl_pw_aff_list_eq_set(
6736 __isl_take isl_pw_aff_list *list1,
6737 __isl_take isl_pw_aff_list *list2);
6738 __isl_give isl_set *isl_pw_aff_list_ne_set(
6739 __isl_take isl_pw_aff_list *list1,
6740 __isl_take isl_pw_aff_list *list2);
6741 __isl_give isl_set *isl_pw_aff_list_le_set(
6742 __isl_take isl_pw_aff_list *list1,
6743 __isl_take isl_pw_aff_list *list2);
6744 __isl_give isl_set *isl_pw_aff_list_lt_set(
6745 __isl_take isl_pw_aff_list *list1,
6746 __isl_take isl_pw_aff_list *list2);
6747 __isl_give isl_set *isl_pw_aff_list_ge_set(
6748 __isl_take isl_pw_aff_list *list1,
6749 __isl_take isl_pw_aff_list *list2);
6750 __isl_give isl_set *isl_pw_aff_list_gt_set(
6751 __isl_take isl_pw_aff_list *list1,
6752 __isl_take isl_pw_aff_list *list2);
6754 The function C<isl_aff_ge_basic_set> returns a basic set
6755 containing those elements in the shared space
6756 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6757 The function C<isl_pw_aff_ge_set> returns a set
6758 containing those elements in the shared domain
6759 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6760 greater than or equal to C<pwaff2>.
6761 The function C<isl_multi_aff_lex_le_set> returns a set
6762 containing those elements in the shared domain space
6763 where C<ma1> is lexicographically smaller than or
6765 The functions operating on C<isl_pw_aff_list> apply the corresponding
6766 C<isl_pw_aff> function to each pair of elements in the two lists.
6768 #include <isl/aff.h>
6769 __isl_give isl_map *isl_pw_aff_eq_map(
6770 __isl_take isl_pw_aff *pa1,
6771 __isl_take isl_pw_aff *pa2);
6772 __isl_give isl_map *isl_pw_aff_lt_map(
6773 __isl_take isl_pw_aff *pa1,
6774 __isl_take isl_pw_aff *pa2);
6775 __isl_give isl_map *isl_pw_aff_gt_map(
6776 __isl_take isl_pw_aff *pa1,
6777 __isl_take isl_pw_aff *pa2);
6779 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6780 __isl_take isl_multi_pw_aff *mpa1,
6781 __isl_take isl_multi_pw_aff *mpa2);
6782 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6783 __isl_take isl_multi_pw_aff *mpa1,
6784 __isl_take isl_multi_pw_aff *mpa2);
6785 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6786 __isl_take isl_multi_pw_aff *mpa1,
6787 __isl_take isl_multi_pw_aff *mpa2);
6789 These functions return a map between domain elements of the arguments
6790 where the function values satisfy the given relation.
6792 #include <isl/union_map.h>
6793 __isl_give isl_union_map *
6794 isl_union_map_eq_at_multi_union_pw_aff(
6795 __isl_take isl_union_map *umap,
6796 __isl_take isl_multi_union_pw_aff *mupa);
6797 __isl_give isl_union_map *
6798 isl_union_map_lex_lt_at_multi_union_pw_aff(
6799 __isl_take isl_union_map *umap,
6800 __isl_take isl_multi_union_pw_aff *mupa);
6801 __isl_give isl_union_map *
6802 isl_union_map_lex_gt_at_multi_union_pw_aff(
6803 __isl_take isl_union_map *umap,
6804 __isl_take isl_multi_union_pw_aff *mupa);
6806 These functions select the subset of elements in the union map
6807 that have an equal or lexicographically smaller function value.
6809 =item * Cartesian Product
6811 #include <isl/space.h>
6812 __isl_give isl_space *isl_space_product(
6813 __isl_take isl_space *space1,
6814 __isl_take isl_space *space2);
6815 __isl_give isl_space *isl_space_domain_product(
6816 __isl_take isl_space *space1,
6817 __isl_take isl_space *space2);
6818 __isl_give isl_space *isl_space_range_product(
6819 __isl_take isl_space *space1,
6820 __isl_take isl_space *space2);
6823 C<isl_space_product>, C<isl_space_domain_product>
6824 and C<isl_space_range_product> take pairs or relation spaces and
6825 produce a single relations space, where either the domain, the range
6826 or both domain and range are wrapped spaces of relations between
6827 the domains and/or ranges of the input spaces.
6828 If the product is only constructed over the domain or the range
6829 then the ranges or the domains of the inputs should be the same.
6830 The function C<isl_space_product> also accepts a pair of set spaces,
6831 in which case it returns a wrapped space of a relation between the
6834 #include <isl/set.h>
6835 __isl_give isl_set *isl_set_product(
6836 __isl_take isl_set *set1,
6837 __isl_take isl_set *set2);
6839 #include <isl/map.h>
6840 __isl_give isl_basic_map *isl_basic_map_domain_product(
6841 __isl_take isl_basic_map *bmap1,
6842 __isl_take isl_basic_map *bmap2);
6843 __isl_give isl_basic_map *isl_basic_map_range_product(
6844 __isl_take isl_basic_map *bmap1,
6845 __isl_take isl_basic_map *bmap2);
6846 __isl_give isl_basic_map *isl_basic_map_product(
6847 __isl_take isl_basic_map *bmap1,
6848 __isl_take isl_basic_map *bmap2);
6849 __isl_give isl_map *isl_map_domain_product(
6850 __isl_take isl_map *map1,
6851 __isl_take isl_map *map2);
6852 __isl_give isl_map *isl_map_range_product(
6853 __isl_take isl_map *map1,
6854 __isl_take isl_map *map2);
6855 __isl_give isl_map *isl_map_product(
6856 __isl_take isl_map *map1,
6857 __isl_take isl_map *map2);
6859 #include <isl/union_set.h>
6860 __isl_give isl_union_set *isl_union_set_product(
6861 __isl_take isl_union_set *uset1,
6862 __isl_take isl_union_set *uset2);
6864 #include <isl/union_map.h>
6865 __isl_give isl_union_map *isl_union_map_domain_product(
6866 __isl_take isl_union_map *umap1,
6867 __isl_take isl_union_map *umap2);
6868 __isl_give isl_union_map *isl_union_map_range_product(
6869 __isl_take isl_union_map *umap1,
6870 __isl_take isl_union_map *umap2);
6871 __isl_give isl_union_map *isl_union_map_product(
6872 __isl_take isl_union_map *umap1,
6873 __isl_take isl_union_map *umap2);
6875 #include <isl/val.h>
6876 __isl_give isl_multi_val *isl_multi_val_range_product(
6877 __isl_take isl_multi_val *mv1,
6878 __isl_take isl_multi_val *mv2);
6879 __isl_give isl_multi_val *isl_multi_val_product(
6880 __isl_take isl_multi_val *mv1,
6881 __isl_take isl_multi_val *mv2);
6883 #include <isl/aff.h>
6884 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6885 __isl_take isl_multi_aff *ma1,
6886 __isl_take isl_multi_aff *ma2);
6887 __isl_give isl_multi_aff *isl_multi_aff_product(
6888 __isl_take isl_multi_aff *ma1,
6889 __isl_take isl_multi_aff *ma2);
6890 __isl_give isl_multi_pw_aff *
6891 isl_multi_pw_aff_range_product(
6892 __isl_take isl_multi_pw_aff *mpa1,
6893 __isl_take isl_multi_pw_aff *mpa2);
6894 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6895 __isl_take isl_multi_pw_aff *mpa1,
6896 __isl_take isl_multi_pw_aff *mpa2);
6897 __isl_give isl_pw_multi_aff *
6898 isl_pw_multi_aff_range_product(
6899 __isl_take isl_pw_multi_aff *pma1,
6900 __isl_take isl_pw_multi_aff *pma2);
6901 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6902 __isl_take isl_pw_multi_aff *pma1,
6903 __isl_take isl_pw_multi_aff *pma2);
6904 __isl_give isl_multi_union_pw_aff *
6905 isl_multi_union_pw_aff_range_product(
6906 __isl_take isl_multi_union_pw_aff *mupa1,
6907 __isl_take isl_multi_union_pw_aff *mupa2);
6909 The above functions compute the cross product of the given
6910 sets, relations or functions. The domains and ranges of the results
6911 are wrapped maps between domains and ranges of the inputs.
6912 To obtain a ``flat'' product, use the following functions
6915 #include <isl/set.h>
6916 __isl_give isl_basic_set *isl_basic_set_flat_product(
6917 __isl_take isl_basic_set *bset1,
6918 __isl_take isl_basic_set *bset2);
6919 __isl_give isl_set *isl_set_flat_product(
6920 __isl_take isl_set *set1,
6921 __isl_take isl_set *set2);
6923 #include <isl/map.h>
6924 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6925 __isl_take isl_basic_map *bmap1,
6926 __isl_take isl_basic_map *bmap2);
6927 __isl_give isl_map *isl_map_flat_domain_product(
6928 __isl_take isl_map *map1,
6929 __isl_take isl_map *map2);
6930 __isl_give isl_map *isl_map_flat_range_product(
6931 __isl_take isl_map *map1,
6932 __isl_take isl_map *map2);
6933 __isl_give isl_basic_map *isl_basic_map_flat_product(
6934 __isl_take isl_basic_map *bmap1,
6935 __isl_take isl_basic_map *bmap2);
6936 __isl_give isl_map *isl_map_flat_product(
6937 __isl_take isl_map *map1,
6938 __isl_take isl_map *map2);
6940 #include <isl/union_map.h>
6941 __isl_give isl_union_map *
6942 isl_union_map_flat_domain_product(
6943 __isl_take isl_union_map *umap1,
6944 __isl_take isl_union_map *umap2);
6945 __isl_give isl_union_map *
6946 isl_union_map_flat_range_product(
6947 __isl_take isl_union_map *umap1,
6948 __isl_take isl_union_map *umap2);
6950 #include <isl/val.h>
6951 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6952 __isl_take isl_multi_val *mv1,
6953 __isl_take isl_multi_val *mv2);
6955 #include <isl/aff.h>
6956 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6957 __isl_take isl_multi_aff *ma1,
6958 __isl_take isl_multi_aff *ma2);
6959 __isl_give isl_pw_multi_aff *
6960 isl_pw_multi_aff_flat_range_product(
6961 __isl_take isl_pw_multi_aff *pma1,
6962 __isl_take isl_pw_multi_aff *pma2);
6963 __isl_give isl_multi_pw_aff *
6964 isl_multi_pw_aff_flat_range_product(
6965 __isl_take isl_multi_pw_aff *mpa1,
6966 __isl_take isl_multi_pw_aff *mpa2);
6967 __isl_give isl_union_pw_multi_aff *
6968 isl_union_pw_multi_aff_flat_range_product(
6969 __isl_take isl_union_pw_multi_aff *upma1,
6970 __isl_take isl_union_pw_multi_aff *upma2);
6971 __isl_give isl_multi_union_pw_aff *
6972 isl_multi_union_pw_aff_flat_range_product(
6973 __isl_take isl_multi_union_pw_aff *mupa1,
6974 __isl_take isl_multi_union_pw_aff *mupa2);
6976 #include <isl/space.h>
6977 __isl_give isl_space *isl_space_factor_domain(
6978 __isl_take isl_space *space);
6979 __isl_give isl_space *isl_space_factor_range(
6980 __isl_take isl_space *space);
6981 __isl_give isl_space *isl_space_domain_factor_domain(
6982 __isl_take isl_space *space);
6983 __isl_give isl_space *isl_space_domain_factor_range(
6984 __isl_take isl_space *space);
6985 __isl_give isl_space *isl_space_range_factor_domain(
6986 __isl_take isl_space *space);
6987 __isl_give isl_space *isl_space_range_factor_range(
6988 __isl_take isl_space *space);
6990 The functions C<isl_space_range_factor_domain> and
6991 C<isl_space_range_factor_range> extract the two arguments from
6992 the result of a call to C<isl_space_range_product>.
6994 The arguments of a call to a product can be extracted
6995 from the result using the following functions.
6997 #include <isl/map.h>
6998 __isl_give isl_map *isl_map_factor_domain(
6999 __isl_take isl_map *map);
7000 __isl_give isl_map *isl_map_factor_range(
7001 __isl_take isl_map *map);
7002 __isl_give isl_map *isl_map_domain_factor_domain(
7003 __isl_take isl_map *map);
7004 __isl_give isl_map *isl_map_domain_factor_range(
7005 __isl_take isl_map *map);
7006 __isl_give isl_map *isl_map_range_factor_domain(
7007 __isl_take isl_map *map);
7008 __isl_give isl_map *isl_map_range_factor_range(
7009 __isl_take isl_map *map);
7011 #include <isl/union_map.h>
7012 __isl_give isl_union_map *isl_union_map_factor_domain(
7013 __isl_take isl_union_map *umap);
7014 __isl_give isl_union_map *isl_union_map_factor_range(
7015 __isl_take isl_union_map *umap);
7016 __isl_give isl_union_map *
7017 isl_union_map_domain_factor_domain(
7018 __isl_take isl_union_map *umap);
7019 __isl_give isl_union_map *
7020 isl_union_map_domain_factor_range(
7021 __isl_take isl_union_map *umap);
7022 __isl_give isl_union_map *
7023 isl_union_map_range_factor_domain(
7024 __isl_take isl_union_map *umap);
7025 __isl_give isl_union_map *
7026 isl_union_map_range_factor_range(
7027 __isl_take isl_union_map *umap);
7029 #include <isl/val.h>
7030 __isl_give isl_multi_val *isl_multi_val_factor_range(
7031 __isl_take isl_multi_val *mv);
7032 __isl_give isl_multi_val *
7033 isl_multi_val_range_factor_domain(
7034 __isl_take isl_multi_val *mv);
7035 __isl_give isl_multi_val *
7036 isl_multi_val_range_factor_range(
7037 __isl_take isl_multi_val *mv);
7039 #include <isl/aff.h>
7040 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
7041 __isl_take isl_multi_aff *ma);
7042 __isl_give isl_multi_aff *
7043 isl_multi_aff_range_factor_domain(
7044 __isl_take isl_multi_aff *ma);
7045 __isl_give isl_multi_aff *
7046 isl_multi_aff_range_factor_range(
7047 __isl_take isl_multi_aff *ma);
7048 __isl_give isl_multi_pw_aff *
7049 isl_multi_pw_aff_factor_range(
7050 __isl_take isl_multi_pw_aff *mpa);
7051 __isl_give isl_multi_pw_aff *
7052 isl_multi_pw_aff_range_factor_domain(
7053 __isl_take isl_multi_pw_aff *mpa);
7054 __isl_give isl_multi_pw_aff *
7055 isl_multi_pw_aff_range_factor_range(
7056 __isl_take isl_multi_pw_aff *mpa);
7057 __isl_give isl_multi_union_pw_aff *
7058 isl_multi_union_pw_aff_factor_range(
7059 __isl_take isl_multi_union_pw_aff *mupa);
7060 __isl_give isl_multi_union_pw_aff *
7061 isl_multi_union_pw_aff_range_factor_domain(
7062 __isl_take isl_multi_union_pw_aff *mupa);
7063 __isl_give isl_multi_union_pw_aff *
7064 isl_multi_union_pw_aff_range_factor_range(
7065 __isl_take isl_multi_union_pw_aff *mupa);
7067 The splice functions are a generalization of the flat product functions,
7068 where the second argument may be inserted at any position inside
7069 the first argument rather than being placed at the end.
7070 The functions C<isl_multi_val_factor_range>,
7071 C<isl_multi_aff_factor_range>,
7072 C<isl_multi_pw_aff_factor_range> and
7073 C<isl_multi_union_pw_aff_factor_range>
7074 take functions that live in a set space.
7076 #include <isl/val.h>
7077 __isl_give isl_multi_val *isl_multi_val_range_splice(
7078 __isl_take isl_multi_val *mv1, unsigned pos,
7079 __isl_take isl_multi_val *mv2);
7081 #include <isl/aff.h>
7082 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
7083 __isl_take isl_multi_aff *ma1, unsigned pos,
7084 __isl_take isl_multi_aff *ma2);
7085 __isl_give isl_multi_aff *isl_multi_aff_splice(
7086 __isl_take isl_multi_aff *ma1,
7087 unsigned in_pos, unsigned out_pos,
7088 __isl_take isl_multi_aff *ma2);
7089 __isl_give isl_multi_pw_aff *
7090 isl_multi_pw_aff_range_splice(
7091 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
7092 __isl_take isl_multi_pw_aff *mpa2);
7093 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
7094 __isl_take isl_multi_pw_aff *mpa1,
7095 unsigned in_pos, unsigned out_pos,
7096 __isl_take isl_multi_pw_aff *mpa2);
7097 __isl_give isl_multi_union_pw_aff *
7098 isl_multi_union_pw_aff_range_splice(
7099 __isl_take isl_multi_union_pw_aff *mupa1,
7101 __isl_take isl_multi_union_pw_aff *mupa2);
7103 =item * Simplification
7105 When applied to a set or relation,
7106 the gist operation returns a set or relation that has the
7107 same intersection with the context as the input set or relation.
7108 Any implicit equality in the intersection is made explicit in the result,
7109 while all inequalities that are redundant with respect to the intersection
7111 In case of union sets and relations, the gist operation is performed
7114 When applied to a function,
7115 the gist operation applies the set gist operation to each of
7116 the cells in the domain of the input piecewise expression.
7117 The context is also exploited
7118 to simplify the expression associated to each cell.
7120 #include <isl/set.h>
7121 __isl_give isl_basic_set *isl_basic_set_gist(
7122 __isl_take isl_basic_set *bset,
7123 __isl_take isl_basic_set *context);
7124 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
7125 __isl_take isl_set *context);
7126 __isl_give isl_set *isl_set_gist_params(
7127 __isl_take isl_set *set,
7128 __isl_take isl_set *context);
7130 #include <isl/map.h>
7131 __isl_give isl_basic_map *isl_basic_map_gist(
7132 __isl_take isl_basic_map *bmap,
7133 __isl_take isl_basic_map *context);
7134 __isl_give isl_basic_map *isl_basic_map_gist_domain(
7135 __isl_take isl_basic_map *bmap,
7136 __isl_take isl_basic_set *context);
7137 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
7138 __isl_take isl_map *context);
7139 __isl_give isl_map *isl_map_gist_params(
7140 __isl_take isl_map *map,
7141 __isl_take isl_set *context);
7142 __isl_give isl_map *isl_map_gist_domain(
7143 __isl_take isl_map *map,
7144 __isl_take isl_set *context);
7145 __isl_give isl_map *isl_map_gist_range(
7146 __isl_take isl_map *map,
7147 __isl_take isl_set *context);
7149 #include <isl/union_set.h>
7150 __isl_give isl_union_set *isl_union_set_gist(
7151 __isl_take isl_union_set *uset,
7152 __isl_take isl_union_set *context);
7153 __isl_give isl_union_set *isl_union_set_gist_params(
7154 __isl_take isl_union_set *uset,
7155 __isl_take isl_set *set);
7157 #include <isl/union_map.h>
7158 __isl_give isl_union_map *isl_union_map_gist(
7159 __isl_take isl_union_map *umap,
7160 __isl_take isl_union_map *context);
7161 __isl_give isl_union_map *isl_union_map_gist_params(
7162 __isl_take isl_union_map *umap,
7163 __isl_take isl_set *set);
7164 __isl_give isl_union_map *isl_union_map_gist_domain(
7165 __isl_take isl_union_map *umap,
7166 __isl_take isl_union_set *uset);
7167 __isl_give isl_union_map *isl_union_map_gist_range(
7168 __isl_take isl_union_map *umap,
7169 __isl_take isl_union_set *uset);
7171 #include <isl/aff.h>
7172 __isl_give isl_aff *isl_aff_gist_params(
7173 __isl_take isl_aff *aff,
7174 __isl_take isl_set *context);
7175 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
7176 __isl_take isl_set *context);
7177 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
7178 __isl_take isl_multi_aff *maff,
7179 __isl_take isl_set *context);
7180 __isl_give isl_multi_aff *isl_multi_aff_gist(
7181 __isl_take isl_multi_aff *maff,
7182 __isl_take isl_set *context);
7183 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
7184 __isl_take isl_pw_aff *pwaff,
7185 __isl_take isl_set *context);
7186 __isl_give isl_pw_aff *isl_pw_aff_gist(
7187 __isl_take isl_pw_aff *pwaff,
7188 __isl_take isl_set *context);
7189 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
7190 __isl_take isl_pw_multi_aff *pma,
7191 __isl_take isl_set *set);
7192 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
7193 __isl_take isl_pw_multi_aff *pma,
7194 __isl_take isl_set *set);
7195 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
7196 __isl_take isl_multi_pw_aff *mpa,
7197 __isl_take isl_set *set);
7198 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
7199 __isl_take isl_multi_pw_aff *mpa,
7200 __isl_take isl_set *set);
7201 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
7202 __isl_take isl_union_pw_aff *upa,
7203 __isl_take isl_union_set *context);
7204 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
7205 __isl_take isl_union_pw_aff *upa,
7206 __isl_take isl_set *context);
7207 __isl_give isl_union_pw_multi_aff *
7208 isl_union_pw_multi_aff_gist_params(
7209 __isl_take isl_union_pw_multi_aff *upma,
7210 __isl_take isl_set *context);
7211 __isl_give isl_union_pw_multi_aff *
7212 isl_union_pw_multi_aff_gist(
7213 __isl_take isl_union_pw_multi_aff *upma,
7214 __isl_take isl_union_set *context);
7215 __isl_give isl_multi_union_pw_aff *
7216 isl_multi_union_pw_aff_gist_params(
7217 __isl_take isl_multi_union_pw_aff *aff,
7218 __isl_take isl_set *context);
7219 __isl_give isl_multi_union_pw_aff *
7220 isl_multi_union_pw_aff_gist(
7221 __isl_take isl_multi_union_pw_aff *aff,
7222 __isl_take isl_union_set *context);
7224 #include <isl/polynomial.h>
7225 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
7226 __isl_take isl_qpolynomial *qp,
7227 __isl_take isl_set *context);
7228 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
7229 __isl_take isl_qpolynomial *qp,
7230 __isl_take isl_set *context);
7231 __isl_give isl_qpolynomial_fold *
7232 isl_qpolynomial_fold_gist_params(
7233 __isl_take isl_qpolynomial_fold *fold,
7234 __isl_take isl_set *context);
7235 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7236 __isl_take isl_qpolynomial_fold *fold,
7237 __isl_take isl_set *context);
7238 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7239 __isl_take isl_pw_qpolynomial *pwqp,
7240 __isl_take isl_set *context);
7241 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7242 __isl_take isl_pw_qpolynomial *pwqp,
7243 __isl_take isl_set *context);
7244 __isl_give isl_pw_qpolynomial_fold *
7245 isl_pw_qpolynomial_fold_gist(
7246 __isl_take isl_pw_qpolynomial_fold *pwf,
7247 __isl_take isl_set *context);
7248 __isl_give isl_pw_qpolynomial_fold *
7249 isl_pw_qpolynomial_fold_gist_params(
7250 __isl_take isl_pw_qpolynomial_fold *pwf,
7251 __isl_take isl_set *context);
7252 __isl_give isl_union_pw_qpolynomial *
7253 isl_union_pw_qpolynomial_gist_params(
7254 __isl_take isl_union_pw_qpolynomial *upwqp,
7255 __isl_take isl_set *context);
7256 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7257 __isl_take isl_union_pw_qpolynomial *upwqp,
7258 __isl_take isl_union_set *context);
7259 __isl_give isl_union_pw_qpolynomial_fold *
7260 isl_union_pw_qpolynomial_fold_gist(
7261 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7262 __isl_take isl_union_set *context);
7263 __isl_give isl_union_pw_qpolynomial_fold *
7264 isl_union_pw_qpolynomial_fold_gist_params(
7265 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7266 __isl_take isl_set *context);
7268 =item * Binary Arithmetic Operations
7270 #include <isl/set.h>
7271 __isl_give isl_set *isl_set_sum(
7272 __isl_take isl_set *set1,
7273 __isl_take isl_set *set2);
7274 #include <isl/map.h>
7275 __isl_give isl_map *isl_map_sum(
7276 __isl_take isl_map *map1,
7277 __isl_take isl_map *map2);
7279 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7280 i.e., the set containing the sums of pairs of elements from
7281 C<set1> and C<set2>.
7282 The domain of the result of C<isl_map_sum> is the intersection
7283 of the domains of its two arguments. The corresponding range
7284 elements are the sums of the corresponding range elements
7285 in the two arguments.
7287 #include <isl/val.h>
7288 __isl_give isl_multi_val *isl_multi_val_add(
7289 __isl_take isl_multi_val *mv1,
7290 __isl_take isl_multi_val *mv2);
7291 __isl_give isl_multi_val *isl_multi_val_sub(
7292 __isl_take isl_multi_val *mv1,
7293 __isl_take isl_multi_val *mv2);
7295 #include <isl/aff.h>
7296 __isl_give isl_aff *isl_aff_add(
7297 __isl_take isl_aff *aff1,
7298 __isl_take isl_aff *aff2);
7299 __isl_give isl_multi_aff *isl_multi_aff_add(
7300 __isl_take isl_multi_aff *maff1,
7301 __isl_take isl_multi_aff *maff2);
7302 __isl_give isl_pw_aff *isl_pw_aff_add(
7303 __isl_take isl_pw_aff *pwaff1,
7304 __isl_take isl_pw_aff *pwaff2);
7305 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7306 __isl_take isl_multi_pw_aff *mpa1,
7307 __isl_take isl_multi_pw_aff *mpa2);
7308 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7309 __isl_take isl_pw_multi_aff *pma1,
7310 __isl_take isl_pw_multi_aff *pma2);
7311 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7312 __isl_take isl_union_pw_aff *upa1,
7313 __isl_take isl_union_pw_aff *upa2);
7314 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7315 __isl_take isl_union_pw_multi_aff *upma1,
7316 __isl_take isl_union_pw_multi_aff *upma2);
7317 __isl_give isl_multi_union_pw_aff *
7318 isl_multi_union_pw_aff_add(
7319 __isl_take isl_multi_union_pw_aff *mupa1,
7320 __isl_take isl_multi_union_pw_aff *mupa2);
7321 __isl_give isl_pw_aff *isl_pw_aff_min(
7322 __isl_take isl_pw_aff *pwaff1,
7323 __isl_take isl_pw_aff *pwaff2);
7324 __isl_give isl_pw_aff *isl_pw_aff_max(
7325 __isl_take isl_pw_aff *pwaff1,
7326 __isl_take isl_pw_aff *pwaff2);
7327 __isl_give isl_aff *isl_aff_sub(
7328 __isl_take isl_aff *aff1,
7329 __isl_take isl_aff *aff2);
7330 __isl_give isl_multi_aff *isl_multi_aff_sub(
7331 __isl_take isl_multi_aff *ma1,
7332 __isl_take isl_multi_aff *ma2);
7333 __isl_give isl_pw_aff *isl_pw_aff_sub(
7334 __isl_take isl_pw_aff *pwaff1,
7335 __isl_take isl_pw_aff *pwaff2);
7336 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7337 __isl_take isl_multi_pw_aff *mpa1,
7338 __isl_take isl_multi_pw_aff *mpa2);
7339 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7340 __isl_take isl_pw_multi_aff *pma1,
7341 __isl_take isl_pw_multi_aff *pma2);
7342 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7343 __isl_take isl_union_pw_aff *upa1,
7344 __isl_take isl_union_pw_aff *upa2);
7345 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7346 __isl_take isl_union_pw_multi_aff *upma1,
7347 __isl_take isl_union_pw_multi_aff *upma2);
7348 __isl_give isl_multi_union_pw_aff *
7349 isl_multi_union_pw_aff_sub(
7350 __isl_take isl_multi_union_pw_aff *mupa1,
7351 __isl_take isl_multi_union_pw_aff *mupa2);
7353 C<isl_aff_sub> subtracts the second argument from the first.
7355 #include <isl/polynomial.h>
7356 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7357 __isl_take isl_qpolynomial *qp1,
7358 __isl_take isl_qpolynomial *qp2);
7359 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7360 __isl_take isl_pw_qpolynomial *pwqp1,
7361 __isl_take isl_pw_qpolynomial *pwqp2);
7362 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7363 __isl_take isl_pw_qpolynomial *pwqp1,
7364 __isl_take isl_pw_qpolynomial *pwqp2);
7365 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7366 __isl_take isl_pw_qpolynomial_fold *pwf1,
7367 __isl_take isl_pw_qpolynomial_fold *pwf2);
7368 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7369 __isl_take isl_union_pw_qpolynomial *upwqp1,
7370 __isl_take isl_union_pw_qpolynomial *upwqp2);
7371 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7372 __isl_take isl_qpolynomial *qp1,
7373 __isl_take isl_qpolynomial *qp2);
7374 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7375 __isl_take isl_pw_qpolynomial *pwqp1,
7376 __isl_take isl_pw_qpolynomial *pwqp2);
7377 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7378 __isl_take isl_union_pw_qpolynomial *upwqp1,
7379 __isl_take isl_union_pw_qpolynomial *upwqp2);
7380 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7381 __isl_take isl_pw_qpolynomial_fold *pwf1,
7382 __isl_take isl_pw_qpolynomial_fold *pwf2);
7383 __isl_give isl_union_pw_qpolynomial_fold *
7384 isl_union_pw_qpolynomial_fold_fold(
7385 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7386 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7388 #include <isl/aff.h>
7389 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7390 __isl_take isl_pw_aff *pwaff1,
7391 __isl_take isl_pw_aff *pwaff2);
7392 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7393 __isl_take isl_pw_multi_aff *pma1,
7394 __isl_take isl_pw_multi_aff *pma2);
7395 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7396 __isl_take isl_union_pw_aff *upa1,
7397 __isl_take isl_union_pw_aff *upa2);
7398 __isl_give isl_union_pw_multi_aff *
7399 isl_union_pw_multi_aff_union_add(
7400 __isl_take isl_union_pw_multi_aff *upma1,
7401 __isl_take isl_union_pw_multi_aff *upma2);
7402 __isl_give isl_multi_union_pw_aff *
7403 isl_multi_union_pw_aff_union_add(
7404 __isl_take isl_multi_union_pw_aff *mupa1,
7405 __isl_take isl_multi_union_pw_aff *mupa2);
7406 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7407 __isl_take isl_pw_aff *pwaff1,
7408 __isl_take isl_pw_aff *pwaff2);
7409 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7410 __isl_take isl_pw_aff *pwaff1,
7411 __isl_take isl_pw_aff *pwaff2);
7413 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7414 expression with a domain that is the union of those of C<pwaff1> and
7415 C<pwaff2> and such that on each cell, the quasi-affine expression is
7416 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7417 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7418 associated expression is the defined one.
7419 This in contrast to the C<isl_pw_aff_max> function, which is
7420 only defined on the shared definition domain of the arguments.
7422 #include <isl/val.h>
7423 __isl_give isl_multi_val *isl_multi_val_add_val(
7424 __isl_take isl_multi_val *mv,
7425 __isl_take isl_val *v);
7426 __isl_give isl_multi_val *isl_multi_val_mod_val(
7427 __isl_take isl_multi_val *mv,
7428 __isl_take isl_val *v);
7429 __isl_give isl_multi_val *isl_multi_val_scale_val(
7430 __isl_take isl_multi_val *mv,
7431 __isl_take isl_val *v);
7432 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7433 __isl_take isl_multi_val *mv,
7434 __isl_take isl_val *v);
7436 #include <isl/aff.h>
7437 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7438 __isl_take isl_val *mod);
7439 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7440 __isl_take isl_pw_aff *pa,
7441 __isl_take isl_val *mod);
7442 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7443 __isl_take isl_union_pw_aff *upa,
7444 __isl_take isl_val *f);
7445 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7446 __isl_take isl_val *v);
7447 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7448 __isl_take isl_multi_aff *ma,
7449 __isl_take isl_val *v);
7450 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7451 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7452 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7453 __isl_take isl_multi_pw_aff *mpa,
7454 __isl_take isl_val *v);
7455 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7456 __isl_take isl_pw_multi_aff *pma,
7457 __isl_take isl_val *v);
7458 __isl_give isl_union_pw_multi_aff *
7459 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7460 __isl_take isl_union_pw_aff *upa,
7461 __isl_take isl_val *f);
7462 isl_union_pw_multi_aff_scale_val(
7463 __isl_take isl_union_pw_multi_aff *upma,
7464 __isl_take isl_val *val);
7465 __isl_give isl_multi_union_pw_aff *
7466 isl_multi_union_pw_aff_scale_val(
7467 __isl_take isl_multi_union_pw_aff *mupa,
7468 __isl_take isl_val *v);
7469 __isl_give isl_aff *isl_aff_scale_down_ui(
7470 __isl_take isl_aff *aff, unsigned f);
7471 __isl_give isl_aff *isl_aff_scale_down_val(
7472 __isl_take isl_aff *aff, __isl_take isl_val *v);
7473 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7474 __isl_take isl_multi_aff *ma,
7475 __isl_take isl_val *v);
7476 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7477 __isl_take isl_pw_aff *pa,
7478 __isl_take isl_val *f);
7479 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7480 __isl_take isl_multi_pw_aff *mpa,
7481 __isl_take isl_val *v);
7482 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7483 __isl_take isl_pw_multi_aff *pma,
7484 __isl_take isl_val *v);
7485 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7486 __isl_take isl_union_pw_aff *upa,
7487 __isl_take isl_val *v);
7488 __isl_give isl_union_pw_multi_aff *
7489 isl_union_pw_multi_aff_scale_down_val(
7490 __isl_take isl_union_pw_multi_aff *upma,
7491 __isl_take isl_val *val);
7492 __isl_give isl_multi_union_pw_aff *
7493 isl_multi_union_pw_aff_scale_down_val(
7494 __isl_take isl_multi_union_pw_aff *mupa,
7495 __isl_take isl_val *v);
7497 #include <isl/polynomial.h>
7498 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7499 __isl_take isl_qpolynomial *qp,
7500 __isl_take isl_val *v);
7501 __isl_give isl_qpolynomial_fold *
7502 isl_qpolynomial_fold_scale_val(
7503 __isl_take isl_qpolynomial_fold *fold,
7504 __isl_take isl_val *v);
7505 __isl_give isl_pw_qpolynomial *
7506 isl_pw_qpolynomial_scale_val(
7507 __isl_take isl_pw_qpolynomial *pwqp,
7508 __isl_take isl_val *v);
7509 __isl_give isl_pw_qpolynomial_fold *
7510 isl_pw_qpolynomial_fold_scale_val(
7511 __isl_take isl_pw_qpolynomial_fold *pwf,
7512 __isl_take isl_val *v);
7513 __isl_give isl_union_pw_qpolynomial *
7514 isl_union_pw_qpolynomial_scale_val(
7515 __isl_take isl_union_pw_qpolynomial *upwqp,
7516 __isl_take isl_val *v);
7517 __isl_give isl_union_pw_qpolynomial_fold *
7518 isl_union_pw_qpolynomial_fold_scale_val(
7519 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7520 __isl_take isl_val *v);
7521 __isl_give isl_qpolynomial *
7522 isl_qpolynomial_scale_down_val(
7523 __isl_take isl_qpolynomial *qp,
7524 __isl_take isl_val *v);
7525 __isl_give isl_qpolynomial_fold *
7526 isl_qpolynomial_fold_scale_down_val(
7527 __isl_take isl_qpolynomial_fold *fold,
7528 __isl_take isl_val *v);
7529 __isl_give isl_pw_qpolynomial *
7530 isl_pw_qpolynomial_scale_down_val(
7531 __isl_take isl_pw_qpolynomial *pwqp,
7532 __isl_take isl_val *v);
7533 __isl_give isl_pw_qpolynomial_fold *
7534 isl_pw_qpolynomial_fold_scale_down_val(
7535 __isl_take isl_pw_qpolynomial_fold *pwf,
7536 __isl_take isl_val *v);
7537 __isl_give isl_union_pw_qpolynomial *
7538 isl_union_pw_qpolynomial_scale_down_val(
7539 __isl_take isl_union_pw_qpolynomial *upwqp,
7540 __isl_take isl_val *v);
7541 __isl_give isl_union_pw_qpolynomial_fold *
7542 isl_union_pw_qpolynomial_fold_scale_down_val(
7543 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7544 __isl_take isl_val *v);
7546 #include <isl/val.h>
7547 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7548 __isl_take isl_multi_val *mv1,
7549 __isl_take isl_multi_val *mv2);
7550 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7551 __isl_take isl_multi_val *mv1,
7552 __isl_take isl_multi_val *mv2);
7553 __isl_give isl_multi_val *
7554 isl_multi_val_scale_down_multi_val(
7555 __isl_take isl_multi_val *mv1,
7556 __isl_take isl_multi_val *mv2);
7558 #include <isl/aff.h>
7559 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7560 __isl_take isl_multi_aff *ma,
7561 __isl_take isl_multi_val *mv);
7562 __isl_give isl_multi_union_pw_aff *
7563 isl_multi_union_pw_aff_mod_multi_val(
7564 __isl_take isl_multi_union_pw_aff *upma,
7565 __isl_take isl_multi_val *mv);
7566 __isl_give isl_multi_pw_aff *
7567 isl_multi_pw_aff_mod_multi_val(
7568 __isl_take isl_multi_pw_aff *mpa,
7569 __isl_take isl_multi_val *mv);
7570 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7571 __isl_take isl_multi_aff *ma,
7572 __isl_take isl_multi_val *mv);
7573 __isl_give isl_pw_multi_aff *
7574 isl_pw_multi_aff_scale_multi_val(
7575 __isl_take isl_pw_multi_aff *pma,
7576 __isl_take isl_multi_val *mv);
7577 __isl_give isl_multi_pw_aff *
7578 isl_multi_pw_aff_scale_multi_val(
7579 __isl_take isl_multi_pw_aff *mpa,
7580 __isl_take isl_multi_val *mv);
7581 __isl_give isl_multi_union_pw_aff *
7582 isl_multi_union_pw_aff_scale_multi_val(
7583 __isl_take isl_multi_union_pw_aff *mupa,
7584 __isl_take isl_multi_val *mv);
7585 __isl_give isl_union_pw_multi_aff *
7586 isl_union_pw_multi_aff_scale_multi_val(
7587 __isl_take isl_union_pw_multi_aff *upma,
7588 __isl_take isl_multi_val *mv);
7589 __isl_give isl_multi_aff *
7590 isl_multi_aff_scale_down_multi_val(
7591 __isl_take isl_multi_aff *ma,
7592 __isl_take isl_multi_val *mv);
7593 __isl_give isl_multi_pw_aff *
7594 isl_multi_pw_aff_scale_down_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_down_multi_val(
7599 __isl_take isl_multi_union_pw_aff *mupa,
7600 __isl_take isl_multi_val *mv);
7602 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7603 by the corresponding elements of C<mv>.
7605 #include <isl/aff.h>
7606 __isl_give isl_aff *isl_aff_mul(
7607 __isl_take isl_aff *aff1,
7608 __isl_take isl_aff *aff2);
7609 __isl_give isl_aff *isl_aff_div(
7610 __isl_take isl_aff *aff1,
7611 __isl_take isl_aff *aff2);
7612 __isl_give isl_pw_aff *isl_pw_aff_mul(
7613 __isl_take isl_pw_aff *pwaff1,
7614 __isl_take isl_pw_aff *pwaff2);
7615 __isl_give isl_pw_aff *isl_pw_aff_div(
7616 __isl_take isl_pw_aff *pa1,
7617 __isl_take isl_pw_aff *pa2);
7618 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7619 __isl_take isl_pw_aff *pa1,
7620 __isl_take isl_pw_aff *pa2);
7621 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7622 __isl_take isl_pw_aff *pa1,
7623 __isl_take isl_pw_aff *pa2);
7625 When multiplying two affine expressions, at least one of the two needs
7626 to be a constant. Similarly, when dividing an affine expression by another,
7627 the second expression needs to be a constant.
7628 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7629 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7632 #include <isl/polynomial.h>
7633 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7634 __isl_take isl_qpolynomial *qp1,
7635 __isl_take isl_qpolynomial *qp2);
7636 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7637 __isl_take isl_pw_qpolynomial *pwqp1,
7638 __isl_take isl_pw_qpolynomial *pwqp2);
7639 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7640 __isl_take isl_union_pw_qpolynomial *upwqp1,
7641 __isl_take isl_union_pw_qpolynomial *upwqp2);
7645 =head3 Lexicographic Optimization
7647 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7648 the following functions
7649 compute a set that contains the lexicographic minimum or maximum
7650 of the elements in C<set> (or C<bset>) for those values of the parameters
7651 that satisfy C<dom>.
7652 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7653 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7655 In other words, the union of the parameter values
7656 for which the result is non-empty and of C<*empty>
7659 #include <isl/set.h>
7660 __isl_give isl_set *isl_basic_set_partial_lexmin(
7661 __isl_take isl_basic_set *bset,
7662 __isl_take isl_basic_set *dom,
7663 __isl_give isl_set **empty);
7664 __isl_give isl_set *isl_basic_set_partial_lexmax(
7665 __isl_take isl_basic_set *bset,
7666 __isl_take isl_basic_set *dom,
7667 __isl_give isl_set **empty);
7668 __isl_give isl_set *isl_set_partial_lexmin(
7669 __isl_take isl_set *set, __isl_take isl_set *dom,
7670 __isl_give isl_set **empty);
7671 __isl_give isl_set *isl_set_partial_lexmax(
7672 __isl_take isl_set *set, __isl_take isl_set *dom,
7673 __isl_give isl_set **empty);
7675 Given a (basic) set C<set> (or C<bset>), the following functions simply
7676 return a set containing the lexicographic minimum or maximum
7677 of the elements in C<set> (or C<bset>).
7678 In case of union sets, the optimum is computed per space.
7680 #include <isl/set.h>
7681 __isl_give isl_set *isl_basic_set_lexmin(
7682 __isl_take isl_basic_set *bset);
7683 __isl_give isl_set *isl_basic_set_lexmax(
7684 __isl_take isl_basic_set *bset);
7685 __isl_give isl_set *isl_set_lexmin(
7686 __isl_take isl_set *set);
7687 __isl_give isl_set *isl_set_lexmax(
7688 __isl_take isl_set *set);
7689 __isl_give isl_union_set *isl_union_set_lexmin(
7690 __isl_take isl_union_set *uset);
7691 __isl_give isl_union_set *isl_union_set_lexmax(
7692 __isl_take isl_union_set *uset);
7694 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7695 the following functions
7696 compute a relation that maps each element of C<dom>
7697 to the single lexicographic minimum or maximum
7698 of the elements that are associated to that same
7699 element in C<map> (or C<bmap>).
7700 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7701 that contains the elements in C<dom> that do not map
7702 to any elements in C<map> (or C<bmap>).
7703 In other words, the union of the domain of the result and of C<*empty>
7706 #include <isl/map.h>
7707 __isl_give isl_map *isl_basic_map_partial_lexmax(
7708 __isl_take isl_basic_map *bmap,
7709 __isl_take isl_basic_set *dom,
7710 __isl_give isl_set **empty);
7711 __isl_give isl_map *isl_basic_map_partial_lexmin(
7712 __isl_take isl_basic_map *bmap,
7713 __isl_take isl_basic_set *dom,
7714 __isl_give isl_set **empty);
7715 __isl_give isl_map *isl_map_partial_lexmax(
7716 __isl_take isl_map *map, __isl_take isl_set *dom,
7717 __isl_give isl_set **empty);
7718 __isl_give isl_map *isl_map_partial_lexmin(
7719 __isl_take isl_map *map, __isl_take isl_set *dom,
7720 __isl_give isl_set **empty);
7722 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7723 return a map mapping each element in the domain of
7724 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7725 of all elements associated to that element.
7726 In case of union relations, the optimum is computed per space.
7728 #include <isl/map.h>
7729 __isl_give isl_map *isl_basic_map_lexmin(
7730 __isl_take isl_basic_map *bmap);
7731 __isl_give isl_map *isl_basic_map_lexmax(
7732 __isl_take isl_basic_map *bmap);
7733 __isl_give isl_map *isl_map_lexmin(
7734 __isl_take isl_map *map);
7735 __isl_give isl_map *isl_map_lexmax(
7736 __isl_take isl_map *map);
7737 __isl_give isl_union_map *isl_union_map_lexmin(
7738 __isl_take isl_union_map *umap);
7739 __isl_give isl_union_map *isl_union_map_lexmax(
7740 __isl_take isl_union_map *umap);
7742 The following functions return their result in the form of
7743 a piecewise multi-affine expression,
7744 but are otherwise equivalent to the corresponding functions
7745 returning a basic set or relation.
7747 #include <isl/set.h>
7748 __isl_give isl_pw_multi_aff *
7749 isl_basic_set_partial_lexmin_pw_multi_aff(
7750 __isl_take isl_basic_set *bset,
7751 __isl_take isl_basic_set *dom,
7752 __isl_give isl_set **empty);
7753 __isl_give isl_pw_multi_aff *
7754 isl_basic_set_partial_lexmax_pw_multi_aff(
7755 __isl_take isl_basic_set *bset,
7756 __isl_take isl_basic_set *dom,
7757 __isl_give isl_set **empty);
7758 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7759 __isl_take isl_set *set);
7760 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7761 __isl_take isl_set *set);
7763 #include <isl/map.h>
7764 __isl_give isl_pw_multi_aff *
7765 isl_basic_map_lexmin_pw_multi_aff(
7766 __isl_take isl_basic_map *bmap);
7767 __isl_give isl_pw_multi_aff *
7768 isl_basic_map_partial_lexmin_pw_multi_aff(
7769 __isl_take isl_basic_map *bmap,
7770 __isl_take isl_basic_set *dom,
7771 __isl_give isl_set **empty);
7772 __isl_give isl_pw_multi_aff *
7773 isl_basic_map_partial_lexmax_pw_multi_aff(
7774 __isl_take isl_basic_map *bmap,
7775 __isl_take isl_basic_set *dom,
7776 __isl_give isl_set **empty);
7777 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7778 __isl_take isl_map *map);
7779 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7780 __isl_take isl_map *map);
7782 The following functions return the lexicographic minimum or maximum
7783 on the shared domain of the inputs and the single defined function
7784 on those parts of the domain where only a single function is defined.
7786 #include <isl/aff.h>
7787 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7788 __isl_take isl_pw_multi_aff *pma1,
7789 __isl_take isl_pw_multi_aff *pma2);
7790 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7791 __isl_take isl_pw_multi_aff *pma1,
7792 __isl_take isl_pw_multi_aff *pma2);
7794 If the input to a lexicographic optimization problem has
7795 multiple constraints with the same coefficients for the optimized
7796 variables, then, by default, this symmetry is exploited by
7797 replacing those constraints by a single constraint with
7798 an abstract bound, which is in turn bounded by the corresponding terms
7799 in the original constraints.
7800 Without this optimization, the solver would typically consider
7801 all possible orderings of those original bounds, resulting in a needless
7802 decomposition of the domain.
7803 However, the optimization can also result in slowdowns since
7804 an extra parameter is introduced that may get used in additional
7806 The following option determines whether symmetry detection is applied
7807 during lexicographic optimization.
7809 #include <isl/options.h>
7810 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7812 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7816 See also \autoref{s:offline}.
7820 =head2 Ternary Operations
7822 #include <isl/aff.h>
7823 __isl_give isl_pw_aff *isl_pw_aff_cond(
7824 __isl_take isl_pw_aff *cond,
7825 __isl_take isl_pw_aff *pwaff_true,
7826 __isl_take isl_pw_aff *pwaff_false);
7828 The function C<isl_pw_aff_cond> performs a conditional operator
7829 and returns an expression that is equal to C<pwaff_true>
7830 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7831 where C<cond> is zero.
7835 Lists are defined over several element types, including
7836 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
7837 C<isl_union_pw_aff>,
7838 C<isl_union_pw_multi_aff>,
7839 C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
7841 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7842 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7843 Here we take lists of C<isl_set>s as an example.
7844 Lists can be created, copied, modified and freed using the following functions.
7846 #include <isl/set.h>
7847 __isl_give isl_set_list *isl_set_list_from_set(
7848 __isl_take isl_set *el);
7849 __isl_give isl_set_list *isl_set_list_alloc(
7850 isl_ctx *ctx, int n);
7851 __isl_give isl_set_list *isl_set_list_copy(
7852 __isl_keep isl_set_list *list);
7853 __isl_give isl_set_list *isl_set_list_insert(
7854 __isl_take isl_set_list *list, unsigned pos,
7855 __isl_take isl_set *el);
7856 __isl_give isl_set_list *isl_set_list_add(
7857 __isl_take isl_set_list *list,
7858 __isl_take isl_set *el);
7859 __isl_give isl_set_list *isl_set_list_drop(
7860 __isl_take isl_set_list *list,
7861 unsigned first, unsigned n);
7862 __isl_give isl_set_list *isl_set_list_swap(
7863 __isl_take isl_set_list *list,
7864 unsigned pos1, unsigned pos2);
7865 __isl_give isl_set_list *isl_set_list_reverse(
7866 __isl_take isl_set_list *list);
7867 __isl_give isl_set_list *isl_set_list_set_set(
7868 __isl_take isl_set_list *list, int index,
7869 __isl_take isl_set *set);
7870 __isl_give isl_set_list *isl_set_list_concat(
7871 __isl_take isl_set_list *list1,
7872 __isl_take isl_set_list *list2);
7873 __isl_give isl_set_list *isl_set_list_map(
7874 __isl_take isl_set_list *list,
7875 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7878 __isl_give isl_set_list *isl_set_list_sort(
7879 __isl_take isl_set_list *list,
7880 int (*cmp)(__isl_keep isl_set *a,
7881 __isl_keep isl_set *b, void *user),
7883 __isl_null isl_set_list *isl_set_list_free(
7884 __isl_take isl_set_list *list);
7886 C<isl_set_list_alloc> creates an empty list with an initial capacity
7887 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7888 add elements to a list, increasing its capacity as needed.
7889 C<isl_set_list_from_set> creates a list with a single element.
7890 C<isl_set_list_swap> swaps the elements at the specified locations.
7891 C<isl_set_list_reverse> reverses the elements in the list.
7893 Lists can be inspected using the following functions.
7895 #include <isl/set.h>
7896 int isl_set_list_size(__isl_keep isl_set_list *list);
7897 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7898 __isl_give isl_set *isl_set_list_get_at(
7899 __isl_keep isl_set_list *list, int index);
7900 __isl_give isl_set *isl_set_list_get_set(
7901 __isl_keep isl_set_list *list, int index);
7902 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7903 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7905 isl_stat isl_set_list_foreach_scc(
7906 __isl_keep isl_set_list *list,
7907 isl_bool (*follows)(__isl_keep isl_set *a,
7908 __isl_keep isl_set *b, void *user),
7910 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7913 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
7915 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
7916 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7917 strongly connected components of the graph with as vertices the elements
7918 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7919 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7920 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7922 Lists can be printed using
7924 #include <isl/set.h>
7925 __isl_give isl_printer *isl_printer_print_set_list(
7926 __isl_take isl_printer *p,
7927 __isl_keep isl_set_list *list);
7929 =head2 Associative arrays
7931 Associative arrays map isl objects of a specific type to isl objects
7932 of some (other) specific type. They are defined for several pairs
7933 of types, including (C<isl_map>, C<isl_basic_set>),
7934 (C<isl_id>, C<isl_ast_expr>),
7935 (C<isl_id>, C<isl_id>) and
7936 (C<isl_id>, C<isl_pw_aff>).
7937 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7940 Associative arrays can be created, copied and freed using
7941 the following functions.
7943 #include <isl/id_to_ast_expr.h>
7944 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7945 isl_ctx *ctx, int min_size);
7946 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7947 __isl_keep isl_id_to_ast_expr *id2expr);
7948 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7949 __isl_take isl_id_to_ast_expr *id2expr);
7951 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7952 to specify the expected size of the associative array.
7953 The associative array will be grown automatically as needed.
7955 Associative arrays can be inspected using the following functions.
7957 #include <isl/id_to_ast_expr.h>
7958 __isl_give isl_maybe_isl_ast_expr
7959 isl_id_to_ast_expr_try_get(
7960 __isl_keep isl_id_to_ast_expr *id2expr,
7961 __isl_keep isl_id *key);
7962 isl_bool isl_id_to_ast_expr_has(
7963 __isl_keep isl_id_to_ast_expr *id2expr,
7964 __isl_keep isl_id *key);
7965 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7966 __isl_keep isl_id_to_ast_expr *id2expr,
7967 __isl_take isl_id *key);
7968 isl_stat isl_id_to_ast_expr_foreach(
7969 __isl_keep isl_id_to_ast_expr *id2expr,
7970 isl_stat (*fn)(__isl_take isl_id *key,
7971 __isl_take isl_ast_expr *val, void *user),
7974 The function C<isl_id_to_ast_expr_try_get> returns a structure
7975 containing two elements, C<valid> and C<value>.
7976 If there is a value associated to the key, then C<valid>
7977 is set to C<isl_bool_true> and C<value> contains a copy of
7978 the associated value. Otherwise C<value> is C<NULL> and
7979 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7980 on whether some error has occurred or there simply is no associated value.
7981 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7982 in the structure and
7983 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7985 Associative arrays can be modified using the following functions.
7987 #include <isl/id_to_ast_expr.h>
7988 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7989 __isl_take isl_id_to_ast_expr *id2expr,
7990 __isl_take isl_id *key,
7991 __isl_take isl_ast_expr *val);
7992 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7993 __isl_take isl_id_to_ast_expr *id2expr,
7994 __isl_take isl_id *key);
7996 Associative arrays can be printed using the following function.
7998 #include <isl/id_to_ast_expr.h>
7999 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
8000 __isl_take isl_printer *p,
8001 __isl_keep isl_id_to_ast_expr *id2expr);
8005 Vectors can be created, copied and freed using the following functions.
8007 #include <isl/vec.h>
8008 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
8010 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
8012 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
8013 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
8015 Note that the elements of a vector created by C<isl_vec_alloc>
8016 may have arbitrary values.
8017 A vector created by C<isl_vec_zero> has elements with value zero.
8018 The elements can be changed and inspected using the following functions.
8020 int isl_vec_size(__isl_keep isl_vec *vec);
8021 __isl_give isl_val *isl_vec_get_element_val(
8022 __isl_keep isl_vec *vec, int pos);
8023 __isl_give isl_vec *isl_vec_set_element_si(
8024 __isl_take isl_vec *vec, int pos, int v);
8025 __isl_give isl_vec *isl_vec_set_element_val(
8026 __isl_take isl_vec *vec, int pos,
8027 __isl_take isl_val *v);
8028 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
8030 __isl_give isl_vec *isl_vec_set_val(
8031 __isl_take isl_vec *vec, __isl_take isl_val *v);
8032 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
8033 __isl_keep isl_vec *vec2, int pos);
8035 C<isl_vec_get_element> will return a negative value if anything went wrong.
8036 In that case, the value of C<*v> is undefined.
8038 The following function can be used to concatenate two vectors.
8040 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
8041 __isl_take isl_vec *vec2);
8045 Matrices can be created, copied and freed using the following functions.
8047 #include <isl/mat.h>
8048 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
8049 unsigned n_row, unsigned n_col);
8050 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
8051 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
8053 Note that the elements of a newly created matrix may have arbitrary values.
8054 The elements can be changed and inspected using the following functions.
8056 int isl_mat_rows(__isl_keep isl_mat *mat);
8057 int isl_mat_cols(__isl_keep isl_mat *mat);
8058 __isl_give isl_val *isl_mat_get_element_val(
8059 __isl_keep isl_mat *mat, int row, int col);
8060 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
8061 int row, int col, int v);
8062 __isl_give isl_mat *isl_mat_set_element_val(
8063 __isl_take isl_mat *mat, int row, int col,
8064 __isl_take isl_val *v);
8066 The following function computes the rank of a matrix.
8067 The return value may be -1 if some error occurred.
8069 #include <isl/mat.h>
8070 int isl_mat_rank(__isl_keep isl_mat *mat);
8072 The following function can be used to compute the (right) inverse
8073 of a matrix, i.e., a matrix such that the product of the original
8074 and the inverse (in that order) is a multiple of the identity matrix.
8075 The input matrix is assumed to be of full row-rank.
8077 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
8079 The following function can be used to compute the (right) kernel
8080 (or null space) of a matrix, i.e., a matrix such that the product of
8081 the original and the kernel (in that order) is the zero matrix.
8083 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
8085 The following function computes a basis for the space spanned
8086 by the rows of a matrix.
8088 __isl_give isl_mat *isl_mat_row_basis(
8089 __isl_take isl_mat *mat);
8091 The following function computes rows that extend a basis of C<mat1>
8092 to a basis that also covers C<mat2>.
8094 __isl_give isl_mat *isl_mat_row_basis_extension(
8095 __isl_take isl_mat *mat1,
8096 __isl_take isl_mat *mat2);
8098 The following function checks whether there is no linear dependence
8099 among the combined rows of "mat1" and "mat2" that is not already present
8100 in "mat1" or "mat2" individually.
8101 If "mat1" and "mat2" have linearly independent rows by themselves,
8102 then this means that there is no linear dependence among all rows together.
8104 isl_bool isl_mat_has_linearly_independent_rows(
8105 __isl_keep isl_mat *mat1,
8106 __isl_keep isl_mat *mat2);
8108 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
8110 The following functions determine
8111 an upper or lower bound on a quasipolynomial over its domain.
8113 __isl_give isl_pw_qpolynomial_fold *
8114 isl_pw_qpolynomial_bound(
8115 __isl_take isl_pw_qpolynomial *pwqp,
8116 enum isl_fold type, int *tight);
8118 __isl_give isl_union_pw_qpolynomial_fold *
8119 isl_union_pw_qpolynomial_bound(
8120 __isl_take isl_union_pw_qpolynomial *upwqp,
8121 enum isl_fold type, int *tight);
8123 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
8124 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
8125 is the returned bound is known be tight, i.e., for each value
8126 of the parameters there is at least
8127 one element in the domain that reaches the bound.
8128 If the domain of C<pwqp> is not wrapping, then the bound is computed
8129 over all elements in that domain and the result has a purely parametric
8130 domain. If the domain of C<pwqp> is wrapping, then the bound is
8131 computed over the range of the wrapped relation. The domain of the
8132 wrapped relation becomes the domain of the result.
8134 =head2 Parametric Vertex Enumeration
8136 The parametric vertex enumeration described in this section
8137 is mainly intended to be used internally and by the C<barvinok>
8140 #include <isl/vertices.h>
8141 __isl_give isl_vertices *isl_basic_set_compute_vertices(
8142 __isl_keep isl_basic_set *bset);
8144 The function C<isl_basic_set_compute_vertices> performs the
8145 actual computation of the parametric vertices and the chamber
8146 decomposition and stores the result in an C<isl_vertices> object.
8147 This information can be queried by either iterating over all
8148 the vertices or iterating over all the chambers or cells
8149 and then iterating over all vertices that are active on the chamber.
8151 isl_stat isl_vertices_foreach_vertex(
8152 __isl_keep isl_vertices *vertices,
8153 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8154 void *user), void *user);
8156 isl_stat isl_vertices_foreach_cell(
8157 __isl_keep isl_vertices *vertices,
8158 isl_stat (*fn)(__isl_take isl_cell *cell,
8159 void *user), void *user);
8160 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
8161 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8162 void *user), void *user);
8164 Other operations that can be performed on an C<isl_vertices> object are
8167 int isl_vertices_get_n_vertices(
8168 __isl_keep isl_vertices *vertices);
8169 __isl_null isl_vertices *isl_vertices_free(
8170 __isl_take isl_vertices *vertices);
8172 Vertices can be inspected and destroyed using the following functions.
8174 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
8175 __isl_give isl_basic_set *isl_vertex_get_domain(
8176 __isl_keep isl_vertex *vertex);
8177 __isl_give isl_multi_aff *isl_vertex_get_expr(
8178 __isl_keep isl_vertex *vertex);
8179 __isl_null isl_vertex *isl_vertex_free(
8180 __isl_take isl_vertex *vertex);
8182 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
8183 describing the vertex in terms of the parameters,
8184 while C<isl_vertex_get_domain> returns the activity domain
8187 Chambers can be inspected and destroyed using the following functions.
8189 __isl_give isl_basic_set *isl_cell_get_domain(
8190 __isl_keep isl_cell *cell);
8191 __isl_null isl_cell *isl_cell_free(
8192 __isl_take isl_cell *cell);
8194 =head1 Polyhedral Compilation Library
8196 This section collects functionality in C<isl> that has been specifically
8197 designed for use during polyhedral compilation.
8199 =head2 Schedule Trees
8201 A schedule tree is a structured representation of a schedule,
8202 assigning a relative order to a set of domain elements.
8203 The relative order expressed by the schedule tree is
8204 defined recursively. In particular, the order between
8205 two domain elements is determined by the node that is closest
8206 to the root that refers to both elements and that orders them apart.
8207 Each node in the tree is of one of several types.
8208 The root node is always of type C<isl_schedule_node_domain>
8209 (or C<isl_schedule_node_extension>)
8210 and it describes the (extra) domain elements to which the schedule applies.
8211 The other types of nodes are as follows.
8215 =item C<isl_schedule_node_band>
8217 A band of schedule dimensions. Each schedule dimension is represented
8218 by a union piecewise quasi-affine expression. If this expression
8219 assigns a different value to two domain elements, while all previous
8220 schedule dimensions in the same band assign them the same value,
8221 then the two domain elements are ordered according to these two
8223 Each expression is required to be total in the domain elements
8224 that reach the band node.
8226 =item C<isl_schedule_node_expansion>
8228 An expansion node maps each of the domain elements that reach the node
8229 to one or more domain elements. The image of this mapping forms
8230 the set of domain elements that reach the child of the expansion node.
8231 The function that maps each of the expanded domain elements
8232 to the original domain element from which it was expanded
8233 is called the contraction.
8235 =item C<isl_schedule_node_filter>
8237 A filter node does not impose any ordering, but rather intersects
8238 the set of domain elements that the current subtree refers to
8239 with a given union set. The subtree of the filter node only
8240 refers to domain elements in the intersection.
8241 A filter node is typically only used as a child of a sequence or
8244 =item C<isl_schedule_node_leaf>
8246 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
8248 =item C<isl_schedule_node_mark>
8250 A mark node can be used to attach any kind of information to a subtree
8251 of the schedule tree.
8253 =item C<isl_schedule_node_sequence>
8255 A sequence node has one or more children, each of which is a filter node.
8256 The filters on these filter nodes form a partition of
8257 the domain elements that the current subtree refers to.
8258 If two domain elements appear in distinct filters then the sequence
8259 node orders them according to the child positions of the corresponding
8262 =item C<isl_schedule_node_set>
8264 A set node is similar to a sequence node, except that
8265 it expresses that domain elements appearing in distinct filters
8266 may have any order. The order of the children of a set node
8267 is therefore also immaterial.
8271 The following node types are only supported by the AST generator.
8275 =item C<isl_schedule_node_context>
8277 The context describes constraints on the parameters and
8278 the schedule dimensions of outer
8279 bands that the AST generator may assume to hold. It is also the only
8280 kind of node that may introduce additional parameters.
8281 The space of the context is that of the flat product of the outer
8282 band nodes. In particular, if there are no outer band nodes, then
8283 this space is the unnamed zero-dimensional space.
8284 Since a context node references the outer band nodes, any tree
8285 containing a context node is considered to be anchored.
8287 =item C<isl_schedule_node_extension>
8289 An extension node instructs the AST generator to add additional
8290 domain elements that need to be scheduled.
8291 The additional domain elements are described by the range of
8292 the extension map in terms of the outer schedule dimensions,
8293 i.e., the flat product of the outer band nodes.
8294 Note that domain elements are added whenever the AST generator
8295 reaches the extension node, meaning that there are still some
8296 active domain elements for which an AST needs to be generated.
8297 The conditions under which some domain elements are still active
8298 may however not be completely described by the outer AST nodes
8299 generated at that point.
8300 Since an extension node references the outer band nodes, any tree
8301 containing an extension node is considered to be anchored.
8303 An extension node may also appear as the root of a schedule tree,
8304 when it is intended to be inserted into another tree
8305 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8306 In this case, the domain of the extension node should
8307 correspond to the flat product of the outer band nodes
8308 in this other schedule tree at the point where the extension tree
8311 =item C<isl_schedule_node_guard>
8313 The guard describes constraints on the parameters and
8314 the schedule dimensions of outer
8315 bands that need to be enforced by the outer nodes
8316 in the generated AST.
8317 That is, the part of the AST that is generated from descendants
8318 of the guard node can assume that these constraints are satisfied.
8319 The space of the guard is that of the flat product of the outer
8320 band nodes. In particular, if there are no outer band nodes, then
8321 this space is the unnamed zero-dimensional space.
8322 Since a guard node references the outer band nodes, any tree
8323 containing a guard node is considered to be anchored.
8327 Except for the C<isl_schedule_node_context> nodes,
8328 none of the nodes may introduce any parameters that were not
8329 already present in the root domain node.
8331 A schedule tree is encapsulated in an C<isl_schedule> object.
8332 The simplest such objects, those with a tree consisting of single domain node,
8333 can be created using the following functions with either an empty
8334 domain or a given domain.
8336 #include <isl/schedule.h>
8337 __isl_give isl_schedule *isl_schedule_empty(
8338 __isl_take isl_space *space);
8339 __isl_give isl_schedule *isl_schedule_from_domain(
8340 __isl_take isl_union_set *domain);
8342 The function C<isl_schedule_constraints_compute_schedule> described
8343 in L</"Scheduling"> can also be used to construct schedules.
8345 C<isl_schedule> objects may be copied and freed using the following functions.
8347 #include <isl/schedule.h>
8348 __isl_give isl_schedule *isl_schedule_copy(
8349 __isl_keep isl_schedule *sched);
8350 __isl_null isl_schedule *isl_schedule_free(
8351 __isl_take isl_schedule *sched);
8353 The following functions checks whether two C<isl_schedule> objects
8354 are obviously the same.
8356 #include <isl/schedule.h>
8357 isl_bool isl_schedule_plain_is_equal(
8358 __isl_keep isl_schedule *schedule1,
8359 __isl_keep isl_schedule *schedule2);
8361 The domain of the schedule, i.e., the domain described by the root node,
8362 can be obtained using the following function.
8364 #include <isl/schedule.h>
8365 __isl_give isl_union_set *isl_schedule_get_domain(
8366 __isl_keep isl_schedule *schedule);
8368 An extra top-level band node (right underneath the domain node) can
8369 be introduced into the schedule using the following function.
8370 The schedule tree is assumed not to have any anchored nodes.
8372 #include <isl/schedule.h>
8373 __isl_give isl_schedule *
8374 isl_schedule_insert_partial_schedule(
8375 __isl_take isl_schedule *schedule,
8376 __isl_take isl_multi_union_pw_aff *partial);
8378 A top-level context node (right underneath the domain node) can
8379 be introduced into the schedule using the following function.
8381 #include <isl/schedule.h>
8382 __isl_give isl_schedule *isl_schedule_insert_context(
8383 __isl_take isl_schedule *schedule,
8384 __isl_take isl_set *context)
8386 A top-level guard node (right underneath the domain node) can
8387 be introduced into the schedule using the following function.
8389 #include <isl/schedule.h>
8390 __isl_give isl_schedule *isl_schedule_insert_guard(
8391 __isl_take isl_schedule *schedule,
8392 __isl_take isl_set *guard)
8394 A schedule that combines two schedules either in the given
8395 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8396 or an C<isl_schedule_node_set> node,
8397 can be created using the following functions.
8399 #include <isl/schedule.h>
8400 __isl_give isl_schedule *isl_schedule_sequence(
8401 __isl_take isl_schedule *schedule1,
8402 __isl_take isl_schedule *schedule2);
8403 __isl_give isl_schedule *isl_schedule_set(
8404 __isl_take isl_schedule *schedule1,
8405 __isl_take isl_schedule *schedule2);
8407 The domains of the two input schedules need to be disjoint.
8409 The following function can be used to restrict the domain
8410 of a schedule with a domain node as root to be a subset of the given union set.
8411 This operation may remove nodes in the tree that have become
8414 #include <isl/schedule.h>
8415 __isl_give isl_schedule *isl_schedule_intersect_domain(
8416 __isl_take isl_schedule *schedule,
8417 __isl_take isl_union_set *domain);
8419 The following function can be used to simplify the domain
8420 of a schedule with a domain node as root with respect to the given
8423 #include <isl/schedule.h>
8424 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8425 __isl_take isl_schedule *schedule,
8426 __isl_take isl_set *context);
8428 The following function resets the user pointers on all parameter
8429 and tuple identifiers referenced by the nodes of the given schedule.
8431 #include <isl/schedule.h>
8432 __isl_give isl_schedule *isl_schedule_reset_user(
8433 __isl_take isl_schedule *schedule);
8435 The following function aligns the parameters of all nodes
8436 in the given schedule to the given space.
8438 #include <isl/schedule.h>
8439 __isl_give isl_schedule *isl_schedule_align_params(
8440 __isl_take isl_schedule *schedule,
8441 __isl_take isl_space *space);
8443 The following function allows the user to plug in a given function
8444 in the iteration domains. The input schedule is not allowed to contain
8445 any expansion nodes.
8447 #include <isl/schedule.h>
8448 __isl_give isl_schedule *
8449 isl_schedule_pullback_union_pw_multi_aff(
8450 __isl_take isl_schedule *schedule,
8451 __isl_take isl_union_pw_multi_aff *upma);
8453 The following function can be used to plug in the schedule C<expansion>
8454 in the leaves of C<schedule>, where C<contraction> describes how
8455 the domain elements of C<expansion> map to the domain elements
8456 at the original leaves of C<schedule>.
8457 The resulting schedule will contain expansion nodes, unless
8458 C<contraction> is an identity function.
8460 #include <isl/schedule.h>
8461 __isl_give isl_schedule *isl_schedule_expand(
8462 __isl_take isl_schedule *schedule,
8463 __isl_take isl_union_pw_multi_aff *contraction,
8464 __isl_take isl_schedule *expansion);
8466 An C<isl_union_map> representation of the schedule can be obtained
8467 from an C<isl_schedule> using the following function.
8469 #include <isl/schedule.h>
8470 __isl_give isl_union_map *isl_schedule_get_map(
8471 __isl_keep isl_schedule *sched);
8473 The resulting relation encodes the same relative ordering as
8474 the schedule by mapping the domain elements to a common schedule space.
8475 If the schedule_separate_components option is set, then the order
8476 of the children of a set node is explicitly encoded in the result.
8477 If the tree contains any expansion nodes, then the relation
8478 is formulated in terms of the expanded domain elements.
8480 Schedules can be read from input using the following functions.
8482 #include <isl/schedule.h>
8483 __isl_give isl_schedule *isl_schedule_read_from_file(
8484 isl_ctx *ctx, FILE *input);
8485 __isl_give isl_schedule *isl_schedule_read_from_str(
8486 isl_ctx *ctx, const char *str);
8488 A representation of the schedule can be printed using
8490 #include <isl/schedule.h>
8491 __isl_give isl_printer *isl_printer_print_schedule(
8492 __isl_take isl_printer *p,
8493 __isl_keep isl_schedule *schedule);
8494 __isl_give char *isl_schedule_to_str(
8495 __isl_keep isl_schedule *schedule);
8497 C<isl_schedule_to_str> prints the schedule in flow format.
8499 The schedule tree can be traversed through the use of
8500 C<isl_schedule_node> objects that point to a particular
8501 position in the schedule tree. Whenever a C<isl_schedule_node>
8502 is used to modify a node in the schedule tree, the original schedule
8503 tree is left untouched and the modifications are performed to a copy
8504 of the tree. The returned C<isl_schedule_node> then points to
8505 this modified copy of the tree.
8507 The root of the schedule tree can be obtained using the following function.
8509 #include <isl/schedule.h>
8510 __isl_give isl_schedule_node *isl_schedule_get_root(
8511 __isl_keep isl_schedule *schedule);
8513 A pointer to a newly created schedule tree with a single domain
8514 node can be created using the following functions.
8516 #include <isl/schedule_node.h>
8517 __isl_give isl_schedule_node *
8518 isl_schedule_node_from_domain(
8519 __isl_take isl_union_set *domain);
8520 __isl_give isl_schedule_node *
8521 isl_schedule_node_from_extension(
8522 __isl_take isl_union_map *extension);
8524 C<isl_schedule_node_from_extension> creates a tree with an extension
8527 Schedule nodes can be copied and freed using the following functions.
8529 #include <isl/schedule_node.h>
8530 __isl_give isl_schedule_node *isl_schedule_node_copy(
8531 __isl_keep isl_schedule_node *node);
8532 __isl_null isl_schedule_node *isl_schedule_node_free(
8533 __isl_take isl_schedule_node *node);
8535 The following functions can be used to check if two schedule
8536 nodes point to the same position in the same schedule.
8538 #include <isl/schedule_node.h>
8539 isl_bool isl_schedule_node_is_equal(
8540 __isl_keep isl_schedule_node *node1,
8541 __isl_keep isl_schedule_node *node2);
8543 The following properties can be obtained from a schedule node.
8545 #include <isl/schedule_node.h>
8546 enum isl_schedule_node_type isl_schedule_node_get_type(
8547 __isl_keep isl_schedule_node *node);
8548 enum isl_schedule_node_type
8549 isl_schedule_node_get_parent_type(
8550 __isl_keep isl_schedule_node *node);
8551 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8552 __isl_keep isl_schedule_node *node);
8554 The function C<isl_schedule_node_get_type> returns the type of
8555 the node, while C<isl_schedule_node_get_parent_type> returns
8556 type of the parent of the node, which is required to exist.
8557 The function C<isl_schedule_node_get_schedule> returns a copy
8558 to the schedule to which the node belongs.
8560 The following functions can be used to move the schedule node
8561 to a different position in the tree or to check if such a position
8564 #include <isl/schedule_node.h>
8565 isl_bool isl_schedule_node_has_parent(
8566 __isl_keep isl_schedule_node *node);
8567 __isl_give isl_schedule_node *isl_schedule_node_parent(
8568 __isl_take isl_schedule_node *node);
8569 __isl_give isl_schedule_node *isl_schedule_node_root(
8570 __isl_take isl_schedule_node *node);
8571 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8572 __isl_take isl_schedule_node *node,
8574 int isl_schedule_node_n_children(
8575 __isl_keep isl_schedule_node *node);
8576 __isl_give isl_schedule_node *isl_schedule_node_child(
8577 __isl_take isl_schedule_node *node, int pos);
8578 isl_bool isl_schedule_node_has_children(
8579 __isl_keep isl_schedule_node *node);
8580 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8581 __isl_take isl_schedule_node *node);
8582 isl_bool isl_schedule_node_has_previous_sibling(
8583 __isl_keep isl_schedule_node *node);
8584 __isl_give isl_schedule_node *
8585 isl_schedule_node_previous_sibling(
8586 __isl_take isl_schedule_node *node);
8587 isl_bool isl_schedule_node_has_next_sibling(
8588 __isl_keep isl_schedule_node *node);
8589 __isl_give isl_schedule_node *
8590 isl_schedule_node_next_sibling(
8591 __isl_take isl_schedule_node *node);
8593 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8594 is the node itself, the ancestor of generation 1 is its parent and so on.
8596 It is also possible to query the number of ancestors of a node,
8597 the position of the current node
8598 within the children of its parent, the position of the subtree
8599 containing a node within the children of an ancestor
8600 or to obtain a copy of a given
8601 child without destroying the current node.
8602 Given two nodes that point to the same schedule, their closest
8603 shared ancestor can be obtained using
8604 C<isl_schedule_node_get_shared_ancestor>.
8606 #include <isl/schedule_node.h>
8607 int isl_schedule_node_get_tree_depth(
8608 __isl_keep isl_schedule_node *node);
8609 int isl_schedule_node_get_child_position(
8610 __isl_keep isl_schedule_node *node);
8611 int isl_schedule_node_get_ancestor_child_position(
8612 __isl_keep isl_schedule_node *node,
8613 __isl_keep isl_schedule_node *ancestor);
8614 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8615 __isl_keep isl_schedule_node *node, int pos);
8616 __isl_give isl_schedule_node *
8617 isl_schedule_node_get_shared_ancestor(
8618 __isl_keep isl_schedule_node *node1,
8619 __isl_keep isl_schedule_node *node2);
8621 All nodes in a schedule tree or
8622 all descendants of a specific node (including the node) can be visited
8623 in depth-first pre-order using the following functions.
8625 #include <isl/schedule.h>
8626 isl_stat isl_schedule_foreach_schedule_node_top_down(
8627 __isl_keep isl_schedule *sched,
8628 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8629 void *user), void *user);
8631 #include <isl/schedule_node.h>
8632 isl_stat isl_schedule_node_foreach_descendant_top_down(
8633 __isl_keep isl_schedule_node *node,
8634 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8635 void *user), void *user);
8637 The callback function is slightly different from the usual
8638 callbacks in that it not only indicates success (non-negative result)
8639 or failure (negative result), but also indicates whether the children
8640 of the given node should be visited. In particular, if the callback
8641 returns a positive value, then the children are visited, but if
8642 the callback returns zero, then the children are not visited.
8644 The following functions checks whether
8645 all descendants of a specific node (including the node itself)
8646 satisfy a user-specified test.
8648 #include <isl/schedule_node.h>
8649 isl_bool isl_schedule_node_every_descendant(
8650 __isl_keep isl_schedule_node *node,
8651 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8652 void *user), void *user)
8654 The ancestors of a node in a schedule tree can be visited from
8655 the root down to and including the parent of the node using
8656 the following function.
8658 #include <isl/schedule_node.h>
8659 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8660 __isl_keep isl_schedule_node *node,
8661 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8662 void *user), void *user);
8664 The following functions allows for a depth-first post-order
8665 traversal of the nodes in a schedule tree or
8666 of the descendants of a specific node (including the node
8667 itself), where the user callback is allowed to modify the
8670 #include <isl/schedule.h>
8671 __isl_give isl_schedule *
8672 isl_schedule_map_schedule_node_bottom_up(
8673 __isl_take isl_schedule *schedule,
8674 __isl_give isl_schedule_node *(*fn)(
8675 __isl_take isl_schedule_node *node,
8676 void *user), void *user);
8678 #include <isl/schedule_node.h>
8679 __isl_give isl_schedule_node *
8680 isl_schedule_node_map_descendant_bottom_up(
8681 __isl_take isl_schedule_node *node,
8682 __isl_give isl_schedule_node *(*fn)(
8683 __isl_take isl_schedule_node *node,
8684 void *user), void *user);
8686 The traversal continues from the node returned by the callback function.
8687 It is the responsibility of the user to ensure that this does not
8688 lead to an infinite loop. It is safest to always return a pointer
8689 to the same position (same ancestors and child positions) as the input node.
8691 The following function removes a node (along with its descendants)
8692 from a schedule tree and returns a pointer to the leaf at the
8693 same position in the updated tree.
8694 It is not allowed to remove the root of a schedule tree or
8695 a child of a set or sequence node.
8697 #include <isl/schedule_node.h>
8698 __isl_give isl_schedule_node *isl_schedule_node_cut(
8699 __isl_take isl_schedule_node *node);
8701 The following function removes a single node
8702 from a schedule tree and returns a pointer to the child
8703 of the node, now located at the position of the original node
8704 or to a leaf node at that position if there was no child.
8705 It is not allowed to remove the root of a schedule tree,
8706 a set or sequence node, a child of a set or sequence node or
8707 a band node with an anchored subtree.
8709 #include <isl/schedule_node.h>
8710 __isl_give isl_schedule_node *isl_schedule_node_delete(
8711 __isl_take isl_schedule_node *node);
8713 Most nodes in a schedule tree only contain local information.
8714 In some cases, however, a node may also refer to the schedule dimensions
8715 of its outer band nodes.
8716 This means that the position of the node within the tree should
8717 not be changed, or at least that no changes are performed to the
8718 outer band nodes. The following function can be used to test
8719 whether the subtree rooted at a given node contains any such nodes.
8721 #include <isl/schedule_node.h>
8722 isl_bool isl_schedule_node_is_subtree_anchored(
8723 __isl_keep isl_schedule_node *node);
8725 The following function resets the user pointers on all parameter
8726 and tuple identifiers referenced by the given schedule node.
8728 #include <isl/schedule_node.h>
8729 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8730 __isl_take isl_schedule_node *node);
8732 The following function aligns the parameters of the given schedule
8733 node to the given space.
8735 #include <isl/schedule_node.h>
8736 __isl_give isl_schedule_node *
8737 isl_schedule_node_align_params(
8738 __isl_take isl_schedule_node *node,
8739 __isl_take isl_space *space);
8741 Several node types have their own functions for querying
8742 (and in some cases setting) some node type specific properties.
8744 #include <isl/schedule_node.h>
8745 __isl_give isl_space *isl_schedule_node_band_get_space(
8746 __isl_keep isl_schedule_node *node);
8747 __isl_give isl_multi_union_pw_aff *
8748 isl_schedule_node_band_get_partial_schedule(
8749 __isl_keep isl_schedule_node *node);
8750 __isl_give isl_union_map *
8751 isl_schedule_node_band_get_partial_schedule_union_map(
8752 __isl_keep isl_schedule_node *node);
8753 unsigned isl_schedule_node_band_n_member(
8754 __isl_keep isl_schedule_node *node);
8755 isl_bool isl_schedule_node_band_member_get_coincident(
8756 __isl_keep isl_schedule_node *node, int pos);
8757 __isl_give isl_schedule_node *
8758 isl_schedule_node_band_member_set_coincident(
8759 __isl_take isl_schedule_node *node, int pos,
8761 isl_bool isl_schedule_node_band_get_permutable(
8762 __isl_keep isl_schedule_node *node);
8763 __isl_give isl_schedule_node *
8764 isl_schedule_node_band_set_permutable(
8765 __isl_take isl_schedule_node *node, int permutable);
8766 enum isl_ast_loop_type
8767 isl_schedule_node_band_member_get_ast_loop_type(
8768 __isl_keep isl_schedule_node *node, int pos);
8769 __isl_give isl_schedule_node *
8770 isl_schedule_node_band_member_set_ast_loop_type(
8771 __isl_take isl_schedule_node *node, int pos,
8772 enum isl_ast_loop_type type);
8773 __isl_give isl_union_set *
8774 enum isl_ast_loop_type
8775 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8776 __isl_keep isl_schedule_node *node, int pos);
8777 __isl_give isl_schedule_node *
8778 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8779 __isl_take isl_schedule_node *node, int pos,
8780 enum isl_ast_loop_type type);
8781 isl_schedule_node_band_get_ast_build_options(
8782 __isl_keep isl_schedule_node *node);
8783 __isl_give isl_schedule_node *
8784 isl_schedule_node_band_set_ast_build_options(
8785 __isl_take isl_schedule_node *node,
8786 __isl_take isl_union_set *options);
8787 __isl_give isl_set *
8788 isl_schedule_node_band_get_ast_isolate_option(
8789 __isl_keep isl_schedule_node *node);
8791 The function C<isl_schedule_node_band_get_space> returns the space
8792 of the partial schedule of the band.
8793 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8794 returns a representation of the partial schedule of the band node
8795 in the form of an C<isl_union_map>.
8796 The coincident and permutable properties are set by
8797 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8799 A scheduling dimension is considered to be ``coincident''
8800 if it satisfies the coincidence constraints within its band.
8801 That is, if the dependence distances of the coincidence
8802 constraints are all zero in that direction (for fixed
8803 iterations of outer bands).
8804 A band is marked permutable if it was produced using the Pluto-like scheduler.
8805 Note that the scheduler may have to resort to a Feautrier style scheduling
8806 step even if the default scheduler is used.
8807 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8808 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8809 For the meaning of these loop AST generation types and the difference
8810 between the regular loop AST generation type and the isolate
8811 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8812 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8813 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8814 may return C<isl_ast_loop_error> if an error occurs.
8815 The AST build options govern how an AST is generated for
8816 the individual schedule dimensions during AST generation.
8817 See L</"AST Generation Options (Schedule Tree)">.
8818 The isolate option for the given node can be extracted from these
8819 AST build options using the function
8820 C<isl_schedule_node_band_get_ast_isolate_option>.
8822 #include <isl/schedule_node.h>
8823 __isl_give isl_set *
8824 isl_schedule_node_context_get_context(
8825 __isl_keep isl_schedule_node *node);
8827 #include <isl/schedule_node.h>
8828 __isl_give isl_union_set *
8829 isl_schedule_node_domain_get_domain(
8830 __isl_keep isl_schedule_node *node);
8832 #include <isl/schedule_node.h>
8833 __isl_give isl_union_map *
8834 isl_schedule_node_expansion_get_expansion(
8835 __isl_keep isl_schedule_node *node);
8836 __isl_give isl_union_pw_multi_aff *
8837 isl_schedule_node_expansion_get_contraction(
8838 __isl_keep isl_schedule_node *node);
8840 #include <isl/schedule_node.h>
8841 __isl_give isl_union_map *
8842 isl_schedule_node_extension_get_extension(
8843 __isl_keep isl_schedule_node *node);
8845 #include <isl/schedule_node.h>
8846 __isl_give isl_union_set *
8847 isl_schedule_node_filter_get_filter(
8848 __isl_keep isl_schedule_node *node);
8850 #include <isl/schedule_node.h>
8851 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8852 __isl_keep isl_schedule_node *node);
8854 #include <isl/schedule_node.h>
8855 __isl_give isl_id *isl_schedule_node_mark_get_id(
8856 __isl_keep isl_schedule_node *node);
8858 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8859 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8860 partial schedules related to the node.
8862 #include <isl/schedule_node.h>
8863 __isl_give isl_multi_union_pw_aff *
8864 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8865 __isl_keep isl_schedule_node *node);
8866 __isl_give isl_union_pw_multi_aff *
8867 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8868 __isl_keep isl_schedule_node *node);
8869 __isl_give isl_union_map *
8870 isl_schedule_node_get_prefix_schedule_union_map(
8871 __isl_keep isl_schedule_node *node);
8872 __isl_give isl_union_map *
8873 isl_schedule_node_get_prefix_schedule_relation(
8874 __isl_keep isl_schedule_node *node);
8875 __isl_give isl_union_map *
8876 isl_schedule_node_get_subtree_schedule_union_map(
8877 __isl_keep isl_schedule_node *node);
8879 In particular, the functions
8880 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8881 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8882 and C<isl_schedule_node_get_prefix_schedule_union_map>
8883 return a relative ordering on the domain elements that reach the given
8884 node determined by its ancestors.
8885 The function C<isl_schedule_node_get_prefix_schedule_relation>
8886 additionally includes the domain constraints in the result.
8887 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8888 returns a representation of the partial schedule defined by the
8889 subtree rooted at the given node.
8890 If the tree contains any expansion nodes, then the subtree schedule
8891 is formulated in terms of the expanded domain elements.
8892 The tree passed to functions returning a prefix schedule
8893 may only contain extension nodes if these would not affect
8894 the result of these functions. That is, if one of the ancestors
8895 is an extension node, then all of the domain elements that were
8896 added by the extension node need to have been filtered out
8897 by filter nodes between the extension node and the input node.
8898 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8899 may not contain in extension nodes in the selected subtree.
8901 The expansion/contraction defined by an entire subtree, combining
8902 the expansions/contractions
8903 on the expansion nodes in the subtree, can be obtained using
8904 the following functions.
8906 #include <isl/schedule_node.h>
8907 __isl_give isl_union_map *
8908 isl_schedule_node_get_subtree_expansion(
8909 __isl_keep isl_schedule_node *node);
8910 __isl_give isl_union_pw_multi_aff *
8911 isl_schedule_node_get_subtree_contraction(
8912 __isl_keep isl_schedule_node *node);
8914 The total number of outer band members of given node, i.e.,
8915 the shared output dimension of the maps in the result
8916 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8917 using the following function.
8919 #include <isl/schedule_node.h>
8920 int isl_schedule_node_get_schedule_depth(
8921 __isl_keep isl_schedule_node *node);
8923 The following functions return the elements that reach the given node
8924 or the union of universes in the spaces that contain these elements.
8926 #include <isl/schedule_node.h>
8927 __isl_give isl_union_set *
8928 isl_schedule_node_get_domain(
8929 __isl_keep isl_schedule_node *node);
8930 __isl_give isl_union_set *
8931 isl_schedule_node_get_universe_domain(
8932 __isl_keep isl_schedule_node *node);
8934 The input tree of C<isl_schedule_node_get_domain>
8935 may only contain extension nodes if these would not affect
8936 the result of this function. That is, if one of the ancestors
8937 is an extension node, then all of the domain elements that were
8938 added by the extension node need to have been filtered out
8939 by filter nodes between the extension node and the input node.
8941 The following functions can be used to introduce additional nodes
8942 in the schedule tree. The new node is introduced at the point
8943 in the tree where the C<isl_schedule_node> points to and
8944 the results points to the new node.
8946 #include <isl/schedule_node.h>
8947 __isl_give isl_schedule_node *
8948 isl_schedule_node_insert_partial_schedule(
8949 __isl_take isl_schedule_node *node,
8950 __isl_take isl_multi_union_pw_aff *schedule);
8952 This function inserts a new band node with (the greatest integer
8953 part of) the given partial schedule.
8954 The subtree rooted at the given node is assumed not to have
8957 #include <isl/schedule_node.h>
8958 __isl_give isl_schedule_node *
8959 isl_schedule_node_insert_context(
8960 __isl_take isl_schedule_node *node,
8961 __isl_take isl_set *context);
8963 This function inserts a new context node with the given context constraints.
8965 #include <isl/schedule_node.h>
8966 __isl_give isl_schedule_node *
8967 isl_schedule_node_insert_filter(
8968 __isl_take isl_schedule_node *node,
8969 __isl_take isl_union_set *filter);
8971 This function inserts a new filter node with the given filter.
8972 If the original node already pointed to a filter node, then the
8973 two filter nodes are merged into one.
8975 #include <isl/schedule_node.h>
8976 __isl_give isl_schedule_node *
8977 isl_schedule_node_insert_guard(
8978 __isl_take isl_schedule_node *node,
8979 __isl_take isl_set *guard);
8981 This function inserts a new guard node with the given guard constraints.
8983 #include <isl/schedule_node.h>
8984 __isl_give isl_schedule_node *
8985 isl_schedule_node_insert_mark(
8986 __isl_take isl_schedule_node *node,
8987 __isl_take isl_id *mark);
8989 This function inserts a new mark node with the give mark identifier.
8991 #include <isl/schedule_node.h>
8992 __isl_give isl_schedule_node *
8993 isl_schedule_node_insert_sequence(
8994 __isl_take isl_schedule_node *node,
8995 __isl_take isl_union_set_list *filters);
8996 __isl_give isl_schedule_node *
8997 isl_schedule_node_insert_set(
8998 __isl_take isl_schedule_node *node,
8999 __isl_take isl_union_set_list *filters);
9001 These functions insert a new sequence or set node with the given
9002 filters as children.
9004 #include <isl/schedule_node.h>
9005 __isl_give isl_schedule_node *isl_schedule_node_group(
9006 __isl_take isl_schedule_node *node,
9007 __isl_take isl_id *group_id);
9009 This function introduces an expansion node in between the current
9010 node and its parent that expands instances of a space with tuple
9011 identifier C<group_id> to the original domain elements that reach
9012 the node. The group instances are identified by the prefix schedule
9013 of those domain elements. The ancestors of the node are adjusted
9014 to refer to the group instances instead of the original domain
9015 elements. The return value points to the same node in the updated
9016 schedule tree as the input node, i.e., to the child of the newly
9017 introduced expansion node. Grouping instances of different statements
9018 ensures that they will be treated as a single statement by the
9019 AST generator up to the point of the expansion node.
9021 The following function can be used to flatten a nested
9024 #include <isl/schedule_node.h>
9025 __isl_give isl_schedule_node *
9026 isl_schedule_node_sequence_splice_child(
9027 __isl_take isl_schedule_node *node, int pos);
9029 That is, given a sequence node C<node> that has another sequence node
9030 in its child at position C<pos> (in particular, the child of that filter
9031 node is a sequence node), attach the children of that other sequence
9032 node as children of C<node>, replacing the original child at position
9035 The partial schedule of a band node can be scaled (down) or reduced using
9036 the following functions.
9038 #include <isl/schedule_node.h>
9039 __isl_give isl_schedule_node *
9040 isl_schedule_node_band_scale(
9041 __isl_take isl_schedule_node *node,
9042 __isl_take isl_multi_val *mv);
9043 __isl_give isl_schedule_node *
9044 isl_schedule_node_band_scale_down(
9045 __isl_take isl_schedule_node *node,
9046 __isl_take isl_multi_val *mv);
9047 __isl_give isl_schedule_node *
9048 isl_schedule_node_band_mod(
9049 __isl_take isl_schedule_node *node,
9050 __isl_take isl_multi_val *mv);
9052 The spaces of the two arguments need to match.
9053 After scaling, the partial schedule is replaced by its greatest
9054 integer part to ensure that the schedule remains integral.
9056 The partial schedule of a band node can be shifted by an
9057 C<isl_multi_union_pw_aff> with a domain that is a superset
9058 of the domain of the partial schedule using
9059 the following function.
9061 #include <isl/schedule_node.h>
9062 __isl_give isl_schedule_node *
9063 isl_schedule_node_band_shift(
9064 __isl_take isl_schedule_node *node,
9065 __isl_take isl_multi_union_pw_aff *shift);
9067 A band node can be tiled using the following function.
9069 #include <isl/schedule_node.h>
9070 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
9071 __isl_take isl_schedule_node *node,
9072 __isl_take isl_multi_val *sizes);
9074 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
9076 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
9077 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
9079 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
9081 The C<isl_schedule_node_band_tile> function tiles
9082 the band using the given tile sizes inside its schedule.
9083 A new child band node is created to represent the point loops and it is
9084 inserted between the modified band and its children.
9085 The subtree rooted at the given node is assumed not to have
9087 The C<tile_scale_tile_loops> option specifies whether the tile
9088 loops iterators should be scaled by the tile sizes.
9089 If the C<tile_shift_point_loops> option is set, then the point loops
9090 are shifted to start at zero.
9092 A band node can be split into two nested band nodes
9093 using the following function.
9095 #include <isl/schedule_node.h>
9096 __isl_give isl_schedule_node *isl_schedule_node_band_split(
9097 __isl_take isl_schedule_node *node, int pos);
9099 The resulting outer band node contains the first C<pos> dimensions of
9100 the schedule of C<node> while the inner band contains the remaining dimensions.
9101 The schedules of the two band nodes live in anonymous spaces.
9102 The loop AST generation type options and the isolate option
9103 are split over the two band nodes.
9105 A band node can be moved down to the leaves of the subtree rooted
9106 at the band node using the following function.
9108 #include <isl/schedule_node.h>
9109 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
9110 __isl_take isl_schedule_node *node);
9112 The subtree rooted at the given node is assumed not to have
9114 The result points to the node in the resulting tree that is in the same
9115 position as the node pointed to by C<node> in the original tree.
9117 #include <isl/schedule_node.h>
9118 __isl_give isl_schedule_node *
9119 isl_schedule_node_order_before(
9120 __isl_take isl_schedule_node *node,
9121 __isl_take isl_union_set *filter);
9122 __isl_give isl_schedule_node *
9123 isl_schedule_node_order_after(
9124 __isl_take isl_schedule_node *node,
9125 __isl_take isl_union_set *filter);
9127 These functions split the domain elements that reach C<node>
9128 into those that satisfy C<filter> and those that do not and
9129 arranges for the elements that do satisfy the filter to be
9130 executed before (in case of C<isl_schedule_node_order_before>)
9131 or after (in case of C<isl_schedule_node_order_after>)
9132 those that do not. The order is imposed by
9133 a sequence node, possibly reusing the grandparent of C<node>
9134 on two copies of the subtree attached to the original C<node>.
9135 Both copies are simplified with respect to their filter.
9137 Return a pointer to the copy of the subtree that does not
9138 satisfy C<filter>. If there is no such copy (because all
9139 reaching domain elements satisfy the filter), then return
9140 the original pointer.
9142 #include <isl/schedule_node.h>
9143 __isl_give isl_schedule_node *
9144 isl_schedule_node_graft_before(
9145 __isl_take isl_schedule_node *node,
9146 __isl_take isl_schedule_node *graft);
9147 __isl_give isl_schedule_node *
9148 isl_schedule_node_graft_after(
9149 __isl_take isl_schedule_node *node,
9150 __isl_take isl_schedule_node *graft);
9152 This function inserts the C<graft> tree into the tree containing C<node>
9153 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
9154 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
9155 The root node of C<graft>
9156 should be an extension node where the domain of the extension
9157 is the flat product of all outer band nodes of C<node>.
9158 The root node may also be a domain node.
9159 The elements of the domain or the range of the extension may not
9160 intersect with the domain elements that reach "node".
9161 The schedule tree of C<graft> may not be anchored.
9163 The schedule tree of C<node> is modified to include an extension node
9164 corresponding to the root node of C<graft> as a child of the original
9165 parent of C<node>. The original node that C<node> points to and the
9166 child of the root node of C<graft> are attached to this extension node
9167 through a sequence, with appropriate filters and with the child
9168 of C<graft> appearing before or after the original C<node>.
9170 If C<node> already appears inside a sequence that is the child of
9171 an extension node and if the spaces of the new domain elements
9172 do not overlap with those of the original domain elements,
9173 then that extension node is extended with the new extension
9174 rather than introducing a new segment of extension and sequence nodes.
9176 Return a pointer to the same node in the modified tree that
9177 C<node> pointed to in the original tree.
9179 A representation of the schedule node can be printed using
9181 #include <isl/schedule_node.h>
9182 __isl_give isl_printer *isl_printer_print_schedule_node(
9183 __isl_take isl_printer *p,
9184 __isl_keep isl_schedule_node *node);
9185 __isl_give char *isl_schedule_node_to_str(
9186 __isl_keep isl_schedule_node *node);
9188 C<isl_schedule_node_to_str> prints the schedule node in block format.
9190 =head2 Dependence Analysis
9192 C<isl> contains specialized functionality for performing
9193 array dataflow analysis. That is, given a I<sink> access relation,
9194 a collection of possible I<source> accesses and
9195 a collection of I<kill> accesses,
9196 C<isl> can compute relations that describe
9197 for each iteration of the sink access, which iterations
9198 of which of the source access relations may have
9199 accessed the same data element before the given iteration
9200 of the sink access without any intermediate kill of that data element.
9201 The resulting dependence relations map source iterations
9202 to either the corresponding sink iterations or
9203 pairs of corresponding sink iterations and accessed data elements.
9204 To compute standard flow dependences, the sink should be
9205 a read, while the sources should be writes.
9206 If no kills are specified,
9207 then memory based dependence analysis is performed.
9208 If, on the other hand, all sources are also kills,
9209 then value based dependence analysis is performed.
9210 If any of the source accesses are marked as being I<must>
9211 accesses, then they are also treated as kills.
9212 Furthermore, the specification of must-sources results
9213 in the computation of must-dependences.
9214 Only dependences originating in a must access not coscheduled
9215 with any other access to the same element and without
9216 any may accesses between the must access and the sink access
9217 are considered to be must dependences.
9219 =head3 High-level Interface
9221 A high-level interface to dependence analysis is provided
9222 by the following function.
9224 #include <isl/flow.h>
9225 __isl_give isl_union_flow *
9226 isl_union_access_info_compute_flow(
9227 __isl_take isl_union_access_info *access);
9229 The input C<isl_union_access_info> object describes the sink
9230 access relations, the source access relations and a schedule,
9231 while the output C<isl_union_flow> object describes
9232 the resulting dependence relations and the subsets of the
9233 sink relations for which no source was found.
9235 An C<isl_union_access_info> is created, modified, copied and freed using
9236 the following functions.
9238 #include <isl/flow.h>
9239 __isl_give isl_union_access_info *
9240 isl_union_access_info_from_sink(
9241 __isl_take isl_union_map *sink);
9242 __isl_give isl_union_access_info *
9243 isl_union_access_info_set_kill(
9244 __isl_take isl_union_access_info *access,
9245 __isl_take isl_union_map *kill);
9246 __isl_give isl_union_access_info *
9247 isl_union_access_info_set_may_source(
9248 __isl_take isl_union_access_info *access,
9249 __isl_take isl_union_map *may_source);
9250 __isl_give isl_union_access_info *
9251 isl_union_access_info_set_must_source(
9252 __isl_take isl_union_access_info *access,
9253 __isl_take isl_union_map *must_source);
9254 __isl_give isl_union_access_info *
9255 isl_union_access_info_set_schedule(
9256 __isl_take isl_union_access_info *access,
9257 __isl_take isl_schedule *schedule);
9258 __isl_give isl_union_access_info *
9259 isl_union_access_info_set_schedule_map(
9260 __isl_take isl_union_access_info *access,
9261 __isl_take isl_union_map *schedule_map);
9262 __isl_give isl_union_access_info *
9263 isl_union_access_info_copy(
9264 __isl_keep isl_union_access_info *access);
9265 __isl_null isl_union_access_info *
9266 isl_union_access_info_free(
9267 __isl_take isl_union_access_info *access);
9269 The may sources set by C<isl_union_access_info_set_may_source>
9270 do not need to include the must sources set by
9271 C<isl_union_access_info_set_must_source> as a subset.
9272 The kills set by C<isl_union_access_info_set_kill> may overlap
9273 with the may-sources and/or must-sources.
9274 The user is free not to call one (or more) of these functions,
9275 in which case the corresponding set is kept to its empty default.
9276 Similarly, the default schedule initialized by
9277 C<isl_union_access_info_from_sink> is empty.
9278 The current schedule is determined by the last call to either
9279 C<isl_union_access_info_set_schedule> or
9280 C<isl_union_access_info_set_schedule_map>.
9281 The domain of the schedule corresponds to the domains of
9282 the access relations. In particular, the domains of the access
9283 relations are effectively intersected with the domain of the schedule
9284 and only the resulting accesses are considered by the dependence analysis.
9286 An C<isl_union_access_info> object can be read from input
9287 using the following function.
9289 #include <isl/flow.h>
9290 __isl_give isl_union_access_info *
9291 isl_union_access_info_read_from_file(isl_ctx *ctx,
9294 A representation of the information contained in an object
9295 of type C<isl_union_access_info> can be obtained using
9297 #include <isl/flow.h>
9298 __isl_give isl_printer *
9299 isl_printer_print_union_access_info(
9300 __isl_take isl_printer *p,
9301 __isl_keep isl_union_access_info *access);
9302 __isl_give char *isl_union_access_info_to_str(
9303 __isl_keep isl_union_access_info *access);
9305 C<isl_union_access_info_to_str> prints the information in flow format.
9307 The output of C<isl_union_access_info_compute_flow> can be examined,
9308 copied, and freed using the following functions.
9310 #include <isl/flow.h>
9311 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9312 __isl_keep isl_union_flow *flow);
9313 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9314 __isl_keep isl_union_flow *flow);
9315 __isl_give isl_union_map *
9316 isl_union_flow_get_full_must_dependence(
9317 __isl_keep isl_union_flow *flow);
9318 __isl_give isl_union_map *
9319 isl_union_flow_get_full_may_dependence(
9320 __isl_keep isl_union_flow *flow);
9321 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9322 __isl_keep isl_union_flow *flow);
9323 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9324 __isl_keep isl_union_flow *flow);
9325 __isl_give isl_union_flow *isl_union_flow_copy(
9326 __isl_keep isl_union_flow *flow);
9327 __isl_null isl_union_flow *isl_union_flow_free(
9328 __isl_take isl_union_flow *flow);
9330 The relation returned by C<isl_union_flow_get_must_dependence>
9331 relates domain elements of must sources to domain elements of the sink.
9332 The relation returned by C<isl_union_flow_get_may_dependence>
9333 relates domain elements of must or may sources to domain elements of the sink
9334 and includes the previous relation as a subset.
9335 The relation returned by C<isl_union_flow_get_full_must_dependence>
9336 relates domain elements of must sources to pairs of domain elements of the sink
9337 and accessed data elements.
9338 The relation returned by C<isl_union_flow_get_full_may_dependence>
9339 relates domain elements of must or may sources to pairs of
9340 domain elements of the sink and accessed data elements.
9341 This relation includes the previous relation as a subset.
9342 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9343 of the sink relation for which no dependences have been found.
9344 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9345 of the sink relation for which no definite dependences have been found.
9346 That is, it contains those sink access that do not contribute to any
9347 of the elements in the relation returned
9348 by C<isl_union_flow_get_must_dependence>.
9350 A representation of the information contained in an object
9351 of type C<isl_union_flow> can be obtained using
9353 #include <isl/flow.h>
9354 __isl_give isl_printer *isl_printer_print_union_flow(
9355 __isl_take isl_printer *p,
9356 __isl_keep isl_union_flow *flow);
9357 __isl_give char *isl_union_flow_to_str(
9358 __isl_keep isl_union_flow *flow);
9360 C<isl_union_flow_to_str> prints the information in flow format.
9362 =head3 Low-level Interface
9364 A lower-level interface is provided by the following functions.
9366 #include <isl/flow.h>
9368 typedef int (*isl_access_level_before)(void *first, void *second);
9370 __isl_give isl_access_info *isl_access_info_alloc(
9371 __isl_take isl_map *sink,
9372 void *sink_user, isl_access_level_before fn,
9374 __isl_give isl_access_info *isl_access_info_add_source(
9375 __isl_take isl_access_info *acc,
9376 __isl_take isl_map *source, int must,
9378 __isl_null isl_access_info *isl_access_info_free(
9379 __isl_take isl_access_info *acc);
9381 __isl_give isl_flow *isl_access_info_compute_flow(
9382 __isl_take isl_access_info *acc);
9384 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9385 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9386 void *dep_user, void *user),
9388 __isl_give isl_map *isl_flow_get_no_source(
9389 __isl_keep isl_flow *deps, int must);
9390 __isl_null isl_flow *isl_flow_free(
9391 __isl_take isl_flow *deps);
9393 The function C<isl_access_info_compute_flow> performs the actual
9394 dependence analysis. The other functions are used to construct
9395 the input for this function or to read off the output.
9397 The input is collected in an C<isl_access_info>, which can
9398 be created through a call to C<isl_access_info_alloc>.
9399 The arguments to this functions are the sink access relation
9400 C<sink>, a token C<sink_user> used to identify the sink
9401 access to the user, a callback function for specifying the
9402 relative order of source and sink accesses, and the number
9403 of source access relations that will be added.
9405 The callback function has type C<int (*)(void *first, void *second)>.
9406 The function is called with two user supplied tokens identifying
9407 either a source or the sink and it should return the shared nesting
9408 level and the relative order of the two accesses.
9409 In particular, let I<n> be the number of loops shared by
9410 the two accesses. If C<first> precedes C<second> textually,
9411 then the function should return I<2 * n + 1>; otherwise,
9412 it should return I<2 * n>.
9413 The low-level interface assumes that no sources are coscheduled.
9414 If the information returned by the callback does not allow
9415 the relative order to be determined, then one of the sources
9416 is arbitrarily taken to be executed after the other(s).
9418 The sources can be added to the C<isl_access_info> object by performing
9419 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9420 C<must> indicates whether the source is a I<must> access
9421 or a I<may> access. Note that a multi-valued access relation
9422 should only be marked I<must> if every iteration in the domain
9423 of the relation accesses I<all> elements in its image.
9424 The C<source_user> token is again used to identify
9425 the source access. The range of the source access relation
9426 C<source> should have the same dimension as the range
9427 of the sink access relation.
9428 The C<isl_access_info_free> function should usually not be
9429 called explicitly, because it is already called implicitly by
9430 C<isl_access_info_compute_flow>.
9432 The result of the dependence analysis is collected in an
9433 C<isl_flow>. There may be elements of
9434 the sink access for which no preceding source access could be
9435 found or for which all preceding sources are I<may> accesses.
9436 The relations containing these elements can be obtained through
9437 calls to C<isl_flow_get_no_source>, the first with C<must> set
9438 and the second with C<must> unset.
9439 In the case of standard flow dependence analysis,
9440 with the sink a read and the sources I<must> writes,
9441 the first relation corresponds to the reads from uninitialized
9442 array elements and the second relation is empty.
9443 The actual flow dependences can be extracted using
9444 C<isl_flow_foreach>. This function will call the user-specified
9445 callback function C<fn> for each B<non-empty> dependence between
9446 a source and the sink. The callback function is called
9447 with four arguments, the actual flow dependence relation
9448 mapping source iterations to sink iterations, a boolean that
9449 indicates whether it is a I<must> or I<may> dependence, a token
9450 identifying the source and an additional C<void *> with value
9451 equal to the third argument of the C<isl_flow_foreach> call.
9452 A dependence is marked I<must> if it originates from a I<must>
9453 source and if it is not followed by any I<may> sources.
9455 After finishing with an C<isl_flow>, the user should call
9456 C<isl_flow_free> to free all associated memory.
9458 =head3 Interaction with the Low-level Interface
9460 During the dependence analysis, we frequently need to perform
9461 the following operation. Given a relation between sink iterations
9462 and potential source iterations from a particular source domain,
9463 what is the last potential source iteration corresponding to each
9464 sink iteration. It can sometimes be convenient to adjust
9465 the set of potential source iterations before or after each such operation.
9466 The prototypical example is fuzzy array dataflow analysis,
9467 where we need to analyze if, based on data-dependent constraints,
9468 the sink iteration can ever be executed without one or more of
9469 the corresponding potential source iterations being executed.
9470 If so, we can introduce extra parameters and select an unknown
9471 but fixed source iteration from the potential source iterations.
9472 To be able to perform such manipulations, C<isl> provides the following
9475 #include <isl/flow.h>
9477 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9478 __isl_keep isl_map *source_map,
9479 __isl_keep isl_set *sink, void *source_user,
9481 __isl_give isl_access_info *isl_access_info_set_restrict(
9482 __isl_take isl_access_info *acc,
9483 isl_access_restrict fn, void *user);
9485 The function C<isl_access_info_set_restrict> should be called
9486 before calling C<isl_access_info_compute_flow> and registers a callback function
9487 that will be called any time C<isl> is about to compute the last
9488 potential source. The first argument is the (reverse) proto-dependence,
9489 mapping sink iterations to potential source iterations.
9490 The second argument represents the sink iterations for which
9491 we want to compute the last source iteration.
9492 The third argument is the token corresponding to the source
9493 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9494 The callback is expected to return a restriction on either the input or
9495 the output of the operation computing the last potential source.
9496 If the input needs to be restricted then restrictions are needed
9497 for both the source and the sink iterations. The sink iterations
9498 and the potential source iterations will be intersected with these sets.
9499 If the output needs to be restricted then only a restriction on the source
9500 iterations is required.
9501 If any error occurs, the callback should return C<NULL>.
9502 An C<isl_restriction> object can be created, freed and inspected
9503 using the following functions.
9505 #include <isl/flow.h>
9507 __isl_give isl_restriction *isl_restriction_input(
9508 __isl_take isl_set *source_restr,
9509 __isl_take isl_set *sink_restr);
9510 __isl_give isl_restriction *isl_restriction_output(
9511 __isl_take isl_set *source_restr);
9512 __isl_give isl_restriction *isl_restriction_none(
9513 __isl_take isl_map *source_map);
9514 __isl_give isl_restriction *isl_restriction_empty(
9515 __isl_take isl_map *source_map);
9516 __isl_null isl_restriction *isl_restriction_free(
9517 __isl_take isl_restriction *restr);
9519 C<isl_restriction_none> and C<isl_restriction_empty> are special
9520 cases of C<isl_restriction_input>. C<isl_restriction_none>
9521 is essentially equivalent to
9523 isl_restriction_input(isl_set_universe(
9524 isl_space_range(isl_map_get_space(source_map))),
9526 isl_space_domain(isl_map_get_space(source_map))));
9528 whereas C<isl_restriction_empty> is essentially equivalent to
9530 isl_restriction_input(isl_set_empty(
9531 isl_space_range(isl_map_get_space(source_map))),
9533 isl_space_domain(isl_map_get_space(source_map))));
9537 #include <isl/schedule.h>
9538 __isl_give isl_schedule *
9539 isl_schedule_constraints_compute_schedule(
9540 __isl_take isl_schedule_constraints *sc);
9542 The function C<isl_schedule_constraints_compute_schedule> can be
9543 used to compute a schedule that satisfies the given schedule constraints.
9544 These schedule constraints include the iteration domain for which
9545 a schedule should be computed and dependences between pairs of
9546 iterations. In particular, these dependences include
9547 I<validity> dependences and I<proximity> dependences.
9548 By default, the algorithm used to construct the schedule is similar
9549 to that of C<Pluto>.
9550 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9552 The generated schedule respects all validity dependences.
9553 That is, all dependence distances over these dependences in the
9554 scheduled space are lexicographically positive.
9556 The default algorithm tries to ensure that the dependence distances
9557 over coincidence constraints are zero and to minimize the
9558 dependence distances over proximity dependences.
9559 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9560 for groups of domains where the dependence distances over validity
9561 dependences have only non-negative values.
9562 Note that when minimizing the maximal dependence distance
9563 over proximity dependences, a single affine expression in the parameters
9564 is constructed that bounds all dependence distances. If no such expression
9565 exists, then the algorithm will fail and resort to an alternative
9566 scheduling algorithm. In particular, this means that adding proximity
9567 dependences may eliminate valid solutions. A typical example where this
9568 phenomenon may occur is when some subset of the proximity dependences
9569 has no restriction on some parameter, forcing the coefficient of that
9570 parameter to be zero, while some other subset forces the dependence
9571 distance to depend on that parameter, requiring the same coefficient
9573 When using Feautrier's algorithm, the coincidence and proximity constraints
9574 are only taken into account during the extension to a
9575 full-dimensional schedule.
9577 An C<isl_schedule_constraints> object can be constructed
9578 and manipulated using the following functions.
9580 #include <isl/schedule.h>
9581 __isl_give isl_schedule_constraints *
9582 isl_schedule_constraints_copy(
9583 __isl_keep isl_schedule_constraints *sc);
9584 __isl_give isl_schedule_constraints *
9585 isl_schedule_constraints_on_domain(
9586 __isl_take isl_union_set *domain);
9587 __isl_give isl_schedule_constraints *
9588 isl_schedule_constraints_set_context(
9589 __isl_take isl_schedule_constraints *sc,
9590 __isl_take isl_set *context);
9591 __isl_give isl_schedule_constraints *
9592 isl_schedule_constraints_set_validity(
9593 __isl_take isl_schedule_constraints *sc,
9594 __isl_take isl_union_map *validity);
9595 __isl_give isl_schedule_constraints *
9596 isl_schedule_constraints_set_coincidence(
9597 __isl_take isl_schedule_constraints *sc,
9598 __isl_take isl_union_map *coincidence);
9599 __isl_give isl_schedule_constraints *
9600 isl_schedule_constraints_set_proximity(
9601 __isl_take isl_schedule_constraints *sc,
9602 __isl_take isl_union_map *proximity);
9603 __isl_give isl_schedule_constraints *
9604 isl_schedule_constraints_set_conditional_validity(
9605 __isl_take isl_schedule_constraints *sc,
9606 __isl_take isl_union_map *condition,
9607 __isl_take isl_union_map *validity);
9608 __isl_give isl_schedule_constraints *
9609 isl_schedule_constraints_apply(
9610 __isl_take isl_schedule_constraints *sc,
9611 __isl_take isl_union_map *umap);
9612 __isl_null isl_schedule_constraints *
9613 isl_schedule_constraints_free(
9614 __isl_take isl_schedule_constraints *sc);
9616 The initial C<isl_schedule_constraints> object created by
9617 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9618 That is, it has an empty set of dependences.
9619 The function C<isl_schedule_constraints_set_context> allows the user
9620 to specify additional constraints on the parameters that may
9621 be assumed to hold during the construction of the schedule.
9622 The function C<isl_schedule_constraints_set_validity> replaces the
9623 validity dependences, mapping domain elements I<i> to domain
9624 elements that should be scheduled after I<i>.
9625 The function C<isl_schedule_constraints_set_coincidence> replaces the
9626 coincidence dependences, mapping domain elements I<i> to domain
9627 elements that should be scheduled together with I<I>, if possible.
9628 The function C<isl_schedule_constraints_set_proximity> replaces the
9629 proximity dependences, mapping domain elements I<i> to domain
9630 elements that should be scheduled either before I<I>
9631 or as early as possible after I<i>.
9633 The function C<isl_schedule_constraints_set_conditional_validity>
9634 replaces the conditional validity constraints.
9635 A conditional validity constraint is only imposed when any of the corresponding
9636 conditions is satisfied, i.e., when any of them is non-zero.
9637 That is, the scheduler ensures that within each band if the dependence
9638 distances over the condition constraints are not all zero
9639 then all corresponding conditional validity constraints are respected.
9640 A conditional validity constraint corresponds to a condition
9641 if the two are adjacent, i.e., if the domain of one relation intersect
9642 the range of the other relation.
9643 The typical use case of conditional validity constraints is
9644 to allow order constraints between live ranges to be violated
9645 as long as the live ranges themselves are local to the band.
9646 To allow more fine-grained control over which conditions correspond
9647 to which conditional validity constraints, the domains and ranges
9648 of these relations may include I<tags>. That is, the domains and
9649 ranges of those relation may themselves be wrapped relations
9650 where the iteration domain appears in the domain of those wrapped relations
9651 and the range of the wrapped relations can be arbitrarily chosen
9652 by the user. Conditions and conditional validity constraints are only
9653 considered adjacent to each other if the entire wrapped relation matches.
9654 In particular, a relation with a tag will never be considered adjacent
9655 to a relation without a tag.
9657 The function C<isl_schedule_constraints_apply> takes
9658 schedule constraints that are defined on some set of domain elements
9659 and transforms them to schedule constraints on the elements
9660 to which these domain elements are mapped by the given transformation.
9662 An C<isl_schedule_constraints> object can be inspected
9663 using the following functions.
9665 #include <isl/schedule.h>
9666 __isl_give isl_union_set *
9667 isl_schedule_constraints_get_domain(
9668 __isl_keep isl_schedule_constraints *sc);
9669 __isl_give isl_set *isl_schedule_constraints_get_context(
9670 __isl_keep isl_schedule_constraints *sc);
9671 __isl_give isl_union_map *
9672 isl_schedule_constraints_get_validity(
9673 __isl_keep isl_schedule_constraints *sc);
9674 __isl_give isl_union_map *
9675 isl_schedule_constraints_get_coincidence(
9676 __isl_keep isl_schedule_constraints *sc);
9677 __isl_give isl_union_map *
9678 isl_schedule_constraints_get_proximity(
9679 __isl_keep isl_schedule_constraints *sc);
9680 __isl_give isl_union_map *
9681 isl_schedule_constraints_get_conditional_validity(
9682 __isl_keep isl_schedule_constraints *sc);
9683 __isl_give isl_union_map *
9684 isl_schedule_constraints_get_conditional_validity_condition(
9685 __isl_keep isl_schedule_constraints *sc);
9687 An C<isl_schedule_constraints> object can be read from input
9688 using the following functions.
9690 #include <isl/schedule.h>
9691 __isl_give isl_schedule_constraints *
9692 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9694 __isl_give isl_schedule_constraints *
9695 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9698 The contents of an C<isl_schedule_constraints> object can be printed
9699 using the following functions.
9701 #include <isl/schedule.h>
9702 __isl_give isl_printer *
9703 isl_printer_print_schedule_constraints(
9704 __isl_take isl_printer *p,
9705 __isl_keep isl_schedule_constraints *sc);
9706 __isl_give char *isl_schedule_constraints_to_str(
9707 __isl_keep isl_schedule_constraints *sc);
9709 The following function computes a schedule directly from
9710 an iteration domain and validity and proximity dependences
9711 and is implemented in terms of the functions described above.
9712 The use of C<isl_union_set_compute_schedule> is discouraged.
9714 #include <isl/schedule.h>
9715 __isl_give isl_schedule *isl_union_set_compute_schedule(
9716 __isl_take isl_union_set *domain,
9717 __isl_take isl_union_map *validity,
9718 __isl_take isl_union_map *proximity);
9720 The generated schedule represents a schedule tree.
9721 For more information on schedule trees, see
9722 L</"Schedule Trees">.
9726 #include <isl/schedule.h>
9727 isl_stat isl_options_set_schedule_max_coefficient(
9728 isl_ctx *ctx, int val);
9729 int isl_options_get_schedule_max_coefficient(
9731 isl_stat isl_options_set_schedule_max_constant_term(
9732 isl_ctx *ctx, int val);
9733 int isl_options_get_schedule_max_constant_term(
9735 isl_stat isl_options_set_schedule_serialize_sccs(
9736 isl_ctx *ctx, int val);
9737 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9738 isl_stat isl_options_set_schedule_whole_component(
9739 isl_ctx *ctx, int val);
9740 int isl_options_get_schedule_whole_component(
9742 isl_stat isl_options_set_schedule_maximize_band_depth(
9743 isl_ctx *ctx, int val);
9744 int isl_options_get_schedule_maximize_band_depth(
9746 isl_stat isl_options_set_schedule_maximize_coincidence(
9747 isl_ctx *ctx, int val);
9748 int isl_options_get_schedule_maximize_coincidence(
9750 isl_stat isl_options_set_schedule_outer_coincidence(
9751 isl_ctx *ctx, int val);
9752 int isl_options_get_schedule_outer_coincidence(
9754 isl_stat isl_options_set_schedule_split_scaled(
9755 isl_ctx *ctx, int val);
9756 int isl_options_get_schedule_split_scaled(
9758 isl_stat isl_options_set_schedule_treat_coalescing(
9759 isl_ctx *ctx, int val);
9760 int isl_options_get_schedule_treat_coalescing(
9762 isl_stat isl_options_set_schedule_algorithm(
9763 isl_ctx *ctx, int val);
9764 int isl_options_get_schedule_algorithm(
9766 isl_stat isl_options_set_schedule_carry_self_first(
9767 isl_ctx *ctx, int val);
9768 int isl_options_get_schedule_carry_self_first(
9770 isl_stat isl_options_set_schedule_separate_components(
9771 isl_ctx *ctx, int val);
9772 int isl_options_get_schedule_separate_components(
9777 =item * schedule_max_coefficient
9779 This option enforces that the coefficients for variable and parameter
9780 dimensions in the calculated schedule are not larger than the specified value.
9781 This option can significantly increase the speed of the scheduling calculation
9782 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9783 this option does not introduce bounds on the variable or parameter
9785 This option has no effect on the Feautrier style scheduler.
9787 =item * schedule_max_constant_term
9789 This option enforces that the constant coefficients in the calculated schedule
9790 are not larger than the maximal constant term. This option can significantly
9791 increase the speed of the scheduling calculation and may also prevent fusing of
9792 unrelated dimensions. A value of -1 means that this option does not introduce
9793 bounds on the constant coefficients.
9795 =item * schedule_serialize_sccs
9797 If this option is set, then all strongly connected components
9798 in the dependence graph are serialized as soon as they are detected.
9799 This means in particular that instances of statements will only
9800 appear in the same band node if these statements belong
9801 to the same strongly connected component at the point where
9802 the band node is constructed.
9804 =item * schedule_whole_component
9806 If this option is set, then entire (weakly) connected
9807 components in the dependence graph are scheduled together
9809 Otherwise, each strongly connected component within
9810 such a weakly connected component is first scheduled separately
9811 and then combined with other strongly connected components.
9812 This option has no effect if C<schedule_serialize_sccs> is set.
9814 =item * schedule_maximize_band_depth
9816 If this option is set, then the scheduler tries to maximize
9817 the width of the bands. Wider bands give more possibilities for tiling.
9818 In particular, if the C<schedule_whole_component> option is set,
9819 then bands are split if this might result in wider bands.
9820 Otherwise, the effect of this option is to only allow
9821 strongly connected components to be combined if this does
9822 not reduce the width of the bands.
9823 Note that if the C<schedule_serialize_sccs> options is set, then
9824 the C<schedule_maximize_band_depth> option therefore has no effect.
9826 =item * schedule_maximize_coincidence
9828 This option is only effective if the C<schedule_whole_component>
9829 option is turned off.
9830 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9831 strongly connected components are only combined with each other
9832 if this does not reduce the number of coincident band members.
9834 =item * schedule_outer_coincidence
9836 If this option is set, then we try to construct schedules
9837 where the outermost scheduling dimension in each band
9838 satisfies the coincidence constraints.
9840 =item * schedule_algorithm
9842 Selects the scheduling algorithm to be used.
9843 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9844 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9846 =item * schedule_split_scaled
9848 If this option is set, then we try to construct schedules in which the
9849 constant term is split off from the linear part if the linear parts of
9850 the scheduling rows for all nodes in the graph have a common non-trivial
9852 The constant term is then dropped and the linear
9854 This option is only effective when the Feautrier style scheduler is
9855 being used, either as the main scheduler or as a fallback for the
9856 Pluto-like scheduler.
9858 =item * schedule_treat_coalescing
9860 If this option is set, then the scheduler will try and avoid
9861 producing schedules that perform loop coalescing.
9862 In particular, for the Pluto-like scheduler, this option places
9863 bounds on the schedule coefficients based on the sizes of the instance sets.
9864 For the Feautrier style scheduler, this option detects potentially
9865 coalescing schedules and then tries to adjust the schedule to avoid
9868 =item * schedule_carry_self_first
9870 If this option is set, then the Feautrier style scheduler
9871 (when used as a fallback for the Pluto-like scheduler) will
9872 first try to only carry self-dependences.
9874 =item * schedule_separate_components
9876 If this option is set then the function C<isl_schedule_get_map>
9877 will treat set nodes in the same way as sequence nodes.
9881 =head2 AST Generation
9883 This section describes the C<isl> functionality for generating
9884 ASTs that visit all the elements
9885 in a domain in an order specified by a schedule tree or
9887 In case the schedule given as a C<isl_union_map>, an AST is generated
9888 that visits all the elements in the domain of the C<isl_union_map>
9889 according to the lexicographic order of the corresponding image
9890 element(s). If the range of the C<isl_union_map> consists of
9891 elements in more than one space, then each of these spaces is handled
9892 separately in an arbitrary order.
9893 It should be noted that the schedule tree or the image elements
9894 in a schedule map only specify the I<order>
9895 in which the corresponding domain elements should be visited.
9896 No direct relation between the partial schedule values
9897 or the image elements on the one hand and the loop iterators
9898 in the generated AST on the other hand should be assumed.
9900 Each AST is generated within a build. The initial build
9901 simply specifies the constraints on the parameters (if any)
9902 and can be created, inspected, copied and freed using the following functions.
9904 #include <isl/ast_build.h>
9905 __isl_give isl_ast_build *isl_ast_build_alloc(
9907 __isl_give isl_ast_build *isl_ast_build_from_context(
9908 __isl_take isl_set *set);
9909 __isl_give isl_ast_build *isl_ast_build_copy(
9910 __isl_keep isl_ast_build *build);
9911 __isl_null isl_ast_build *isl_ast_build_free(
9912 __isl_take isl_ast_build *build);
9914 The C<set> argument is usually a parameter set with zero or more parameters.
9915 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9916 this set is required to be a parameter set.
9917 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9918 specify any parameter constraints.
9919 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9920 and L</"Fine-grained Control over AST Generation">.
9921 Finally, the AST itself can be constructed using one of the following
9924 #include <isl/ast_build.h>
9925 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9926 __isl_keep isl_ast_build *build,
9927 __isl_take isl_schedule *schedule);
9928 __isl_give isl_ast_node *
9929 isl_ast_build_node_from_schedule_map(
9930 __isl_keep isl_ast_build *build,
9931 __isl_take isl_union_map *schedule);
9933 =head3 Inspecting the AST
9935 The basic properties of an AST node can be obtained as follows.
9937 #include <isl/ast.h>
9938 enum isl_ast_node_type isl_ast_node_get_type(
9939 __isl_keep isl_ast_node *node);
9941 The type of an AST node is one of
9942 C<isl_ast_node_for>,
9944 C<isl_ast_node_block>,
9945 C<isl_ast_node_mark> or
9946 C<isl_ast_node_user>.
9947 An C<isl_ast_node_for> represents a for node.
9948 An C<isl_ast_node_if> represents an if node.
9949 An C<isl_ast_node_block> represents a compound node.
9950 An C<isl_ast_node_mark> introduces a mark in the AST.
9951 An C<isl_ast_node_user> represents an expression statement.
9952 An expression statement typically corresponds to a domain element, i.e.,
9953 one of the elements that is visited by the AST.
9955 Each type of node has its own additional properties.
9957 #include <isl/ast.h>
9958 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9959 __isl_keep isl_ast_node *node);
9960 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9961 __isl_keep isl_ast_node *node);
9962 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9963 __isl_keep isl_ast_node *node);
9964 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9965 __isl_keep isl_ast_node *node);
9966 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9967 __isl_keep isl_ast_node *node);
9968 isl_bool isl_ast_node_for_is_degenerate(
9969 __isl_keep isl_ast_node *node);
9971 An C<isl_ast_for> is considered degenerate if it is known to execute
9974 #include <isl/ast.h>
9975 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9976 __isl_keep isl_ast_node *node);
9977 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9978 __isl_keep isl_ast_node *node);
9979 isl_bool isl_ast_node_if_has_else(
9980 __isl_keep isl_ast_node *node);
9981 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9982 __isl_keep isl_ast_node *node);
9984 __isl_give isl_ast_node_list *
9985 isl_ast_node_block_get_children(
9986 __isl_keep isl_ast_node *node);
9988 __isl_give isl_id *isl_ast_node_mark_get_id(
9989 __isl_keep isl_ast_node *node);
9990 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9991 __isl_keep isl_ast_node *node);
9993 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9994 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9996 #include <isl/ast.h>
9997 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9998 __isl_keep isl_ast_node *node);
10000 All descendants of a specific node in the AST (including the node itself)
10002 in depth-first pre-order using the following function.
10004 #include <isl/ast.h>
10005 isl_stat isl_ast_node_foreach_descendant_top_down(
10006 __isl_keep isl_ast_node *node,
10007 isl_bool (*fn)(__isl_keep isl_ast_node *node,
10008 void *user), void *user);
10010 The callback function should return C<isl_bool_true> if the children
10011 of the given node should be visited and C<isl_bool_false> if they should not.
10012 It should return C<isl_bool_error> in case of failure, in which case
10013 the entire traversal is aborted.
10015 Each of the returned C<isl_ast_expr>s can in turn be inspected using
10016 the following functions.
10018 #include <isl/ast.h>
10019 enum isl_ast_expr_type isl_ast_expr_get_type(
10020 __isl_keep isl_ast_expr *expr);
10022 The type of an AST expression is one of
10023 C<isl_ast_expr_op>,
10024 C<isl_ast_expr_id> or
10025 C<isl_ast_expr_int>.
10026 An C<isl_ast_expr_op> represents the result of an operation.
10027 An C<isl_ast_expr_id> represents an identifier.
10028 An C<isl_ast_expr_int> represents an integer value.
10030 Each type of expression has its own additional properties.
10032 #include <isl/ast.h>
10033 enum isl_ast_op_type isl_ast_expr_get_op_type(
10034 __isl_keep isl_ast_expr *expr);
10035 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
10036 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
10037 __isl_keep isl_ast_expr *expr, int pos);
10038 isl_stat isl_ast_expr_foreach_ast_op_type(
10039 __isl_keep isl_ast_expr *expr,
10040 isl_stat (*fn)(enum isl_ast_op_type type,
10041 void *user), void *user);
10042 isl_stat isl_ast_node_foreach_ast_op_type(
10043 __isl_keep isl_ast_node *node,
10044 isl_stat (*fn)(enum isl_ast_op_type type,
10045 void *user), void *user);
10047 C<isl_ast_expr_get_op_type> returns the type of the operation
10048 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
10049 arguments. C<isl_ast_expr_get_op_arg> returns the specified
10051 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
10052 C<isl_ast_op_type> that appears in C<expr>.
10053 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
10054 C<isl_ast_op_type> that appears in C<node>.
10055 The operation type is one of the following.
10059 =item C<isl_ast_op_and>
10061 Logical I<and> of two arguments.
10062 Both arguments can be evaluated.
10064 =item C<isl_ast_op_and_then>
10066 Logical I<and> of two arguments.
10067 The second argument can only be evaluated if the first evaluates to true.
10069 =item C<isl_ast_op_or>
10071 Logical I<or> of two arguments.
10072 Both arguments can be evaluated.
10074 =item C<isl_ast_op_or_else>
10076 Logical I<or> of two arguments.
10077 The second argument can only be evaluated if the first evaluates to false.
10079 =item C<isl_ast_op_max>
10081 Maximum of two or more arguments.
10083 =item C<isl_ast_op_min>
10085 Minimum of two or more arguments.
10087 =item C<isl_ast_op_minus>
10091 =item C<isl_ast_op_add>
10093 Sum of two arguments.
10095 =item C<isl_ast_op_sub>
10097 Difference of two arguments.
10099 =item C<isl_ast_op_mul>
10101 Product of two arguments.
10103 =item C<isl_ast_op_div>
10105 Exact division. That is, the result is known to be an integer.
10107 =item C<isl_ast_op_fdiv_q>
10109 Result of integer division, rounded towards negative
10111 The divisor is known to be positive.
10113 =item C<isl_ast_op_pdiv_q>
10115 Result of integer division, where dividend is known to be non-negative.
10116 The divisor is known to be positive.
10118 =item C<isl_ast_op_pdiv_r>
10120 Remainder of integer division, where dividend is known to be non-negative.
10121 The divisor is known to be positive.
10123 =item C<isl_ast_op_zdiv_r>
10125 Equal to zero iff the remainder on integer division is zero.
10126 The divisor is known to be positive.
10128 =item C<isl_ast_op_cond>
10130 Conditional operator defined on three arguments.
10131 If the first argument evaluates to true, then the result
10132 is equal to the second argument. Otherwise, the result
10133 is equal to the third argument.
10134 The second and third argument may only be evaluated if
10135 the first argument evaluates to true and false, respectively.
10136 Corresponds to C<a ? b : c> in C.
10138 =item C<isl_ast_op_select>
10140 Conditional operator defined on three arguments.
10141 If the first argument evaluates to true, then the result
10142 is equal to the second argument. Otherwise, the result
10143 is equal to the third argument.
10144 The second and third argument may be evaluated independently
10145 of the value of the first argument.
10146 Corresponds to C<a * b + (1 - a) * c> in C.
10148 =item C<isl_ast_op_eq>
10152 =item C<isl_ast_op_le>
10154 Less than or equal relation.
10156 =item C<isl_ast_op_lt>
10158 Less than relation.
10160 =item C<isl_ast_op_ge>
10162 Greater than or equal relation.
10164 =item C<isl_ast_op_gt>
10166 Greater than relation.
10168 =item C<isl_ast_op_call>
10171 The number of arguments of the C<isl_ast_expr> is one more than
10172 the number of arguments in the function call, the first argument
10173 representing the function being called.
10175 =item C<isl_ast_op_access>
10178 The number of arguments of the C<isl_ast_expr> is one more than
10179 the number of index expressions in the array access, the first argument
10180 representing the array being accessed.
10182 =item C<isl_ast_op_member>
10185 This operation has two arguments, a structure and the name of
10186 the member of the structure being accessed.
10190 #include <isl/ast.h>
10191 __isl_give isl_id *isl_ast_expr_get_id(
10192 __isl_keep isl_ast_expr *expr);
10194 Return the identifier represented by the AST expression.
10196 #include <isl/ast.h>
10197 __isl_give isl_val *isl_ast_expr_get_val(
10198 __isl_keep isl_ast_expr *expr);
10200 Return the integer represented by the AST expression.
10202 =head3 Properties of ASTs
10204 #include <isl/ast.h>
10205 isl_bool isl_ast_expr_is_equal(
10206 __isl_keep isl_ast_expr *expr1,
10207 __isl_keep isl_ast_expr *expr2);
10209 Check if two C<isl_ast_expr>s are equal to each other.
10211 =head3 Manipulating and printing the AST
10213 AST nodes can be copied and freed using the following functions.
10215 #include <isl/ast.h>
10216 __isl_give isl_ast_node *isl_ast_node_copy(
10217 __isl_keep isl_ast_node *node);
10218 __isl_null isl_ast_node *isl_ast_node_free(
10219 __isl_take isl_ast_node *node);
10221 AST expressions can be copied and freed using the following functions.
10223 #include <isl/ast.h>
10224 __isl_give isl_ast_expr *isl_ast_expr_copy(
10225 __isl_keep isl_ast_expr *expr);
10226 __isl_null isl_ast_expr *isl_ast_expr_free(
10227 __isl_take isl_ast_expr *expr);
10229 New AST expressions can be created either directly or within
10230 the context of an C<isl_ast_build>.
10232 #include <isl/ast.h>
10233 __isl_give isl_ast_expr *isl_ast_expr_from_val(
10234 __isl_take isl_val *v);
10235 __isl_give isl_ast_expr *isl_ast_expr_from_id(
10236 __isl_take isl_id *id);
10237 __isl_give isl_ast_expr *isl_ast_expr_neg(
10238 __isl_take isl_ast_expr *expr);
10239 __isl_give isl_ast_expr *isl_ast_expr_address_of(
10240 __isl_take isl_ast_expr *expr);
10241 __isl_give isl_ast_expr *isl_ast_expr_add(
10242 __isl_take isl_ast_expr *expr1,
10243 __isl_take isl_ast_expr *expr2);
10244 __isl_give isl_ast_expr *isl_ast_expr_sub(
10245 __isl_take isl_ast_expr *expr1,
10246 __isl_take isl_ast_expr *expr2);
10247 __isl_give isl_ast_expr *isl_ast_expr_mul(
10248 __isl_take isl_ast_expr *expr1,
10249 __isl_take isl_ast_expr *expr2);
10250 __isl_give isl_ast_expr *isl_ast_expr_div(
10251 __isl_take isl_ast_expr *expr1,
10252 __isl_take isl_ast_expr *expr2);
10253 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
10254 __isl_take isl_ast_expr *expr1,
10255 __isl_take isl_ast_expr *expr2);
10256 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
10257 __isl_take isl_ast_expr *expr1,
10258 __isl_take isl_ast_expr *expr2);
10259 __isl_give isl_ast_expr *isl_ast_expr_and(
10260 __isl_take isl_ast_expr *expr1,
10261 __isl_take isl_ast_expr *expr2)
10262 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10263 __isl_take isl_ast_expr *expr1,
10264 __isl_take isl_ast_expr *expr2)
10265 __isl_give isl_ast_expr *isl_ast_expr_or(
10266 __isl_take isl_ast_expr *expr1,
10267 __isl_take isl_ast_expr *expr2)
10268 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10269 __isl_take isl_ast_expr *expr1,
10270 __isl_take isl_ast_expr *expr2)
10271 __isl_give isl_ast_expr *isl_ast_expr_eq(
10272 __isl_take isl_ast_expr *expr1,
10273 __isl_take isl_ast_expr *expr2);
10274 __isl_give isl_ast_expr *isl_ast_expr_le(
10275 __isl_take isl_ast_expr *expr1,
10276 __isl_take isl_ast_expr *expr2);
10277 __isl_give isl_ast_expr *isl_ast_expr_lt(
10278 __isl_take isl_ast_expr *expr1,
10279 __isl_take isl_ast_expr *expr2);
10280 __isl_give isl_ast_expr *isl_ast_expr_ge(
10281 __isl_take isl_ast_expr *expr1,
10282 __isl_take isl_ast_expr *expr2);
10283 __isl_give isl_ast_expr *isl_ast_expr_gt(
10284 __isl_take isl_ast_expr *expr1,
10285 __isl_take isl_ast_expr *expr2);
10286 __isl_give isl_ast_expr *isl_ast_expr_access(
10287 __isl_take isl_ast_expr *array,
10288 __isl_take isl_ast_expr_list *indices);
10289 __isl_give isl_ast_expr *isl_ast_expr_call(
10290 __isl_take isl_ast_expr *function,
10291 __isl_take isl_ast_expr_list *arguments);
10293 The function C<isl_ast_expr_address_of> can be applied to an
10294 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10295 to represent the address of the C<isl_ast_expr_access>.
10296 The second argument of the functions C<isl_ast_expr_pdiv_q> and
10297 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
10299 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10300 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10302 #include <isl/ast_build.h>
10303 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10304 __isl_keep isl_ast_build *build,
10305 __isl_take isl_set *set);
10306 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10307 __isl_keep isl_ast_build *build,
10308 __isl_take isl_pw_aff *pa);
10309 __isl_give isl_ast_expr *
10310 isl_ast_build_access_from_pw_multi_aff(
10311 __isl_keep isl_ast_build *build,
10312 __isl_take isl_pw_multi_aff *pma);
10313 __isl_give isl_ast_expr *
10314 isl_ast_build_access_from_multi_pw_aff(
10315 __isl_keep isl_ast_build *build,
10316 __isl_take isl_multi_pw_aff *mpa);
10317 __isl_give isl_ast_expr *
10318 isl_ast_build_call_from_pw_multi_aff(
10319 __isl_keep isl_ast_build *build,
10320 __isl_take isl_pw_multi_aff *pma);
10321 __isl_give isl_ast_expr *
10322 isl_ast_build_call_from_multi_pw_aff(
10323 __isl_keep isl_ast_build *build,
10324 __isl_take isl_multi_pw_aff *mpa);
10327 the domains of C<pa>, C<mpa> and C<pma> should correspond
10328 to the schedule space of C<build>.
10329 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10330 the function being called.
10331 If the accessed space is a nested relation, then it is taken
10332 to represent an access of the member specified by the range
10333 of this nested relation of the structure specified by the domain
10334 of the nested relation.
10336 The following functions can be used to modify an C<isl_ast_expr>.
10338 #include <isl/ast.h>
10339 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10340 __isl_take isl_ast_expr *expr, int pos,
10341 __isl_take isl_ast_expr *arg);
10343 Replace the argument of C<expr> at position C<pos> by C<arg>.
10345 #include <isl/ast.h>
10346 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10347 __isl_take isl_ast_expr *expr,
10348 __isl_take isl_id_to_ast_expr *id2expr);
10350 The function C<isl_ast_expr_substitute_ids> replaces the
10351 subexpressions of C<expr> of type C<isl_ast_expr_id>
10352 by the corresponding expression in C<id2expr>, if there is any.
10355 User specified data can be attached to an C<isl_ast_node> and obtained
10356 from the same C<isl_ast_node> using the following functions.
10358 #include <isl/ast.h>
10359 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10360 __isl_take isl_ast_node *node,
10361 __isl_take isl_id *annotation);
10362 __isl_give isl_id *isl_ast_node_get_annotation(
10363 __isl_keep isl_ast_node *node);
10365 Basic printing can be performed using the following functions.
10367 #include <isl/ast.h>
10368 __isl_give isl_printer *isl_printer_print_ast_expr(
10369 __isl_take isl_printer *p,
10370 __isl_keep isl_ast_expr *expr);
10371 __isl_give isl_printer *isl_printer_print_ast_node(
10372 __isl_take isl_printer *p,
10373 __isl_keep isl_ast_node *node);
10374 __isl_give char *isl_ast_expr_to_str(
10375 __isl_keep isl_ast_expr *expr);
10376 __isl_give char *isl_ast_node_to_str(
10377 __isl_keep isl_ast_node *node);
10378 __isl_give char *isl_ast_expr_to_C_str(
10379 __isl_keep isl_ast_expr *expr);
10380 __isl_give char *isl_ast_node_to_C_str(
10381 __isl_keep isl_ast_node *node);
10383 The functions C<isl_ast_expr_to_C_str> and
10384 C<isl_ast_node_to_C_str> are convenience functions
10385 that return a string representation of the input in C format.
10387 More advanced printing can be performed using the following functions.
10389 #include <isl/ast.h>
10390 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10391 __isl_take isl_printer *p,
10392 enum isl_ast_op_type type,
10393 __isl_keep const char *name);
10394 isl_stat isl_options_set_ast_print_macro_once(
10395 isl_ctx *ctx, int val);
10396 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10397 __isl_give isl_printer *isl_ast_op_type_print_macro(
10398 enum isl_ast_op_type type,
10399 __isl_take isl_printer *p);
10400 __isl_give isl_printer *isl_ast_expr_print_macros(
10401 __isl_keep isl_ast_expr *expr,
10402 __isl_take isl_printer *p);
10403 __isl_give isl_printer *isl_ast_node_print_macros(
10404 __isl_keep isl_ast_node *node,
10405 __isl_take isl_printer *p);
10406 __isl_give isl_printer *isl_ast_node_print(
10407 __isl_keep isl_ast_node *node,
10408 __isl_take isl_printer *p,
10409 __isl_take isl_ast_print_options *options);
10410 __isl_give isl_printer *isl_ast_node_for_print(
10411 __isl_keep isl_ast_node *node,
10412 __isl_take isl_printer *p,
10413 __isl_take isl_ast_print_options *options);
10414 __isl_give isl_printer *isl_ast_node_if_print(
10415 __isl_keep isl_ast_node *node,
10416 __isl_take isl_printer *p,
10417 __isl_take isl_ast_print_options *options);
10419 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10420 C<isl> may print out an AST that makes use of macros such
10421 as C<floord>, C<min> and C<max>.
10422 The names of these macros may be modified by a call
10423 to C<isl_ast_op_type_set_print_name>. The user-specified
10424 names are associated to the printer object.
10425 C<isl_ast_op_type_print_macro> prints out the macro
10426 corresponding to a specific C<isl_ast_op_type>.
10427 If the print-macro-once option is set, then a given macro definition
10428 is only printed once to any given printer object.
10429 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10430 for subexpressions where these macros would be used and prints
10431 out the required macro definitions.
10432 Essentially, C<isl_ast_expr_print_macros> calls
10433 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10434 as function argument.
10435 C<isl_ast_node_print_macros> does the same
10436 for expressions in its C<isl_ast_node> argument.
10437 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10438 C<isl_ast_node_if_print> print an C<isl_ast_node>
10439 in C<ISL_FORMAT_C>, but allow for some extra control
10440 through an C<isl_ast_print_options> object.
10441 This object can be created using the following functions.
10443 #include <isl/ast.h>
10444 __isl_give isl_ast_print_options *
10445 isl_ast_print_options_alloc(isl_ctx *ctx);
10446 __isl_give isl_ast_print_options *
10447 isl_ast_print_options_copy(
10448 __isl_keep isl_ast_print_options *options);
10449 __isl_null isl_ast_print_options *
10450 isl_ast_print_options_free(
10451 __isl_take isl_ast_print_options *options);
10453 __isl_give isl_ast_print_options *
10454 isl_ast_print_options_set_print_user(
10455 __isl_take isl_ast_print_options *options,
10456 __isl_give isl_printer *(*print_user)(
10457 __isl_take isl_printer *p,
10458 __isl_take isl_ast_print_options *options,
10459 __isl_keep isl_ast_node *node, void *user),
10461 __isl_give isl_ast_print_options *
10462 isl_ast_print_options_set_print_for(
10463 __isl_take isl_ast_print_options *options,
10464 __isl_give isl_printer *(*print_for)(
10465 __isl_take isl_printer *p,
10466 __isl_take isl_ast_print_options *options,
10467 __isl_keep isl_ast_node *node, void *user),
10470 The callback set by C<isl_ast_print_options_set_print_user>
10471 is called whenever a node of type C<isl_ast_node_user> needs to
10473 The callback set by C<isl_ast_print_options_set_print_for>
10474 is called whenever a node of type C<isl_ast_node_for> needs to
10476 Note that C<isl_ast_node_for_print> will I<not> call the
10477 callback set by C<isl_ast_print_options_set_print_for> on the node
10478 on which C<isl_ast_node_for_print> is called, but only on nested
10479 nodes of type C<isl_ast_node_for>. It is therefore safe to
10480 call C<isl_ast_node_for_print> from within the callback set by
10481 C<isl_ast_print_options_set_print_for>.
10483 The following option determines the type to be used for iterators
10484 while printing the AST.
10486 isl_stat isl_options_set_ast_iterator_type(
10487 isl_ctx *ctx, const char *val);
10488 const char *isl_options_get_ast_iterator_type(
10491 The AST printer only prints body nodes as blocks if these
10492 blocks cannot be safely omitted.
10493 For example, a C<for> node with one body node will not be
10494 surrounded with braces in C<ISL_FORMAT_C>.
10495 A block will always be printed by setting the following option.
10497 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10499 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10503 #include <isl/ast_build.h>
10504 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10505 isl_ctx *ctx, int val);
10506 int isl_options_get_ast_build_atomic_upper_bound(
10508 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10510 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10511 isl_stat isl_options_set_ast_build_detect_min_max(
10512 isl_ctx *ctx, int val);
10513 int isl_options_get_ast_build_detect_min_max(
10515 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10516 isl_ctx *ctx, int val);
10517 int isl_options_get_ast_build_exploit_nested_bounds(
10519 isl_stat isl_options_set_ast_build_group_coscheduled(
10520 isl_ctx *ctx, int val);
10521 int isl_options_get_ast_build_group_coscheduled(
10523 isl_stat isl_options_set_ast_build_separation_bounds(
10524 isl_ctx *ctx, int val);
10525 int isl_options_get_ast_build_separation_bounds(
10527 isl_stat isl_options_set_ast_build_scale_strides(
10528 isl_ctx *ctx, int val);
10529 int isl_options_get_ast_build_scale_strides(
10531 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10533 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10534 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10536 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10540 =item * ast_build_atomic_upper_bound
10542 Generate loop upper bounds that consist of the current loop iterator,
10543 an operator and an expression not involving the iterator.
10544 If this option is not set, then the current loop iterator may appear
10545 several times in the upper bound.
10546 For example, when this option is turned off, AST generation
10549 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10553 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10556 When the option is turned on, the following AST is generated
10558 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10561 =item * ast_build_prefer_pdiv
10563 If this option is turned off, then the AST generation will
10564 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10565 operators, but no C<isl_ast_op_pdiv_q> or
10566 C<isl_ast_op_pdiv_r> operators.
10567 If this option is turned on, then C<isl> will try to convert
10568 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10569 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10571 =item * ast_build_detect_min_max
10573 If this option is turned on, then C<isl> will try and detect
10574 min or max-expressions when building AST expressions from
10575 piecewise affine expressions.
10577 =item * ast_build_exploit_nested_bounds
10579 Simplify conditions based on bounds of nested for loops.
10580 In particular, remove conditions that are implied by the fact
10581 that one or more nested loops have at least one iteration,
10582 meaning that the upper bound is at least as large as the lower bound.
10583 For example, when this option is turned off, AST generation
10586 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10592 for (int c0 = 0; c0 <= N; c0 += 1)
10593 for (int c1 = 0; c1 <= M; c1 += 1)
10596 When the option is turned on, the following AST is generated
10598 for (int c0 = 0; c0 <= N; c0 += 1)
10599 for (int c1 = 0; c1 <= M; c1 += 1)
10602 =item * ast_build_group_coscheduled
10604 If two domain elements are assigned the same schedule point, then
10605 they may be executed in any order and they may even appear in different
10606 loops. If this options is set, then the AST generator will make
10607 sure that coscheduled domain elements do not appear in separate parts
10608 of the AST. This is useful in case of nested AST generation
10609 if the outer AST generation is given only part of a schedule
10610 and the inner AST generation should handle the domains that are
10611 coscheduled by this initial part of the schedule together.
10612 For example if an AST is generated for a schedule
10614 { A[i] -> [0]; B[i] -> [0] }
10616 then the C<isl_ast_build_set_create_leaf> callback described
10617 below may get called twice, once for each domain.
10618 Setting this option ensures that the callback is only called once
10619 on both domains together.
10621 =item * ast_build_separation_bounds
10623 This option specifies which bounds to use during separation.
10624 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10625 then all (possibly implicit) bounds on the current dimension will
10626 be used during separation.
10627 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10628 then only those bounds that are explicitly available will
10629 be used during separation.
10631 =item * ast_build_scale_strides
10633 This option specifies whether the AST generator is allowed
10634 to scale down iterators of strided loops.
10636 =item * ast_build_allow_else
10638 This option specifies whether the AST generator is allowed
10639 to construct if statements with else branches.
10641 =item * ast_build_allow_or
10643 This option specifies whether the AST generator is allowed
10644 to construct if conditions with disjunctions.
10648 =head3 AST Generation Options (Schedule Tree)
10650 In case of AST construction from a schedule tree, the options
10651 that control how an AST is created from the individual schedule
10652 dimensions are stored in the band nodes of the tree
10653 (see L</"Schedule Trees">).
10655 In particular, a schedule dimension can be handled in four
10656 different ways, atomic, separate, unroll or the default.
10657 This loop AST generation type can be set using
10658 C<isl_schedule_node_band_member_set_ast_loop_type>.
10660 the first three can be selected by including a one-dimensional
10661 element with as value the position of the schedule dimension
10662 within the band and as name one of C<atomic>, C<separate>
10663 or C<unroll> in the options
10664 set by C<isl_schedule_node_band_set_ast_build_options>.
10665 Only one of these three may be specified for
10666 any given schedule dimension within a band node.
10667 If none of these is specified, then the default
10668 is used. The meaning of the options is as follows.
10674 When this option is specified, the AST generator will make
10675 sure that a given domains space only appears in a single
10676 loop at the specified level.
10678 For example, for the schedule tree
10680 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10682 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10683 options: "{ atomic[x] }"
10685 the following AST will be generated
10687 for (int c0 = 0; c0 <= 10; c0 += 1) {
10694 On the other hand, 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: "{ separate[x] }"
10701 the following AST will be generated
10705 for (int c0 = 1; c0 <= 9; c0 += 1) {
10712 If neither C<atomic> nor C<separate> is specified, then the AST generator
10713 may produce either of these two results or some intermediate form.
10717 When this option is specified, the AST generator will
10718 split the domain of the specified schedule dimension
10719 into pieces with a fixed set of statements for which
10720 instances need to be executed by the iterations in
10721 the schedule domain part. This option tends to avoid
10722 the generation of guards inside the corresponding loops.
10723 See also the C<atomic> option.
10727 When this option is specified, the AST generator will
10728 I<completely> unroll the corresponding schedule dimension.
10729 It is the responsibility of the user to ensure that such
10730 unrolling is possible.
10731 To obtain a partial unrolling, the user should apply an additional
10732 strip-mining to the schedule and fully unroll the inner schedule
10737 The C<isolate> option is a bit more involved. It allows the user
10738 to isolate a range of schedule dimension values from smaller and
10739 greater values. Additionally, the user may specify a different
10740 atomic/separate/unroll choice for the isolated part and the remaining
10741 parts. The typical use case of the C<isolate> option is to isolate
10742 full tiles from partial tiles.
10743 The part that needs to be isolated may depend on outer schedule dimensions.
10744 The option therefore needs to be able to reference those outer schedule
10745 dimensions. In particular, the space of the C<isolate> option is that
10746 of a wrapped map with as domain the flat product of all outer band nodes
10747 and as range the space of the current band node.
10748 The atomic/separate/unroll choice for the isolated part is determined
10749 by an option that lives in an unnamed wrapped space with as domain
10750 a zero-dimensional C<isolate> space and as range the regular
10751 C<atomic>, C<separate> or C<unroll> space.
10752 This option may also be set directly using
10753 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10754 The atomic/separate/unroll choice for the remaining part is determined
10755 by the regular C<atomic>, C<separate> or C<unroll> option.
10756 Since the C<isolate> option references outer schedule dimensions,
10757 its use in a band node causes any tree containing the node
10758 to be considered anchored.
10760 As an example, consider the isolation of full tiles from partial tiles
10761 in a tiling of a triangular domain. The original schedule is as follows.
10763 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10765 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10766 { A[i,j] -> [floor(j/10)] }, \
10767 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10771 for (int c0 = 0; c0 <= 10; c0 += 1)
10772 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10773 for (int c2 = 10 * c0;
10774 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10775 for (int c3 = 10 * c1;
10776 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10779 Isolating the full tiles, we have the following input
10781 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10783 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10784 { A[i,j] -> [floor(j/10)] }, \
10785 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10786 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10787 10a+9+10b+9 <= 100 }"
10792 for (int c0 = 0; c0 <= 8; c0 += 1) {
10793 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10794 for (int c2 = 10 * c0;
10795 c2 <= 10 * c0 + 9; c2 += 1)
10796 for (int c3 = 10 * c1;
10797 c3 <= 10 * c1 + 9; c3 += 1)
10799 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10800 for (int c2 = 10 * c0;
10801 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10802 for (int c3 = 10 * c1;
10803 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10806 for (int c0 = 9; c0 <= 10; c0 += 1)
10807 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10808 for (int c2 = 10 * c0;
10809 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10810 for (int c3 = 10 * c1;
10811 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10815 We may then additionally unroll the innermost loop of the isolated part
10817 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10819 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10820 { A[i,j] -> [floor(j/10)] }, \
10821 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10822 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10823 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10828 for (int c0 = 0; c0 <= 8; c0 += 1) {
10829 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10830 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10832 A(c2, 10 * c1 + 1);
10833 A(c2, 10 * c1 + 2);
10834 A(c2, 10 * c1 + 3);
10835 A(c2, 10 * c1 + 4);
10836 A(c2, 10 * c1 + 5);
10837 A(c2, 10 * c1 + 6);
10838 A(c2, 10 * c1 + 7);
10839 A(c2, 10 * c1 + 8);
10840 A(c2, 10 * c1 + 9);
10842 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10843 for (int c2 = 10 * c0;
10844 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10845 for (int c3 = 10 * c1;
10846 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10849 for (int c0 = 9; c0 <= 10; c0 += 1)
10850 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10851 for (int c2 = 10 * c0;
10852 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10853 for (int c3 = 10 * c1;
10854 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10859 =head3 AST Generation Options (Schedule Map)
10861 In case of AST construction using
10862 C<isl_ast_build_node_from_schedule_map>, the options
10863 that control how an AST is created from the individual schedule
10864 dimensions are stored in the C<isl_ast_build>.
10865 They can be set using the following function.
10867 #include <isl/ast_build.h>
10868 __isl_give isl_ast_build *
10869 isl_ast_build_set_options(
10870 __isl_take isl_ast_build *build,
10871 __isl_take isl_union_map *options);
10873 The options are encoded in an C<isl_union_map>.
10874 The domain of this union relation refers to the schedule domain,
10875 i.e., the range of the schedule passed
10876 to C<isl_ast_build_node_from_schedule_map>.
10877 In the case of nested AST generation (see L</"Nested AST Generation">),
10878 the domain of C<options> should refer to the extra piece of the schedule.
10879 That is, it should be equal to the range of the wrapped relation in the
10880 range of the schedule.
10881 The range of the options can consist of elements in one or more spaces,
10882 the names of which determine the effect of the option.
10883 The values of the range typically also refer to the schedule dimension
10884 to which the option applies, with value C<0> representing
10885 the outermost schedule dimension. In case of nested AST generation
10886 (see L</"Nested AST Generation">), these values refer to the position
10887 of the schedule dimension within the innermost AST generation.
10888 The constraints on the domain elements of
10889 the option should only refer to this dimension and earlier dimensions.
10890 We consider the following spaces.
10894 =item C<separation_class>
10896 B<This option has been deprecated. Use the isolate option on
10897 schedule trees instead.>
10899 This space is a wrapped relation between two one dimensional spaces.
10900 The input space represents the schedule dimension to which the option
10901 applies and the output space represents the separation class.
10902 While constructing a loop corresponding to the specified schedule
10903 dimension(s), the AST generator will try to generate separate loops
10904 for domain elements that are assigned different classes.
10905 If only some of the elements are assigned a class, then those elements
10906 that are not assigned any class will be treated as belonging to a class
10907 that is separate from the explicitly assigned classes.
10908 The typical use case for this option is to separate full tiles from
10910 The other options, described below, are applied after the separation
10913 As an example, consider the separation into full and partial tiles
10914 of a tiling of a triangular domain.
10915 Take, for example, the domain
10917 { A[i,j] : 0 <= i,j and i + j <= 100 }
10919 and a tiling into tiles of 10 by 10. The input to the AST generator
10920 is then the schedule
10922 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10925 Without any options, the following AST is generated
10927 for (int c0 = 0; c0 <= 10; c0 += 1)
10928 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10929 for (int c2 = 10 * c0;
10930 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10932 for (int c3 = 10 * c1;
10933 c3 <= min(10 * c1 + 9, -c2 + 100);
10937 Separation into full and partial tiles can be obtained by assigning
10938 a class, say C<0>, to the full tiles. The full tiles are represented by those
10939 values of the first and second schedule dimensions for which there are
10940 values of the third and fourth dimensions to cover an entire tile.
10941 That is, we need to specify the following option
10943 { [a,b,c,d] -> separation_class[[0]->[0]] :
10944 exists b': 0 <= 10a,10b' and
10945 10a+9+10b'+9 <= 100;
10946 [a,b,c,d] -> separation_class[[1]->[0]] :
10947 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10949 which simplifies to
10951 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10952 a >= 0 and b >= 0 and b <= 8 - a;
10953 [a, b, c, d] -> separation_class[[0] -> [0]] :
10954 a >= 0 and a <= 8 }
10956 With this option, the generated AST is as follows
10959 for (int c0 = 0; c0 <= 8; c0 += 1) {
10960 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10961 for (int c2 = 10 * c0;
10962 c2 <= 10 * c0 + 9; c2 += 1)
10963 for (int c3 = 10 * c1;
10964 c3 <= 10 * c1 + 9; c3 += 1)
10966 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10967 for (int c2 = 10 * c0;
10968 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10970 for (int c3 = 10 * c1;
10971 c3 <= min(-c2 + 100, 10 * c1 + 9);
10975 for (int c0 = 9; c0 <= 10; c0 += 1)
10976 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10977 for (int c2 = 10 * c0;
10978 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10980 for (int c3 = 10 * c1;
10981 c3 <= min(10 * c1 + 9, -c2 + 100);
10988 This is a single-dimensional space representing the schedule dimension(s)
10989 to which ``separation'' should be applied. Separation tries to split
10990 a loop into several pieces if this can avoid the generation of guards
10992 See also the C<atomic> option.
10996 This is a single-dimensional space representing the schedule dimension(s)
10997 for which the domains should be considered ``atomic''. That is, the
10998 AST generator will make sure that any given domain space will only appear
10999 in a single loop at the specified level.
11001 Consider the following schedule
11003 { a[i] -> [i] : 0 <= i < 10;
11004 b[i] -> [i+1] : 0 <= i < 10 }
11006 If the following option is specified
11008 { [i] -> separate[x] }
11010 then the following AST will be generated
11014 for (int c0 = 1; c0 <= 9; c0 += 1) {
11021 If, on the other hand, the following option is specified
11023 { [i] -> atomic[x] }
11025 then the following AST will be generated
11027 for (int c0 = 0; c0 <= 10; c0 += 1) {
11034 If neither C<atomic> nor C<separate> is specified, then the AST generator
11035 may produce either of these two results or some intermediate form.
11039 This is a single-dimensional space representing the schedule dimension(s)
11040 that should be I<completely> unrolled.
11041 To obtain a partial unrolling, the user should apply an additional
11042 strip-mining to the schedule and fully unroll the inner loop.
11046 =head3 Fine-grained Control over AST Generation
11048 Besides specifying the constraints on the parameters,
11049 an C<isl_ast_build> object can be used to control
11050 various aspects of the AST generation process.
11051 In case of AST construction using
11052 C<isl_ast_build_node_from_schedule_map>,
11053 the most prominent way of control is through ``options'',
11054 as explained above.
11056 Additional control is available through the following functions.
11058 #include <isl/ast_build.h>
11059 __isl_give isl_ast_build *
11060 isl_ast_build_set_iterators(
11061 __isl_take isl_ast_build *build,
11062 __isl_take isl_id_list *iterators);
11064 The function C<isl_ast_build_set_iterators> allows the user to
11065 specify a list of iterator C<isl_id>s to be used as iterators.
11066 If the input schedule is injective, then
11067 the number of elements in this list should be as large as the dimension
11068 of the schedule space, but no direct correspondence should be assumed
11069 between dimensions and elements.
11070 If the input schedule is not injective, then an additional number
11071 of C<isl_id>s equal to the largest dimension of the input domains
11073 If the number of provided C<isl_id>s is insufficient, then additional
11074 names are automatically generated.
11076 #include <isl/ast_build.h>
11077 __isl_give isl_ast_build *
11078 isl_ast_build_set_create_leaf(
11079 __isl_take isl_ast_build *build,
11080 __isl_give isl_ast_node *(*fn)(
11081 __isl_take isl_ast_build *build,
11082 void *user), void *user);
11085 C<isl_ast_build_set_create_leaf> function allows for the
11086 specification of a callback that should be called whenever the AST
11087 generator arrives at an element of the schedule domain.
11088 The callback should return an AST node that should be inserted
11089 at the corresponding position of the AST. The default action (when
11090 the callback is not set) is to continue generating parts of the AST to scan
11091 all the domain elements associated to the schedule domain element
11092 and to insert user nodes, ``calling'' the domain element, for each of them.
11093 The C<build> argument contains the current state of the C<isl_ast_build>.
11094 To ease nested AST generation (see L</"Nested AST Generation">),
11095 all control information that is
11096 specific to the current AST generation such as the options and
11097 the callbacks has been removed from this C<isl_ast_build>.
11098 The callback would typically return the result of a nested
11099 AST generation or a
11100 user defined node created using the following function.
11102 #include <isl/ast.h>
11103 __isl_give isl_ast_node *isl_ast_node_alloc_user(
11104 __isl_take isl_ast_expr *expr);
11106 #include <isl/ast_build.h>
11107 __isl_give isl_ast_build *
11108 isl_ast_build_set_at_each_domain(
11109 __isl_take isl_ast_build *build,
11110 __isl_give isl_ast_node *(*fn)(
11111 __isl_take isl_ast_node *node,
11112 __isl_keep isl_ast_build *build,
11113 void *user), void *user);
11114 __isl_give isl_ast_build *
11115 isl_ast_build_set_before_each_for(
11116 __isl_take isl_ast_build *build,
11117 __isl_give isl_id *(*fn)(
11118 __isl_keep isl_ast_build *build,
11119 void *user), void *user);
11120 __isl_give isl_ast_build *
11121 isl_ast_build_set_after_each_for(
11122 __isl_take isl_ast_build *build,
11123 __isl_give isl_ast_node *(*fn)(
11124 __isl_take isl_ast_node *node,
11125 __isl_keep isl_ast_build *build,
11126 void *user), void *user);
11127 __isl_give isl_ast_build *
11128 isl_ast_build_set_before_each_mark(
11129 __isl_take isl_ast_build *build,
11130 isl_stat (*fn)(__isl_keep isl_id *mark,
11131 __isl_keep isl_ast_build *build,
11132 void *user), void *user);
11133 __isl_give isl_ast_build *
11134 isl_ast_build_set_after_each_mark(
11135 __isl_take isl_ast_build *build,
11136 __isl_give isl_ast_node *(*fn)(
11137 __isl_take isl_ast_node *node,
11138 __isl_keep isl_ast_build *build,
11139 void *user), void *user);
11141 The callback set by C<isl_ast_build_set_at_each_domain> will
11142 be called for each domain AST node.
11143 The callbacks set by C<isl_ast_build_set_before_each_for>
11144 and C<isl_ast_build_set_after_each_for> will be called
11145 for each for AST node. The first will be called in depth-first
11146 pre-order, while the second will be called in depth-first post-order.
11147 Since C<isl_ast_build_set_before_each_for> is called before the for
11148 node is actually constructed, it is only passed an C<isl_ast_build>.
11149 The returned C<isl_id> will be added as an annotation (using
11150 C<isl_ast_node_set_annotation>) to the constructed for node.
11151 In particular, if the user has also specified an C<after_each_for>
11152 callback, then the annotation can be retrieved from the node passed to
11153 that callback using C<isl_ast_node_get_annotation>.
11154 The callbacks set by C<isl_ast_build_set_before_each_mark>
11155 and C<isl_ast_build_set_after_each_mark> will be called for each
11156 mark AST node that is created, i.e., for each mark schedule node
11157 in the input schedule tree. The first will be called in depth-first
11158 pre-order, while the second will be called in depth-first post-order.
11159 Since the callback set by C<isl_ast_build_set_before_each_mark>
11160 is called before the mark AST node is actually constructed, it is passed
11161 the identifier of the mark node.
11162 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
11163 The given C<isl_ast_build> can be used to create new
11164 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
11165 or C<isl_ast_build_call_from_pw_multi_aff>.
11167 =head3 Nested AST Generation
11169 C<isl> allows the user to create an AST within the context
11170 of another AST. These nested ASTs are created using the
11171 same C<isl_ast_build_node_from_schedule_map> function that is used to create
11172 the outer AST. The C<build> argument should be an C<isl_ast_build>
11173 passed to a callback set by
11174 C<isl_ast_build_set_create_leaf>.
11175 The space of the range of the C<schedule> argument should refer
11176 to this build. In particular, the space should be a wrapped
11177 relation and the domain of this wrapped relation should be the
11178 same as that of the range of the schedule returned by
11179 C<isl_ast_build_get_schedule> below.
11180 In practice, the new schedule is typically
11181 created by calling C<isl_union_map_range_product> on the old schedule
11182 and some extra piece of the schedule.
11183 The space of the schedule domain is also available from
11184 the C<isl_ast_build>.
11186 #include <isl/ast_build.h>
11187 __isl_give isl_union_map *isl_ast_build_get_schedule(
11188 __isl_keep isl_ast_build *build);
11189 __isl_give isl_space *isl_ast_build_get_schedule_space(
11190 __isl_keep isl_ast_build *build);
11191 __isl_give isl_ast_build *isl_ast_build_restrict(
11192 __isl_take isl_ast_build *build,
11193 __isl_take isl_set *set);
11195 The C<isl_ast_build_get_schedule> function returns a (partial)
11196 schedule for the domains elements for which part of the AST still needs to
11197 be generated in the current build.
11198 In particular, the domain elements are mapped to those iterations of the loops
11199 enclosing the current point of the AST generation inside which
11200 the domain elements are executed.
11201 No direct correspondence between
11202 the input schedule and this schedule should be assumed.
11203 The space obtained from C<isl_ast_build_get_schedule_space> can be used
11204 to create a set for C<isl_ast_build_restrict> to intersect
11205 with the current build. In particular, the set passed to
11206 C<isl_ast_build_restrict> can have additional parameters.
11207 The ids of the set dimensions in the space returned by
11208 C<isl_ast_build_get_schedule_space> correspond to the
11209 iterators of the already generated loops.
11210 The user should not rely on the ids of the output dimensions
11211 of the relations in the union relation returned by
11212 C<isl_ast_build_get_schedule> having any particular value.
11214 =head1 Applications
11216 Although C<isl> is mainly meant to be used as a library,
11217 it also contains some basic applications that use some
11218 of the functionality of C<isl>.
11219 For applications that take one or more polytopes or polyhedra
11220 as input, this input may be specified in either the L<isl format>
11221 or the L<PolyLib format>.
11223 =head2 C<isl_polyhedron_sample>
11225 C<isl_polyhedron_sample> takes a polyhedron as input and prints
11226 an integer element of the polyhedron, if there is any.
11227 The first column in the output is the denominator and is always
11228 equal to 1. If the polyhedron contains no integer points,
11229 then a vector of length zero is printed.
11233 C<isl_pip> takes the same input as the C<example> program
11234 from the C<piplib> distribution, i.e., a set of constraints
11235 on the parameters, a line containing only -1 and finally a set
11236 of constraints on a parametric polyhedron.
11237 The coefficients of the parameters appear in the last columns
11238 (but before the final constant column).
11239 The output is the lexicographic minimum of the parametric polyhedron.
11240 As C<isl> currently does not have its own output format, the output
11241 is just a dump of the internal state.
11243 =head2 C<isl_polyhedron_minimize>
11245 C<isl_polyhedron_minimize> computes the minimum of some linear
11246 or affine objective function over the integer points in a polyhedron.
11247 If an affine objective function
11248 is given, then the constant should appear in the last column.
11250 =head2 C<isl_polytope_scan>
11252 Given a polytope, C<isl_polytope_scan> prints
11253 all integer points in the polytope.
11257 Given an C<isl_union_access_info> object as input,
11258 C<isl_flow> prints out the corresponding dependences,
11259 as computed by C<isl_union_access_info_compute_flow>.
11261 =head2 C<isl_codegen>
11263 Given either a schedule tree or a sequence consisting of
11264 a schedule map, a context set and an options relation,
11265 C<isl_codegen> prints out an AST that scans the domain elements
11266 of the schedule in the order of their image(s) taking into account
11267 the constraints in the context set.
11269 =head2 C<isl_schedule>
11271 Given an C<isl_schedule_constraints> object as input,
11272 C<isl_schedule> prints out a schedule that satisfies the given