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);
612 C<isl> uses two special return types for functions that either return
613 a boolean or that in principle do not return anything.
614 In particular, the C<isl_bool> type has three possible values:
615 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
616 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
617 C<isl_bool_error> (a negative integer value), indicating that something
618 went wrong. The following function can be used to negate an C<isl_bool>,
619 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
622 isl_bool isl_bool_not(isl_bool b);
624 The C<isl_stat> type has two possible values:
625 C<isl_stat_ok> (the integer value zero), indicating a successful
627 C<isl_stat_error> (a negative integer value), indicating that something
629 See L</"Error Handling"> for more information on
630 C<isl_bool_error> and C<isl_stat_error>.
634 An C<isl_val> represents an integer value, a rational value
635 or one of three special values, infinity, negative infinity and NaN.
636 Some predefined values can be created using the following functions.
639 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
640 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
641 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
642 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
643 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
644 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
646 Specific integer values can be created using the following functions.
649 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
651 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
653 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
654 size_t n, size_t size, const void *chunks);
656 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
657 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
658 The least significant digit is assumed to be stored first.
660 Value objects can be copied and freed using the following functions.
663 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
664 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
666 They can be inspected using the following functions.
669 long isl_val_get_num_si(__isl_keep isl_val *v);
670 long isl_val_get_den_si(__isl_keep isl_val *v);
671 __isl_give isl_val *isl_val_get_den_val(
672 __isl_keep isl_val *v);
673 double isl_val_get_d(__isl_keep isl_val *v);
674 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
676 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
677 size_t size, void *chunks);
679 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
680 of C<size> bytes needed to store the absolute value of the
682 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
683 which is assumed to have been preallocated by the caller.
684 The least significant digit is stored first.
685 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
686 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
687 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
689 An C<isl_val> can be modified using the following function.
692 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
695 The following unary properties are defined on C<isl_val>s.
698 int isl_val_sgn(__isl_keep isl_val *v);
699 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
700 isl_bool isl_val_is_one(__isl_keep isl_val *v);
701 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
702 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
703 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
704 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
705 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
706 isl_bool isl_val_is_int(__isl_keep isl_val *v);
707 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
708 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
709 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
710 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
712 Note that the sign of NaN is undefined.
714 The following binary properties are defined on pairs of C<isl_val>s.
717 isl_bool isl_val_lt(__isl_keep isl_val *v1,
718 __isl_keep isl_val *v2);
719 isl_bool isl_val_le(__isl_keep isl_val *v1,
720 __isl_keep isl_val *v2);
721 isl_bool isl_val_gt(__isl_keep isl_val *v1,
722 __isl_keep isl_val *v2);
723 isl_bool isl_val_ge(__isl_keep isl_val *v1,
724 __isl_keep isl_val *v2);
725 isl_bool isl_val_eq(__isl_keep isl_val *v1,
726 __isl_keep isl_val *v2);
727 isl_bool isl_val_ne(__isl_keep isl_val *v1,
728 __isl_keep isl_val *v2);
729 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
730 __isl_keep isl_val *v2);
732 Comparisons to NaN always return false.
733 That is, a NaN is not considered to hold any relative position
734 with respect to any value. In particular, a NaN
735 is neither considered to be equal to nor to be different from
736 any value (including another NaN).
737 The function C<isl_val_abs_eq> checks whether its two arguments
738 are equal in absolute value.
740 For integer C<isl_val>s we additionally have the following binary property.
743 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
744 __isl_keep isl_val *v2);
746 An C<isl_val> can also be compared to an integer using the following
747 functions. The result of C<isl_val_cmp_si> undefined for NaN.
750 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
751 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
753 The following unary operations are available on C<isl_val>s.
756 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
757 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
758 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
759 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
760 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
761 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
762 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
764 The following binary operations are available on C<isl_val>s.
767 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
768 __isl_take isl_val *v2);
769 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
770 __isl_take isl_val *v2);
771 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
772 __isl_take isl_val *v2);
773 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
775 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
776 __isl_take isl_val *v2);
777 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
779 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
780 __isl_take isl_val *v2);
781 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
783 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
784 __isl_take isl_val *v2);
785 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
788 On integer values, we additionally have the following operations.
791 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
792 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
793 __isl_take isl_val *v2);
794 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
795 __isl_take isl_val *v2);
796 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
797 __isl_take isl_val *v2, __isl_give isl_val **x,
798 __isl_give isl_val **y);
800 The function C<isl_val_gcdext> returns the greatest common divisor g
801 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
802 that C<*x> * C<v1> + C<*y> * C<v2> = g.
804 =head3 GMP specific functions
806 These functions are only available if C<isl> has been compiled with C<GMP>
809 Specific integer and rational values can be created from C<GMP> values using
810 the following functions.
812 #include <isl/val_gmp.h>
813 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
815 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
816 const mpz_t n, const mpz_t d);
818 The numerator and denominator of a rational value can be extracted as
819 C<GMP> values using the following functions.
821 #include <isl/val_gmp.h>
822 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
823 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
825 =head2 Sets and Relations
827 C<isl> uses six types of objects for representing sets and relations,
828 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
829 C<isl_union_set> and C<isl_union_map>.
830 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
831 can be described as a conjunction of affine constraints, while
832 C<isl_set> and C<isl_map> represent unions of
833 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
834 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
835 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
836 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
837 where spaces are considered different if they have a different number
838 of dimensions and/or different names (see L<"Spaces">).
839 The difference between sets and relations (maps) is that sets have
840 one set of variables, while relations have two sets of variables,
841 input variables and output variables.
843 =head2 Error Handling
845 C<isl> supports different ways to react in case a runtime error is triggered.
846 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
847 with two maps that have incompatible spaces. There are three possible ways
848 to react on error: to warn, to continue or to abort.
850 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
851 the last error in the corresponding C<isl_ctx> and the function in which the
852 error was triggered returns a value indicating that some error has
853 occurred. In case of functions returning a pointer, this value is
854 C<NULL>. In case of functions returning an C<isl_bool> or an
855 C<isl_stat>, this value is C<isl_bool_error> or C<isl_stat_error>.
856 An error does not corrupt internal state,
857 such that isl can continue to be used. C<isl> also provides functions to
858 read the last error, including the specific error message,
859 the isl source file where the error occurred and the line number,
860 and to reset all information about the last error. The
861 last error is only stored for information purposes. Its presence does not
862 change the behavior of C<isl>. Hence, resetting an error is not required to
863 continue to use isl, but only to observe new errors.
866 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
867 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
868 const char *isl_ctx_last_error_file(isl_ctx *ctx);
869 int isl_ctx_last_error_line(isl_ctx *ctx);
870 void isl_ctx_reset_error(isl_ctx *ctx);
872 If no error has occurred since the last call to C<isl_ctx_reset_error>,
873 then the functions C<isl_ctx_last_error_msg> and
874 C<isl_ctx_last_error_file> return C<NULL>.
876 Another option is to continue on error. This is similar to warn on error mode,
877 except that C<isl> does not print any warning. This allows a program to
878 implement its own error reporting.
880 The last option is to directly abort the execution of the program from within
881 the isl library. This makes it obviously impossible to recover from an error,
882 but it allows to directly spot the error location. By aborting on error,
883 debuggers break at the location the error occurred and can provide a stack
884 trace. Other tools that automatically provide stack traces on abort or that do
885 not want to continue execution after an error was triggered may also prefer to
888 The on error behavior of isl can be specified by calling
889 C<isl_options_set_on_error> or by setting the command line option
890 C<--isl-on-error>. Valid arguments for the function call are
891 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
892 choices for the command line option are C<warn>, C<continue> and C<abort>.
893 It is also possible to query the current error mode.
895 #include <isl/options.h>
896 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
897 int isl_options_get_on_error(isl_ctx *ctx);
901 Identifiers are used to identify both individual dimensions
902 and tuples of dimensions. They consist of an optional name and an optional
903 user pointer. The name and the user pointer cannot both be C<NULL>, however.
904 Identifiers with the same name but different pointer values
905 are considered to be distinct.
906 Similarly, identifiers with different names but the same pointer value
907 are also considered to be distinct.
908 Equal identifiers are represented using the same object.
909 Pairs of identifiers can therefore be tested for equality using the
911 Identifiers can be constructed, copied, freed, inspected and printed
912 using the following functions.
915 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
916 __isl_keep const char *name, void *user);
917 __isl_give isl_id *isl_id_set_free_user(
918 __isl_take isl_id *id,
919 void (*free_user)(void *user));
920 __isl_give isl_id *isl_id_copy(isl_id *id);
921 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
923 void *isl_id_get_user(__isl_keep isl_id *id);
924 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
926 __isl_give isl_printer *isl_printer_print_id(
927 __isl_take isl_printer *p, __isl_keep isl_id *id);
929 The callback set by C<isl_id_set_free_user> is called on the user
930 pointer when the last reference to the C<isl_id> is freed.
931 Note that C<isl_id_get_name> returns a pointer to some internal
932 data structure, so the result can only be used while the
933 corresponding C<isl_id> is alive.
937 Whenever a new set, relation or similar object is created from scratch,
938 the space in which it lives needs to be specified using an C<isl_space>.
939 Each space involves zero or more parameters and zero, one or two
940 tuples of set or input/output dimensions. The parameters and dimensions
941 are identified by an C<isl_dim_type> and a position.
942 The type C<isl_dim_param> refers to parameters,
943 the type C<isl_dim_set> refers to set dimensions (for spaces
944 with a single tuple of dimensions) and the types C<isl_dim_in>
945 and C<isl_dim_out> refer to input and output dimensions
946 (for spaces with two tuples of dimensions).
947 Local spaces (see L</"Local Spaces">) also contain dimensions
948 of type C<isl_dim_div>.
949 Note that parameters are only identified by their position within
950 a given object. Across different objects, parameters are (usually)
951 identified by their names or identifiers. Only unnamed parameters
952 are identified by their positions across objects. The use of unnamed
953 parameters is discouraged.
955 #include <isl/space.h>
956 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
957 unsigned nparam, unsigned n_in, unsigned n_out);
958 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
960 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
961 unsigned nparam, unsigned dim);
962 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
963 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
965 The space used for creating a parameter domain
966 needs to be created using C<isl_space_params_alloc>.
967 For other sets, the space
968 needs to be created using C<isl_space_set_alloc>, while
969 for a relation, the space
970 needs to be created using C<isl_space_alloc>.
972 To check whether a given space is that of a set or a map
973 or whether it is a parameter space, use these functions:
975 #include <isl/space.h>
976 isl_bool isl_space_is_params(__isl_keep isl_space *space);
977 isl_bool isl_space_is_set(__isl_keep isl_space *space);
978 isl_bool isl_space_is_map(__isl_keep isl_space *space);
980 Spaces can be compared using the following functions:
982 #include <isl/space.h>
983 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
984 __isl_keep isl_space *space2);
985 isl_bool isl_space_has_equal_params(
986 __isl_keep isl_space *space1,
987 __isl_keep isl_space *space2);
988 isl_bool isl_space_has_equal_tuples(
989 __isl_keep isl_space *space1,
990 __isl_keep isl_space *space2);
991 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
992 __isl_keep isl_space *space2);
993 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
994 __isl_keep isl_space *space2);
995 isl_bool isl_space_tuple_is_equal(
996 __isl_keep isl_space *space1,
997 enum isl_dim_type type1,
998 __isl_keep isl_space *space2,
999 enum isl_dim_type type2);
1001 C<isl_space_is_domain> checks whether the first argument is equal
1002 to the domain of the second argument. This requires in particular that
1003 the first argument is a set space and that the second argument
1004 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1005 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1006 spaces are the same. That is, it checks if they have the same
1007 identifier (if any), the same dimension and the same internal structure
1010 C<isl_space_has_equal_params> checks whether two spaces
1011 have the same parameters in the same order.
1012 C<isl_space_has_equal_tuples> check whether two spaces have
1013 the same tuples. In contrast to C<isl_space_is_equal> below,
1014 it does not check the
1015 parameters. This is useful because many C<isl> functions align the
1016 parameters before they perform their operations, such that equivalence
1018 C<isl_space_is_equal> checks whether two spaces are identical,
1019 meaning that they have the same parameters and the same tuples.
1020 That is, it checks whether both C<isl_space_has_equal_params> and
1021 C<isl_space_has_equal_tuples> hold.
1023 It is often useful to create objects that live in the
1024 same space as some other object. This can be accomplished
1025 by creating the new objects
1026 (see L</"Creating New Sets and Relations"> or
1027 L</"Functions">) based on the space
1028 of the original object.
1030 #include <isl/set.h>
1031 __isl_give isl_space *isl_basic_set_get_space(
1032 __isl_keep isl_basic_set *bset);
1033 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1035 #include <isl/union_set.h>
1036 __isl_give isl_space *isl_union_set_get_space(
1037 __isl_keep isl_union_set *uset);
1039 #include <isl/map.h>
1040 __isl_give isl_space *isl_basic_map_get_space(
1041 __isl_keep isl_basic_map *bmap);
1042 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1044 #include <isl/union_map.h>
1045 __isl_give isl_space *isl_union_map_get_space(
1046 __isl_keep isl_union_map *umap);
1048 #include <isl/constraint.h>
1049 __isl_give isl_space *isl_constraint_get_space(
1050 __isl_keep isl_constraint *constraint);
1052 #include <isl/polynomial.h>
1053 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1054 __isl_keep isl_qpolynomial *qp);
1055 __isl_give isl_space *isl_qpolynomial_get_space(
1056 __isl_keep isl_qpolynomial *qp);
1057 __isl_give isl_space *
1058 isl_qpolynomial_fold_get_domain_space(
1059 __isl_keep isl_qpolynomial_fold *fold);
1060 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1061 __isl_keep isl_qpolynomial_fold *fold);
1062 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1063 __isl_keep isl_pw_qpolynomial *pwqp);
1064 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1065 __isl_keep isl_pw_qpolynomial *pwqp);
1066 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1067 __isl_keep isl_pw_qpolynomial_fold *pwf);
1068 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1069 __isl_keep isl_pw_qpolynomial_fold *pwf);
1070 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1071 __isl_keep isl_union_pw_qpolynomial *upwqp);
1072 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1073 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1075 #include <isl/val.h>
1076 __isl_give isl_space *isl_multi_val_get_space(
1077 __isl_keep isl_multi_val *mv);
1079 #include <isl/aff.h>
1080 __isl_give isl_space *isl_aff_get_domain_space(
1081 __isl_keep isl_aff *aff);
1082 __isl_give isl_space *isl_aff_get_space(
1083 __isl_keep isl_aff *aff);
1084 __isl_give isl_space *isl_pw_aff_get_domain_space(
1085 __isl_keep isl_pw_aff *pwaff);
1086 __isl_give isl_space *isl_pw_aff_get_space(
1087 __isl_keep isl_pw_aff *pwaff);
1088 __isl_give isl_space *isl_multi_aff_get_domain_space(
1089 __isl_keep isl_multi_aff *maff);
1090 __isl_give isl_space *isl_multi_aff_get_space(
1091 __isl_keep isl_multi_aff *maff);
1092 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1093 __isl_keep isl_pw_multi_aff *pma);
1094 __isl_give isl_space *isl_pw_multi_aff_get_space(
1095 __isl_keep isl_pw_multi_aff *pma);
1096 __isl_give isl_space *isl_union_pw_aff_get_space(
1097 __isl_keep isl_union_pw_aff *upa);
1098 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1099 __isl_keep isl_union_pw_multi_aff *upma);
1100 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1101 __isl_keep isl_multi_pw_aff *mpa);
1102 __isl_give isl_space *isl_multi_pw_aff_get_space(
1103 __isl_keep isl_multi_pw_aff *mpa);
1104 __isl_give isl_space *
1105 isl_multi_union_pw_aff_get_domain_space(
1106 __isl_keep isl_multi_union_pw_aff *mupa);
1107 __isl_give isl_space *
1108 isl_multi_union_pw_aff_get_space(
1109 __isl_keep isl_multi_union_pw_aff *mupa);
1111 #include <isl/point.h>
1112 __isl_give isl_space *isl_point_get_space(
1113 __isl_keep isl_point *pnt);
1115 The number of dimensions of a given type of space
1116 may be read off from a space or an object that lives
1117 in a space using the following functions.
1118 In case of C<isl_space_dim>, type may be
1119 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1120 C<isl_dim_out> (only for relations), C<isl_dim_set>
1121 (only for sets) or C<isl_dim_all>.
1123 #include <isl/space.h>
1124 unsigned isl_space_dim(__isl_keep isl_space *space,
1125 enum isl_dim_type type);
1127 #include <isl/local_space.h>
1128 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1129 enum isl_dim_type type);
1131 #include <isl/set.h>
1132 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1133 enum isl_dim_type type);
1134 unsigned isl_set_dim(__isl_keep isl_set *set,
1135 enum isl_dim_type type);
1137 #include <isl/union_set.h>
1138 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1139 enum isl_dim_type type);
1141 #include <isl/map.h>
1142 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1143 enum isl_dim_type type);
1144 unsigned isl_map_dim(__isl_keep isl_map *map,
1145 enum isl_dim_type type);
1147 #include <isl/union_map.h>
1148 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1149 enum isl_dim_type type);
1151 #include <isl/val.h>
1152 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1153 enum isl_dim_type type);
1155 #include <isl/aff.h>
1156 int isl_aff_dim(__isl_keep isl_aff *aff,
1157 enum isl_dim_type type);
1158 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1159 enum isl_dim_type type);
1160 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1161 enum isl_dim_type type);
1162 unsigned isl_pw_multi_aff_dim(
1163 __isl_keep isl_pw_multi_aff *pma,
1164 enum isl_dim_type type);
1165 unsigned isl_multi_pw_aff_dim(
1166 __isl_keep isl_multi_pw_aff *mpa,
1167 enum isl_dim_type type);
1168 unsigned isl_union_pw_aff_dim(
1169 __isl_keep isl_union_pw_aff *upa,
1170 enum isl_dim_type type);
1171 unsigned isl_union_pw_multi_aff_dim(
1172 __isl_keep isl_union_pw_multi_aff *upma,
1173 enum isl_dim_type type);
1174 unsigned isl_multi_union_pw_aff_dim(
1175 __isl_keep isl_multi_union_pw_aff *mupa,
1176 enum isl_dim_type type);
1178 #include <isl/polynomial.h>
1179 unsigned isl_union_pw_qpolynomial_dim(
1180 __isl_keep isl_union_pw_qpolynomial *upwqp,
1181 enum isl_dim_type type);
1182 unsigned isl_union_pw_qpolynomial_fold_dim(
1183 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1184 enum isl_dim_type type);
1186 Note that an C<isl_union_set>, an C<isl_union_map>,
1187 an C<isl_union_pw_multi_aff>,
1188 an C<isl_union_pw_qpolynomial> and
1189 an C<isl_union_pw_qpolynomial_fold>
1190 only have parameters.
1192 Additional parameters can be added to a space using the following function.
1194 #include <isl/space.h>
1195 __isl_give isl_space *isl_space_add_param_id(
1196 __isl_take isl_space *space,
1197 __isl_take isl_id *id);
1199 If a parameter with the given identifier already appears in the space,
1200 then it is not added again.
1202 The identifiers or names of the individual dimensions of spaces
1203 may be set or read off using the following functions on spaces
1204 or objects that live in spaces.
1205 These functions are mostly useful to obtain the identifiers, positions
1206 or names of the parameters. Identifiers of individual dimensions are
1207 essentially only useful for printing. They are ignored by all other
1208 operations and may not be preserved across those operations.
1210 #include <isl/space.h>
1211 __isl_give isl_space *isl_space_set_dim_id(
1212 __isl_take isl_space *space,
1213 enum isl_dim_type type, unsigned pos,
1214 __isl_take isl_id *id);
1215 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1216 enum isl_dim_type type, unsigned pos);
1217 __isl_give isl_id *isl_space_get_dim_id(
1218 __isl_keep isl_space *space,
1219 enum isl_dim_type type, unsigned pos);
1220 __isl_give isl_space *isl_space_set_dim_name(
1221 __isl_take isl_space *space,
1222 enum isl_dim_type type, unsigned pos,
1223 __isl_keep const char *name);
1224 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1225 enum isl_dim_type type, unsigned pos);
1226 __isl_keep const char *isl_space_get_dim_name(
1227 __isl_keep isl_space *space,
1228 enum isl_dim_type type, unsigned pos);
1230 #include <isl/local_space.h>
1231 __isl_give isl_local_space *isl_local_space_set_dim_id(
1232 __isl_take isl_local_space *ls,
1233 enum isl_dim_type type, unsigned pos,
1234 __isl_take isl_id *id);
1235 isl_bool isl_local_space_has_dim_id(
1236 __isl_keep isl_local_space *ls,
1237 enum isl_dim_type type, unsigned pos);
1238 __isl_give isl_id *isl_local_space_get_dim_id(
1239 __isl_keep isl_local_space *ls,
1240 enum isl_dim_type type, unsigned pos);
1241 __isl_give isl_local_space *isl_local_space_set_dim_name(
1242 __isl_take isl_local_space *ls,
1243 enum isl_dim_type type, unsigned pos, const char *s);
1244 isl_bool isl_local_space_has_dim_name(
1245 __isl_keep isl_local_space *ls,
1246 enum isl_dim_type type, unsigned pos)
1247 const char *isl_local_space_get_dim_name(
1248 __isl_keep isl_local_space *ls,
1249 enum isl_dim_type type, unsigned pos);
1251 #include <isl/constraint.h>
1252 const char *isl_constraint_get_dim_name(
1253 __isl_keep isl_constraint *constraint,
1254 enum isl_dim_type type, unsigned pos);
1256 #include <isl/set.h>
1257 __isl_give isl_id *isl_basic_set_get_dim_id(
1258 __isl_keep isl_basic_set *bset,
1259 enum isl_dim_type type, unsigned pos);
1260 __isl_give isl_set *isl_set_set_dim_id(
1261 __isl_take isl_set *set, enum isl_dim_type type,
1262 unsigned pos, __isl_take isl_id *id);
1263 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1264 enum isl_dim_type type, unsigned pos);
1265 __isl_give isl_id *isl_set_get_dim_id(
1266 __isl_keep isl_set *set, enum isl_dim_type type,
1268 const char *isl_basic_set_get_dim_name(
1269 __isl_keep isl_basic_set *bset,
1270 enum isl_dim_type type, unsigned pos);
1271 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1272 enum isl_dim_type type, unsigned pos);
1273 const char *isl_set_get_dim_name(
1274 __isl_keep isl_set *set,
1275 enum isl_dim_type type, unsigned pos);
1277 #include <isl/map.h>
1278 __isl_give isl_map *isl_map_set_dim_id(
1279 __isl_take isl_map *map, enum isl_dim_type type,
1280 unsigned pos, __isl_take isl_id *id);
1281 isl_bool isl_basic_map_has_dim_id(
1282 __isl_keep isl_basic_map *bmap,
1283 enum isl_dim_type type, unsigned pos);
1284 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1285 enum isl_dim_type type, unsigned pos);
1286 __isl_give isl_id *isl_map_get_dim_id(
1287 __isl_keep isl_map *map, enum isl_dim_type type,
1289 __isl_give isl_id *isl_union_map_get_dim_id(
1290 __isl_keep isl_union_map *umap,
1291 enum isl_dim_type type, unsigned pos);
1292 const char *isl_basic_map_get_dim_name(
1293 __isl_keep isl_basic_map *bmap,
1294 enum isl_dim_type type, unsigned pos);
1295 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1296 enum isl_dim_type type, unsigned pos);
1297 const char *isl_map_get_dim_name(
1298 __isl_keep isl_map *map,
1299 enum isl_dim_type type, unsigned pos);
1301 #include <isl/val.h>
1302 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1303 __isl_take isl_multi_val *mv,
1304 enum isl_dim_type type, unsigned pos,
1305 __isl_take isl_id *id);
1306 __isl_give isl_id *isl_multi_val_get_dim_id(
1307 __isl_keep isl_multi_val *mv,
1308 enum isl_dim_type type, unsigned pos);
1309 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1310 __isl_take isl_multi_val *mv,
1311 enum isl_dim_type type, unsigned pos, const char *s);
1313 #include <isl/aff.h>
1314 __isl_give isl_aff *isl_aff_set_dim_id(
1315 __isl_take isl_aff *aff, enum isl_dim_type type,
1316 unsigned pos, __isl_take isl_id *id);
1317 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1318 __isl_take isl_multi_aff *maff,
1319 enum isl_dim_type type, unsigned pos,
1320 __isl_take isl_id *id);
1321 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1322 __isl_take isl_pw_aff *pma,
1323 enum isl_dim_type type, unsigned pos,
1324 __isl_take isl_id *id);
1325 __isl_give isl_multi_pw_aff *
1326 isl_multi_pw_aff_set_dim_id(
1327 __isl_take isl_multi_pw_aff *mpa,
1328 enum isl_dim_type type, unsigned pos,
1329 __isl_take isl_id *id);
1330 __isl_give isl_multi_union_pw_aff *
1331 isl_multi_union_pw_aff_set_dim_id(
1332 __isl_take isl_multi_union_pw_aff *mupa,
1333 enum isl_dim_type type, unsigned pos,
1334 __isl_take isl_id *id);
1335 __isl_give isl_id *isl_multi_aff_get_dim_id(
1336 __isl_keep isl_multi_aff *ma,
1337 enum isl_dim_type type, unsigned pos);
1338 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1339 enum isl_dim_type type, unsigned pos);
1340 __isl_give isl_id *isl_pw_aff_get_dim_id(
1341 __isl_keep isl_pw_aff *pa,
1342 enum isl_dim_type type, unsigned pos);
1343 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1344 __isl_keep isl_pw_multi_aff *pma,
1345 enum isl_dim_type type, unsigned pos);
1346 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1347 __isl_keep isl_multi_pw_aff *mpa,
1348 enum isl_dim_type type, unsigned pos);
1349 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1350 __isl_keep isl_multi_union_pw_aff *mupa,
1351 enum isl_dim_type type, unsigned pos);
1352 __isl_give isl_aff *isl_aff_set_dim_name(
1353 __isl_take isl_aff *aff, enum isl_dim_type type,
1354 unsigned pos, const char *s);
1355 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1356 __isl_take isl_multi_aff *maff,
1357 enum isl_dim_type type, unsigned pos, const char *s);
1358 __isl_give isl_multi_pw_aff *
1359 isl_multi_pw_aff_set_dim_name(
1360 __isl_take isl_multi_pw_aff *mpa,
1361 enum isl_dim_type type, unsigned pos, const char *s);
1362 __isl_give isl_union_pw_aff *
1363 isl_union_pw_aff_set_dim_name(
1364 __isl_take isl_union_pw_aff *upa,
1365 enum isl_dim_type type, unsigned pos,
1367 __isl_give isl_union_pw_multi_aff *
1368 isl_union_pw_multi_aff_set_dim_name(
1369 __isl_take isl_union_pw_multi_aff *upma,
1370 enum isl_dim_type type, unsigned pos,
1372 __isl_give isl_multi_union_pw_aff *
1373 isl_multi_union_pw_aff_set_dim_name(
1374 __isl_take isl_multi_union_pw_aff *mupa,
1375 enum isl_dim_type type, unsigned pos,
1376 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1377 enum isl_dim_type type, unsigned pos);
1378 const char *isl_pw_aff_get_dim_name(
1379 __isl_keep isl_pw_aff *pa,
1380 enum isl_dim_type type, unsigned pos);
1381 const char *isl_pw_multi_aff_get_dim_name(
1382 __isl_keep isl_pw_multi_aff *pma,
1383 enum isl_dim_type type, unsigned pos);
1385 #include <isl/polynomial.h>
1386 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1387 __isl_take isl_qpolynomial *qp,
1388 enum isl_dim_type type, unsigned pos,
1390 __isl_give isl_pw_qpolynomial *
1391 isl_pw_qpolynomial_set_dim_name(
1392 __isl_take isl_pw_qpolynomial *pwqp,
1393 enum isl_dim_type type, unsigned pos,
1395 __isl_give isl_pw_qpolynomial_fold *
1396 isl_pw_qpolynomial_fold_set_dim_name(
1397 __isl_take isl_pw_qpolynomial_fold *pwf,
1398 enum isl_dim_type type, unsigned pos,
1400 __isl_give isl_union_pw_qpolynomial *
1401 isl_union_pw_qpolynomial_set_dim_name(
1402 __isl_take isl_union_pw_qpolynomial *upwqp,
1403 enum isl_dim_type type, unsigned pos,
1405 __isl_give isl_union_pw_qpolynomial_fold *
1406 isl_union_pw_qpolynomial_fold_set_dim_name(
1407 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1408 enum isl_dim_type type, unsigned pos,
1411 Note that C<isl_space_get_name> returns a pointer to some internal
1412 data structure, so the result can only be used while the
1413 corresponding C<isl_space> is alive.
1414 Also note that every function that operates on two sets or relations
1415 requires that both arguments have the same parameters. This also
1416 means that if one of the arguments has named parameters, then the
1417 other needs to have named parameters too and the names need to match.
1418 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1419 arguments may have different parameters (as long as they are named),
1420 in which case the result will have as parameters the union of the parameters of
1423 Given the identifier or name of a dimension (typically a parameter),
1424 its position can be obtained from the following functions.
1426 #include <isl/space.h>
1427 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1428 enum isl_dim_type type, __isl_keep isl_id *id);
1429 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1430 enum isl_dim_type type, const char *name);
1432 #include <isl/local_space.h>
1433 int isl_local_space_find_dim_by_name(
1434 __isl_keep isl_local_space *ls,
1435 enum isl_dim_type type, const char *name);
1437 #include <isl/val.h>
1438 int isl_multi_val_find_dim_by_id(
1439 __isl_keep isl_multi_val *mv,
1440 enum isl_dim_type type, __isl_keep isl_id *id);
1441 int isl_multi_val_find_dim_by_name(
1442 __isl_keep isl_multi_val *mv,
1443 enum isl_dim_type type, const char *name);
1445 #include <isl/set.h>
1446 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1447 enum isl_dim_type type, __isl_keep isl_id *id);
1448 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1449 enum isl_dim_type type, const char *name);
1451 #include <isl/map.h>
1452 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1453 enum isl_dim_type type, __isl_keep isl_id *id);
1454 int isl_basic_map_find_dim_by_name(
1455 __isl_keep isl_basic_map *bmap,
1456 enum isl_dim_type type, const char *name);
1457 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1458 enum isl_dim_type type, const char *name);
1459 int isl_union_map_find_dim_by_name(
1460 __isl_keep isl_union_map *umap,
1461 enum isl_dim_type type, const char *name);
1463 #include <isl/aff.h>
1464 int isl_multi_aff_find_dim_by_id(
1465 __isl_keep isl_multi_aff *ma,
1466 enum isl_dim_type type, __isl_keep isl_id *id);
1467 int isl_multi_pw_aff_find_dim_by_id(
1468 __isl_keep isl_multi_pw_aff *mpa,
1469 enum isl_dim_type type, __isl_keep isl_id *id);
1470 int isl_multi_union_pw_aff_find_dim_by_id(
1471 __isl_keep isl_union_multi_pw_aff *mupa,
1472 enum isl_dim_type type, __isl_keep isl_id *id);
1473 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1474 enum isl_dim_type type, const char *name);
1475 int isl_multi_aff_find_dim_by_name(
1476 __isl_keep isl_multi_aff *ma,
1477 enum isl_dim_type type, const char *name);
1478 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1479 enum isl_dim_type type, const char *name);
1480 int isl_multi_pw_aff_find_dim_by_name(
1481 __isl_keep isl_multi_pw_aff *mpa,
1482 enum isl_dim_type type, const char *name);
1483 int isl_pw_multi_aff_find_dim_by_name(
1484 __isl_keep isl_pw_multi_aff *pma,
1485 enum isl_dim_type type, const char *name);
1486 int isl_union_pw_aff_find_dim_by_name(
1487 __isl_keep isl_union_pw_aff *upa,
1488 enum isl_dim_type type, const char *name);
1489 int isl_union_pw_multi_aff_find_dim_by_name(
1490 __isl_keep isl_union_pw_multi_aff *upma,
1491 enum isl_dim_type type, const char *name);
1492 int isl_multi_union_pw_aff_find_dim_by_name(
1493 __isl_keep isl_multi_union_pw_aff *mupa,
1494 enum isl_dim_type type, const char *name);
1496 #include <isl/polynomial.h>
1497 int isl_pw_qpolynomial_find_dim_by_name(
1498 __isl_keep isl_pw_qpolynomial *pwqp,
1499 enum isl_dim_type type, const char *name);
1500 int isl_pw_qpolynomial_fold_find_dim_by_name(
1501 __isl_keep isl_pw_qpolynomial_fold *pwf,
1502 enum isl_dim_type type, const char *name);
1503 int isl_union_pw_qpolynomial_find_dim_by_name(
1504 __isl_keep isl_union_pw_qpolynomial *upwqp,
1505 enum isl_dim_type type, const char *name);
1506 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1507 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1508 enum isl_dim_type type, const char *name);
1510 The identifiers or names of entire spaces may be set or read off
1511 using the following functions.
1513 #include <isl/space.h>
1514 __isl_give isl_space *isl_space_set_tuple_id(
1515 __isl_take isl_space *space,
1516 enum isl_dim_type type, __isl_take isl_id *id);
1517 __isl_give isl_space *isl_space_reset_tuple_id(
1518 __isl_take isl_space *space, enum isl_dim_type type);
1519 isl_bool isl_space_has_tuple_id(
1520 __isl_keep isl_space *space,
1521 enum isl_dim_type type);
1522 __isl_give isl_id *isl_space_get_tuple_id(
1523 __isl_keep isl_space *space, enum isl_dim_type type);
1524 __isl_give isl_space *isl_space_set_tuple_name(
1525 __isl_take isl_space *space,
1526 enum isl_dim_type type, const char *s);
1527 isl_bool isl_space_has_tuple_name(
1528 __isl_keep isl_space *space,
1529 enum isl_dim_type type);
1530 __isl_keep const char *isl_space_get_tuple_name(
1531 __isl_keep isl_space *space,
1532 enum isl_dim_type type);
1534 #include <isl/local_space.h>
1535 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1536 __isl_take isl_local_space *ls,
1537 enum isl_dim_type type, __isl_take isl_id *id);
1539 #include <isl/set.h>
1540 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1541 __isl_take isl_basic_set *bset,
1542 __isl_take isl_id *id);
1543 __isl_give isl_set *isl_set_set_tuple_id(
1544 __isl_take isl_set *set, __isl_take isl_id *id);
1545 __isl_give isl_set *isl_set_reset_tuple_id(
1546 __isl_take isl_set *set);
1547 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1548 __isl_give isl_id *isl_set_get_tuple_id(
1549 __isl_keep isl_set *set);
1550 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1551 __isl_take isl_basic_set *set, const char *s);
1552 __isl_give isl_set *isl_set_set_tuple_name(
1553 __isl_take isl_set *set, const char *s);
1554 const char *isl_basic_set_get_tuple_name(
1555 __isl_keep isl_basic_set *bset);
1556 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1557 const char *isl_set_get_tuple_name(
1558 __isl_keep isl_set *set);
1560 #include <isl/map.h>
1561 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1562 __isl_take isl_basic_map *bmap,
1563 enum isl_dim_type type, __isl_take isl_id *id);
1564 __isl_give isl_map *isl_map_set_tuple_id(
1565 __isl_take isl_map *map, enum isl_dim_type type,
1566 __isl_take isl_id *id);
1567 __isl_give isl_map *isl_map_reset_tuple_id(
1568 __isl_take isl_map *map, enum isl_dim_type type);
1569 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1570 enum isl_dim_type type);
1571 __isl_give isl_id *isl_map_get_tuple_id(
1572 __isl_keep isl_map *map, enum isl_dim_type type);
1573 __isl_give isl_map *isl_map_set_tuple_name(
1574 __isl_take isl_map *map,
1575 enum isl_dim_type type, const char *s);
1576 const char *isl_basic_map_get_tuple_name(
1577 __isl_keep isl_basic_map *bmap,
1578 enum isl_dim_type type);
1579 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1580 __isl_take isl_basic_map *bmap,
1581 enum isl_dim_type type, const char *s);
1582 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1583 enum isl_dim_type type);
1584 const char *isl_map_get_tuple_name(
1585 __isl_keep isl_map *map,
1586 enum isl_dim_type type);
1588 #include <isl/val.h>
1589 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1590 __isl_take isl_multi_val *mv,
1591 enum isl_dim_type type, __isl_take isl_id *id);
1592 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1593 __isl_take isl_multi_val *mv,
1594 enum isl_dim_type type);
1595 isl_bool isl_multi_val_has_tuple_id(
1596 __isl_keep isl_multi_val *mv,
1597 enum isl_dim_type type);
1598 __isl_give isl_id *isl_multi_val_get_tuple_id(
1599 __isl_keep isl_multi_val *mv,
1600 enum isl_dim_type type);
1601 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1602 __isl_take isl_multi_val *mv,
1603 enum isl_dim_type type, const char *s);
1604 const char *isl_multi_val_get_tuple_name(
1605 __isl_keep isl_multi_val *mv,
1606 enum isl_dim_type type);
1608 #include <isl/aff.h>
1609 __isl_give isl_aff *isl_aff_set_tuple_id(
1610 __isl_take isl_aff *aff,
1611 enum isl_dim_type type, __isl_take isl_id *id);
1612 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1613 __isl_take isl_multi_aff *maff,
1614 enum isl_dim_type type, __isl_take isl_id *id);
1615 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1616 __isl_take isl_pw_aff *pwaff,
1617 enum isl_dim_type type, __isl_take isl_id *id);
1618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1619 __isl_take isl_pw_multi_aff *pma,
1620 enum isl_dim_type type, __isl_take isl_id *id);
1621 __isl_give isl_multi_union_pw_aff *
1622 isl_multi_union_pw_aff_set_tuple_id(
1623 __isl_take isl_multi_union_pw_aff *mupa,
1624 enum isl_dim_type type, __isl_take isl_id *id);
1625 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1626 __isl_take isl_multi_aff *ma,
1627 enum isl_dim_type type);
1628 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1629 __isl_take isl_pw_aff *pa,
1630 enum isl_dim_type type);
1631 __isl_give isl_multi_pw_aff *
1632 isl_multi_pw_aff_reset_tuple_id(
1633 __isl_take isl_multi_pw_aff *mpa,
1634 enum isl_dim_type type);
1635 __isl_give isl_pw_multi_aff *
1636 isl_pw_multi_aff_reset_tuple_id(
1637 __isl_take isl_pw_multi_aff *pma,
1638 enum isl_dim_type type);
1639 __isl_give isl_multi_union_pw_aff *
1640 isl_multi_union_pw_aff_reset_tuple_id(
1641 __isl_take isl_multi_union_pw_aff *mupa,
1642 enum isl_dim_type type);
1643 isl_bool isl_multi_aff_has_tuple_id(
1644 __isl_keep isl_multi_aff *ma,
1645 enum isl_dim_type type);
1646 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1647 __isl_keep isl_multi_aff *ma,
1648 enum isl_dim_type type);
1649 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1650 enum isl_dim_type type);
1651 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1652 __isl_keep isl_pw_aff *pa,
1653 enum isl_dim_type type);
1654 isl_bool isl_pw_multi_aff_has_tuple_id(
1655 __isl_keep isl_pw_multi_aff *pma,
1656 enum isl_dim_type type);
1657 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1658 __isl_keep isl_pw_multi_aff *pma,
1659 enum isl_dim_type type);
1660 isl_bool isl_multi_pw_aff_has_tuple_id(
1661 __isl_keep isl_multi_pw_aff *mpa,
1662 enum isl_dim_type type);
1663 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1664 __isl_keep isl_multi_pw_aff *mpa,
1665 enum isl_dim_type type);
1666 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1667 __isl_keep isl_multi_union_pw_aff *mupa,
1668 enum isl_dim_type type);
1669 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1670 __isl_keep isl_multi_union_pw_aff *mupa,
1671 enum isl_dim_type type);
1672 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1673 __isl_take isl_multi_aff *maff,
1674 enum isl_dim_type type, const char *s);
1675 __isl_give isl_multi_pw_aff *
1676 isl_multi_pw_aff_set_tuple_name(
1677 __isl_take isl_multi_pw_aff *mpa,
1678 enum isl_dim_type type, const char *s);
1679 __isl_give isl_multi_union_pw_aff *
1680 isl_multi_union_pw_aff_set_tuple_name(
1681 __isl_take isl_multi_union_pw_aff *mupa,
1682 enum isl_dim_type type, const char *s);
1683 const char *isl_multi_aff_get_tuple_name(
1684 __isl_keep isl_multi_aff *multi,
1685 enum isl_dim_type type);
1686 isl_bool isl_pw_multi_aff_has_tuple_name(
1687 __isl_keep isl_pw_multi_aff *pma,
1688 enum isl_dim_type type);
1689 const char *isl_pw_multi_aff_get_tuple_name(
1690 __isl_keep isl_pw_multi_aff *pma,
1691 enum isl_dim_type type);
1692 const char *isl_multi_union_pw_aff_get_tuple_name(
1693 __isl_keep isl_multi_union_pw_aff *mupa,
1694 enum isl_dim_type type);
1696 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1697 or C<isl_dim_set>. As with C<isl_space_get_name>,
1698 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1700 Binary operations require the corresponding spaces of their arguments
1701 to have the same name.
1703 To keep the names of all parameters and tuples, but reset the user pointers
1704 of all the corresponding identifiers, use the following function.
1706 #include <isl/space.h>
1707 __isl_give isl_space *isl_space_reset_user(
1708 __isl_take isl_space *space);
1710 #include <isl/set.h>
1711 __isl_give isl_set *isl_set_reset_user(
1712 __isl_take isl_set *set);
1714 #include <isl/map.h>
1715 __isl_give isl_map *isl_map_reset_user(
1716 __isl_take isl_map *map);
1718 #include <isl/union_set.h>
1719 __isl_give isl_union_set *isl_union_set_reset_user(
1720 __isl_take isl_union_set *uset);
1722 #include <isl/union_map.h>
1723 __isl_give isl_union_map *isl_union_map_reset_user(
1724 __isl_take isl_union_map *umap);
1726 #include <isl/val.h>
1727 __isl_give isl_multi_val *isl_multi_val_reset_user(
1728 __isl_take isl_multi_val *mv);
1730 #include <isl/aff.h>
1731 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1732 __isl_take isl_multi_aff *ma);
1733 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1734 __isl_take isl_pw_aff *pa);
1735 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1736 __isl_take isl_multi_pw_aff *mpa);
1737 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1738 __isl_take isl_pw_multi_aff *pma);
1739 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1740 __isl_take isl_union_pw_aff *upa);
1741 __isl_give isl_multi_union_pw_aff *
1742 isl_multi_union_pw_aff_reset_user(
1743 __isl_take isl_multi_union_pw_aff *mupa);
1744 __isl_give isl_union_pw_multi_aff *
1745 isl_union_pw_multi_aff_reset_user(
1746 __isl_take isl_union_pw_multi_aff *upma);
1748 #include <isl/polynomial.h>
1749 __isl_give isl_pw_qpolynomial *
1750 isl_pw_qpolynomial_reset_user(
1751 __isl_take isl_pw_qpolynomial *pwqp);
1752 __isl_give isl_union_pw_qpolynomial *
1753 isl_union_pw_qpolynomial_reset_user(
1754 __isl_take isl_union_pw_qpolynomial *upwqp);
1755 __isl_give isl_pw_qpolynomial_fold *
1756 isl_pw_qpolynomial_fold_reset_user(
1757 __isl_take isl_pw_qpolynomial_fold *pwf);
1758 __isl_give isl_union_pw_qpolynomial_fold *
1759 isl_union_pw_qpolynomial_fold_reset_user(
1760 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1762 Spaces can be nested. In particular, the domain of a set or
1763 the domain or range of a relation can be a nested relation.
1764 This process is also called I<wrapping>.
1765 The functions for detecting, constructing and deconstructing
1766 such nested spaces can be found in the wrapping properties
1767 of L</"Unary Properties">, the wrapping operations
1768 of L</"Unary Operations"> and the Cartesian product operations
1769 of L</"Basic Operations">.
1771 Spaces can be created from other spaces
1772 using the functions described in L</"Unary Operations">
1773 and L</"Binary Operations">.
1777 A local space is essentially a space with
1778 zero or more existentially quantified variables.
1779 The local space of various objects can be obtained
1780 using the following functions.
1782 #include <isl/constraint.h>
1783 __isl_give isl_local_space *isl_constraint_get_local_space(
1784 __isl_keep isl_constraint *constraint);
1786 #include <isl/set.h>
1787 __isl_give isl_local_space *isl_basic_set_get_local_space(
1788 __isl_keep isl_basic_set *bset);
1790 #include <isl/map.h>
1791 __isl_give isl_local_space *isl_basic_map_get_local_space(
1792 __isl_keep isl_basic_map *bmap);
1794 #include <isl/aff.h>
1795 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1796 __isl_keep isl_aff *aff);
1797 __isl_give isl_local_space *isl_aff_get_local_space(
1798 __isl_keep isl_aff *aff);
1800 A new local space can be created from a space using
1802 #include <isl/local_space.h>
1803 __isl_give isl_local_space *isl_local_space_from_space(
1804 __isl_take isl_space *space);
1806 They can be inspected, modified, copied and freed using the following functions.
1808 #include <isl/local_space.h>
1809 isl_bool isl_local_space_is_params(
1810 __isl_keep isl_local_space *ls);
1811 isl_bool isl_local_space_is_set(
1812 __isl_keep isl_local_space *ls);
1813 __isl_give isl_space *isl_local_space_get_space(
1814 __isl_keep isl_local_space *ls);
1815 __isl_give isl_aff *isl_local_space_get_div(
1816 __isl_keep isl_local_space *ls, int pos);
1817 __isl_give isl_local_space *isl_local_space_copy(
1818 __isl_keep isl_local_space *ls);
1819 __isl_null isl_local_space *isl_local_space_free(
1820 __isl_take isl_local_space *ls);
1822 Note that C<isl_local_space_get_div> can only be used on local spaces
1825 Two local spaces can be compared using
1827 isl_bool isl_local_space_is_equal(
1828 __isl_keep isl_local_space *ls1,
1829 __isl_keep isl_local_space *ls2);
1831 Local spaces can be created from other local spaces
1832 using the functions described in L</"Unary Operations">
1833 and L</"Binary Operations">.
1835 =head2 Creating New Sets and Relations
1837 C<isl> has functions for creating some standard sets and relations.
1841 =item * Empty sets and relations
1843 __isl_give isl_basic_set *isl_basic_set_empty(
1844 __isl_take isl_space *space);
1845 __isl_give isl_basic_map *isl_basic_map_empty(
1846 __isl_take isl_space *space);
1847 __isl_give isl_set *isl_set_empty(
1848 __isl_take isl_space *space);
1849 __isl_give isl_map *isl_map_empty(
1850 __isl_take isl_space *space);
1851 __isl_give isl_union_set *isl_union_set_empty(
1852 __isl_take isl_space *space);
1853 __isl_give isl_union_map *isl_union_map_empty(
1854 __isl_take isl_space *space);
1856 For C<isl_union_set>s and C<isl_union_map>s, the space
1857 is only used to specify the parameters.
1859 =item * Universe sets and relations
1861 __isl_give isl_basic_set *isl_basic_set_universe(
1862 __isl_take isl_space *space);
1863 __isl_give isl_basic_map *isl_basic_map_universe(
1864 __isl_take isl_space *space);
1865 __isl_give isl_set *isl_set_universe(
1866 __isl_take isl_space *space);
1867 __isl_give isl_map *isl_map_universe(
1868 __isl_take isl_space *space);
1869 __isl_give isl_union_set *isl_union_set_universe(
1870 __isl_take isl_union_set *uset);
1871 __isl_give isl_union_map *isl_union_map_universe(
1872 __isl_take isl_union_map *umap);
1874 The sets and relations constructed by the functions above
1875 contain all integer values, while those constructed by the
1876 functions below only contain non-negative values.
1878 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1879 __isl_take isl_space *space);
1880 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1881 __isl_take isl_space *space);
1882 __isl_give isl_set *isl_set_nat_universe(
1883 __isl_take isl_space *space);
1884 __isl_give isl_map *isl_map_nat_universe(
1885 __isl_take isl_space *space);
1887 =item * Identity relations
1889 __isl_give isl_basic_map *isl_basic_map_identity(
1890 __isl_take isl_space *space);
1891 __isl_give isl_map *isl_map_identity(
1892 __isl_take isl_space *space);
1894 The number of input and output dimensions in C<space> needs
1897 =item * Lexicographic order
1899 __isl_give isl_map *isl_map_lex_lt(
1900 __isl_take isl_space *set_space);
1901 __isl_give isl_map *isl_map_lex_le(
1902 __isl_take isl_space *set_space);
1903 __isl_give isl_map *isl_map_lex_gt(
1904 __isl_take isl_space *set_space);
1905 __isl_give isl_map *isl_map_lex_ge(
1906 __isl_take isl_space *set_space);
1907 __isl_give isl_map *isl_map_lex_lt_first(
1908 __isl_take isl_space *space, unsigned n);
1909 __isl_give isl_map *isl_map_lex_le_first(
1910 __isl_take isl_space *space, unsigned n);
1911 __isl_give isl_map *isl_map_lex_gt_first(
1912 __isl_take isl_space *space, unsigned n);
1913 __isl_give isl_map *isl_map_lex_ge_first(
1914 __isl_take isl_space *space, unsigned n);
1916 The first four functions take a space for a B<set>
1917 and return relations that express that the elements in the domain
1918 are lexicographically less
1919 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1920 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1921 than the elements in the range.
1922 The last four functions take a space for a map
1923 and return relations that express that the first C<n> dimensions
1924 in the domain are lexicographically less
1925 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1926 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1927 than the first C<n> dimensions in the range.
1931 A basic set or relation can be converted to a set or relation
1932 using the following functions.
1934 __isl_give isl_set *isl_set_from_basic_set(
1935 __isl_take isl_basic_set *bset);
1936 __isl_give isl_map *isl_map_from_basic_map(
1937 __isl_take isl_basic_map *bmap);
1939 Sets and relations can be converted to union sets and relations
1940 using the following functions.
1942 __isl_give isl_union_set *isl_union_set_from_basic_set(
1943 __isl_take isl_basic_set *bset);
1944 __isl_give isl_union_map *isl_union_map_from_basic_map(
1945 __isl_take isl_basic_map *bmap);
1946 __isl_give isl_union_set *isl_union_set_from_set(
1947 __isl_take isl_set *set);
1948 __isl_give isl_union_map *isl_union_map_from_map(
1949 __isl_take isl_map *map);
1951 The inverse conversions below can only be used if the input
1952 union set or relation is known to contain elements in exactly one
1955 __isl_give isl_set *isl_set_from_union_set(
1956 __isl_take isl_union_set *uset);
1957 __isl_give isl_map *isl_map_from_union_map(
1958 __isl_take isl_union_map *umap);
1960 Sets and relations can be copied and freed again using the following
1963 __isl_give isl_basic_set *isl_basic_set_copy(
1964 __isl_keep isl_basic_set *bset);
1965 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1966 __isl_give isl_union_set *isl_union_set_copy(
1967 __isl_keep isl_union_set *uset);
1968 __isl_give isl_basic_map *isl_basic_map_copy(
1969 __isl_keep isl_basic_map *bmap);
1970 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1971 __isl_give isl_union_map *isl_union_map_copy(
1972 __isl_keep isl_union_map *umap);
1973 __isl_null isl_basic_set *isl_basic_set_free(
1974 __isl_take isl_basic_set *bset);
1975 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1976 __isl_null isl_union_set *isl_union_set_free(
1977 __isl_take isl_union_set *uset);
1978 __isl_null isl_basic_map *isl_basic_map_free(
1979 __isl_take isl_basic_map *bmap);
1980 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1981 __isl_null isl_union_map *isl_union_map_free(
1982 __isl_take isl_union_map *umap);
1984 Other sets and relations can be constructed by starting
1985 from a universe set or relation, adding equality and/or
1986 inequality constraints and then projecting out the
1987 existentially quantified variables, if any.
1988 Constraints can be constructed, manipulated and
1989 added to (or removed from) (basic) sets and relations
1990 using the following functions.
1992 #include <isl/constraint.h>
1993 __isl_give isl_constraint *isl_constraint_alloc_equality(
1994 __isl_take isl_local_space *ls);
1995 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1996 __isl_take isl_local_space *ls);
1997 __isl_give isl_constraint *isl_constraint_set_constant_si(
1998 __isl_take isl_constraint *constraint, int v);
1999 __isl_give isl_constraint *isl_constraint_set_constant_val(
2000 __isl_take isl_constraint *constraint,
2001 __isl_take isl_val *v);
2002 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2003 __isl_take isl_constraint *constraint,
2004 enum isl_dim_type type, int pos, int v);
2005 __isl_give isl_constraint *
2006 isl_constraint_set_coefficient_val(
2007 __isl_take isl_constraint *constraint,
2008 enum isl_dim_type type, int pos,
2009 __isl_take isl_val *v);
2010 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2011 __isl_take isl_basic_map *bmap,
2012 __isl_take isl_constraint *constraint);
2013 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2014 __isl_take isl_basic_set *bset,
2015 __isl_take isl_constraint *constraint);
2016 __isl_give isl_map *isl_map_add_constraint(
2017 __isl_take isl_map *map,
2018 __isl_take isl_constraint *constraint);
2019 __isl_give isl_set *isl_set_add_constraint(
2020 __isl_take isl_set *set,
2021 __isl_take isl_constraint *constraint);
2023 For example, to create a set containing the even integers
2024 between 10 and 42, you would use the following code.
2027 isl_local_space *ls;
2029 isl_basic_set *bset;
2031 space = isl_space_set_alloc(ctx, 0, 2);
2032 bset = isl_basic_set_universe(isl_space_copy(space));
2033 ls = isl_local_space_from_space(space);
2035 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2036 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2037 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2038 bset = isl_basic_set_add_constraint(bset, c);
2040 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2041 c = isl_constraint_set_constant_si(c, -10);
2042 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2043 bset = isl_basic_set_add_constraint(bset, c);
2045 c = isl_constraint_alloc_inequality(ls);
2046 c = isl_constraint_set_constant_si(c, 42);
2047 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2048 bset = isl_basic_set_add_constraint(bset, c);
2050 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2054 isl_basic_set *bset;
2055 bset = isl_basic_set_read_from_str(ctx,
2056 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2058 A basic set or relation can also be constructed from two matrices
2059 describing the equalities and the inequalities.
2061 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2062 __isl_take isl_space *space,
2063 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2064 enum isl_dim_type c1,
2065 enum isl_dim_type c2, enum isl_dim_type c3,
2066 enum isl_dim_type c4);
2067 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2068 __isl_take isl_space *space,
2069 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2070 enum isl_dim_type c1,
2071 enum isl_dim_type c2, enum isl_dim_type c3,
2072 enum isl_dim_type c4, enum isl_dim_type c5);
2074 The C<isl_dim_type> arguments indicate the order in which
2075 different kinds of variables appear in the input matrices
2076 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2077 C<isl_dim_set> and C<isl_dim_div> for sets and
2078 of C<isl_dim_cst>, C<isl_dim_param>,
2079 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2081 A (basic or union) set or relation can also be constructed from a
2082 (union) (piecewise) (multiple) affine expression
2083 or a list of affine expressions
2084 (See L</"Functions">), provided these affine expressions do not
2087 __isl_give isl_basic_map *isl_basic_map_from_aff(
2088 __isl_take isl_aff *aff);
2089 __isl_give isl_map *isl_map_from_aff(
2090 __isl_take isl_aff *aff);
2091 __isl_give isl_set *isl_set_from_pw_aff(
2092 __isl_take isl_pw_aff *pwaff);
2093 __isl_give isl_map *isl_map_from_pw_aff(
2094 __isl_take isl_pw_aff *pwaff);
2095 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2096 __isl_take isl_space *domain_space,
2097 __isl_take isl_aff_list *list);
2098 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2099 __isl_take isl_multi_aff *maff)
2100 __isl_give isl_map *isl_map_from_multi_aff(
2101 __isl_take isl_multi_aff *maff)
2102 __isl_give isl_set *isl_set_from_pw_multi_aff(
2103 __isl_take isl_pw_multi_aff *pma);
2104 __isl_give isl_map *isl_map_from_pw_multi_aff(
2105 __isl_take isl_pw_multi_aff *pma);
2106 __isl_give isl_set *isl_set_from_multi_pw_aff(
2107 __isl_take isl_multi_pw_aff *mpa);
2108 __isl_give isl_map *isl_map_from_multi_pw_aff(
2109 __isl_take isl_multi_pw_aff *mpa);
2110 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2111 __isl_take isl_union_pw_aff *upa);
2112 __isl_give isl_union_map *
2113 isl_union_map_from_union_pw_multi_aff(
2114 __isl_take isl_union_pw_multi_aff *upma);
2115 __isl_give isl_union_map *
2116 isl_union_map_from_multi_union_pw_aff(
2117 __isl_take isl_multi_union_pw_aff *mupa);
2119 The C<domain_space> argument describes the domain of the resulting
2120 basic relation. It is required because the C<list> may consist
2121 of zero affine expressions.
2122 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2123 is not allowed to be zero-dimensional. The domain of the result
2124 is the shared domain of the union piecewise affine elements.
2126 =head2 Inspecting Sets and Relations
2128 Usually, the user should not have to care about the actual constraints
2129 of the sets and maps, but should instead apply the abstract operations
2130 explained in the following sections.
2131 Occasionally, however, it may be required to inspect the individual
2132 coefficients of the constraints. This section explains how to do so.
2133 In these cases, it may also be useful to have C<isl> compute
2134 an explicit representation of the existentially quantified variables.
2136 __isl_give isl_set *isl_set_compute_divs(
2137 __isl_take isl_set *set);
2138 __isl_give isl_map *isl_map_compute_divs(
2139 __isl_take isl_map *map);
2140 __isl_give isl_union_set *isl_union_set_compute_divs(
2141 __isl_take isl_union_set *uset);
2142 __isl_give isl_union_map *isl_union_map_compute_divs(
2143 __isl_take isl_union_map *umap);
2145 This explicit representation defines the existentially quantified
2146 variables as integer divisions of the other variables, possibly
2147 including earlier existentially quantified variables.
2148 An explicitly represented existentially quantified variable therefore
2149 has a unique value when the values of the other variables are known.
2151 Alternatively, the existentially quantified variables can be removed
2152 using the following functions, which compute an overapproximation.
2154 #include <isl/set.h>
2155 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2156 __isl_take isl_basic_set *bset);
2157 __isl_give isl_set *isl_set_remove_divs(
2158 __isl_take isl_set *set);
2160 #include <isl/map.h>
2161 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2162 __isl_take isl_basic_map *bmap);
2163 __isl_give isl_map *isl_map_remove_divs(
2164 __isl_take isl_map *map);
2166 #include <isl/union_set.h>
2167 __isl_give isl_union_set *isl_union_set_remove_divs(
2168 __isl_take isl_union_set *bset);
2170 #include <isl/union_map.h>
2171 __isl_give isl_union_map *isl_union_map_remove_divs(
2172 __isl_take isl_union_map *bmap);
2174 It is also possible to only remove those divs that are defined
2175 in terms of a given range of dimensions or only those for which
2176 no explicit representation is known.
2178 __isl_give isl_basic_set *
2179 isl_basic_set_remove_divs_involving_dims(
2180 __isl_take isl_basic_set *bset,
2181 enum isl_dim_type type,
2182 unsigned first, unsigned n);
2183 __isl_give isl_basic_map *
2184 isl_basic_map_remove_divs_involving_dims(
2185 __isl_take isl_basic_map *bmap,
2186 enum isl_dim_type type,
2187 unsigned first, unsigned n);
2188 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2189 __isl_take isl_set *set, enum isl_dim_type type,
2190 unsigned first, unsigned n);
2191 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2192 __isl_take isl_map *map, enum isl_dim_type type,
2193 unsigned first, unsigned n);
2195 __isl_give isl_basic_set *
2196 isl_basic_set_remove_unknown_divs(
2197 __isl_take isl_basic_set *bset);
2198 __isl_give isl_set *isl_set_remove_unknown_divs(
2199 __isl_take isl_set *set);
2200 __isl_give isl_map *isl_map_remove_unknown_divs(
2201 __isl_take isl_map *map);
2203 To iterate over all the sets or maps in a union set or map, use
2205 #include <isl/union_set.h>
2206 isl_stat isl_union_set_foreach_set(
2207 __isl_keep isl_union_set *uset,
2208 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2211 #include <isl/union_map.h>
2212 isl_stat isl_union_map_foreach_map(
2213 __isl_keep isl_union_map *umap,
2214 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2216 isl_bool isl_union_map_every_map(
2217 __isl_keep isl_union_map *umap,
2218 isl_bool (*test)(__isl_keep isl_map *map,
2222 These functions call the callback function once for each
2223 (pair of) space(s) for which there are elements in the input.
2224 The argument to the callback contains all elements in the input
2225 with that (pair of) space(s).
2226 The C<isl_union_map_every_map> variant check whether each
2227 call to the callback returns true and stops checking as soon as one
2228 of these calls returns false.
2230 The number of sets or maps in a union set or map can be obtained
2233 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2234 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2236 To extract the set or map in a given space from a union, use
2238 __isl_give isl_set *isl_union_set_extract_set(
2239 __isl_keep isl_union_set *uset,
2240 __isl_take isl_space *space);
2241 __isl_give isl_map *isl_union_map_extract_map(
2242 __isl_keep isl_union_map *umap,
2243 __isl_take isl_space *space);
2245 To iterate over all the basic sets or maps in a set or map, use
2247 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2248 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2251 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2252 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2256 The callback function C<fn> should return C<isl_stat_ok> if successful and
2257 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2258 occurs, the above functions will return C<isl_stat_error>.
2260 It should be noted that C<isl> does not guarantee that
2261 the basic sets or maps passed to C<fn> are disjoint.
2262 If this is required, then the user should call one of
2263 the following functions first.
2265 __isl_give isl_set *isl_set_make_disjoint(
2266 __isl_take isl_set *set);
2267 __isl_give isl_map *isl_map_make_disjoint(
2268 __isl_take isl_map *map);
2270 The number of basic sets in a set can be obtained
2271 or the number of basic maps in a map can be obtained
2274 #include <isl/set.h>
2275 int isl_set_n_basic_set(__isl_keep isl_set *set);
2277 #include <isl/map.h>
2278 int isl_map_n_basic_map(__isl_keep isl_map *map);
2280 It is also possible to obtain a list of basic sets from a set
2283 #include <isl/set.h>
2284 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2285 __isl_keep isl_set *set);
2287 #include <isl/union_set.h>
2288 __isl_give isl_basic_set_list *
2289 isl_union_set_get_basic_set_list(
2290 __isl_keep isl_union_set *uset);
2292 The returned list can be manipulated using the functions in L<"Lists">.
2294 To iterate over the constraints of a basic set or map, use
2296 #include <isl/constraint.h>
2298 int isl_basic_set_n_constraint(
2299 __isl_keep isl_basic_set *bset);
2300 isl_stat isl_basic_set_foreach_constraint(
2301 __isl_keep isl_basic_set *bset,
2302 isl_stat (*fn)(__isl_take isl_constraint *c,
2305 int isl_basic_map_n_constraint(
2306 __isl_keep isl_basic_map *bmap);
2307 isl_stat isl_basic_map_foreach_constraint(
2308 __isl_keep isl_basic_map *bmap,
2309 isl_stat (*fn)(__isl_take isl_constraint *c,
2312 __isl_null isl_constraint *isl_constraint_free(
2313 __isl_take isl_constraint *c);
2315 Again, the callback function C<fn> should return C<isl_stat_ok>
2317 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2318 occurs, the above functions will return C<isl_stat_error>.
2319 The constraint C<c> represents either an equality or an inequality.
2320 Use the following function to find out whether a constraint
2321 represents an equality. If not, it represents an inequality.
2323 isl_bool isl_constraint_is_equality(
2324 __isl_keep isl_constraint *constraint);
2326 It is also possible to obtain a list of constraints from a basic
2329 #include <isl/constraint.h>
2330 __isl_give isl_constraint_list *
2331 isl_basic_map_get_constraint_list(
2332 __isl_keep isl_basic_map *bmap);
2333 __isl_give isl_constraint_list *
2334 isl_basic_set_get_constraint_list(
2335 __isl_keep isl_basic_set *bset);
2337 These functions require that all existentially quantified variables
2338 have an explicit representation.
2339 The returned list can be manipulated using the functions in L<"Lists">.
2341 The coefficients of the constraints can be inspected using
2342 the following functions.
2344 isl_bool isl_constraint_is_lower_bound(
2345 __isl_keep isl_constraint *constraint,
2346 enum isl_dim_type type, unsigned pos);
2347 isl_bool isl_constraint_is_upper_bound(
2348 __isl_keep isl_constraint *constraint,
2349 enum isl_dim_type type, unsigned pos);
2350 __isl_give isl_val *isl_constraint_get_constant_val(
2351 __isl_keep isl_constraint *constraint);
2352 __isl_give isl_val *isl_constraint_get_coefficient_val(
2353 __isl_keep isl_constraint *constraint,
2354 enum isl_dim_type type, int pos);
2356 The explicit representations of the existentially quantified
2357 variables can be inspected using the following function.
2358 Note that the user is only allowed to use this function
2359 if the inspected set or map is the result of a call
2360 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2361 The existentially quantified variable is equal to the floor
2362 of the returned affine expression. The affine expression
2363 itself can be inspected using the functions in
2366 __isl_give isl_aff *isl_constraint_get_div(
2367 __isl_keep isl_constraint *constraint, int pos);
2369 To obtain the constraints of a basic set or map in matrix
2370 form, use the following functions.
2372 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2373 __isl_keep isl_basic_set *bset,
2374 enum isl_dim_type c1, enum isl_dim_type c2,
2375 enum isl_dim_type c3, enum isl_dim_type c4);
2376 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2377 __isl_keep isl_basic_set *bset,
2378 enum isl_dim_type c1, enum isl_dim_type c2,
2379 enum isl_dim_type c3, enum isl_dim_type c4);
2380 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2381 __isl_keep isl_basic_map *bmap,
2382 enum isl_dim_type c1,
2383 enum isl_dim_type c2, enum isl_dim_type c3,
2384 enum isl_dim_type c4, enum isl_dim_type c5);
2385 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2386 __isl_keep isl_basic_map *bmap,
2387 enum isl_dim_type c1,
2388 enum isl_dim_type c2, enum isl_dim_type c3,
2389 enum isl_dim_type c4, enum isl_dim_type c5);
2391 The C<isl_dim_type> arguments dictate the order in which
2392 different kinds of variables appear in the resulting matrix.
2393 For set inputs, they should be a permutation of
2394 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2395 For map inputs, they should be a permutation of
2396 C<isl_dim_cst>, C<isl_dim_param>,
2397 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2401 Points are elements of a set. They can be used to construct
2402 simple sets (boxes) or they can be used to represent the
2403 individual elements of a set.
2404 The zero point (the origin) can be created using
2406 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2408 The coordinates of a point can be inspected, set and changed
2411 __isl_give isl_val *isl_point_get_coordinate_val(
2412 __isl_keep isl_point *pnt,
2413 enum isl_dim_type type, int pos);
2414 __isl_give isl_point *isl_point_set_coordinate_val(
2415 __isl_take isl_point *pnt,
2416 enum isl_dim_type type, int pos,
2417 __isl_take isl_val *v);
2419 __isl_give isl_point *isl_point_add_ui(
2420 __isl_take isl_point *pnt,
2421 enum isl_dim_type type, int pos, unsigned val);
2422 __isl_give isl_point *isl_point_sub_ui(
2423 __isl_take isl_point *pnt,
2424 enum isl_dim_type type, int pos, unsigned val);
2426 Points can be copied or freed using
2428 __isl_give isl_point *isl_point_copy(
2429 __isl_keep isl_point *pnt);
2430 __isl_null isl_point *isl_point_free(
2431 __isl_take isl_point *pnt);
2433 A singleton set can be created from a point using
2435 __isl_give isl_basic_set *isl_basic_set_from_point(
2436 __isl_take isl_point *pnt);
2437 __isl_give isl_set *isl_set_from_point(
2438 __isl_take isl_point *pnt);
2439 __isl_give isl_union_set *isl_union_set_from_point(
2440 __isl_take isl_point *pnt);
2442 and a box can be created from two opposite extremal points using
2444 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2445 __isl_take isl_point *pnt1,
2446 __isl_take isl_point *pnt2);
2447 __isl_give isl_set *isl_set_box_from_points(
2448 __isl_take isl_point *pnt1,
2449 __isl_take isl_point *pnt2);
2451 All elements of a B<bounded> (union) set can be enumerated using
2452 the following functions.
2454 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2455 isl_stat (*fn)(__isl_take isl_point *pnt,
2458 isl_stat isl_union_set_foreach_point(
2459 __isl_keep isl_union_set *uset,
2460 isl_stat (*fn)(__isl_take isl_point *pnt,
2464 The function C<fn> is called for each integer point in
2465 C<set> with as second argument the last argument of
2466 the C<isl_set_foreach_point> call. The function C<fn>
2467 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2468 In the latter case, C<isl_set_foreach_point> will stop
2469 enumerating and return C<isl_stat_error> as well.
2470 If the enumeration is performed successfully and to completion,
2471 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2473 To obtain a single point of a (basic or union) set, use
2475 __isl_give isl_point *isl_basic_set_sample_point(
2476 __isl_take isl_basic_set *bset);
2477 __isl_give isl_point *isl_set_sample_point(
2478 __isl_take isl_set *set);
2479 __isl_give isl_point *isl_union_set_sample_point(
2480 __isl_take isl_union_set *uset);
2482 If C<set> does not contain any (integer) points, then the
2483 resulting point will be ``void'', a property that can be
2486 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2490 Besides sets and relation, C<isl> also supports various types of functions.
2491 Each of these types is derived from the value type (see L</"Values">)
2492 or from one of two primitive function types
2493 through the application of zero or more type constructors.
2494 We first describe the primitive type and then we describe
2495 the types derived from these primitive types.
2497 =head3 Primitive Functions
2499 C<isl> support two primitive function types, quasi-affine
2500 expressions and quasipolynomials.
2501 A quasi-affine expression is defined either over a parameter
2502 space or over a set and is composed of integer constants,
2503 parameters and set variables, addition, subtraction and
2504 integer division by an integer constant.
2505 For example, the quasi-affine expression
2507 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2509 maps C<x> to C<2*floor((4 n + x)/9>.
2510 A quasipolynomial is a polynomial expression in quasi-affine
2511 expression. That is, it additionally allows for multiplication.
2512 Note, though, that it is not allowed to construct an integer
2513 division of an expression involving multiplications.
2514 Here is an example of a quasipolynomial that is not
2515 quasi-affine expression
2517 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2519 Note that the external representations of quasi-affine expressions
2520 and quasipolynomials are different. Quasi-affine expressions
2521 use a notation with square brackets just like binary relations,
2522 while quasipolynomials do not. This might change at some point.
2524 If a primitive function is defined over a parameter space,
2525 then the space of the function itself is that of a set.
2526 If it is defined over a set, then the space of the function
2527 is that of a relation. In both cases, the set space (or
2528 the output space) is single-dimensional, anonymous and unstructured.
2529 To create functions with multiple dimensions or with other kinds
2530 of set or output spaces, use multiple expressions
2531 (see L</"Multiple Expressions">).
2535 =item * Quasi-affine Expressions
2537 Besides the expressions described above, a quasi-affine
2538 expression can also be set to NaN. Such expressions
2539 typically represent a failure to represent a result
2540 as a quasi-affine expression.
2542 The zero quasi affine expression or the quasi affine expression
2543 that is equal to a given value, parameter or
2544 a specified dimension on a given domain can be created using
2546 #include <isl/aff.h>
2547 __isl_give isl_aff *isl_aff_zero_on_domain(
2548 __isl_take isl_local_space *ls);
2549 __isl_give isl_aff *isl_aff_val_on_domain(
2550 __isl_take isl_local_space *ls,
2551 __isl_take isl_val *val);
2552 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2553 __isl_take isl_space *space,
2554 __isl_take isl_id *id);
2555 __isl_give isl_aff *isl_aff_var_on_domain(
2556 __isl_take isl_local_space *ls,
2557 enum isl_dim_type type, unsigned pos);
2558 __isl_give isl_aff *isl_aff_nan_on_domain(
2559 __isl_take isl_local_space *ls);
2561 The space passed to C<isl_aff_param_on_domain_space_id>
2562 is required to have a parameter with the given identifier.
2564 Quasi affine expressions can be copied and freed using
2566 #include <isl/aff.h>
2567 __isl_give isl_aff *isl_aff_copy(
2568 __isl_keep isl_aff *aff);
2569 __isl_null isl_aff *isl_aff_free(
2570 __isl_take isl_aff *aff);
2572 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2573 using the following function. The constraint is required to have
2574 a non-zero coefficient for the specified dimension.
2576 #include <isl/constraint.h>
2577 __isl_give isl_aff *isl_constraint_get_bound(
2578 __isl_keep isl_constraint *constraint,
2579 enum isl_dim_type type, int pos);
2581 The entire affine expression of the constraint can also be extracted
2582 using the following function.
2584 #include <isl/constraint.h>
2585 __isl_give isl_aff *isl_constraint_get_aff(
2586 __isl_keep isl_constraint *constraint);
2588 Conversely, an equality constraint equating
2589 the affine expression to zero or an inequality constraint enforcing
2590 the affine expression to be non-negative, can be constructed using
2592 __isl_give isl_constraint *isl_equality_from_aff(
2593 __isl_take isl_aff *aff);
2594 __isl_give isl_constraint *isl_inequality_from_aff(
2595 __isl_take isl_aff *aff);
2597 The coefficients and the integer divisions of an affine expression
2598 can be inspected using the following functions.
2600 #include <isl/aff.h>
2601 __isl_give isl_val *isl_aff_get_constant_val(
2602 __isl_keep isl_aff *aff);
2603 __isl_give isl_val *isl_aff_get_coefficient_val(
2604 __isl_keep isl_aff *aff,
2605 enum isl_dim_type type, int pos);
2606 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2607 enum isl_dim_type type, int pos);
2608 __isl_give isl_val *isl_aff_get_denominator_val(
2609 __isl_keep isl_aff *aff);
2610 __isl_give isl_aff *isl_aff_get_div(
2611 __isl_keep isl_aff *aff, int pos);
2613 They can be modified using the following functions.
2615 #include <isl/aff.h>
2616 __isl_give isl_aff *isl_aff_set_constant_si(
2617 __isl_take isl_aff *aff, int v);
2618 __isl_give isl_aff *isl_aff_set_constant_val(
2619 __isl_take isl_aff *aff, __isl_take isl_val *v);
2620 __isl_give isl_aff *isl_aff_set_coefficient_si(
2621 __isl_take isl_aff *aff,
2622 enum isl_dim_type type, int pos, int v);
2623 __isl_give isl_aff *isl_aff_set_coefficient_val(
2624 __isl_take isl_aff *aff,
2625 enum isl_dim_type type, int pos,
2626 __isl_take isl_val *v);
2628 __isl_give isl_aff *isl_aff_add_constant_si(
2629 __isl_take isl_aff *aff, int v);
2630 __isl_give isl_aff *isl_aff_add_constant_val(
2631 __isl_take isl_aff *aff, __isl_take isl_val *v);
2632 __isl_give isl_aff *isl_aff_add_constant_num_si(
2633 __isl_take isl_aff *aff, int v);
2634 __isl_give isl_aff *isl_aff_add_coefficient_si(
2635 __isl_take isl_aff *aff,
2636 enum isl_dim_type type, int pos, int v);
2637 __isl_give isl_aff *isl_aff_add_coefficient_val(
2638 __isl_take isl_aff *aff,
2639 enum isl_dim_type type, int pos,
2640 __isl_take isl_val *v);
2642 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2643 set the I<numerator> of the constant or coefficient, while
2644 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2645 the constant or coefficient as a whole.
2646 The C<add_constant> and C<add_coefficient> functions add an integer
2647 or rational value to
2648 the possibly rational constant or coefficient.
2649 The C<add_constant_num> functions add an integer value to
2652 =item * Quasipolynomials
2654 Some simple quasipolynomials can be created using the following functions.
2656 #include <isl/polynomial.h>
2657 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2658 __isl_take isl_space *domain);
2659 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2660 __isl_take isl_space *domain);
2661 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2662 __isl_take isl_space *domain);
2663 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2664 __isl_take isl_space *domain);
2665 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2666 __isl_take isl_space *domain);
2667 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2668 __isl_take isl_space *domain,
2669 __isl_take isl_val *val);
2670 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2671 __isl_take isl_space *domain,
2672 enum isl_dim_type type, unsigned pos);
2673 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2674 __isl_take isl_aff *aff);
2676 Recall that the space in which a quasipolynomial lives is a map space
2677 with a one-dimensional range. The C<domain> argument in some of
2678 the functions above corresponds to the domain of this map space.
2680 Quasipolynomials can be copied and freed again using the following
2683 #include <isl/polynomial.h>
2684 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2685 __isl_keep isl_qpolynomial *qp);
2686 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2687 __isl_take isl_qpolynomial *qp);
2689 The constant term of a quasipolynomial can be extracted using
2691 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2692 __isl_keep isl_qpolynomial *qp);
2694 To iterate over all terms in a quasipolynomial,
2697 isl_stat isl_qpolynomial_foreach_term(
2698 __isl_keep isl_qpolynomial *qp,
2699 isl_stat (*fn)(__isl_take isl_term *term,
2700 void *user), void *user);
2702 The terms themselves can be inspected and freed using
2705 unsigned isl_term_dim(__isl_keep isl_term *term,
2706 enum isl_dim_type type);
2707 __isl_give isl_val *isl_term_get_coefficient_val(
2708 __isl_keep isl_term *term);
2709 int isl_term_get_exp(__isl_keep isl_term *term,
2710 enum isl_dim_type type, unsigned pos);
2711 __isl_give isl_aff *isl_term_get_div(
2712 __isl_keep isl_term *term, unsigned pos);
2713 void isl_term_free(__isl_take isl_term *term);
2715 Each term is a product of parameters, set variables and
2716 integer divisions. The function C<isl_term_get_exp>
2717 returns the exponent of a given dimensions in the given term.
2723 A reduction represents a maximum or a minimum of its
2725 The only reduction type defined by C<isl> is
2726 C<isl_qpolynomial_fold>.
2728 There are currently no functions to directly create such
2729 objects, but they do appear in the piecewise quasipolynomial
2730 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2732 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2734 Reductions can be copied and freed using
2735 the following functions.
2737 #include <isl/polynomial.h>
2738 __isl_give isl_qpolynomial_fold *
2739 isl_qpolynomial_fold_copy(
2740 __isl_keep isl_qpolynomial_fold *fold);
2741 void isl_qpolynomial_fold_free(
2742 __isl_take isl_qpolynomial_fold *fold);
2744 To iterate over all quasipolynomials in a reduction, use
2746 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2747 __isl_keep isl_qpolynomial_fold *fold,
2748 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2749 void *user), void *user);
2751 =head3 Multiple Expressions
2753 A multiple expression represents a sequence of zero or
2754 more base expressions, all defined on the same domain space.
2755 The domain space of the multiple expression is the same
2756 as that of the base expressions, but the range space
2757 can be any space. In case the base expressions have
2758 a set space, the corresponding multiple expression
2759 also has a set space.
2760 Objects of the value type do not have an associated space.
2761 The space of a multiple value is therefore always a set space.
2762 Similarly, the space of a multiple union piecewise
2763 affine expression is always a set space.
2764 If the base expressions are not total, then
2765 a corresponding zero-dimensional multiple expression may
2766 have an explicit domain that keeps track of the domain
2767 outside of any base expressions.
2769 The multiple expression types defined by C<isl>
2770 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2771 C<isl_multi_union_pw_aff>.
2773 A multiple expression with the value zero for
2774 each output (or set) dimension can be created
2775 using the following functions.
2777 #include <isl/val.h>
2778 __isl_give isl_multi_val *isl_multi_val_zero(
2779 __isl_take isl_space *space);
2781 #include <isl/aff.h>
2782 __isl_give isl_multi_aff *isl_multi_aff_zero(
2783 __isl_take isl_space *space);
2784 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2785 __isl_take isl_space *space);
2786 __isl_give isl_multi_union_pw_aff *
2787 isl_multi_union_pw_aff_zero(
2788 __isl_take isl_space *space);
2790 Since there is no canonical way of representing a zero
2791 value of type C<isl_union_pw_aff>, the space passed
2792 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2794 An identity function can be created using the following
2795 functions. The space needs to be that of a relation
2796 with the same number of input and output dimensions.
2798 #include <isl/aff.h>
2799 __isl_give isl_multi_aff *isl_multi_aff_identity(
2800 __isl_take isl_space *space);
2801 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2802 __isl_take isl_space *space);
2804 A function that performs a projection on a universe
2805 relation or set can be created using the following functions.
2806 See also the corresponding
2807 projection operations in L</"Unary Operations">.
2809 #include <isl/aff.h>
2810 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2811 __isl_take isl_space *space);
2812 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2813 __isl_take isl_space *space);
2814 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2815 __isl_take isl_space *space,
2816 enum isl_dim_type type,
2817 unsigned first, unsigned n);
2819 A multiple expression can be created from a single
2820 base expression using the following functions.
2821 The space of the created multiple expression is the same
2822 as that of the base expression, except for
2823 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2824 lives in a parameter space and the output lives
2825 in a single-dimensional set space.
2827 #include <isl/aff.h>
2828 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2829 __isl_take isl_aff *aff);
2830 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2831 __isl_take isl_pw_aff *pa);
2832 __isl_give isl_multi_union_pw_aff *
2833 isl_multi_union_pw_aff_from_union_pw_aff(
2834 __isl_take isl_union_pw_aff *upa);
2836 A multiple expression can be created from a list
2837 of base expression in a specified space.
2838 The domain of this space needs to be the same
2839 as the domains of the base expressions in the list.
2840 If the base expressions have a set space (or no associated space),
2841 then this space also needs to be a set space.
2843 #include <isl/val.h>
2844 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2845 __isl_take isl_space *space,
2846 __isl_take isl_val_list *list);
2848 #include <isl/aff.h>
2849 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2850 __isl_take isl_space *space,
2851 __isl_take isl_aff_list *list);
2852 __isl_give isl_multi_pw_aff *
2853 isl_multi_pw_aff_from_pw_aff_list(
2854 __isl_take isl_space *space,
2855 __isl_take isl_pw_aff_list *list);
2856 __isl_give isl_multi_union_pw_aff *
2857 isl_multi_union_pw_aff_from_union_pw_aff_list(
2858 __isl_take isl_space *space,
2859 __isl_take isl_union_pw_aff_list *list);
2861 As a convenience, a multiple piecewise expression can
2862 also be created from a multiple expression.
2863 Each piecewise expression in the result has a single
2866 #include <isl/aff.h>
2867 __isl_give isl_multi_pw_aff *
2868 isl_multi_pw_aff_from_multi_aff(
2869 __isl_take isl_multi_aff *ma);
2871 Similarly, a multiple union expression can be
2872 created from a multiple expression.
2874 #include <isl/aff.h>
2875 __isl_give isl_multi_union_pw_aff *
2876 isl_multi_union_pw_aff_from_multi_aff(
2877 __isl_take isl_multi_aff *ma);
2878 __isl_give isl_multi_union_pw_aff *
2879 isl_multi_union_pw_aff_from_multi_pw_aff(
2880 __isl_take isl_multi_pw_aff *mpa);
2882 A multiple quasi-affine expression can be created from
2883 a multiple value with a given domain space using the following
2886 #include <isl/aff.h>
2887 __isl_give isl_multi_aff *
2888 isl_multi_aff_multi_val_on_space(
2889 __isl_take isl_space *space,
2890 __isl_take isl_multi_val *mv);
2893 a multiple union piecewise affine expression can be created from
2894 a multiple value with a given domain or
2895 a (piecewise) multiple affine expression with a given domain
2896 using the following functions.
2898 #include <isl/aff.h>
2899 __isl_give isl_multi_union_pw_aff *
2900 isl_multi_union_pw_aff_multi_val_on_domain(
2901 __isl_take isl_union_set *domain,
2902 __isl_take isl_multi_val *mv);
2903 __isl_give isl_multi_union_pw_aff *
2904 isl_multi_union_pw_aff_multi_aff_on_domain(
2905 __isl_take isl_union_set *domain,
2906 __isl_take isl_multi_aff *ma);
2907 __isl_give isl_multi_union_pw_aff *
2908 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2909 __isl_take isl_union_set *domain,
2910 __isl_take isl_pw_multi_aff *pma);
2912 Multiple expressions can be copied and freed using
2913 the following functions.
2915 #include <isl/val.h>
2916 __isl_give isl_multi_val *isl_multi_val_copy(
2917 __isl_keep isl_multi_val *mv);
2918 __isl_null isl_multi_val *isl_multi_val_free(
2919 __isl_take isl_multi_val *mv);
2921 #include <isl/aff.h>
2922 __isl_give isl_multi_aff *isl_multi_aff_copy(
2923 __isl_keep isl_multi_aff *maff);
2924 __isl_null isl_multi_aff *isl_multi_aff_free(
2925 __isl_take isl_multi_aff *maff);
2926 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2927 __isl_keep isl_multi_pw_aff *mpa);
2928 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2929 __isl_take isl_multi_pw_aff *mpa);
2930 __isl_give isl_multi_union_pw_aff *
2931 isl_multi_union_pw_aff_copy(
2932 __isl_keep isl_multi_union_pw_aff *mupa);
2933 __isl_null isl_multi_union_pw_aff *
2934 isl_multi_union_pw_aff_free(
2935 __isl_take isl_multi_union_pw_aff *mupa);
2937 The base expression at a given position of a multiple
2938 expression can be extracted using the following functions.
2940 #include <isl/val.h>
2941 __isl_give isl_val *isl_multi_val_get_val(
2942 __isl_keep isl_multi_val *mv, int pos);
2944 #include <isl/aff.h>
2945 __isl_give isl_aff *isl_multi_aff_get_aff(
2946 __isl_keep isl_multi_aff *multi, int pos);
2947 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2948 __isl_keep isl_multi_pw_aff *mpa, int pos);
2949 __isl_give isl_union_pw_aff *
2950 isl_multi_union_pw_aff_get_union_pw_aff(
2951 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2953 It can be replaced using the following functions.
2955 #include <isl/val.h>
2956 __isl_give isl_multi_val *isl_multi_val_set_val(
2957 __isl_take isl_multi_val *mv, int pos,
2958 __isl_take isl_val *val);
2960 #include <isl/aff.h>
2961 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2962 __isl_take isl_multi_aff *multi, int pos,
2963 __isl_take isl_aff *aff);
2964 __isl_give isl_multi_union_pw_aff *
2965 isl_multi_union_pw_aff_set_union_pw_aff(
2966 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2967 __isl_take isl_union_pw_aff *upa);
2969 As a convenience, a sequence of base expressions that have
2970 their domains in a given space can be extracted from a sequence
2971 of union expressions using the following function.
2973 #include <isl/aff.h>
2974 __isl_give isl_multi_pw_aff *
2975 isl_multi_union_pw_aff_extract_multi_pw_aff(
2976 __isl_keep isl_multi_union_pw_aff *mupa,
2977 __isl_take isl_space *space);
2979 Note that there is a difference between C<isl_multi_union_pw_aff>
2980 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2981 of unions of piecewise expressions, while the second is a union
2982 of piecewise sequences. In particular, multiple affine expressions
2983 in an C<isl_union_pw_multi_aff> may live in different spaces,
2984 while there is only a single multiple expression in
2985 an C<isl_multi_union_pw_aff>, which can therefore only live
2986 in a single space. This means that not every
2987 C<isl_union_pw_multi_aff> can be converted to
2988 an C<isl_multi_union_pw_aff>. Conversely, the elements
2989 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2990 while each multiple expression inside an C<isl_union_pw_multi_aff>
2991 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2992 of dimension greater than one may therefore not be exact.
2993 The following functions can
2994 be used to perform these conversions when they are possible.
2996 #include <isl/aff.h>
2997 __isl_give isl_multi_union_pw_aff *
2998 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2999 __isl_take isl_union_pw_multi_aff *upma);
3000 __isl_give isl_union_pw_multi_aff *
3001 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3002 __isl_take isl_multi_union_pw_aff *mupa);
3004 =head3 Piecewise Expressions
3006 A piecewise expression is an expression that is described
3007 using zero or more base expression defined over the same
3008 number of cells in the domain space of the base expressions.
3009 All base expressions are defined over the same
3010 domain space and the cells are disjoint.
3011 The space of a piecewise expression is the same as
3012 that of the base expressions.
3013 If the union of the cells is a strict subset of the domain
3014 space, then the value of the piecewise expression outside
3015 this union is different for types derived from quasi-affine
3016 expressions and those derived from quasipolynomials.
3017 Piecewise expressions derived from quasi-affine expressions
3018 are considered to be undefined outside the union of their cells.
3019 Piecewise expressions derived from quasipolynomials
3020 are considered to be zero outside the union of their cells.
3022 Piecewise quasipolynomials are mainly used by the C<barvinok>
3023 library for representing the number of elements in a parametric set or map.
3024 For example, the piecewise quasipolynomial
3026 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3028 represents the number of points in the map
3030 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3032 The piecewise expression types defined by C<isl>
3033 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3034 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3036 A piecewise expression with no cells can be created using
3037 the following functions.
3039 #include <isl/aff.h>
3040 __isl_give isl_pw_aff *isl_pw_aff_empty(
3041 __isl_take isl_space *space);
3042 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3043 __isl_take isl_space *space);
3045 A piecewise expression with a single universe cell can be
3046 created using the following functions.
3048 #include <isl/aff.h>
3049 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3050 __isl_take isl_aff *aff);
3051 __isl_give isl_pw_multi_aff *
3052 isl_pw_multi_aff_from_multi_aff(
3053 __isl_take isl_multi_aff *ma);
3055 #include <isl/polynomial.h>
3056 __isl_give isl_pw_qpolynomial *
3057 isl_pw_qpolynomial_from_qpolynomial(
3058 __isl_take isl_qpolynomial *qp);
3060 A piecewise expression with a single specified cell can be
3061 created using the following functions.
3063 #include <isl/aff.h>
3064 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3065 __isl_take isl_set *set, __isl_take isl_aff *aff);
3066 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3067 __isl_take isl_set *set,
3068 __isl_take isl_multi_aff *maff);
3070 #include <isl/polynomial.h>
3071 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3072 __isl_take isl_set *set,
3073 __isl_take isl_qpolynomial *qp);
3075 The following convenience functions first create a base expression and
3076 then create a piecewise expression over a universe domain.
3078 #include <isl/aff.h>
3079 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3080 __isl_take isl_local_space *ls);
3081 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3082 __isl_take isl_local_space *ls,
3083 enum isl_dim_type type, unsigned pos);
3084 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3085 __isl_take isl_local_space *ls);
3086 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3087 __isl_take isl_space *space);
3088 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3089 __isl_take isl_space *space);
3090 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3091 __isl_take isl_space *space);
3092 __isl_give isl_pw_multi_aff *
3093 isl_pw_multi_aff_project_out_map(
3094 __isl_take isl_space *space,
3095 enum isl_dim_type type,
3096 unsigned first, unsigned n);
3098 #include <isl/polynomial.h>
3099 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3100 __isl_take isl_space *space);
3102 The following convenience functions first create a base expression and
3103 then create a piecewise expression over a given domain.
3105 #include <isl/aff.h>
3106 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3107 __isl_take isl_set *domain,
3108 __isl_take isl_val *v);
3109 __isl_give isl_pw_multi_aff *
3110 isl_pw_multi_aff_multi_val_on_domain(
3111 __isl_take isl_set *domain,
3112 __isl_take isl_multi_val *mv);
3114 As a convenience, a piecewise multiple expression can
3115 also be created from a piecewise expression.
3116 Each multiple expression in the result is derived
3117 from the corresponding base expression.
3119 #include <isl/aff.h>
3120 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3121 __isl_take isl_pw_aff *pa);
3123 Similarly, a piecewise quasipolynomial can be
3124 created from a piecewise quasi-affine expression using
3125 the following function.
3127 #include <isl/polynomial.h>
3128 __isl_give isl_pw_qpolynomial *
3129 isl_pw_qpolynomial_from_pw_aff(
3130 __isl_take isl_pw_aff *pwaff);
3132 Piecewise expressions can be copied and freed using the following functions.
3134 #include <isl/aff.h>
3135 __isl_give isl_pw_aff *isl_pw_aff_copy(
3136 __isl_keep isl_pw_aff *pwaff);
3137 __isl_null isl_pw_aff *isl_pw_aff_free(
3138 __isl_take isl_pw_aff *pwaff);
3139 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3140 __isl_keep isl_pw_multi_aff *pma);
3141 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3142 __isl_take isl_pw_multi_aff *pma);
3144 #include <isl/polynomial.h>
3145 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3146 __isl_keep isl_pw_qpolynomial *pwqp);
3147 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3148 __isl_take isl_pw_qpolynomial *pwqp);
3149 __isl_give isl_pw_qpolynomial_fold *
3150 isl_pw_qpolynomial_fold_copy(
3151 __isl_keep isl_pw_qpolynomial_fold *pwf);
3152 __isl_null isl_pw_qpolynomial_fold *
3153 isl_pw_qpolynomial_fold_free(
3154 __isl_take isl_pw_qpolynomial_fold *pwf);
3156 To iterate over the different cells of a piecewise expression,
3157 use the following functions.
3159 #include <isl/aff.h>
3160 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3161 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3162 isl_stat isl_pw_aff_foreach_piece(
3163 __isl_keep isl_pw_aff *pwaff,
3164 isl_stat (*fn)(__isl_take isl_set *set,
3165 __isl_take isl_aff *aff,
3166 void *user), void *user);
3167 int isl_pw_multi_aff_n_piece(
3168 __isl_keep isl_pw_multi_aff *pma);
3169 isl_stat isl_pw_multi_aff_foreach_piece(
3170 __isl_keep isl_pw_multi_aff *pma,
3171 isl_stat (*fn)(__isl_take isl_set *set,
3172 __isl_take isl_multi_aff *maff,
3173 void *user), void *user);
3175 #include <isl/polynomial.h>
3176 int isl_pw_qpolynomial_n_piece(
3177 __isl_keep isl_pw_qpolynomial *pwqp);
3178 isl_stat isl_pw_qpolynomial_foreach_piece(
3179 __isl_keep isl_pw_qpolynomial *pwqp,
3180 isl_stat (*fn)(__isl_take isl_set *set,
3181 __isl_take isl_qpolynomial *qp,
3182 void *user), void *user);
3183 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3184 __isl_keep isl_pw_qpolynomial *pwqp,
3185 isl_stat (*fn)(__isl_take isl_set *set,
3186 __isl_take isl_qpolynomial *qp,
3187 void *user), void *user);
3188 int isl_pw_qpolynomial_fold_n_piece(
3189 __isl_keep isl_pw_qpolynomial_fold *pwf);
3190 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3191 __isl_keep isl_pw_qpolynomial_fold *pwf,
3192 isl_stat (*fn)(__isl_take isl_set *set,
3193 __isl_take isl_qpolynomial_fold *fold,
3194 void *user), void *user);
3195 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3196 __isl_keep isl_pw_qpolynomial_fold *pwf,
3197 isl_stat (*fn)(__isl_take isl_set *set,
3198 __isl_take isl_qpolynomial_fold *fold,
3199 void *user), void *user);
3201 As usual, the function C<fn> should return C<isl_stat_ok> on success
3202 and C<isl_stat_error> on failure. The difference between
3203 C<isl_pw_qpolynomial_foreach_piece> and
3204 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3205 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3206 compute unique representations for all existentially quantified
3207 variables and then turn these existentially quantified variables
3208 into extra set variables, adapting the associated quasipolynomial
3209 accordingly. This means that the C<set> passed to C<fn>
3210 will not have any existentially quantified variables, but that
3211 the dimensions of the sets may be different for different
3212 invocations of C<fn>.
3213 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3214 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3216 A piecewise expression consisting of the expressions at a given
3217 position of a piecewise multiple expression can be extracted
3218 using the following function.
3220 #include <isl/aff.h>
3221 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3222 __isl_keep isl_pw_multi_aff *pma, int pos);
3224 These expressions can be replaced using the following function.
3226 #include <isl/aff.h>
3227 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3228 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3229 __isl_take isl_pw_aff *pa);
3231 Note that there is a difference between C<isl_multi_pw_aff> and
3232 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3233 affine expressions, while the second is a piecewise sequence
3234 of affine expressions. In particular, each of the piecewise
3235 affine expressions in an C<isl_multi_pw_aff> may have a different
3236 domain, while all multiple expressions associated to a cell
3237 in an C<isl_pw_multi_aff> have the same domain.
3238 It is possible to convert between the two, but when converting
3239 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3240 of the result is the intersection of the domains of the input.
3241 The reverse conversion is exact.
3243 #include <isl/aff.h>
3244 __isl_give isl_pw_multi_aff *
3245 isl_pw_multi_aff_from_multi_pw_aff(
3246 __isl_take isl_multi_pw_aff *mpa);
3247 __isl_give isl_multi_pw_aff *
3248 isl_multi_pw_aff_from_pw_multi_aff(
3249 __isl_take isl_pw_multi_aff *pma);
3251 =head3 Union Expressions
3253 A union expression collects base expressions defined
3254 over different domains. The space of a union expression
3255 is that of the shared parameter space.
3257 The union expression types defined by C<isl>
3258 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3259 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3261 C<isl_union_pw_aff>,
3262 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3263 there can be at most one base expression for a given domain space.
3265 C<isl_union_pw_multi_aff>,
3266 there can be multiple such expressions for a given domain space,
3267 but the domains of these expressions need to be disjoint.
3269 An empty union expression can be created using the following functions.
3271 #include <isl/aff.h>
3272 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3273 __isl_take isl_space *space);
3274 __isl_give isl_union_pw_multi_aff *
3275 isl_union_pw_multi_aff_empty(
3276 __isl_take isl_space *space);
3278 #include <isl/polynomial.h>
3279 __isl_give isl_union_pw_qpolynomial *
3280 isl_union_pw_qpolynomial_zero(
3281 __isl_take isl_space *space);
3283 A union expression containing a single base expression
3284 can be created using the following functions.
3286 #include <isl/aff.h>
3287 __isl_give isl_union_pw_aff *
3288 isl_union_pw_aff_from_pw_aff(
3289 __isl_take isl_pw_aff *pa);
3290 __isl_give isl_union_pw_multi_aff *
3291 isl_union_pw_multi_aff_from_aff(
3292 __isl_take isl_aff *aff);
3293 __isl_give isl_union_pw_multi_aff *
3294 isl_union_pw_multi_aff_from_pw_multi_aff(
3295 __isl_take isl_pw_multi_aff *pma);
3297 #include <isl/polynomial.h>
3298 __isl_give isl_union_pw_qpolynomial *
3299 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3300 __isl_take isl_pw_qpolynomial *pwqp);
3302 The following functions create a base expression on each
3303 of the sets in the union set and collect the results.
3305 #include <isl/aff.h>
3306 __isl_give isl_union_pw_multi_aff *
3307 isl_union_pw_multi_aff_from_union_pw_aff(
3308 __isl_take isl_union_pw_aff *upa);
3309 __isl_give isl_union_pw_aff *
3310 isl_union_pw_multi_aff_get_union_pw_aff(
3311 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3312 __isl_give isl_union_pw_aff *
3313 isl_union_pw_aff_val_on_domain(
3314 __isl_take isl_union_set *domain,
3315 __isl_take isl_val *v);
3316 __isl_give isl_union_pw_multi_aff *
3317 isl_union_pw_multi_aff_multi_val_on_domain(
3318 __isl_take isl_union_set *domain,
3319 __isl_take isl_multi_val *mv);
3320 __isl_give isl_union_pw_aff *
3321 isl_union_pw_aff_param_on_domain_id(
3322 __isl_take isl_union_set *domain,
3323 __isl_take isl_id *id);
3325 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3326 is the identifier of a parameter that may or may not already
3327 be present in C<domain>.
3329 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3331 expression on a given domain can be created using the following
3334 #include <isl/aff.h>
3335 __isl_give isl_union_pw_aff *
3336 isl_union_pw_aff_aff_on_domain(
3337 __isl_take isl_union_set *domain,
3338 __isl_take isl_aff *aff);
3339 __isl_give isl_union_pw_aff *
3340 isl_union_pw_aff_pw_aff_on_domain(
3341 __isl_take isl_union_set *domain,
3342 __isl_take isl_pw_aff *pa);
3344 A base expression can be added to a union expression using
3345 the following functions.
3347 #include <isl/aff.h>
3348 __isl_give isl_union_pw_aff *
3349 isl_union_pw_aff_add_pw_aff(
3350 __isl_take isl_union_pw_aff *upa,
3351 __isl_take isl_pw_aff *pa);
3352 __isl_give isl_union_pw_multi_aff *
3353 isl_union_pw_multi_aff_add_pw_multi_aff(
3354 __isl_take isl_union_pw_multi_aff *upma,
3355 __isl_take isl_pw_multi_aff *pma);
3357 #include <isl/polynomial.h>
3358 __isl_give isl_union_pw_qpolynomial *
3359 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3360 __isl_take isl_union_pw_qpolynomial *upwqp,
3361 __isl_take isl_pw_qpolynomial *pwqp);
3363 Union expressions can be copied and freed using
3364 the following functions.
3366 #include <isl/aff.h>
3367 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3368 __isl_keep isl_union_pw_aff *upa);
3369 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3370 __isl_take isl_union_pw_aff *upa);
3371 __isl_give isl_union_pw_multi_aff *
3372 isl_union_pw_multi_aff_copy(
3373 __isl_keep isl_union_pw_multi_aff *upma);
3374 __isl_null isl_union_pw_multi_aff *
3375 isl_union_pw_multi_aff_free(
3376 __isl_take isl_union_pw_multi_aff *upma);
3378 #include <isl/polynomial.h>
3379 __isl_give isl_union_pw_qpolynomial *
3380 isl_union_pw_qpolynomial_copy(
3381 __isl_keep isl_union_pw_qpolynomial *upwqp);
3382 __isl_null isl_union_pw_qpolynomial *
3383 isl_union_pw_qpolynomial_free(
3384 __isl_take isl_union_pw_qpolynomial *upwqp);
3385 __isl_give isl_union_pw_qpolynomial_fold *
3386 isl_union_pw_qpolynomial_fold_copy(
3387 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3388 __isl_null isl_union_pw_qpolynomial_fold *
3389 isl_union_pw_qpolynomial_fold_free(
3390 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3392 To iterate over the base expressions in a union expression,
3393 use the following functions.
3395 #include <isl/aff.h>
3396 int isl_union_pw_aff_n_pw_aff(
3397 __isl_keep isl_union_pw_aff *upa);
3398 isl_stat isl_union_pw_aff_foreach_pw_aff(
3399 __isl_keep isl_union_pw_aff *upa,
3400 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3401 void *user), void *user);
3402 int isl_union_pw_multi_aff_n_pw_multi_aff(
3403 __isl_keep isl_union_pw_multi_aff *upma);
3404 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3405 __isl_keep isl_union_pw_multi_aff *upma,
3406 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3407 void *user), void *user);
3409 #include <isl/polynomial.h>
3410 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3411 __isl_keep isl_union_pw_qpolynomial *upwqp);
3412 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3413 __isl_keep isl_union_pw_qpolynomial *upwqp,
3414 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3415 void *user), void *user);
3416 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3417 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3418 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3419 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3420 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3421 void *user), void *user);
3423 To extract the base expression in a given space from a union, use
3424 the following functions.
3426 #include <isl/aff.h>
3427 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3428 __isl_keep isl_union_pw_aff *upa,
3429 __isl_take isl_space *space);
3430 __isl_give isl_pw_multi_aff *
3431 isl_union_pw_multi_aff_extract_pw_multi_aff(
3432 __isl_keep isl_union_pw_multi_aff *upma,
3433 __isl_take isl_space *space);
3435 #include <isl/polynomial.h>
3436 __isl_give isl_pw_qpolynomial *
3437 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3438 __isl_keep isl_union_pw_qpolynomial *upwqp,
3439 __isl_take isl_space *space);
3441 =head2 Input and Output
3443 For set and relation,
3444 C<isl> supports its own input/output format, which is similar
3445 to the C<Omega> format, but also supports the C<PolyLib> format
3447 For other object types, typically only an C<isl> format is supported.
3449 =head3 C<isl> format
3451 The C<isl> format is similar to that of C<Omega>, but has a different
3452 syntax for describing the parameters and allows for the definition
3453 of an existentially quantified variable as the integer division
3454 of an affine expression.
3455 For example, the set of integers C<i> between C<0> and C<n>
3456 such that C<i % 10 <= 6> can be described as
3458 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3461 A set or relation can have several disjuncts, separated
3462 by the keyword C<or>. Each disjunct is either a conjunction
3463 of constraints or a projection (C<exists>) of a conjunction
3464 of constraints. The constraints are separated by the keyword
3467 =head3 C<PolyLib> format
3469 If the represented set is a union, then the first line
3470 contains a single number representing the number of disjuncts.
3471 Otherwise, a line containing the number C<1> is optional.
3473 Each disjunct is represented by a matrix of constraints.
3474 The first line contains two numbers representing
3475 the number of rows and columns,
3476 where the number of rows is equal to the number of constraints
3477 and the number of columns is equal to two plus the number of variables.
3478 The following lines contain the actual rows of the constraint matrix.
3479 In each row, the first column indicates whether the constraint
3480 is an equality (C<0>) or inequality (C<1>). The final column
3481 corresponds to the constant term.
3483 If the set is parametric, then the coefficients of the parameters
3484 appear in the last columns before the constant column.
3485 The coefficients of any existentially quantified variables appear
3486 between those of the set variables and those of the parameters.
3488 =head3 Extended C<PolyLib> format
3490 The extended C<PolyLib> format is nearly identical to the
3491 C<PolyLib> format. The only difference is that the line
3492 containing the number of rows and columns of a constraint matrix
3493 also contains four additional numbers:
3494 the number of output dimensions, the number of input dimensions,
3495 the number of local dimensions (i.e., the number of existentially
3496 quantified variables) and the number of parameters.
3497 For sets, the number of ``output'' dimensions is equal
3498 to the number of set dimensions, while the number of ``input''
3503 Objects can be read from input using the following functions.
3505 #include <isl/val.h>
3506 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3508 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3509 isl_ctx *ctx, const char *str);
3511 #include <isl/set.h>
3512 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3513 isl_ctx *ctx, FILE *input);
3514 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3515 isl_ctx *ctx, const char *str);
3516 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3518 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3521 #include <isl/map.h>
3522 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3523 isl_ctx *ctx, FILE *input);
3524 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3525 isl_ctx *ctx, const char *str);
3526 __isl_give isl_map *isl_map_read_from_file(
3527 isl_ctx *ctx, FILE *input);
3528 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3531 #include <isl/union_set.h>
3532 __isl_give isl_union_set *isl_union_set_read_from_file(
3533 isl_ctx *ctx, FILE *input);
3534 __isl_give isl_union_set *isl_union_set_read_from_str(
3535 isl_ctx *ctx, const char *str);
3537 #include <isl/union_map.h>
3538 __isl_give isl_union_map *isl_union_map_read_from_file(
3539 isl_ctx *ctx, FILE *input);
3540 __isl_give isl_union_map *isl_union_map_read_from_str(
3541 isl_ctx *ctx, const char *str);
3543 #include <isl/aff.h>
3544 __isl_give isl_aff *isl_aff_read_from_str(
3545 isl_ctx *ctx, const char *str);
3546 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3547 isl_ctx *ctx, const char *str);
3548 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3549 isl_ctx *ctx, const char *str);
3550 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3551 isl_ctx *ctx, const char *str);
3552 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3553 isl_ctx *ctx, const char *str);
3554 __isl_give isl_union_pw_aff *
3555 isl_union_pw_aff_read_from_str(
3556 isl_ctx *ctx, const char *str);
3557 __isl_give isl_union_pw_multi_aff *
3558 isl_union_pw_multi_aff_read_from_str(
3559 isl_ctx *ctx, const char *str);
3560 __isl_give isl_multi_union_pw_aff *
3561 isl_multi_union_pw_aff_read_from_str(
3562 isl_ctx *ctx, const char *str);
3564 #include <isl/polynomial.h>
3565 __isl_give isl_union_pw_qpolynomial *
3566 isl_union_pw_qpolynomial_read_from_str(
3567 isl_ctx *ctx, const char *str);
3569 For sets and relations,
3570 the input format is autodetected and may be either the C<PolyLib> format
3571 or the C<isl> format.
3575 Before anything can be printed, an C<isl_printer> needs to
3578 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3580 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3581 __isl_null isl_printer *isl_printer_free(
3582 __isl_take isl_printer *printer);
3584 C<isl_printer_to_file> prints to the given file, while
3585 C<isl_printer_to_str> prints to a string that can be extracted
3586 using the following function.
3588 #include <isl/printer.h>
3589 __isl_give char *isl_printer_get_str(
3590 __isl_keep isl_printer *printer);
3592 The printer can be inspected using the following functions.
3594 FILE *isl_printer_get_file(
3595 __isl_keep isl_printer *printer);
3596 int isl_printer_get_output_format(
3597 __isl_keep isl_printer *p);
3598 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3600 The behavior of the printer can be modified in various ways
3602 __isl_give isl_printer *isl_printer_set_output_format(
3603 __isl_take isl_printer *p, int output_format);
3604 __isl_give isl_printer *isl_printer_set_indent(
3605 __isl_take isl_printer *p, int indent);
3606 __isl_give isl_printer *isl_printer_set_indent_prefix(
3607 __isl_take isl_printer *p, const char *prefix);
3608 __isl_give isl_printer *isl_printer_indent(
3609 __isl_take isl_printer *p, int indent);
3610 __isl_give isl_printer *isl_printer_set_prefix(
3611 __isl_take isl_printer *p, const char *prefix);
3612 __isl_give isl_printer *isl_printer_set_suffix(
3613 __isl_take isl_printer *p, const char *suffix);
3614 __isl_give isl_printer *isl_printer_set_yaml_style(
3615 __isl_take isl_printer *p, int yaml_style);
3617 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3618 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3619 and defaults to C<ISL_FORMAT_ISL>.
3620 Each line in the output is prefixed by C<indent_prefix>,
3621 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3622 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3623 In the C<PolyLib> format output,
3624 the coefficients of the existentially quantified variables
3625 appear between those of the set variables and those
3627 The function C<isl_printer_indent> increases the indentation
3628 by the specified amount (which may be negative).
3629 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3630 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3633 To actually print something, use
3635 #include <isl/printer.h>
3636 __isl_give isl_printer *isl_printer_print_double(
3637 __isl_take isl_printer *p, double d);
3639 #include <isl/val.h>
3640 __isl_give isl_printer *isl_printer_print_val(
3641 __isl_take isl_printer *p, __isl_keep isl_val *v);
3643 #include <isl/set.h>
3644 __isl_give isl_printer *isl_printer_print_basic_set(
3645 __isl_take isl_printer *printer,
3646 __isl_keep isl_basic_set *bset);
3647 __isl_give isl_printer *isl_printer_print_set(
3648 __isl_take isl_printer *printer,
3649 __isl_keep isl_set *set);
3651 #include <isl/map.h>
3652 __isl_give isl_printer *isl_printer_print_basic_map(
3653 __isl_take isl_printer *printer,
3654 __isl_keep isl_basic_map *bmap);
3655 __isl_give isl_printer *isl_printer_print_map(
3656 __isl_take isl_printer *printer,
3657 __isl_keep isl_map *map);
3659 #include <isl/union_set.h>
3660 __isl_give isl_printer *isl_printer_print_union_set(
3661 __isl_take isl_printer *p,
3662 __isl_keep isl_union_set *uset);
3664 #include <isl/union_map.h>
3665 __isl_give isl_printer *isl_printer_print_union_map(
3666 __isl_take isl_printer *p,
3667 __isl_keep isl_union_map *umap);
3669 #include <isl/val.h>
3670 __isl_give isl_printer *isl_printer_print_multi_val(
3671 __isl_take isl_printer *p,
3672 __isl_keep isl_multi_val *mv);
3674 #include <isl/aff.h>
3675 __isl_give isl_printer *isl_printer_print_aff(
3676 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3677 __isl_give isl_printer *isl_printer_print_multi_aff(
3678 __isl_take isl_printer *p,
3679 __isl_keep isl_multi_aff *maff);
3680 __isl_give isl_printer *isl_printer_print_pw_aff(
3681 __isl_take isl_printer *p,
3682 __isl_keep isl_pw_aff *pwaff);
3683 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3684 __isl_take isl_printer *p,
3685 __isl_keep isl_pw_multi_aff *pma);
3686 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3687 __isl_take isl_printer *p,
3688 __isl_keep isl_multi_pw_aff *mpa);
3689 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3690 __isl_take isl_printer *p,
3691 __isl_keep isl_union_pw_aff *upa);
3692 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3693 __isl_take isl_printer *p,
3694 __isl_keep isl_union_pw_multi_aff *upma);
3695 __isl_give isl_printer *
3696 isl_printer_print_multi_union_pw_aff(
3697 __isl_take isl_printer *p,
3698 __isl_keep isl_multi_union_pw_aff *mupa);
3700 #include <isl/polynomial.h>
3701 __isl_give isl_printer *isl_printer_print_qpolynomial(
3702 __isl_take isl_printer *p,
3703 __isl_keep isl_qpolynomial *qp);
3704 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3705 __isl_take isl_printer *p,
3706 __isl_keep isl_pw_qpolynomial *pwqp);
3707 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3708 __isl_take isl_printer *p,
3709 __isl_keep isl_union_pw_qpolynomial *upwqp);
3711 __isl_give isl_printer *
3712 isl_printer_print_pw_qpolynomial_fold(
3713 __isl_take isl_printer *p,
3714 __isl_keep isl_pw_qpolynomial_fold *pwf);
3715 __isl_give isl_printer *
3716 isl_printer_print_union_pw_qpolynomial_fold(
3717 __isl_take isl_printer *p,
3718 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3720 For C<isl_printer_print_qpolynomial>,
3721 C<isl_printer_print_pw_qpolynomial> and
3722 C<isl_printer_print_pw_qpolynomial_fold>,
3723 the output format of the printer
3724 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3725 For C<isl_printer_print_union_pw_qpolynomial> and
3726 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3728 In case of printing in C<ISL_FORMAT_C>, the user may want
3729 to set the names of all dimensions first.
3731 C<isl> also provides limited support for printing YAML documents,
3732 just enough for the internal use for printing such documents.
3734 #include <isl/printer.h>
3735 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3736 __isl_take isl_printer *p);
3737 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3738 __isl_take isl_printer *p);
3739 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3740 __isl_take isl_printer *p);
3741 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3742 __isl_take isl_printer *p);
3743 __isl_give isl_printer *isl_printer_yaml_next(
3744 __isl_take isl_printer *p);
3746 A document is started by a call to either
3747 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3748 Anything printed to the printer after such a call belong to the
3749 first key of the mapping or the first element in the sequence.
3750 The function C<isl_printer_yaml_next> moves to the value if
3751 we are currently printing a mapping key, the next key if we
3752 are printing a value or the next element if we are printing
3753 an element in a sequence.
3754 Nested mappings and sequences are initiated by the same
3755 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3756 Each call to these functions needs to have a corresponding call to
3757 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3759 When called on a file printer, the following function flushes
3760 the file. When called on a string printer, the buffer is cleared.
3762 __isl_give isl_printer *isl_printer_flush(
3763 __isl_take isl_printer *p);
3765 The following functions allow the user to attach
3766 notes to a printer in order to keep track of additional state.
3768 #include <isl/printer.h>
3769 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3770 __isl_keep isl_id *id);
3771 __isl_give isl_id *isl_printer_get_note(
3772 __isl_keep isl_printer *p, __isl_take isl_id *id);
3773 __isl_give isl_printer *isl_printer_set_note(
3774 __isl_take isl_printer *p,
3775 __isl_take isl_id *id, __isl_take isl_id *note);
3777 C<isl_printer_set_note> associates the given note to the given
3778 identifier in the printer.
3779 C<isl_printer_get_note> retrieves a note associated to an
3781 C<isl_printer_has_note> checks if there is such a note.
3782 C<isl_printer_get_note> fails if the requested note does not exist.
3784 Alternatively, a string representation can be obtained
3785 directly using the following functions, which always print
3789 __isl_give char *isl_id_to_str(
3790 __isl_keep isl_id *id);
3792 #include <isl/space.h>
3793 __isl_give char *isl_space_to_str(
3794 __isl_keep isl_space *space);
3796 #include <isl/val.h>
3797 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3798 __isl_give char *isl_multi_val_to_str(
3799 __isl_keep isl_multi_val *mv);
3801 #include <isl/set.h>
3802 __isl_give char *isl_basic_set_to_str(
3803 __isl_keep isl_basic_set *bset);
3804 __isl_give char *isl_set_to_str(
3805 __isl_keep isl_set *set);
3807 #include <isl/union_set.h>
3808 __isl_give char *isl_union_set_to_str(
3809 __isl_keep isl_union_set *uset);
3811 #include <isl/map.h>
3812 __isl_give char *isl_basic_map_to_str(
3813 __isl_keep isl_basic_map *bmap);
3814 __isl_give char *isl_map_to_str(
3815 __isl_keep isl_map *map);
3817 #include <isl/union_map.h>
3818 __isl_give char *isl_union_map_to_str(
3819 __isl_keep isl_union_map *umap);
3821 #include <isl/aff.h>
3822 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3823 __isl_give char *isl_pw_aff_to_str(
3824 __isl_keep isl_pw_aff *pa);
3825 __isl_give char *isl_multi_aff_to_str(
3826 __isl_keep isl_multi_aff *ma);
3827 __isl_give char *isl_pw_multi_aff_to_str(
3828 __isl_keep isl_pw_multi_aff *pma);
3829 __isl_give char *isl_multi_pw_aff_to_str(
3830 __isl_keep isl_multi_pw_aff *mpa);
3831 __isl_give char *isl_union_pw_aff_to_str(
3832 __isl_keep isl_union_pw_aff *upa);
3833 __isl_give char *isl_union_pw_multi_aff_to_str(
3834 __isl_keep isl_union_pw_multi_aff *upma);
3835 __isl_give char *isl_multi_union_pw_aff_to_str(
3836 __isl_keep isl_multi_union_pw_aff *mupa);
3838 #include <isl/point.h>
3839 __isl_give char *isl_point_to_str(
3840 __isl_keep isl_point *pnt);
3842 #include <isl/polynomial.h>
3843 __isl_give char *isl_pw_qpolynomial_to_str(
3844 __isl_keep isl_pw_qpolynomial *pwqp);
3845 __isl_give char *isl_union_pw_qpolynomial_to_str(
3846 __isl_keep isl_union_pw_qpolynomial *upwqp);
3850 =head3 Unary Properties
3856 The following functions test whether the given set or relation
3857 contains any integer points. The ``plain'' variants do not perform
3858 any computations, but simply check if the given set or relation
3859 is already known to be empty.
3861 #include <isl/set.h>
3862 isl_bool isl_basic_set_plain_is_empty(
3863 __isl_keep isl_basic_set *bset);
3864 isl_bool isl_basic_set_is_empty(
3865 __isl_keep isl_basic_set *bset);
3866 isl_bool isl_set_plain_is_empty(
3867 __isl_keep isl_set *set);
3868 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3870 #include <isl/union_set.h>
3871 isl_bool isl_union_set_is_empty(
3872 __isl_keep isl_union_set *uset);
3874 #include <isl/map.h>
3875 isl_bool isl_basic_map_plain_is_empty(
3876 __isl_keep isl_basic_map *bmap);
3877 isl_bool isl_basic_map_is_empty(
3878 __isl_keep isl_basic_map *bmap);
3879 isl_bool isl_map_plain_is_empty(
3880 __isl_keep isl_map *map);
3881 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3883 #include <isl/union_map.h>
3884 isl_bool isl_union_map_plain_is_empty(
3885 __isl_keep isl_union_map *umap);
3886 isl_bool isl_union_map_is_empty(
3887 __isl_keep isl_union_map *umap);
3889 =item * Universality
3891 isl_bool isl_basic_set_plain_is_universe(
3892 __isl_keep isl_basic_set *bset);
3893 isl_bool isl_basic_set_is_universe(
3894 __isl_keep isl_basic_set *bset);
3895 isl_bool isl_basic_map_plain_is_universe(
3896 __isl_keep isl_basic_map *bmap);
3897 isl_bool isl_basic_map_is_universe(
3898 __isl_keep isl_basic_map *bmap);
3899 isl_bool isl_set_plain_is_universe(
3900 __isl_keep isl_set *set);
3901 isl_bool isl_map_plain_is_universe(
3902 __isl_keep isl_map *map);
3904 =item * Single-valuedness
3906 #include <isl/set.h>
3907 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3909 #include <isl/map.h>
3910 isl_bool isl_basic_map_is_single_valued(
3911 __isl_keep isl_basic_map *bmap);
3912 isl_bool isl_map_plain_is_single_valued(
3913 __isl_keep isl_map *map);
3914 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3916 #include <isl/union_map.h>
3917 isl_bool isl_union_map_is_single_valued(
3918 __isl_keep isl_union_map *umap);
3922 isl_bool isl_map_plain_is_injective(
3923 __isl_keep isl_map *map);
3924 isl_bool isl_map_is_injective(
3925 __isl_keep isl_map *map);
3926 isl_bool isl_union_map_plain_is_injective(
3927 __isl_keep isl_union_map *umap);
3928 isl_bool isl_union_map_is_injective(
3929 __isl_keep isl_union_map *umap);
3933 isl_bool isl_map_is_bijective(
3934 __isl_keep isl_map *map);
3935 isl_bool isl_union_map_is_bijective(
3936 __isl_keep isl_union_map *umap);
3940 The following functions test whether the given relation
3941 only maps elements to themselves.
3943 #include <isl/map.h>
3944 isl_bool isl_map_is_identity(
3945 __isl_keep isl_map *map);
3947 #include <isl/union_map.h>
3948 isl_bool isl_union_map_is_identity(
3949 __isl_keep isl_union_map *umap);
3953 __isl_give isl_val *
3954 isl_basic_map_plain_get_val_if_fixed(
3955 __isl_keep isl_basic_map *bmap,
3956 enum isl_dim_type type, unsigned pos);
3957 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3958 __isl_keep isl_set *set,
3959 enum isl_dim_type type, unsigned pos);
3960 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3961 __isl_keep isl_map *map,
3962 enum isl_dim_type type, unsigned pos);
3964 If the set or relation obviously lies on a hyperplane where the given dimension
3965 has a fixed value, then return that value.
3966 Otherwise return NaN.
3970 isl_stat isl_set_dim_residue_class_val(
3971 __isl_keep isl_set *set,
3972 int pos, __isl_give isl_val **modulo,
3973 __isl_give isl_val **residue);
3975 Check if the values of the given set dimension are equal to a fixed
3976 value modulo some integer value. If so, assign the modulo to C<*modulo>
3977 and the fixed value to C<*residue>. If the given dimension attains only
3978 a single value, then assign C<0> to C<*modulo> and the fixed value to
3980 If the dimension does not attain only a single value and if no modulo
3981 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3983 #include <isl/set.h>
3984 __isl_give isl_stride_info *isl_set_get_stride_info(
3985 __isl_keep isl_set *set, int pos);
3986 __isl_give isl_val *isl_set_get_stride(
3987 __isl_keep isl_set *set, int pos);
3989 #include <isl/map.h>
3990 __isl_give isl_stride_info *
3991 isl_map_get_range_stride_info(
3992 __isl_keep isl_map *map, int pos);
3994 Check if the values of the given set dimension are equal to
3995 some affine expression of the other dimensions (the offset)
3996 modulo some integer stride or
3997 check if the values of the given output dimensions are equal to
3998 some affine expression of the input dimensions (the offset)
3999 modulo some integer stride.
4000 If no more specific information can be found, then the stride
4001 is taken to be one and the offset is taken to be the zero expression.
4002 The function C<isl_set_get_stride> performs the same
4003 computation as C<isl_set_get_stride_info> but only returns the stride.
4004 For the other functions,
4005 the stride and offset can be extracted from the returned object
4006 using the following functions.
4008 #include <isl/stride_info.h>
4009 __isl_give isl_val *isl_stride_info_get_stride(
4010 __isl_keep isl_stride_info *si);
4011 __isl_give isl_aff *isl_stride_info_get_offset(
4012 __isl_keep isl_stride_info *si);
4014 The stride info object can be released using the following function.
4016 #include <isl/stride_info.h>
4017 __isl_null isl_stride_info *isl_stride_info_free(
4018 __isl_take isl_stride_info *si);
4022 To check whether the description of a set, relation or function depends
4023 on one or more given dimensions,
4024 the following functions can be used.
4026 #include <isl/constraint.h>
4027 isl_bool isl_constraint_involves_dims(
4028 __isl_keep isl_constraint *constraint,
4029 enum isl_dim_type type, unsigned first, unsigned n);
4031 #include <isl/set.h>
4032 isl_bool isl_basic_set_involves_dims(
4033 __isl_keep isl_basic_set *bset,
4034 enum isl_dim_type type, unsigned first, unsigned n);
4035 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4036 enum isl_dim_type type, unsigned first, unsigned n);
4038 #include <isl/map.h>
4039 isl_bool isl_basic_map_involves_dims(
4040 __isl_keep isl_basic_map *bmap,
4041 enum isl_dim_type type, unsigned first, unsigned n);
4042 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4043 enum isl_dim_type type, unsigned first, unsigned n);
4045 #include <isl/union_map.h>
4046 isl_bool isl_union_map_involves_dims(
4047 __isl_keep isl_union_map *umap,
4048 enum isl_dim_type type, unsigned first, unsigned n);
4050 #include <isl/aff.h>
4051 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4052 enum isl_dim_type type, unsigned first, unsigned n);
4053 isl_bool isl_pw_aff_involves_dims(
4054 __isl_keep isl_pw_aff *pwaff,
4055 enum isl_dim_type type, unsigned first, unsigned n);
4056 isl_bool isl_multi_aff_involves_dims(
4057 __isl_keep isl_multi_aff *ma,
4058 enum isl_dim_type type, unsigned first, unsigned n);
4059 isl_bool isl_pw_multi_aff_involves_dims(
4060 __isl_keep isl_pw_multi_aff *pma,
4061 enum isl_dim_type type, unsigned first, unsigned n);
4062 isl_bool isl_multi_pw_aff_involves_dims(
4063 __isl_keep isl_multi_pw_aff *mpa,
4064 enum isl_dim_type type, unsigned first, unsigned n);
4066 #include <isl/polynomial.h>
4067 isl_bool isl_qpolynomial_involves_dims(
4068 __isl_keep isl_qpolynomial *qp,
4069 enum isl_dim_type type, unsigned first, unsigned n);
4071 Similarly, the following functions can be used to check whether
4072 a given dimension is involved in any lower or upper bound.
4074 #include <isl/set.h>
4075 isl_bool isl_set_dim_has_any_lower_bound(
4076 __isl_keep isl_set *set,
4077 enum isl_dim_type type, unsigned pos);
4078 isl_bool isl_set_dim_has_any_upper_bound(
4079 __isl_keep isl_set *set,
4080 enum isl_dim_type type, unsigned pos);
4082 Note that these functions return true even if there is a bound on
4083 the dimension on only some of the basic sets of C<set>.
4084 To check if they have a bound for all of the basic sets in C<set>,
4085 use the following functions instead.
4087 #include <isl/set.h>
4088 isl_bool isl_set_dim_has_lower_bound(
4089 __isl_keep isl_set *set,
4090 enum isl_dim_type type, unsigned pos);
4091 isl_bool isl_set_dim_has_upper_bound(
4092 __isl_keep isl_set *set,
4093 enum isl_dim_type type, unsigned pos);
4097 To check whether a set is a parameter domain, use this function:
4099 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4100 isl_bool isl_union_set_is_params(
4101 __isl_keep isl_union_set *uset);
4105 The following functions check whether the space of the given
4106 (basic) set or relation domain and/or range is a wrapped relation.
4108 #include <isl/space.h>
4109 isl_bool isl_space_is_wrapping(
4110 __isl_keep isl_space *space);
4111 isl_bool isl_space_domain_is_wrapping(
4112 __isl_keep isl_space *space);
4113 isl_bool isl_space_range_is_wrapping(
4114 __isl_keep isl_space *space);
4115 isl_bool isl_space_is_product(
4116 __isl_keep isl_space *space);
4118 #include <isl/set.h>
4119 isl_bool isl_basic_set_is_wrapping(
4120 __isl_keep isl_basic_set *bset);
4121 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4123 #include <isl/map.h>
4124 isl_bool isl_map_domain_is_wrapping(
4125 __isl_keep isl_map *map);
4126 isl_bool isl_map_range_is_wrapping(
4127 __isl_keep isl_map *map);
4128 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4130 #include <isl/val.h>
4131 isl_bool isl_multi_val_range_is_wrapping(
4132 __isl_keep isl_multi_val *mv);
4134 #include <isl/aff.h>
4135 isl_bool isl_multi_aff_range_is_wrapping(
4136 __isl_keep isl_multi_aff *ma);
4137 isl_bool isl_multi_pw_aff_range_is_wrapping(
4138 __isl_keep isl_multi_pw_aff *mpa);
4139 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4140 __isl_keep isl_multi_union_pw_aff *mupa);
4142 The input to C<isl_space_is_wrapping> should
4143 be the space of a set, while that of
4144 C<isl_space_domain_is_wrapping> and
4145 C<isl_space_range_is_wrapping> should be the space of a relation.
4146 The input to C<isl_space_is_product> can be either the space
4147 of a set or that of a binary relation.
4148 In case the input is the space of a binary relation, it checks
4149 whether both domain and range are wrapping.
4151 =item * Internal Product
4153 isl_bool isl_basic_map_can_zip(
4154 __isl_keep isl_basic_map *bmap);
4155 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4157 Check whether the product of domain and range of the given relation
4159 i.e., whether both domain and range are nested relations.
4163 #include <isl/space.h>
4164 isl_bool isl_space_can_curry(
4165 __isl_keep isl_space *space);
4167 #include <isl/map.h>
4168 isl_bool isl_basic_map_can_curry(
4169 __isl_keep isl_basic_map *bmap);
4170 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4172 Check whether the domain of the (basic) relation is a wrapped relation.
4174 #include <isl/space.h>
4175 __isl_give isl_space *isl_space_uncurry(
4176 __isl_take isl_space *space);
4178 #include <isl/map.h>
4179 isl_bool isl_basic_map_can_uncurry(
4180 __isl_keep isl_basic_map *bmap);
4181 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4183 Check whether the range of the (basic) relation is a wrapped relation.
4185 #include <isl/space.h>
4186 isl_bool isl_space_can_range_curry(
4187 __isl_keep isl_space *space);
4189 #include <isl/map.h>
4190 isl_bool isl_map_can_range_curry(
4191 __isl_keep isl_map *map);
4193 Check whether the domain of the relation wrapped in the range of
4194 the input is itself a wrapped relation.
4196 =item * Special Values
4198 #include <isl/aff.h>
4199 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4200 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4201 isl_bool isl_multi_pw_aff_is_cst(
4202 __isl_keep isl_multi_pw_aff *mpa);
4204 Check whether the given expression is a constant.
4206 #include <isl/val.h>
4207 isl_bool isl_multi_val_involves_nan(
4208 __isl_keep isl_multi_val *mv);
4210 #include <isl/aff.h>
4211 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4212 isl_bool isl_multi_aff_involves_nan(
4213 __isl_keep isl_multi_aff *ma);
4214 isl_bool isl_pw_aff_involves_nan(
4215 __isl_keep isl_pw_aff *pa);
4216 isl_bool isl_pw_multi_aff_involves_nan(
4217 __isl_keep isl_pw_multi_aff *pma);
4218 isl_bool isl_multi_pw_aff_involves_nan(
4219 __isl_keep isl_multi_pw_aff *mpa);
4220 isl_bool isl_union_pw_aff_involves_nan(
4221 __isl_keep isl_union_pw_aff *upa);
4222 isl_bool isl_union_pw_multi_aff_involves_nan(
4223 __isl_keep isl_union_pw_multi_aff *upma);
4224 isl_bool isl_multi_union_pw_aff_involves_nan(
4225 __isl_keep isl_multi_union_pw_aff *mupa);
4227 #include <isl/polynomial.h>
4228 isl_bool isl_qpolynomial_is_nan(
4229 __isl_keep isl_qpolynomial *qp);
4230 isl_bool isl_qpolynomial_fold_is_nan(
4231 __isl_keep isl_qpolynomial_fold *fold);
4232 isl_bool isl_pw_qpolynomial_involves_nan(
4233 __isl_keep isl_pw_qpolynomial *pwqp);
4234 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4235 __isl_keep isl_pw_qpolynomial_fold *pwf);
4236 isl_bool isl_union_pw_qpolynomial_involves_nan(
4237 __isl_keep isl_union_pw_qpolynomial *upwqp);
4238 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4239 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4241 Check whether the given expression is equal to or involves NaN.
4243 #include <isl/aff.h>
4244 isl_bool isl_aff_plain_is_zero(
4245 __isl_keep isl_aff *aff);
4247 Check whether the affine expression is obviously zero.
4251 =head3 Binary Properties
4257 The following functions check whether two objects
4258 represent the same set, relation or function.
4259 The C<plain> variants only return true if the objects
4260 are obviously the same. That is, they may return false
4261 even if the objects are the same, but they will never
4262 return true if the objects are not the same.
4264 #include <isl/set.h>
4265 isl_bool isl_basic_set_plain_is_equal(
4266 __isl_keep isl_basic_set *bset1,
4267 __isl_keep isl_basic_set *bset2);
4268 isl_bool isl_basic_set_is_equal(
4269 __isl_keep isl_basic_set *bset1,
4270 __isl_keep isl_basic_set *bset2);
4271 isl_bool isl_set_plain_is_equal(
4272 __isl_keep isl_set *set1,
4273 __isl_keep isl_set *set2);
4274 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4275 __isl_keep isl_set *set2);
4277 #include <isl/map.h>
4278 isl_bool isl_basic_map_is_equal(
4279 __isl_keep isl_basic_map *bmap1,
4280 __isl_keep isl_basic_map *bmap2);
4281 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4282 __isl_keep isl_map *map2);
4283 isl_bool isl_map_plain_is_equal(
4284 __isl_keep isl_map *map1,
4285 __isl_keep isl_map *map2);
4287 #include <isl/union_set.h>
4288 isl_bool isl_union_set_is_equal(
4289 __isl_keep isl_union_set *uset1,
4290 __isl_keep isl_union_set *uset2);
4292 #include <isl/union_map.h>
4293 isl_bool isl_union_map_is_equal(
4294 __isl_keep isl_union_map *umap1,
4295 __isl_keep isl_union_map *umap2);
4297 #include <isl/aff.h>
4298 isl_bool isl_aff_plain_is_equal(
4299 __isl_keep isl_aff *aff1,
4300 __isl_keep isl_aff *aff2);
4301 isl_bool isl_multi_aff_plain_is_equal(
4302 __isl_keep isl_multi_aff *maff1,
4303 __isl_keep isl_multi_aff *maff2);
4304 isl_bool isl_pw_aff_plain_is_equal(
4305 __isl_keep isl_pw_aff *pwaff1,
4306 __isl_keep isl_pw_aff *pwaff2);
4307 isl_bool isl_pw_aff_is_equal(
4308 __isl_keep isl_pw_aff *pa1,
4309 __isl_keep isl_pw_aff *pa2);
4310 isl_bool isl_pw_multi_aff_plain_is_equal(
4311 __isl_keep isl_pw_multi_aff *pma1,
4312 __isl_keep isl_pw_multi_aff *pma2);
4313 isl_bool isl_pw_multi_aff_is_equal(
4314 __isl_keep isl_pw_multi_aff *pma1,
4315 __isl_keep isl_pw_multi_aff *pma2);
4316 isl_bool isl_multi_pw_aff_plain_is_equal(
4317 __isl_keep isl_multi_pw_aff *mpa1,
4318 __isl_keep isl_multi_pw_aff *mpa2);
4319 isl_bool isl_multi_pw_aff_is_equal(
4320 __isl_keep isl_multi_pw_aff *mpa1,
4321 __isl_keep isl_multi_pw_aff *mpa2);
4322 isl_bool isl_union_pw_aff_plain_is_equal(
4323 __isl_keep isl_union_pw_aff *upa1,
4324 __isl_keep isl_union_pw_aff *upa2);
4325 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4326 __isl_keep isl_union_pw_multi_aff *upma1,
4327 __isl_keep isl_union_pw_multi_aff *upma2);
4328 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4329 __isl_keep isl_multi_union_pw_aff *mupa1,
4330 __isl_keep isl_multi_union_pw_aff *mupa2);
4332 #include <isl/polynomial.h>
4333 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4334 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4335 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4336 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4337 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4338 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4340 =item * Disjointness
4342 #include <isl/set.h>
4343 isl_bool isl_basic_set_is_disjoint(
4344 __isl_keep isl_basic_set *bset1,
4345 __isl_keep isl_basic_set *bset2);
4346 isl_bool isl_set_plain_is_disjoint(
4347 __isl_keep isl_set *set1,
4348 __isl_keep isl_set *set2);
4349 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4350 __isl_keep isl_set *set2);
4352 #include <isl/map.h>
4353 isl_bool isl_basic_map_is_disjoint(
4354 __isl_keep isl_basic_map *bmap1,
4355 __isl_keep isl_basic_map *bmap2);
4356 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4357 __isl_keep isl_map *map2);
4359 #include <isl/union_set.h>
4360 isl_bool isl_union_set_is_disjoint(
4361 __isl_keep isl_union_set *uset1,
4362 __isl_keep isl_union_set *uset2);
4364 #include <isl/union_map.h>
4365 isl_bool isl_union_map_is_disjoint(
4366 __isl_keep isl_union_map *umap1,
4367 __isl_keep isl_union_map *umap2);
4371 isl_bool isl_basic_set_is_subset(
4372 __isl_keep isl_basic_set *bset1,
4373 __isl_keep isl_basic_set *bset2);
4374 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4375 __isl_keep isl_set *set2);
4376 isl_bool isl_set_is_strict_subset(
4377 __isl_keep isl_set *set1,
4378 __isl_keep isl_set *set2);
4379 isl_bool isl_union_set_is_subset(
4380 __isl_keep isl_union_set *uset1,
4381 __isl_keep isl_union_set *uset2);
4382 isl_bool isl_union_set_is_strict_subset(
4383 __isl_keep isl_union_set *uset1,
4384 __isl_keep isl_union_set *uset2);
4385 isl_bool isl_basic_map_is_subset(
4386 __isl_keep isl_basic_map *bmap1,
4387 __isl_keep isl_basic_map *bmap2);
4388 isl_bool isl_basic_map_is_strict_subset(
4389 __isl_keep isl_basic_map *bmap1,
4390 __isl_keep isl_basic_map *bmap2);
4391 isl_bool isl_map_is_subset(
4392 __isl_keep isl_map *map1,
4393 __isl_keep isl_map *map2);
4394 isl_bool isl_map_is_strict_subset(
4395 __isl_keep isl_map *map1,
4396 __isl_keep isl_map *map2);
4397 isl_bool isl_union_map_is_subset(
4398 __isl_keep isl_union_map *umap1,
4399 __isl_keep isl_union_map *umap2);
4400 isl_bool isl_union_map_is_strict_subset(
4401 __isl_keep isl_union_map *umap1,
4402 __isl_keep isl_union_map *umap2);
4404 Check whether the first argument is a (strict) subset of the
4409 Every comparison function returns a negative value if the first
4410 argument is considered smaller than the second, a positive value
4411 if the first argument is considered greater and zero if the two
4412 constraints are considered the same by the comparison criterion.
4414 #include <isl/constraint.h>
4415 int isl_constraint_plain_cmp(
4416 __isl_keep isl_constraint *c1,
4417 __isl_keep isl_constraint *c2);
4419 This function is useful for sorting C<isl_constraint>s.
4420 The order depends on the internal representation of the inputs.
4421 The order is fixed over different calls to the function (assuming
4422 the internal representation of the inputs has not changed), but may
4423 change over different versions of C<isl>.
4425 #include <isl/constraint.h>
4426 int isl_constraint_cmp_last_non_zero(
4427 __isl_keep isl_constraint *c1,
4428 __isl_keep isl_constraint *c2);
4430 This function can be used to sort constraints that live in the same
4431 local space. Constraints that involve ``earlier'' dimensions or
4432 that have a smaller coefficient for the shared latest dimension
4433 are considered smaller than other constraints.
4434 This function only defines a B<partial> order.
4436 #include <isl/set.h>
4437 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4438 __isl_keep isl_set *set2);
4440 This function is useful for sorting C<isl_set>s.
4441 The order depends on the internal representation of the inputs.
4442 The order is fixed over different calls to the function (assuming
4443 the internal representation of the inputs has not changed), but may
4444 change over different versions of C<isl>.
4446 #include <isl/aff.h>
4447 int isl_multi_aff_plain_cmp(
4448 __isl_keep isl_multi_aff *ma1,
4449 __isl_keep isl_multi_aff *ma2);
4450 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4451 __isl_keep isl_pw_aff *pa2);
4453 The functions C<isl_multi_aff_plain_cmp> and
4454 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4455 C<isl_pw_aff>s. The order is not strictly defined.
4456 The current order sorts expressions that only involve
4457 earlier dimensions before those that involve later dimensions.
4461 =head2 Unary Operations
4467 __isl_give isl_set *isl_set_complement(
4468 __isl_take isl_set *set);
4469 __isl_give isl_map *isl_map_complement(
4470 __isl_take isl_map *map);
4474 #include <isl/space.h>
4475 __isl_give isl_space *isl_space_reverse(
4476 __isl_take isl_space *space);
4478 #include <isl/map.h>
4479 __isl_give isl_basic_map *isl_basic_map_reverse(
4480 __isl_take isl_basic_map *bmap);
4481 __isl_give isl_map *isl_map_reverse(
4482 __isl_take isl_map *map);
4484 #include <isl/union_map.h>
4485 __isl_give isl_union_map *isl_union_map_reverse(
4486 __isl_take isl_union_map *umap);
4490 #include <isl/space.h>
4491 __isl_give isl_space *isl_space_domain(
4492 __isl_take isl_space *space);
4493 __isl_give isl_space *isl_space_range(
4494 __isl_take isl_space *space);
4495 __isl_give isl_space *isl_space_params(
4496 __isl_take isl_space *space);
4498 #include <isl/local_space.h>
4499 __isl_give isl_local_space *isl_local_space_domain(
4500 __isl_take isl_local_space *ls);
4501 __isl_give isl_local_space *isl_local_space_range(
4502 __isl_take isl_local_space *ls);
4504 #include <isl/set.h>
4505 __isl_give isl_basic_set *isl_basic_set_project_out(
4506 __isl_take isl_basic_set *bset,
4507 enum isl_dim_type type, unsigned first, unsigned n);
4508 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4509 enum isl_dim_type type, unsigned first, unsigned n);
4510 __isl_give isl_map *isl_set_project_onto_map(
4511 __isl_take isl_set *set,
4512 enum isl_dim_type type, unsigned first,
4514 __isl_give isl_basic_set *isl_basic_set_params(
4515 __isl_take isl_basic_set *bset);
4516 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4518 The function C<isl_set_project_onto_map> returns a relation
4519 that projects the input set onto the given set dimensions.
4521 #include <isl/map.h>
4522 __isl_give isl_basic_map *isl_basic_map_project_out(
4523 __isl_take isl_basic_map *bmap,
4524 enum isl_dim_type type, unsigned first, unsigned n);
4525 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4526 enum isl_dim_type type, unsigned first, unsigned n);
4527 __isl_give isl_basic_set *isl_basic_map_domain(
4528 __isl_take isl_basic_map *bmap);
4529 __isl_give isl_basic_set *isl_basic_map_range(
4530 __isl_take isl_basic_map *bmap);
4531 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4532 __isl_give isl_set *isl_map_domain(
4533 __isl_take isl_map *bmap);
4534 __isl_give isl_set *isl_map_range(
4535 __isl_take isl_map *map);
4537 #include <isl/union_set.h>
4538 __isl_give isl_union_set *isl_union_set_project_out(
4539 __isl_take isl_union_set *uset,
4540 enum isl_dim_type type,
4541 unsigned first, unsigned n);
4542 __isl_give isl_set *isl_union_set_params(
4543 __isl_take isl_union_set *uset);
4545 The function C<isl_union_set_project_out> can only project out
4548 #include <isl/union_map.h>
4549 __isl_give isl_union_map *isl_union_map_project_out(
4550 __isl_take isl_union_map *umap,
4551 enum isl_dim_type type, unsigned first, unsigned n);
4552 __isl_give isl_union_map *
4553 isl_union_map_project_out_all_params(
4554 __isl_take isl_union_map *umap);
4555 __isl_give isl_set *isl_union_map_params(
4556 __isl_take isl_union_map *umap);
4557 __isl_give isl_union_set *isl_union_map_domain(
4558 __isl_take isl_union_map *umap);
4559 __isl_give isl_union_set *isl_union_map_range(
4560 __isl_take isl_union_map *umap);
4562 The function C<isl_union_map_project_out> can only project out
4565 #include <isl/aff.h>
4566 __isl_give isl_aff *isl_aff_project_domain_on_params(
4567 __isl_take isl_aff *aff);
4568 __isl_give isl_multi_aff *
4569 isl_multi_aff_project_domain_on_params(
4570 __isl_take isl_multi_aff *ma);
4571 __isl_give isl_pw_aff *
4572 isl_pw_aff_project_domain_on_params(
4573 __isl_take isl_pw_aff *pa);
4574 __isl_give isl_multi_pw_aff *
4575 isl_multi_pw_aff_project_domain_on_params(
4576 __isl_take isl_multi_pw_aff *mpa);
4577 __isl_give isl_pw_multi_aff *
4578 isl_pw_multi_aff_project_domain_on_params(
4579 __isl_take isl_pw_multi_aff *pma);
4580 __isl_give isl_set *isl_pw_aff_domain(
4581 __isl_take isl_pw_aff *pwaff);
4582 __isl_give isl_set *isl_pw_multi_aff_domain(
4583 __isl_take isl_pw_multi_aff *pma);
4584 __isl_give isl_set *isl_multi_pw_aff_domain(
4585 __isl_take isl_multi_pw_aff *mpa);
4586 __isl_give isl_union_set *isl_union_pw_aff_domain(
4587 __isl_take isl_union_pw_aff *upa);
4588 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4589 __isl_take isl_union_pw_multi_aff *upma);
4590 __isl_give isl_union_set *
4591 isl_multi_union_pw_aff_domain(
4592 __isl_take isl_multi_union_pw_aff *mupa);
4593 __isl_give isl_set *isl_pw_aff_params(
4594 __isl_take isl_pw_aff *pwa);
4596 If no explicit domain was set on a zero-dimensional input to
4597 C<isl_multi_union_pw_aff_domain>, then this function will
4598 return a parameter set.
4600 #include <isl/polynomial.h>
4601 __isl_give isl_qpolynomial *
4602 isl_qpolynomial_project_domain_on_params(
4603 __isl_take isl_qpolynomial *qp);
4604 __isl_give isl_pw_qpolynomial *
4605 isl_pw_qpolynomial_project_domain_on_params(
4606 __isl_take isl_pw_qpolynomial *pwqp);
4607 __isl_give isl_pw_qpolynomial_fold *
4608 isl_pw_qpolynomial_fold_project_domain_on_params(
4609 __isl_take isl_pw_qpolynomial_fold *pwf);
4610 __isl_give isl_set *isl_pw_qpolynomial_domain(
4611 __isl_take isl_pw_qpolynomial *pwqp);
4612 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4613 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4614 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4615 __isl_take isl_union_pw_qpolynomial *upwqp);
4617 #include <isl/space.h>
4618 __isl_give isl_space *isl_space_domain_map(
4619 __isl_take isl_space *space);
4620 __isl_give isl_space *isl_space_range_map(
4621 __isl_take isl_space *space);
4623 #include <isl/map.h>
4624 __isl_give isl_map *isl_set_wrapped_domain_map(
4625 __isl_take isl_set *set);
4626 __isl_give isl_basic_map *isl_basic_map_domain_map(
4627 __isl_take isl_basic_map *bmap);
4628 __isl_give isl_basic_map *isl_basic_map_range_map(
4629 __isl_take isl_basic_map *bmap);
4630 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4631 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4633 #include <isl/union_map.h>
4634 __isl_give isl_union_map *isl_union_map_domain_map(
4635 __isl_take isl_union_map *umap);
4636 __isl_give isl_union_pw_multi_aff *
4637 isl_union_map_domain_map_union_pw_multi_aff(
4638 __isl_take isl_union_map *umap);
4639 __isl_give isl_union_map *isl_union_map_range_map(
4640 __isl_take isl_union_map *umap);
4641 __isl_give isl_union_map *
4642 isl_union_set_wrapped_domain_map(
4643 __isl_take isl_union_set *uset);
4645 The functions above construct a (basic, regular or union) relation
4646 that maps (a wrapped version of) the input relation to its domain or range.
4647 C<isl_set_wrapped_domain_map> maps the input set to the domain
4648 of its wrapped relation.
4652 __isl_give isl_basic_set *isl_basic_set_eliminate(
4653 __isl_take isl_basic_set *bset,
4654 enum isl_dim_type type,
4655 unsigned first, unsigned n);
4656 __isl_give isl_set *isl_set_eliminate(
4657 __isl_take isl_set *set, enum isl_dim_type type,
4658 unsigned first, unsigned n);
4659 __isl_give isl_basic_map *isl_basic_map_eliminate(
4660 __isl_take isl_basic_map *bmap,
4661 enum isl_dim_type type,
4662 unsigned first, unsigned n);
4663 __isl_give isl_map *isl_map_eliminate(
4664 __isl_take isl_map *map, enum isl_dim_type type,
4665 unsigned first, unsigned n);
4667 Eliminate the coefficients for the given dimensions from the constraints,
4668 without removing the dimensions.
4670 =item * Constructing a set from a parameter domain
4672 A zero-dimensional (local) space or (basic) set can be constructed
4673 on a given parameter domain using the following functions.
4675 #include <isl/space.h>
4676 __isl_give isl_space *isl_space_set_from_params(
4677 __isl_take isl_space *space);
4679 #include <isl/local_space.h>
4680 __isl_give isl_local_space *
4681 isl_local_space_set_from_params(
4682 __isl_take isl_local_space *ls);
4684 #include <isl/set.h>
4685 __isl_give isl_basic_set *isl_basic_set_from_params(
4686 __isl_take isl_basic_set *bset);
4687 __isl_give isl_set *isl_set_from_params(
4688 __isl_take isl_set *set);
4690 =item * Constructing a relation from one or two sets
4692 Create a relation with the given set(s) as domain and/or range.
4693 If only the domain or the range is specified, then
4694 the range or domain of the created relation is a zero-dimensional
4695 flat anonymous space.
4697 #include <isl/space.h>
4698 __isl_give isl_space *isl_space_from_domain(
4699 __isl_take isl_space *space);
4700 __isl_give isl_space *isl_space_from_range(
4701 __isl_take isl_space *space);
4702 __isl_give isl_space *isl_space_map_from_set(
4703 __isl_take isl_space *space);
4704 __isl_give isl_space *isl_space_map_from_domain_and_range(
4705 __isl_take isl_space *domain,
4706 __isl_take isl_space *range);
4708 #include <isl/local_space.h>
4709 __isl_give isl_local_space *isl_local_space_from_domain(
4710 __isl_take isl_local_space *ls);
4712 #include <isl/map.h>
4713 __isl_give isl_map *isl_map_from_domain(
4714 __isl_take isl_set *set);
4715 __isl_give isl_map *isl_map_from_range(
4716 __isl_take isl_set *set);
4718 #include <isl/union_map.h>
4719 __isl_give isl_union_map *isl_union_map_from_domain(
4720 __isl_take isl_union_set *uset);
4721 __isl_give isl_union_map *isl_union_map_from_range(
4722 __isl_take isl_union_set *uset);
4723 __isl_give isl_union_map *
4724 isl_union_map_from_domain_and_range(
4725 __isl_take isl_union_set *domain,
4726 __isl_take isl_union_set *range);
4728 #include <isl/val.h>
4729 __isl_give isl_multi_val *isl_multi_val_from_range(
4730 __isl_take isl_multi_val *mv);
4732 #include <isl/aff.h>
4733 __isl_give isl_aff *isl_aff_from_range(
4734 __isl_take isl_aff *aff);
4735 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4736 __isl_take isl_multi_aff *ma);
4737 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4738 __isl_take isl_pw_aff *pwa);
4739 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4740 __isl_take isl_multi_pw_aff *mpa);
4741 __isl_give isl_multi_union_pw_aff *
4742 isl_multi_union_pw_aff_from_range(
4743 __isl_take isl_multi_union_pw_aff *mupa);
4744 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4745 __isl_take isl_set *set);
4746 __isl_give isl_union_pw_multi_aff *
4747 isl_union_pw_multi_aff_from_domain(
4748 __isl_take isl_union_set *uset);
4750 #include <isl/polynomial.h>
4751 __isl_give isl_pw_qpolynomial *
4752 isl_pw_qpolynomial_from_range(
4753 __isl_take isl_pw_qpolynomial *pwqp);
4754 __isl_give isl_pw_qpolynomial_fold *
4755 isl_pw_qpolynomial_fold_from_range(
4756 __isl_take isl_pw_qpolynomial_fold *pwf);
4760 #include <isl/set.h>
4761 __isl_give isl_basic_set *isl_basic_set_fix_si(
4762 __isl_take isl_basic_set *bset,
4763 enum isl_dim_type type, unsigned pos, int value);
4764 __isl_give isl_basic_set *isl_basic_set_fix_val(
4765 __isl_take isl_basic_set *bset,
4766 enum isl_dim_type type, unsigned pos,
4767 __isl_take isl_val *v);
4768 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4769 enum isl_dim_type type, unsigned pos, int value);
4770 __isl_give isl_set *isl_set_fix_val(
4771 __isl_take isl_set *set,
4772 enum isl_dim_type type, unsigned pos,
4773 __isl_take isl_val *v);
4775 #include <isl/map.h>
4776 __isl_give isl_basic_map *isl_basic_map_fix_si(
4777 __isl_take isl_basic_map *bmap,
4778 enum isl_dim_type type, unsigned pos, int value);
4779 __isl_give isl_basic_map *isl_basic_map_fix_val(
4780 __isl_take isl_basic_map *bmap,
4781 enum isl_dim_type type, unsigned pos,
4782 __isl_take isl_val *v);
4783 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4784 enum isl_dim_type type, unsigned pos, int value);
4785 __isl_give isl_map *isl_map_fix_val(
4786 __isl_take isl_map *map,
4787 enum isl_dim_type type, unsigned pos,
4788 __isl_take isl_val *v);
4790 #include <isl/aff.h>
4791 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4792 __isl_take isl_pw_multi_aff *pma,
4793 enum isl_dim_type type, unsigned pos, int value);
4795 #include <isl/polynomial.h>
4796 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4797 __isl_take isl_pw_qpolynomial *pwqp,
4798 enum isl_dim_type type, unsigned n,
4799 __isl_take isl_val *v);
4800 __isl_give isl_pw_qpolynomial_fold *
4801 isl_pw_qpolynomial_fold_fix_val(
4802 __isl_take isl_pw_qpolynomial_fold *pwf,
4803 enum isl_dim_type type, unsigned n,
4804 __isl_take isl_val *v);
4806 Intersect the set, relation or function domain
4807 with the hyperplane where the given
4808 dimension has the fixed given value.
4810 #include <isl/set.h>
4811 __isl_give isl_basic_set *
4812 isl_basic_set_lower_bound_val(
4813 __isl_take isl_basic_set *bset,
4814 enum isl_dim_type type, unsigned pos,
4815 __isl_take isl_val *value);
4816 __isl_give isl_basic_set *
4817 isl_basic_set_upper_bound_val(
4818 __isl_take isl_basic_set *bset,
4819 enum isl_dim_type type, unsigned pos,
4820 __isl_take isl_val *value);
4821 __isl_give isl_set *isl_set_lower_bound_si(
4822 __isl_take isl_set *set,
4823 enum isl_dim_type type, unsigned pos, int value);
4824 __isl_give isl_set *isl_set_lower_bound_val(
4825 __isl_take isl_set *set,
4826 enum isl_dim_type type, unsigned pos,
4827 __isl_take isl_val *value);
4828 __isl_give isl_set *isl_set_upper_bound_si(
4829 __isl_take isl_set *set,
4830 enum isl_dim_type type, unsigned pos, int value);
4831 __isl_give isl_set *isl_set_upper_bound_val(
4832 __isl_take isl_set *set,
4833 enum isl_dim_type type, unsigned pos,
4834 __isl_take isl_val *value);
4836 #include <isl/map.h>
4837 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4838 __isl_take isl_basic_map *bmap,
4839 enum isl_dim_type type, unsigned pos, int value);
4840 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4841 __isl_take isl_basic_map *bmap,
4842 enum isl_dim_type type, unsigned pos, int value);
4843 __isl_give isl_map *isl_map_lower_bound_si(
4844 __isl_take isl_map *map,
4845 enum isl_dim_type type, unsigned pos, int value);
4846 __isl_give isl_map *isl_map_upper_bound_si(
4847 __isl_take isl_map *map,
4848 enum isl_dim_type type, unsigned pos, int value);
4850 Intersect the set or relation with the half-space where the given
4851 dimension has a value bounded by the fixed given integer value.
4853 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4854 enum isl_dim_type type1, int pos1,
4855 enum isl_dim_type type2, int pos2);
4856 __isl_give isl_basic_map *isl_basic_map_equate(
4857 __isl_take isl_basic_map *bmap,
4858 enum isl_dim_type type1, int pos1,
4859 enum isl_dim_type type2, int pos2);
4860 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4861 enum isl_dim_type type1, int pos1,
4862 enum isl_dim_type type2, int pos2);
4864 Intersect the set or relation with the hyperplane where the given
4865 dimensions are equal to each other.
4867 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4868 enum isl_dim_type type1, int pos1,
4869 enum isl_dim_type type2, int pos2);
4871 Intersect the relation with the hyperplane where the given
4872 dimensions have opposite values.
4874 __isl_give isl_map *isl_map_order_le(
4875 __isl_take isl_map *map,
4876 enum isl_dim_type type1, int pos1,
4877 enum isl_dim_type type2, int pos2);
4878 __isl_give isl_basic_map *isl_basic_map_order_ge(
4879 __isl_take isl_basic_map *bmap,
4880 enum isl_dim_type type1, int pos1,
4881 enum isl_dim_type type2, int pos2);
4882 __isl_give isl_map *isl_map_order_ge(
4883 __isl_take isl_map *map,
4884 enum isl_dim_type type1, int pos1,
4885 enum isl_dim_type type2, int pos2);
4886 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4887 enum isl_dim_type type1, int pos1,
4888 enum isl_dim_type type2, int pos2);
4889 __isl_give isl_basic_map *isl_basic_map_order_gt(
4890 __isl_take isl_basic_map *bmap,
4891 enum isl_dim_type type1, int pos1,
4892 enum isl_dim_type type2, int pos2);
4893 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4894 enum isl_dim_type type1, int pos1,
4895 enum isl_dim_type type2, int pos2);
4897 Intersect the relation with the half-space where the given
4898 dimensions satisfy the given ordering.
4900 #include <isl/union_set.h>
4901 __isl_give isl_union_map *isl_union_map_remove_map_if(
4902 __isl_take isl_union_map *umap,
4903 isl_bool (*fn)(__isl_keep isl_map *map,
4904 void *user), void *user);
4906 This function calls the callback function once for each
4907 pair of spaces for which there are elements in the input.
4908 If the callback returns C<isl_bool_true>, then all those elements
4909 are removed from the result. The only remaining elements in the output
4910 are then those for which the callback returns C<isl_bool_false>.
4914 #include <isl/aff.h>
4915 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4916 __isl_take isl_aff *aff);
4917 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4918 __isl_take isl_aff *aff);
4919 __isl_give isl_set *isl_pw_aff_pos_set(
4920 __isl_take isl_pw_aff *pa);
4921 __isl_give isl_set *isl_pw_aff_nonneg_set(
4922 __isl_take isl_pw_aff *pwaff);
4923 __isl_give isl_set *isl_pw_aff_zero_set(
4924 __isl_take isl_pw_aff *pwaff);
4925 __isl_give isl_set *isl_pw_aff_non_zero_set(
4926 __isl_take isl_pw_aff *pwaff);
4927 __isl_give isl_union_set *
4928 isl_union_pw_aff_zero_union_set(
4929 __isl_take isl_union_pw_aff *upa);
4930 __isl_give isl_union_set *
4931 isl_multi_union_pw_aff_zero_union_set(
4932 __isl_take isl_multi_union_pw_aff *mupa);
4934 The function C<isl_aff_neg_basic_set> returns a basic set
4935 containing those elements in the domain space
4936 of C<aff> where C<aff> is negative.
4937 The function C<isl_pw_aff_nonneg_set> returns a set
4938 containing those elements in the domain
4939 of C<pwaff> where C<pwaff> is non-negative.
4940 The function C<isl_multi_union_pw_aff_zero_union_set>
4941 returns a union set containing those elements
4942 in the domains of its elements where they are all zero.
4946 __isl_give isl_map *isl_set_identity(
4947 __isl_take isl_set *set);
4948 __isl_give isl_union_map *isl_union_set_identity(
4949 __isl_take isl_union_set *uset);
4950 __isl_give isl_union_pw_multi_aff *
4951 isl_union_set_identity_union_pw_multi_aff(
4952 __isl_take isl_union_set *uset);
4954 Construct an identity relation on the given (union) set.
4956 =item * Function Extraction
4958 A piecewise quasi affine expression that is equal to 1 on a set
4959 and 0 outside the set can be created using the following function.
4961 #include <isl/aff.h>
4962 __isl_give isl_pw_aff *isl_set_indicator_function(
4963 __isl_take isl_set *set);
4965 A piecewise multiple quasi affine expression can be extracted
4966 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4967 and the C<isl_map> is single-valued.
4968 In case of a conversion from an C<isl_union_map>
4969 to an C<isl_union_pw_multi_aff>, these properties need to hold
4970 in each domain space.
4971 A conversion to a C<isl_multi_union_pw_aff> additionally
4972 requires that the input is non-empty and involves only a single
4975 #include <isl/aff.h>
4976 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4977 __isl_take isl_set *set);
4978 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4979 __isl_take isl_map *map);
4981 __isl_give isl_union_pw_multi_aff *
4982 isl_union_pw_multi_aff_from_union_set(
4983 __isl_take isl_union_set *uset);
4984 __isl_give isl_union_pw_multi_aff *
4985 isl_union_pw_multi_aff_from_union_map(
4986 __isl_take isl_union_map *umap);
4988 __isl_give isl_multi_union_pw_aff *
4989 isl_multi_union_pw_aff_from_union_map(
4990 __isl_take isl_union_map *umap);
4994 __isl_give isl_basic_set *isl_basic_map_deltas(
4995 __isl_take isl_basic_map *bmap);
4996 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4997 __isl_give isl_union_set *isl_union_map_deltas(
4998 __isl_take isl_union_map *umap);
5000 These functions return a (basic) set containing the differences
5001 between image elements and corresponding domain elements in the input.
5003 __isl_give isl_basic_map *isl_basic_map_deltas_map(
5004 __isl_take isl_basic_map *bmap);
5005 __isl_give isl_map *isl_map_deltas_map(
5006 __isl_take isl_map *map);
5007 __isl_give isl_union_map *isl_union_map_deltas_map(
5008 __isl_take isl_union_map *umap);
5010 The functions above construct a (basic, regular or union) relation
5011 that maps (a wrapped version of) the input relation to its delta set.
5015 Simplify the representation of a set, relation or functions by trying
5016 to combine pairs of basic sets or relations into a single
5017 basic set or relation.
5019 #include <isl/set.h>
5020 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
5022 #include <isl/map.h>
5023 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5025 #include <isl/union_set.h>
5026 __isl_give isl_union_set *isl_union_set_coalesce(
5027 __isl_take isl_union_set *uset);
5029 #include <isl/union_map.h>
5030 __isl_give isl_union_map *isl_union_map_coalesce(
5031 __isl_take isl_union_map *umap);
5033 #include <isl/aff.h>
5034 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5035 __isl_take isl_pw_aff *pwqp);
5036 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5037 __isl_take isl_pw_multi_aff *pma);
5038 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5039 __isl_take isl_multi_pw_aff *mpa);
5040 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5041 __isl_take isl_union_pw_aff *upa);
5042 __isl_give isl_union_pw_multi_aff *
5043 isl_union_pw_multi_aff_coalesce(
5044 __isl_take isl_union_pw_multi_aff *upma);
5045 __isl_give isl_multi_union_pw_aff *
5046 isl_multi_union_pw_aff_coalesce(
5047 __isl_take isl_multi_union_pw_aff *aff);
5049 #include <isl/polynomial.h>
5050 __isl_give isl_pw_qpolynomial_fold *
5051 isl_pw_qpolynomial_fold_coalesce(
5052 __isl_take isl_pw_qpolynomial_fold *pwf);
5053 __isl_give isl_union_pw_qpolynomial *
5054 isl_union_pw_qpolynomial_coalesce(
5055 __isl_take isl_union_pw_qpolynomial *upwqp);
5056 __isl_give isl_union_pw_qpolynomial_fold *
5057 isl_union_pw_qpolynomial_fold_coalesce(
5058 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5060 One of the methods for combining pairs of basic sets or relations
5061 can result in coefficients that are much larger than those that appear
5062 in the constraints of the input. By default, the coefficients are
5063 not allowed to grow larger, but this can be changed by unsetting
5064 the following option.
5066 isl_stat isl_options_set_coalesce_bounded_wrapping(
5067 isl_ctx *ctx, int val);
5068 int isl_options_get_coalesce_bounded_wrapping(
5071 =item * Detecting equalities
5073 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5074 __isl_take isl_basic_set *bset);
5075 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5076 __isl_take isl_basic_map *bmap);
5077 __isl_give isl_set *isl_set_detect_equalities(
5078 __isl_take isl_set *set);
5079 __isl_give isl_map *isl_map_detect_equalities(
5080 __isl_take isl_map *map);
5081 __isl_give isl_union_set *isl_union_set_detect_equalities(
5082 __isl_take isl_union_set *uset);
5083 __isl_give isl_union_map *isl_union_map_detect_equalities(
5084 __isl_take isl_union_map *umap);
5086 Simplify the representation of a set or relation by detecting implicit
5089 =item * Removing redundant constraints
5091 #include <isl/set.h>
5092 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5093 __isl_take isl_basic_set *bset);
5094 __isl_give isl_set *isl_set_remove_redundancies(
5095 __isl_take isl_set *set);
5097 #include <isl/union_set.h>
5098 __isl_give isl_union_set *
5099 isl_union_set_remove_redundancies(
5100 __isl_take isl_union_set *uset);
5102 #include <isl/map.h>
5103 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5104 __isl_take isl_basic_map *bmap);
5105 __isl_give isl_map *isl_map_remove_redundancies(
5106 __isl_take isl_map *map);
5108 #include <isl/union_map.h>
5109 __isl_give isl_union_map *
5110 isl_union_map_remove_redundancies(
5111 __isl_take isl_union_map *umap);
5115 __isl_give isl_basic_set *isl_set_convex_hull(
5116 __isl_take isl_set *set);
5117 __isl_give isl_basic_map *isl_map_convex_hull(
5118 __isl_take isl_map *map);
5120 If the input set or relation has any existentially quantified
5121 variables, then the result of these operations is currently undefined.
5125 #include <isl/set.h>
5126 __isl_give isl_basic_set *
5127 isl_set_unshifted_simple_hull(
5128 __isl_take isl_set *set);
5129 __isl_give isl_basic_set *isl_set_simple_hull(
5130 __isl_take isl_set *set);
5131 __isl_give isl_basic_set *
5132 isl_set_plain_unshifted_simple_hull(
5133 __isl_take isl_set *set);
5134 __isl_give isl_basic_set *
5135 isl_set_unshifted_simple_hull_from_set_list(
5136 __isl_take isl_set *set,
5137 __isl_take isl_set_list *list);
5139 #include <isl/map.h>
5140 __isl_give isl_basic_map *
5141 isl_map_unshifted_simple_hull(
5142 __isl_take isl_map *map);
5143 __isl_give isl_basic_map *isl_map_simple_hull(
5144 __isl_take isl_map *map);
5145 __isl_give isl_basic_map *
5146 isl_map_plain_unshifted_simple_hull(
5147 __isl_take isl_map *map);
5148 __isl_give isl_basic_map *
5149 isl_map_unshifted_simple_hull_from_map_list(
5150 __isl_take isl_map *map,
5151 __isl_take isl_map_list *list);
5153 #include <isl/union_map.h>
5154 __isl_give isl_union_map *isl_union_map_simple_hull(
5155 __isl_take isl_union_map *umap);
5157 These functions compute a single basic set or relation
5158 that contains the whole input set or relation.
5159 In particular, the output is described by translates
5160 of the constraints describing the basic sets or relations in the input.
5161 In case of C<isl_set_unshifted_simple_hull>, only the original
5162 constraints are used, without any translation.
5163 In case of C<isl_set_plain_unshifted_simple_hull> and
5164 C<isl_map_plain_unshifted_simple_hull>, the result is described
5165 by original constraints that are obviously satisfied
5166 by the entire input set or relation.
5167 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5168 C<isl_map_unshifted_simple_hull_from_map_list>, the
5169 constraints are taken from the elements of the second argument.
5173 (See \autoref{s:simple hull}.)
5179 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5180 __isl_take isl_basic_set *bset);
5181 __isl_give isl_basic_set *isl_set_affine_hull(
5182 __isl_take isl_set *set);
5183 __isl_give isl_union_set *isl_union_set_affine_hull(
5184 __isl_take isl_union_set *uset);
5185 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5186 __isl_take isl_basic_map *bmap);
5187 __isl_give isl_basic_map *isl_map_affine_hull(
5188 __isl_take isl_map *map);
5189 __isl_give isl_union_map *isl_union_map_affine_hull(
5190 __isl_take isl_union_map *umap);
5192 In case of union sets and relations, the affine hull is computed
5195 =item * Polyhedral hull
5197 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5198 __isl_take isl_set *set);
5199 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5200 __isl_take isl_map *map);
5201 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5202 __isl_take isl_union_set *uset);
5203 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5204 __isl_take isl_union_map *umap);
5206 These functions compute a single basic set or relation
5207 not involving any existentially quantified variables
5208 that contains the whole input set or relation.
5209 In case of union sets and relations, the polyhedral hull is computed
5212 =item * Other approximations
5214 #include <isl/set.h>
5215 __isl_give isl_basic_set *
5216 isl_basic_set_drop_constraints_involving_dims(
5217 __isl_take isl_basic_set *bset,
5218 enum isl_dim_type type,
5219 unsigned first, unsigned n);
5220 __isl_give isl_basic_set *
5221 isl_basic_set_drop_constraints_not_involving_dims(
5222 __isl_take isl_basic_set *bset,
5223 enum isl_dim_type type,
5224 unsigned first, unsigned n);
5225 __isl_give isl_set *
5226 isl_set_drop_constraints_involving_dims(
5227 __isl_take isl_set *set,
5228 enum isl_dim_type type,
5229 unsigned first, unsigned n);
5230 __isl_give isl_set *
5231 isl_set_drop_constraints_not_involving_dims(
5232 __isl_take isl_set *set,
5233 enum isl_dim_type type,
5234 unsigned first, unsigned n);
5236 #include <isl/map.h>
5237 __isl_give isl_basic_map *
5238 isl_basic_map_drop_constraints_involving_dims(
5239 __isl_take isl_basic_map *bmap,
5240 enum isl_dim_type type,
5241 unsigned first, unsigned n);
5242 __isl_give isl_basic_map *
5243 isl_basic_map_drop_constraints_not_involving_dims(
5244 __isl_take isl_basic_map *bmap,
5245 enum isl_dim_type type,
5246 unsigned first, unsigned n);
5247 __isl_give isl_map *
5248 isl_map_drop_constraints_involving_dims(
5249 __isl_take isl_map *map,
5250 enum isl_dim_type type,
5251 unsigned first, unsigned n);
5252 __isl_give isl_map *
5253 isl_map_drop_constraints_not_involving_dims(
5254 __isl_take isl_map *map,
5255 enum isl_dim_type type,
5256 unsigned first, unsigned n);
5258 These functions drop any constraints (not) involving the specified dimensions.
5259 Note that the result depends on the representation of the input.
5261 #include <isl/polynomial.h>
5262 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5263 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5264 __isl_give isl_union_pw_qpolynomial *
5265 isl_union_pw_qpolynomial_to_polynomial(
5266 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5268 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5269 the polynomial will be an overapproximation. If C<sign> is negative,
5270 it will be an underapproximation. If C<sign> is zero, the approximation
5271 will lie somewhere in between.
5275 __isl_give isl_basic_set *isl_basic_set_sample(
5276 __isl_take isl_basic_set *bset);
5277 __isl_give isl_basic_set *isl_set_sample(
5278 __isl_take isl_set *set);
5279 __isl_give isl_basic_map *isl_basic_map_sample(
5280 __isl_take isl_basic_map *bmap);
5281 __isl_give isl_basic_map *isl_map_sample(
5282 __isl_take isl_map *map);
5284 If the input (basic) set or relation is non-empty, then return
5285 a singleton subset of the input. Otherwise, return an empty set.
5287 =item * Optimization
5289 #include <isl/ilp.h>
5290 __isl_give isl_val *isl_basic_set_max_val(
5291 __isl_keep isl_basic_set *bset,
5292 __isl_keep isl_aff *obj);
5293 __isl_give isl_val *isl_set_min_val(
5294 __isl_keep isl_set *set,
5295 __isl_keep isl_aff *obj);
5296 __isl_give isl_val *isl_set_max_val(
5297 __isl_keep isl_set *set,
5298 __isl_keep isl_aff *obj);
5299 __isl_give isl_multi_val *
5300 isl_union_set_min_multi_union_pw_aff(
5301 __isl_keep isl_union_set *set,
5302 __isl_keep isl_multi_union_pw_aff *obj);
5304 Compute the minimum or maximum of the integer affine expression C<obj>
5305 over the points in C<set>, returning the result in C<opt>.
5306 The result is C<NULL> in case of an error, the optimal value in case
5307 there is one, negative infinity or infinity if the problem is unbounded and
5308 NaN if the problem is empty.
5310 #include <isl/ilp.h>
5311 __isl_give isl_val *isl_basic_set_dim_max_val(
5312 __isl_take isl_basic_set *bset, int pos);
5314 Return the maximal value attained by the given set dimension,
5315 independently of the parameter values and of any other dimensions.
5316 The result is C<NULL> in case of an error, the optimal value in case
5317 there is one, infinity if the problem is unbounded and
5318 NaN if the input is empty.
5320 =item * Parametric optimization
5322 __isl_give isl_pw_aff *isl_set_dim_min(
5323 __isl_take isl_set *set, int pos);
5324 __isl_give isl_pw_aff *isl_set_dim_max(
5325 __isl_take isl_set *set, int pos);
5326 __isl_give isl_pw_aff *isl_map_dim_min(
5327 __isl_take isl_map *map, int pos);
5328 __isl_give isl_pw_aff *isl_map_dim_max(
5329 __isl_take isl_map *map, int pos);
5331 Compute the minimum or maximum of the given set or output dimension
5332 as a function of the parameters (and input dimensions), but independently
5333 of the other set or output dimensions.
5334 For lexicographic optimization, see L<"Lexicographic Optimization">.
5338 The following functions compute either the set of (rational) coefficient
5339 values of valid constraints for the given set or the set of (rational)
5340 values satisfying the constraints with coefficients from the given set.
5341 Internally, these two sets of functions perform essentially the
5342 same operations, except that the set of coefficients is assumed to
5343 be a cone, while the set of values may be any polyhedron.
5344 The current implementation is based on the Farkas lemma and
5345 Fourier-Motzkin elimination, but this may change or be made optional
5346 in future. In particular, future implementations may use different
5347 dualization algorithms or skip the elimination step.
5349 #include <isl/set.h>
5350 __isl_give isl_basic_set *isl_basic_set_coefficients(
5351 __isl_take isl_basic_set *bset);
5352 __isl_give isl_basic_set_list *
5353 isl_basic_set_list_coefficients(
5354 __isl_take isl_basic_set_list *list);
5355 __isl_give isl_basic_set *isl_set_coefficients(
5356 __isl_take isl_set *set);
5357 __isl_give isl_union_set *isl_union_set_coefficients(
5358 __isl_take isl_union_set *bset);
5359 __isl_give isl_basic_set *isl_basic_set_solutions(
5360 __isl_take isl_basic_set *bset);
5361 __isl_give isl_basic_set *isl_set_solutions(
5362 __isl_take isl_set *set);
5363 __isl_give isl_union_set *isl_union_set_solutions(
5364 __isl_take isl_union_set *bset);
5368 __isl_give isl_map *isl_map_fixed_power_val(
5369 __isl_take isl_map *map,
5370 __isl_take isl_val *exp);
5371 __isl_give isl_union_map *
5372 isl_union_map_fixed_power_val(
5373 __isl_take isl_union_map *umap,
5374 __isl_take isl_val *exp);
5376 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5377 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5378 of C<map> is computed.
5380 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5382 __isl_give isl_union_map *isl_union_map_power(
5383 __isl_take isl_union_map *umap, int *exact);
5385 Compute a parametric representation for all positive powers I<k> of C<map>.
5386 The result maps I<k> to a nested relation corresponding to the
5387 I<k>th power of C<map>.
5388 The result may be an overapproximation. If the result is known to be exact,
5389 then C<*exact> is set to C<1>.
5391 =item * Transitive closure
5393 __isl_give isl_map *isl_map_transitive_closure(
5394 __isl_take isl_map *map, int *exact);
5395 __isl_give isl_union_map *isl_union_map_transitive_closure(
5396 __isl_take isl_union_map *umap, int *exact);
5398 Compute the transitive closure of C<map>.
5399 The result may be an overapproximation. If the result is known to be exact,
5400 then C<*exact> is set to C<1>.
5402 =item * Reaching path lengths
5404 __isl_give isl_map *isl_map_reaching_path_lengths(
5405 __isl_take isl_map *map, int *exact);
5407 Compute a relation that maps each element in the range of C<map>
5408 to the lengths of all paths composed of edges in C<map> that
5409 end up in the given element.
5410 The result may be an overapproximation. If the result is known to be exact,
5411 then C<*exact> is set to C<1>.
5412 To compute the I<maximal> path length, the resulting relation
5413 should be postprocessed by C<isl_map_lexmax>.
5414 In particular, if the input relation is a dependence relation
5415 (mapping sources to sinks), then the maximal path length corresponds
5416 to the free schedule.
5417 Note, however, that C<isl_map_lexmax> expects the maximum to be
5418 finite, so if the path lengths are unbounded (possibly due to
5419 the overapproximation), then you will get an error message.
5423 #include <isl/space.h>
5424 __isl_give isl_space *isl_space_wrap(
5425 __isl_take isl_space *space);
5426 __isl_give isl_space *isl_space_unwrap(
5427 __isl_take isl_space *space);
5429 #include <isl/local_space.h>
5430 __isl_give isl_local_space *isl_local_space_wrap(
5431 __isl_take isl_local_space *ls);
5433 #include <isl/set.h>
5434 __isl_give isl_basic_map *isl_basic_set_unwrap(
5435 __isl_take isl_basic_set *bset);
5436 __isl_give isl_map *isl_set_unwrap(
5437 __isl_take isl_set *set);
5439 #include <isl/map.h>
5440 __isl_give isl_basic_set *isl_basic_map_wrap(
5441 __isl_take isl_basic_map *bmap);
5442 __isl_give isl_set *isl_map_wrap(
5443 __isl_take isl_map *map);
5445 #include <isl/union_set.h>
5446 __isl_give isl_union_map *isl_union_set_unwrap(
5447 __isl_take isl_union_set *uset);
5449 #include <isl/union_map.h>
5450 __isl_give isl_union_set *isl_union_map_wrap(
5451 __isl_take isl_union_map *umap);
5453 The input to C<isl_space_unwrap> should
5454 be the space of a set, while that of
5455 C<isl_space_wrap> should be the space of a relation.
5456 Conversely, the output of C<isl_space_unwrap> is the space
5457 of a relation, while that of C<isl_space_wrap> is the space of a set.
5461 Remove any internal structure of domain (and range) of the given
5462 set or relation. If there is any such internal structure in the input,
5463 then the name of the space is also removed.
5465 #include <isl/space.h>
5466 __isl_give isl_space *isl_space_flatten_domain(
5467 __isl_take isl_space *space);
5468 __isl_give isl_space *isl_space_flatten_range(
5469 __isl_take isl_space *space);
5471 #include <isl/local_space.h>
5472 __isl_give isl_local_space *
5473 isl_local_space_flatten_domain(
5474 __isl_take isl_local_space *ls);
5475 __isl_give isl_local_space *
5476 isl_local_space_flatten_range(
5477 __isl_take isl_local_space *ls);
5479 #include <isl/set.h>
5480 __isl_give isl_basic_set *isl_basic_set_flatten(
5481 __isl_take isl_basic_set *bset);
5482 __isl_give isl_set *isl_set_flatten(
5483 __isl_take isl_set *set);
5485 #include <isl/map.h>
5486 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5487 __isl_take isl_basic_map *bmap);
5488 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5489 __isl_take isl_basic_map *bmap);
5490 __isl_give isl_map *isl_map_flatten_range(
5491 __isl_take isl_map *map);
5492 __isl_give isl_map *isl_map_flatten_domain(
5493 __isl_take isl_map *map);
5494 __isl_give isl_basic_map *isl_basic_map_flatten(
5495 __isl_take isl_basic_map *bmap);
5496 __isl_give isl_map *isl_map_flatten(
5497 __isl_take isl_map *map);
5499 #include <isl/val.h>
5500 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5501 __isl_take isl_multi_val *mv);
5503 #include <isl/aff.h>
5504 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5505 __isl_take isl_multi_aff *ma);
5506 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5507 __isl_take isl_multi_aff *ma);
5508 __isl_give isl_multi_pw_aff *
5509 isl_multi_pw_aff_flatten_range(
5510 __isl_take isl_multi_pw_aff *mpa);
5511 __isl_give isl_multi_union_pw_aff *
5512 isl_multi_union_pw_aff_flatten_range(
5513 __isl_take isl_multi_union_pw_aff *mupa);
5515 #include <isl/map.h>
5516 __isl_give isl_map *isl_set_flatten_map(
5517 __isl_take isl_set *set);
5519 The function above constructs a relation
5520 that maps the input set to a flattened version of the set.
5524 Lift the input set to a space with extra dimensions corresponding
5525 to the existentially quantified variables in the input.
5526 In particular, the result lives in a wrapped map where the domain
5527 is the original space and the range corresponds to the original
5528 existentially quantified variables.
5530 #include <isl/set.h>
5531 __isl_give isl_basic_set *isl_basic_set_lift(
5532 __isl_take isl_basic_set *bset);
5533 __isl_give isl_set *isl_set_lift(
5534 __isl_take isl_set *set);
5535 __isl_give isl_union_set *isl_union_set_lift(
5536 __isl_take isl_union_set *uset);
5538 Given a local space that contains the existentially quantified
5539 variables of a set, a basic relation that, when applied to
5540 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5541 can be constructed using the following function.
5543 #include <isl/local_space.h>
5544 __isl_give isl_basic_map *isl_local_space_lifting(
5545 __isl_take isl_local_space *ls);
5547 #include <isl/aff.h>
5548 __isl_give isl_multi_aff *isl_multi_aff_lift(
5549 __isl_take isl_multi_aff *maff,
5550 __isl_give isl_local_space **ls);
5552 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5553 then it is assigned the local space that lies at the basis of
5554 the lifting applied.
5556 =item * Internal Product
5558 #include <isl/space.h>
5559 __isl_give isl_space *isl_space_zip(
5560 __isl_take isl_space *space);
5562 #include <isl/map.h>
5563 __isl_give isl_basic_map *isl_basic_map_zip(
5564 __isl_take isl_basic_map *bmap);
5565 __isl_give isl_map *isl_map_zip(
5566 __isl_take isl_map *map);
5568 #include <isl/union_map.h>
5569 __isl_give isl_union_map *isl_union_map_zip(
5570 __isl_take isl_union_map *umap);
5572 Given a relation with nested relations for domain and range,
5573 interchange the range of the domain with the domain of the range.
5577 #include <isl/space.h>
5578 __isl_give isl_space *isl_space_curry(
5579 __isl_take isl_space *space);
5580 __isl_give isl_space *isl_space_uncurry(
5581 __isl_take isl_space *space);
5583 #include <isl/map.h>
5584 __isl_give isl_basic_map *isl_basic_map_curry(
5585 __isl_take isl_basic_map *bmap);
5586 __isl_give isl_basic_map *isl_basic_map_uncurry(
5587 __isl_take isl_basic_map *bmap);
5588 __isl_give isl_map *isl_map_curry(
5589 __isl_take isl_map *map);
5590 __isl_give isl_map *isl_map_uncurry(
5591 __isl_take isl_map *map);
5593 #include <isl/union_map.h>
5594 __isl_give isl_union_map *isl_union_map_curry(
5595 __isl_take isl_union_map *umap);
5596 __isl_give isl_union_map *isl_union_map_uncurry(
5597 __isl_take isl_union_map *umap);
5599 Given a relation with a nested relation for domain,
5600 the C<curry> functions
5601 move the range of the nested relation out of the domain
5602 and use it as the domain of a nested relation in the range,
5603 with the original range as range of this nested relation.
5604 The C<uncurry> functions perform the inverse operation.
5606 #include <isl/space.h>
5607 __isl_give isl_space *isl_space_range_curry(
5608 __isl_take isl_space *space);
5610 #include <isl/map.h>
5611 __isl_give isl_map *isl_map_range_curry(
5612 __isl_take isl_map *map);
5614 #include <isl/union_map.h>
5615 __isl_give isl_union_map *isl_union_map_range_curry(
5616 __isl_take isl_union_map *umap);
5618 These functions apply the currying to the relation that
5619 is nested inside the range of the input.
5621 =item * Aligning parameters
5623 Change the order of the parameters of the given set, relation
5625 such that the first parameters match those of C<model>.
5626 This may involve the introduction of extra parameters.
5627 All parameters need to be named.
5629 #include <isl/space.h>
5630 __isl_give isl_space *isl_space_align_params(
5631 __isl_take isl_space *space1,
5632 __isl_take isl_space *space2)
5634 #include <isl/set.h>
5635 __isl_give isl_basic_set *isl_basic_set_align_params(
5636 __isl_take isl_basic_set *bset,
5637 __isl_take isl_space *model);
5638 __isl_give isl_set *isl_set_align_params(
5639 __isl_take isl_set *set,
5640 __isl_take isl_space *model);
5642 #include <isl/map.h>
5643 __isl_give isl_basic_map *isl_basic_map_align_params(
5644 __isl_take isl_basic_map *bmap,
5645 __isl_take isl_space *model);
5646 __isl_give isl_map *isl_map_align_params(
5647 __isl_take isl_map *map,
5648 __isl_take isl_space *model);
5650 #include <isl/val.h>
5651 __isl_give isl_multi_val *isl_multi_val_align_params(
5652 __isl_take isl_multi_val *mv,
5653 __isl_take isl_space *model);
5655 #include <isl/aff.h>
5656 __isl_give isl_aff *isl_aff_align_params(
5657 __isl_take isl_aff *aff,
5658 __isl_take isl_space *model);
5659 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5660 __isl_take isl_multi_aff *multi,
5661 __isl_take isl_space *model);
5662 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5663 __isl_take isl_pw_aff *pwaff,
5664 __isl_take isl_space *model);
5665 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5666 __isl_take isl_pw_multi_aff *pma,
5667 __isl_take isl_space *model);
5668 __isl_give isl_union_pw_aff *
5669 isl_union_pw_aff_align_params(
5670 __isl_take isl_union_pw_aff *upa,
5671 __isl_take isl_space *model);
5672 __isl_give isl_union_pw_multi_aff *
5673 isl_union_pw_multi_aff_align_params(
5674 __isl_take isl_union_pw_multi_aff *upma,
5675 __isl_take isl_space *model);
5676 __isl_give isl_multi_union_pw_aff *
5677 isl_multi_union_pw_aff_align_params(
5678 __isl_take isl_multi_union_pw_aff *mupa,
5679 __isl_take isl_space *model);
5681 #include <isl/polynomial.h>
5682 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5683 __isl_take isl_qpolynomial *qp,
5684 __isl_take isl_space *model);
5686 =item * Drop unused parameters
5688 Drop parameters that are not referenced by the isl object.
5689 All parameters need to be named.
5691 #include <isl/set.h>
5692 __isl_give isl_basic_set *
5693 isl_basic_set_drop_unused_params(
5694 __isl_take isl_basic_set *bset);
5695 __isl_give isl_set *isl_set_drop_unused_params(
5696 __isl_take isl_set *set);
5698 #include <isl/map.h>
5699 __isl_give isl_basic_map *
5700 isl_basic_map_drop_unused_params(
5701 __isl_take isl_basic_map *bmap);
5702 __isl_give isl_map *isl_map_drop_unused_params(
5703 __isl_take isl_map *map);
5705 #include <isl/aff.h>
5706 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
5707 __isl_take isl_pw_aff *pa);
5708 __isl_give isl_pw_multi_aff *
5709 isl_pw_multi_aff_drop_unused_params(
5710 __isl_take isl_pw_multi_aff *pma);
5712 #include <isl/polynomial.h>
5713 __isl_give isl_pw_qpolynomial *
5714 isl_pw_qpolynomial_drop_unused_params(
5715 __isl_take isl_pw_qpolynomial *pwqp);
5716 __isl_give isl_pw_qpolynomial_fold *
5717 isl_pw_qpolynomial_fold_drop_unused_params(
5718 __isl_take isl_pw_qpolynomial_fold *pwf);
5720 =item * Unary Arithmetic Operations
5722 #include <isl/set.h>
5723 __isl_give isl_set *isl_set_neg(
5724 __isl_take isl_set *set);
5725 #include <isl/map.h>
5726 __isl_give isl_map *isl_map_neg(
5727 __isl_take isl_map *map);
5729 C<isl_set_neg> constructs a set containing the opposites of
5730 the elements in its argument.
5731 The domain of the result of C<isl_map_neg> is the same
5732 as the domain of its argument. The corresponding range
5733 elements are the opposites of the corresponding range
5734 elements in the argument.
5736 #include <isl/val.h>
5737 __isl_give isl_multi_val *isl_multi_val_neg(
5738 __isl_take isl_multi_val *mv);
5740 #include <isl/aff.h>
5741 __isl_give isl_aff *isl_aff_neg(
5742 __isl_take isl_aff *aff);
5743 __isl_give isl_multi_aff *isl_multi_aff_neg(
5744 __isl_take isl_multi_aff *ma);
5745 __isl_give isl_pw_aff *isl_pw_aff_neg(
5746 __isl_take isl_pw_aff *pwaff);
5747 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5748 __isl_take isl_pw_multi_aff *pma);
5749 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5750 __isl_take isl_multi_pw_aff *mpa);
5751 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5752 __isl_take isl_union_pw_aff *upa);
5753 __isl_give isl_union_pw_multi_aff *
5754 isl_union_pw_multi_aff_neg(
5755 __isl_take isl_union_pw_multi_aff *upma);
5756 __isl_give isl_multi_union_pw_aff *
5757 isl_multi_union_pw_aff_neg(
5758 __isl_take isl_multi_union_pw_aff *mupa);
5759 __isl_give isl_aff *isl_aff_ceil(
5760 __isl_take isl_aff *aff);
5761 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5762 __isl_take isl_pw_aff *pwaff);
5763 __isl_give isl_aff *isl_aff_floor(
5764 __isl_take isl_aff *aff);
5765 __isl_give isl_multi_aff *isl_multi_aff_floor(
5766 __isl_take isl_multi_aff *ma);
5767 __isl_give isl_pw_aff *isl_pw_aff_floor(
5768 __isl_take isl_pw_aff *pwaff);
5769 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5770 __isl_take isl_union_pw_aff *upa);
5771 __isl_give isl_multi_union_pw_aff *
5772 isl_multi_union_pw_aff_floor(
5773 __isl_take isl_multi_union_pw_aff *mupa);
5775 #include <isl/aff.h>
5776 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5777 __isl_take isl_pw_aff_list *list);
5778 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5779 __isl_take isl_pw_aff_list *list);
5781 #include <isl/polynomial.h>
5782 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5783 __isl_take isl_qpolynomial *qp);
5784 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5785 __isl_take isl_pw_qpolynomial *pwqp);
5786 __isl_give isl_union_pw_qpolynomial *
5787 isl_union_pw_qpolynomial_neg(
5788 __isl_take isl_union_pw_qpolynomial *upwqp);
5789 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5790 __isl_take isl_qpolynomial *qp,
5792 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5793 __isl_take isl_pw_qpolynomial *pwqp,
5798 The following functions evaluate a function in a point.
5800 #include <isl/aff.h>
5801 __isl_give isl_val *isl_aff_eval(
5802 __isl_take isl_aff *aff,
5803 __isl_take isl_point *pnt);
5804 __isl_give isl_val *isl_pw_aff_eval(
5805 __isl_take isl_pw_aff *pa,
5806 __isl_take isl_point *pnt);
5808 #include <isl/polynomial.h>
5809 __isl_give isl_val *isl_pw_qpolynomial_eval(
5810 __isl_take isl_pw_qpolynomial *pwqp,
5811 __isl_take isl_point *pnt);
5812 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5813 __isl_take isl_pw_qpolynomial_fold *pwf,
5814 __isl_take isl_point *pnt);
5815 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5816 __isl_take isl_union_pw_qpolynomial *upwqp,
5817 __isl_take isl_point *pnt);
5818 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5819 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5820 __isl_take isl_point *pnt);
5822 These functions return NaN when evaluated at a void point.
5823 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
5824 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
5825 when the function is evaluated outside its explicit domain.
5827 =item * Dimension manipulation
5829 It is usually not advisable to directly change the (input or output)
5830 space of a set or a relation as this removes the name and the internal
5831 structure of the space. However, the functions below can be useful
5832 to add new parameters, assuming
5833 C<isl_set_align_params> and C<isl_map_align_params>
5836 #include <isl/space.h>
5837 __isl_give isl_space *isl_space_add_dims(
5838 __isl_take isl_space *space,
5839 enum isl_dim_type type, unsigned n);
5840 __isl_give isl_space *isl_space_insert_dims(
5841 __isl_take isl_space *space,
5842 enum isl_dim_type type, unsigned pos, unsigned n);
5843 __isl_give isl_space *isl_space_drop_dims(
5844 __isl_take isl_space *space,
5845 enum isl_dim_type type, unsigned first, unsigned n);
5846 __isl_give isl_space *isl_space_move_dims(
5847 __isl_take isl_space *space,
5848 enum isl_dim_type dst_type, unsigned dst_pos,
5849 enum isl_dim_type src_type, unsigned src_pos,
5852 #include <isl/local_space.h>
5853 __isl_give isl_local_space *isl_local_space_add_dims(
5854 __isl_take isl_local_space *ls,
5855 enum isl_dim_type type, unsigned n);
5856 __isl_give isl_local_space *isl_local_space_insert_dims(
5857 __isl_take isl_local_space *ls,
5858 enum isl_dim_type type, unsigned first, unsigned n);
5859 __isl_give isl_local_space *isl_local_space_drop_dims(
5860 __isl_take isl_local_space *ls,
5861 enum isl_dim_type type, unsigned first, unsigned n);
5863 #include <isl/set.h>
5864 __isl_give isl_basic_set *isl_basic_set_add_dims(
5865 __isl_take isl_basic_set *bset,
5866 enum isl_dim_type type, unsigned n);
5867 __isl_give isl_set *isl_set_add_dims(
5868 __isl_take isl_set *set,
5869 enum isl_dim_type type, unsigned n);
5870 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5871 __isl_take isl_basic_set *bset,
5872 enum isl_dim_type type, unsigned pos,
5874 __isl_give isl_set *isl_set_insert_dims(
5875 __isl_take isl_set *set,
5876 enum isl_dim_type type, unsigned pos, unsigned n);
5877 __isl_give isl_basic_set *isl_basic_set_move_dims(
5878 __isl_take isl_basic_set *bset,
5879 enum isl_dim_type dst_type, unsigned dst_pos,
5880 enum isl_dim_type src_type, unsigned src_pos,
5882 __isl_give isl_set *isl_set_move_dims(
5883 __isl_take isl_set *set,
5884 enum isl_dim_type dst_type, unsigned dst_pos,
5885 enum isl_dim_type src_type, unsigned src_pos,
5888 #include <isl/map.h>
5889 __isl_give isl_basic_map *isl_basic_map_add_dims(
5890 __isl_take isl_basic_map *bmap,
5891 enum isl_dim_type type, unsigned n);
5892 __isl_give isl_map *isl_map_add_dims(
5893 __isl_take isl_map *map,
5894 enum isl_dim_type type, unsigned n);
5895 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5896 __isl_take isl_basic_map *bmap,
5897 enum isl_dim_type type, unsigned pos,
5899 __isl_give isl_map *isl_map_insert_dims(
5900 __isl_take isl_map *map,
5901 enum isl_dim_type type, unsigned pos, unsigned n);
5902 __isl_give isl_basic_map *isl_basic_map_move_dims(
5903 __isl_take isl_basic_map *bmap,
5904 enum isl_dim_type dst_type, unsigned dst_pos,
5905 enum isl_dim_type src_type, unsigned src_pos,
5907 __isl_give isl_map *isl_map_move_dims(
5908 __isl_take isl_map *map,
5909 enum isl_dim_type dst_type, unsigned dst_pos,
5910 enum isl_dim_type src_type, unsigned src_pos,
5913 #include <isl/val.h>
5914 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5915 __isl_take isl_multi_val *mv,
5916 enum isl_dim_type type, unsigned first, unsigned n);
5917 __isl_give isl_multi_val *isl_multi_val_add_dims(
5918 __isl_take isl_multi_val *mv,
5919 enum isl_dim_type type, unsigned n);
5920 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5921 __isl_take isl_multi_val *mv,
5922 enum isl_dim_type type, unsigned first, unsigned n);
5924 #include <isl/aff.h>
5925 __isl_give isl_aff *isl_aff_insert_dims(
5926 __isl_take isl_aff *aff,
5927 enum isl_dim_type type, unsigned first, unsigned n);
5928 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5929 __isl_take isl_multi_aff *ma,
5930 enum isl_dim_type type, unsigned first, unsigned n);
5931 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5932 __isl_take isl_pw_aff *pwaff,
5933 enum isl_dim_type type, unsigned first, unsigned n);
5934 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5935 __isl_take isl_multi_pw_aff *mpa,
5936 enum isl_dim_type type, unsigned first, unsigned n);
5937 __isl_give isl_aff *isl_aff_add_dims(
5938 __isl_take isl_aff *aff,
5939 enum isl_dim_type type, unsigned n);
5940 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5941 __isl_take isl_multi_aff *ma,
5942 enum isl_dim_type type, unsigned n);
5943 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5944 __isl_take isl_pw_aff *pwaff,
5945 enum isl_dim_type type, unsigned n);
5946 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5947 __isl_take isl_multi_pw_aff *mpa,
5948 enum isl_dim_type type, unsigned n);
5949 __isl_give isl_aff *isl_aff_drop_dims(
5950 __isl_take isl_aff *aff,
5951 enum isl_dim_type type, unsigned first, unsigned n);
5952 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5953 __isl_take isl_multi_aff *maff,
5954 enum isl_dim_type type, unsigned first, unsigned n);
5955 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5956 __isl_take isl_pw_aff *pwaff,
5957 enum isl_dim_type type, unsigned first, unsigned n);
5958 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5959 __isl_take isl_pw_multi_aff *pma,
5960 enum isl_dim_type type, unsigned first, unsigned n);
5961 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5962 __isl_take isl_union_pw_aff *upa,
5963 enum isl_dim_type type, unsigned first, unsigned n);
5964 __isl_give isl_union_pw_multi_aff *
5965 isl_union_pw_multi_aff_drop_dims(
5966 __isl_take isl_union_pw_multi_aff *upma,
5967 enum isl_dim_type type,
5968 unsigned first, unsigned n);
5969 __isl_give isl_multi_union_pw_aff *
5970 isl_multi_union_pw_aff_drop_dims(
5971 __isl_take isl_multi_union_pw_aff *mupa,
5972 enum isl_dim_type type, unsigned first,
5974 __isl_give isl_aff *isl_aff_move_dims(
5975 __isl_take isl_aff *aff,
5976 enum isl_dim_type dst_type, unsigned dst_pos,
5977 enum isl_dim_type src_type, unsigned src_pos,
5979 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5980 __isl_take isl_multi_aff *ma,
5981 enum isl_dim_type dst_type, unsigned dst_pos,
5982 enum isl_dim_type src_type, unsigned src_pos,
5984 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5985 __isl_take isl_pw_aff *pa,
5986 enum isl_dim_type dst_type, unsigned dst_pos,
5987 enum isl_dim_type src_type, unsigned src_pos,
5989 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5990 __isl_take isl_multi_pw_aff *pma,
5991 enum isl_dim_type dst_type, unsigned dst_pos,
5992 enum isl_dim_type src_type, unsigned src_pos,
5995 #include <isl/polynomial.h>
5996 __isl_give isl_union_pw_qpolynomial *
5997 isl_union_pw_qpolynomial_drop_dims(
5998 __isl_take isl_union_pw_qpolynomial *upwqp,
5999 enum isl_dim_type type,
6000 unsigned first, unsigned n);
6001 __isl_give isl_union_pw_qpolynomial_fold *
6002 isl_union_pw_qpolynomial_fold_drop_dims(
6003 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6004 enum isl_dim_type type,
6005 unsigned first, unsigned n);
6007 The operations on union expressions can only manipulate parameters.
6011 =head2 Binary Operations
6013 The two arguments of a binary operation not only need to live
6014 in the same C<isl_ctx>, they currently also need to have
6015 the same (number of) parameters.
6017 =head3 Basic Operations
6021 =item * Intersection
6023 #include <isl/local_space.h>
6024 __isl_give isl_local_space *isl_local_space_intersect(
6025 __isl_take isl_local_space *ls1,
6026 __isl_take isl_local_space *ls2);
6028 #include <isl/set.h>
6029 __isl_give isl_basic_set *isl_basic_set_intersect_params(
6030 __isl_take isl_basic_set *bset1,
6031 __isl_take isl_basic_set *bset2);
6032 __isl_give isl_basic_set *isl_basic_set_intersect(
6033 __isl_take isl_basic_set *bset1,
6034 __isl_take isl_basic_set *bset2);
6035 __isl_give isl_basic_set *isl_basic_set_list_intersect(
6036 __isl_take struct isl_basic_set_list *list);
6037 __isl_give isl_set *isl_set_intersect_params(
6038 __isl_take isl_set *set,
6039 __isl_take isl_set *params);
6040 __isl_give isl_set *isl_set_intersect(
6041 __isl_take isl_set *set1,
6042 __isl_take isl_set *set2);
6044 #include <isl/map.h>
6045 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
6046 __isl_take isl_basic_map *bmap,
6047 __isl_take isl_basic_set *bset);
6048 __isl_give isl_basic_map *isl_basic_map_intersect_range(
6049 __isl_take isl_basic_map *bmap,
6050 __isl_take isl_basic_set *bset);
6051 __isl_give isl_basic_map *isl_basic_map_intersect(
6052 __isl_take isl_basic_map *bmap1,
6053 __isl_take isl_basic_map *bmap2);
6054 __isl_give isl_basic_map *isl_basic_map_list_intersect(
6055 __isl_take isl_basic_map_list *list);
6056 __isl_give isl_map *isl_map_intersect_params(
6057 __isl_take isl_map *map,
6058 __isl_take isl_set *params);
6059 __isl_give isl_map *isl_map_intersect_domain(
6060 __isl_take isl_map *map,
6061 __isl_take isl_set *set);
6062 __isl_give isl_map *isl_map_intersect_range(
6063 __isl_take isl_map *map,
6064 __isl_take isl_set *set);
6065 __isl_give isl_map *isl_map_intersect(
6066 __isl_take isl_map *map1,
6067 __isl_take isl_map *map2);
6068 __isl_give isl_map *
6069 isl_map_intersect_domain_factor_range(
6070 __isl_take isl_map *map,
6071 __isl_take isl_map *factor);
6072 __isl_give isl_map *
6073 isl_map_intersect_range_factor_range(
6074 __isl_take isl_map *map,
6075 __isl_take isl_map *factor);
6077 #include <isl/union_set.h>
6078 __isl_give isl_union_set *isl_union_set_intersect_params(
6079 __isl_take isl_union_set *uset,
6080 __isl_take isl_set *set);
6081 __isl_give isl_union_set *isl_union_set_intersect(
6082 __isl_take isl_union_set *uset1,
6083 __isl_take isl_union_set *uset2);
6085 #include <isl/union_map.h>
6086 __isl_give isl_union_map *isl_union_map_intersect_params(
6087 __isl_take isl_union_map *umap,
6088 __isl_take isl_set *set);
6089 __isl_give isl_union_map *isl_union_map_intersect_domain(
6090 __isl_take isl_union_map *umap,
6091 __isl_take isl_union_set *uset);
6092 __isl_give isl_union_map *isl_union_map_intersect_range(
6093 __isl_take isl_union_map *umap,
6094 __isl_take isl_union_set *uset);
6095 __isl_give isl_union_map *isl_union_map_intersect(
6096 __isl_take isl_union_map *umap1,
6097 __isl_take isl_union_map *umap2);
6098 __isl_give isl_union_map *
6099 isl_union_map_intersect_range_factor_range(
6100 __isl_take isl_union_map *umap,
6101 __isl_take isl_union_map *factor);
6103 #include <isl/aff.h>
6104 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6105 __isl_take isl_pw_aff *pa,
6106 __isl_take isl_set *set);
6107 __isl_give isl_multi_pw_aff *
6108 isl_multi_pw_aff_intersect_domain(
6109 __isl_take isl_multi_pw_aff *mpa,
6110 __isl_take isl_set *domain);
6111 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6112 __isl_take isl_pw_multi_aff *pma,
6113 __isl_take isl_set *set);
6114 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6115 __isl_take isl_union_pw_aff *upa,
6116 __isl_take isl_union_set *uset);
6117 __isl_give isl_union_pw_multi_aff *
6118 isl_union_pw_multi_aff_intersect_domain(
6119 __isl_take isl_union_pw_multi_aff *upma,
6120 __isl_take isl_union_set *uset);
6121 __isl_give isl_multi_union_pw_aff *
6122 isl_multi_union_pw_aff_intersect_domain(
6123 __isl_take isl_multi_union_pw_aff *mupa,
6124 __isl_take isl_union_set *uset);
6125 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6126 __isl_take isl_pw_aff *pa,
6127 __isl_take isl_set *set);
6128 __isl_give isl_multi_pw_aff *
6129 isl_multi_pw_aff_intersect_params(
6130 __isl_take isl_multi_pw_aff *mpa,
6131 __isl_take isl_set *set);
6132 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6133 __isl_take isl_pw_multi_aff *pma,
6134 __isl_take isl_set *set);
6135 __isl_give isl_union_pw_aff *
6136 isl_union_pw_aff_intersect_params(
6137 __isl_take isl_union_pw_aff *upa,
6138 __isl_give isl_union_pw_multi_aff *
6139 isl_union_pw_multi_aff_intersect_params(
6140 __isl_take isl_union_pw_multi_aff *upma,
6141 __isl_take isl_set *set);
6142 __isl_give isl_multi_union_pw_aff *
6143 isl_multi_union_pw_aff_intersect_params(
6144 __isl_take isl_multi_union_pw_aff *mupa,
6145 __isl_take isl_set *params);
6146 isl_multi_union_pw_aff_intersect_range(
6147 __isl_take isl_multi_union_pw_aff *mupa,
6148 __isl_take isl_set *set);
6150 #include <isl/polynomial.h>
6151 __isl_give isl_pw_qpolynomial *
6152 isl_pw_qpolynomial_intersect_domain(
6153 __isl_take isl_pw_qpolynomial *pwpq,
6154 __isl_take isl_set *set);
6155 __isl_give isl_union_pw_qpolynomial *
6156 isl_union_pw_qpolynomial_intersect_domain(
6157 __isl_take isl_union_pw_qpolynomial *upwpq,
6158 __isl_take isl_union_set *uset);
6159 __isl_give isl_union_pw_qpolynomial_fold *
6160 isl_union_pw_qpolynomial_fold_intersect_domain(
6161 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6162 __isl_take isl_union_set *uset);
6163 __isl_give isl_pw_qpolynomial *
6164 isl_pw_qpolynomial_intersect_params(
6165 __isl_take isl_pw_qpolynomial *pwpq,
6166 __isl_take isl_set *set);
6167 __isl_give isl_pw_qpolynomial_fold *
6168 isl_pw_qpolynomial_fold_intersect_params(
6169 __isl_take isl_pw_qpolynomial_fold *pwf,
6170 __isl_take isl_set *set);
6171 __isl_give isl_union_pw_qpolynomial *
6172 isl_union_pw_qpolynomial_intersect_params(
6173 __isl_take isl_union_pw_qpolynomial *upwpq,
6174 __isl_take isl_set *set);
6175 __isl_give isl_union_pw_qpolynomial_fold *
6176 isl_union_pw_qpolynomial_fold_intersect_params(
6177 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6178 __isl_take isl_set *set);
6180 The second argument to the C<_params> functions needs to be
6181 a parametric (basic) set. For the other functions, a parametric set
6182 for either argument is only allowed if the other argument is
6183 a parametric set as well.
6184 The list passed to C<isl_basic_set_list_intersect> needs to have
6185 at least one element and all elements need to live in the same space.
6186 The function C<isl_multi_union_pw_aff_intersect_range>
6187 restricts the input function to those shared domain elements
6188 that map to the specified range.
6192 #include <isl/set.h>
6193 __isl_give isl_set *isl_basic_set_union(
6194 __isl_take isl_basic_set *bset1,
6195 __isl_take isl_basic_set *bset2);
6196 __isl_give isl_set *isl_set_union(
6197 __isl_take isl_set *set1,
6198 __isl_take isl_set *set2);
6199 __isl_give isl_set *isl_set_list_union(
6200 __isl_take isl_set_list *list);
6202 #include <isl/map.h>
6203 __isl_give isl_map *isl_basic_map_union(
6204 __isl_take isl_basic_map *bmap1,
6205 __isl_take isl_basic_map *bmap2);
6206 __isl_give isl_map *isl_map_union(
6207 __isl_take isl_map *map1,
6208 __isl_take isl_map *map2);
6210 #include <isl/union_set.h>
6211 __isl_give isl_union_set *isl_union_set_union(
6212 __isl_take isl_union_set *uset1,
6213 __isl_take isl_union_set *uset2);
6214 __isl_give isl_union_set *isl_union_set_list_union(
6215 __isl_take isl_union_set_list *list);
6217 #include <isl/union_map.h>
6218 __isl_give isl_union_map *isl_union_map_union(
6219 __isl_take isl_union_map *umap1,
6220 __isl_take isl_union_map *umap2);
6222 The list passed to C<isl_set_list_union> needs to have
6223 at least one element and all elements need to live in the same space.
6225 =item * Set difference
6227 #include <isl/set.h>
6228 __isl_give isl_set *isl_set_subtract(
6229 __isl_take isl_set *set1,
6230 __isl_take isl_set *set2);
6232 #include <isl/map.h>
6233 __isl_give isl_map *isl_map_subtract(
6234 __isl_take isl_map *map1,
6235 __isl_take isl_map *map2);
6236 __isl_give isl_map *isl_map_subtract_domain(
6237 __isl_take isl_map *map,
6238 __isl_take isl_set *dom);
6239 __isl_give isl_map *isl_map_subtract_range(
6240 __isl_take isl_map *map,
6241 __isl_take isl_set *dom);
6243 #include <isl/union_set.h>
6244 __isl_give isl_union_set *isl_union_set_subtract(
6245 __isl_take isl_union_set *uset1,
6246 __isl_take isl_union_set *uset2);
6248 #include <isl/union_map.h>
6249 __isl_give isl_union_map *isl_union_map_subtract(
6250 __isl_take isl_union_map *umap1,
6251 __isl_take isl_union_map *umap2);
6252 __isl_give isl_union_map *isl_union_map_subtract_domain(
6253 __isl_take isl_union_map *umap,
6254 __isl_take isl_union_set *dom);
6255 __isl_give isl_union_map *isl_union_map_subtract_range(
6256 __isl_take isl_union_map *umap,
6257 __isl_take isl_union_set *dom);
6259 #include <isl/aff.h>
6260 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6261 __isl_take isl_pw_aff *pa,
6262 __isl_take isl_set *set);
6263 __isl_give isl_pw_multi_aff *
6264 isl_pw_multi_aff_subtract_domain(
6265 __isl_take isl_pw_multi_aff *pma,
6266 __isl_take isl_set *set);
6267 __isl_give isl_union_pw_aff *
6268 isl_union_pw_aff_subtract_domain(
6269 __isl_take isl_union_pw_aff *upa,
6270 __isl_take isl_union_set *uset);
6271 __isl_give isl_union_pw_multi_aff *
6272 isl_union_pw_multi_aff_subtract_domain(
6273 __isl_take isl_union_pw_multi_aff *upma,
6274 __isl_take isl_set *set);
6276 #include <isl/polynomial.h>
6277 __isl_give isl_pw_qpolynomial *
6278 isl_pw_qpolynomial_subtract_domain(
6279 __isl_take isl_pw_qpolynomial *pwpq,
6280 __isl_take isl_set *set);
6281 __isl_give isl_pw_qpolynomial_fold *
6282 isl_pw_qpolynomial_fold_subtract_domain(
6283 __isl_take isl_pw_qpolynomial_fold *pwf,
6284 __isl_take isl_set *set);
6285 __isl_give isl_union_pw_qpolynomial *
6286 isl_union_pw_qpolynomial_subtract_domain(
6287 __isl_take isl_union_pw_qpolynomial *upwpq,
6288 __isl_take isl_union_set *uset);
6289 __isl_give isl_union_pw_qpolynomial_fold *
6290 isl_union_pw_qpolynomial_fold_subtract_domain(
6291 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6292 __isl_take isl_union_set *uset);
6296 #include <isl/space.h>
6297 __isl_give isl_space *isl_space_join(
6298 __isl_take isl_space *left,
6299 __isl_take isl_space *right);
6301 #include <isl/map.h>
6302 __isl_give isl_basic_set *isl_basic_set_apply(
6303 __isl_take isl_basic_set *bset,
6304 __isl_take isl_basic_map *bmap);
6305 __isl_give isl_set *isl_set_apply(
6306 __isl_take isl_set *set,
6307 __isl_take isl_map *map);
6308 __isl_give isl_union_set *isl_union_set_apply(
6309 __isl_take isl_union_set *uset,
6310 __isl_take isl_union_map *umap);
6311 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6312 __isl_take isl_basic_map *bmap1,
6313 __isl_take isl_basic_map *bmap2);
6314 __isl_give isl_basic_map *isl_basic_map_apply_range(
6315 __isl_take isl_basic_map *bmap1,
6316 __isl_take isl_basic_map *bmap2);
6317 __isl_give isl_map *isl_map_apply_domain(
6318 __isl_take isl_map *map1,
6319 __isl_take isl_map *map2);
6320 __isl_give isl_map *isl_map_apply_range(
6321 __isl_take isl_map *map1,
6322 __isl_take isl_map *map2);
6324 #include <isl/union_map.h>
6325 __isl_give isl_union_map *isl_union_map_apply_domain(
6326 __isl_take isl_union_map *umap1,
6327 __isl_take isl_union_map *umap2);
6328 __isl_give isl_union_map *isl_union_map_apply_range(
6329 __isl_take isl_union_map *umap1,
6330 __isl_take isl_union_map *umap2);
6332 #include <isl/aff.h>
6333 __isl_give isl_union_pw_aff *
6334 isl_multi_union_pw_aff_apply_aff(
6335 __isl_take isl_multi_union_pw_aff *mupa,
6336 __isl_take isl_aff *aff);
6337 __isl_give isl_union_pw_aff *
6338 isl_multi_union_pw_aff_apply_pw_aff(
6339 __isl_take isl_multi_union_pw_aff *mupa,
6340 __isl_take isl_pw_aff *pa);
6341 __isl_give isl_multi_union_pw_aff *
6342 isl_multi_union_pw_aff_apply_multi_aff(
6343 __isl_take isl_multi_union_pw_aff *mupa,
6344 __isl_take isl_multi_aff *ma);
6345 __isl_give isl_multi_union_pw_aff *
6346 isl_multi_union_pw_aff_apply_pw_multi_aff(
6347 __isl_take isl_multi_union_pw_aff *mupa,
6348 __isl_take isl_pw_multi_aff *pma);
6350 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6351 over the shared domain of the elements of the input. The dimension is
6352 required to be greater than zero.
6353 The C<isl_multi_union_pw_aff> argument of
6354 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6355 but only if the range of the C<isl_multi_aff> argument
6356 is also zero-dimensional.
6357 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6359 #include <isl/polynomial.h>
6360 __isl_give isl_pw_qpolynomial_fold *
6361 isl_set_apply_pw_qpolynomial_fold(
6362 __isl_take isl_set *set,
6363 __isl_take isl_pw_qpolynomial_fold *pwf,
6365 __isl_give isl_pw_qpolynomial_fold *
6366 isl_map_apply_pw_qpolynomial_fold(
6367 __isl_take isl_map *map,
6368 __isl_take isl_pw_qpolynomial_fold *pwf,
6370 __isl_give isl_union_pw_qpolynomial_fold *
6371 isl_union_set_apply_union_pw_qpolynomial_fold(
6372 __isl_take isl_union_set *uset,
6373 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6375 __isl_give isl_union_pw_qpolynomial_fold *
6376 isl_union_map_apply_union_pw_qpolynomial_fold(
6377 __isl_take isl_union_map *umap,
6378 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6381 The functions taking a map
6382 compose the given map with the given piecewise quasipolynomial reduction.
6383 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6384 over all elements in the intersection of the range of the map
6385 and the domain of the piecewise quasipolynomial reduction
6386 as a function of an element in the domain of the map.
6387 The functions taking a set compute a bound over all elements in the
6388 intersection of the set and the domain of the
6389 piecewise quasipolynomial reduction.
6393 #include <isl/set.h>
6394 __isl_give isl_basic_set *
6395 isl_basic_set_preimage_multi_aff(
6396 __isl_take isl_basic_set *bset,
6397 __isl_take isl_multi_aff *ma);
6398 __isl_give isl_set *isl_set_preimage_multi_aff(
6399 __isl_take isl_set *set,
6400 __isl_take isl_multi_aff *ma);
6401 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6402 __isl_take isl_set *set,
6403 __isl_take isl_pw_multi_aff *pma);
6404 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6405 __isl_take isl_set *set,
6406 __isl_take isl_multi_pw_aff *mpa);
6408 #include <isl/union_set.h>
6409 __isl_give isl_union_set *
6410 isl_union_set_preimage_multi_aff(
6411 __isl_take isl_union_set *uset,
6412 __isl_take isl_multi_aff *ma);
6413 __isl_give isl_union_set *
6414 isl_union_set_preimage_pw_multi_aff(
6415 __isl_take isl_union_set *uset,
6416 __isl_take isl_pw_multi_aff *pma);
6417 __isl_give isl_union_set *
6418 isl_union_set_preimage_union_pw_multi_aff(
6419 __isl_take isl_union_set *uset,
6420 __isl_take isl_union_pw_multi_aff *upma);
6422 #include <isl/map.h>
6423 __isl_give isl_basic_map *
6424 isl_basic_map_preimage_domain_multi_aff(
6425 __isl_take isl_basic_map *bmap,
6426 __isl_take isl_multi_aff *ma);
6427 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6428 __isl_take isl_map *map,
6429 __isl_take isl_multi_aff *ma);
6430 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6431 __isl_take isl_map *map,
6432 __isl_take isl_multi_aff *ma);
6433 __isl_give isl_map *
6434 isl_map_preimage_domain_pw_multi_aff(
6435 __isl_take isl_map *map,
6436 __isl_take isl_pw_multi_aff *pma);
6437 __isl_give isl_map *
6438 isl_map_preimage_range_pw_multi_aff(
6439 __isl_take isl_map *map,
6440 __isl_take isl_pw_multi_aff *pma);
6441 __isl_give isl_map *
6442 isl_map_preimage_domain_multi_pw_aff(
6443 __isl_take isl_map *map,
6444 __isl_take isl_multi_pw_aff *mpa);
6445 __isl_give isl_basic_map *
6446 isl_basic_map_preimage_range_multi_aff(
6447 __isl_take isl_basic_map *bmap,
6448 __isl_take isl_multi_aff *ma);
6450 #include <isl/union_map.h>
6451 __isl_give isl_union_map *
6452 isl_union_map_preimage_domain_multi_aff(
6453 __isl_take isl_union_map *umap,
6454 __isl_take isl_multi_aff *ma);
6455 __isl_give isl_union_map *
6456 isl_union_map_preimage_range_multi_aff(
6457 __isl_take isl_union_map *umap,
6458 __isl_take isl_multi_aff *ma);
6459 __isl_give isl_union_map *
6460 isl_union_map_preimage_domain_pw_multi_aff(
6461 __isl_take isl_union_map *umap,
6462 __isl_take isl_pw_multi_aff *pma);
6463 __isl_give isl_union_map *
6464 isl_union_map_preimage_range_pw_multi_aff(
6465 __isl_take isl_union_map *umap,
6466 __isl_take isl_pw_multi_aff *pma);
6467 __isl_give isl_union_map *
6468 isl_union_map_preimage_domain_union_pw_multi_aff(
6469 __isl_take isl_union_map *umap,
6470 __isl_take isl_union_pw_multi_aff *upma);
6471 __isl_give isl_union_map *
6472 isl_union_map_preimage_range_union_pw_multi_aff(
6473 __isl_take isl_union_map *umap,
6474 __isl_take isl_union_pw_multi_aff *upma);
6476 These functions compute the preimage of the given set or map domain/range under
6477 the given function. In other words, the expression is plugged
6478 into the set description or into the domain/range of the map.
6482 #include <isl/aff.h>
6483 __isl_give isl_aff *isl_aff_pullback_aff(
6484 __isl_take isl_aff *aff1,
6485 __isl_take isl_aff *aff2);
6486 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6487 __isl_take isl_aff *aff,
6488 __isl_take isl_multi_aff *ma);
6489 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6490 __isl_take isl_pw_aff *pa,
6491 __isl_take isl_multi_aff *ma);
6492 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6493 __isl_take isl_pw_aff *pa,
6494 __isl_take isl_pw_multi_aff *pma);
6495 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6496 __isl_take isl_pw_aff *pa,
6497 __isl_take isl_multi_pw_aff *mpa);
6498 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6499 __isl_take isl_multi_aff *ma1,
6500 __isl_take isl_multi_aff *ma2);
6501 __isl_give isl_pw_multi_aff *
6502 isl_pw_multi_aff_pullback_multi_aff(
6503 __isl_take isl_pw_multi_aff *pma,
6504 __isl_take isl_multi_aff *ma);
6505 __isl_give isl_multi_pw_aff *
6506 isl_multi_pw_aff_pullback_multi_aff(
6507 __isl_take isl_multi_pw_aff *mpa,
6508 __isl_take isl_multi_aff *ma);
6509 __isl_give isl_pw_multi_aff *
6510 isl_pw_multi_aff_pullback_pw_multi_aff(
6511 __isl_take isl_pw_multi_aff *pma1,
6512 __isl_take isl_pw_multi_aff *pma2);
6513 __isl_give isl_multi_pw_aff *
6514 isl_multi_pw_aff_pullback_pw_multi_aff(
6515 __isl_take isl_multi_pw_aff *mpa,
6516 __isl_take isl_pw_multi_aff *pma);
6517 __isl_give isl_multi_pw_aff *
6518 isl_multi_pw_aff_pullback_multi_pw_aff(
6519 __isl_take isl_multi_pw_aff *mpa1,
6520 __isl_take isl_multi_pw_aff *mpa2);
6521 __isl_give isl_union_pw_aff *
6522 isl_union_pw_aff_pullback_union_pw_multi_aff(
6523 __isl_take isl_union_pw_aff *upa,
6524 __isl_take isl_union_pw_multi_aff *upma);
6525 __isl_give isl_union_pw_multi_aff *
6526 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6527 __isl_take isl_union_pw_multi_aff *upma1,
6528 __isl_take isl_union_pw_multi_aff *upma2);
6529 __isl_give isl_multi_union_pw_aff *
6530 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6531 __isl_take isl_multi_union_pw_aff *mupa,
6532 __isl_take isl_union_pw_multi_aff *upma);
6534 These functions precompose the first expression by the second function.
6535 In other words, the second function is plugged
6536 into the first expression.
6540 #include <isl/aff.h>
6541 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6542 __isl_take isl_aff *aff1,
6543 __isl_take isl_aff *aff2);
6544 __isl_give isl_set *isl_aff_eq_set(
6545 __isl_take isl_aff *aff1,
6546 __isl_take isl_aff *aff2);
6547 __isl_give isl_set *isl_aff_ne_set(
6548 __isl_take isl_aff *aff1,
6549 __isl_take isl_aff *aff2);
6550 __isl_give isl_basic_set *isl_aff_le_basic_set(
6551 __isl_take isl_aff *aff1,
6552 __isl_take isl_aff *aff2);
6553 __isl_give isl_set *isl_aff_le_set(
6554 __isl_take isl_aff *aff1,
6555 __isl_take isl_aff *aff2);
6556 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6557 __isl_take isl_aff *aff1,
6558 __isl_take isl_aff *aff2);
6559 __isl_give isl_set *isl_aff_lt_set(
6560 __isl_take isl_aff *aff1,
6561 __isl_take isl_aff *aff2);
6562 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6563 __isl_take isl_aff *aff1,
6564 __isl_take isl_aff *aff2);
6565 __isl_give isl_set *isl_aff_ge_set(
6566 __isl_take isl_aff *aff1,
6567 __isl_take isl_aff *aff2);
6568 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6569 __isl_take isl_aff *aff1,
6570 __isl_take isl_aff *aff2);
6571 __isl_give isl_set *isl_aff_gt_set(
6572 __isl_take isl_aff *aff1,
6573 __isl_take isl_aff *aff2);
6574 __isl_give isl_set *isl_pw_aff_eq_set(
6575 __isl_take isl_pw_aff *pwaff1,
6576 __isl_take isl_pw_aff *pwaff2);
6577 __isl_give isl_set *isl_pw_aff_ne_set(
6578 __isl_take isl_pw_aff *pwaff1,
6579 __isl_take isl_pw_aff *pwaff2);
6580 __isl_give isl_set *isl_pw_aff_le_set(
6581 __isl_take isl_pw_aff *pwaff1,
6582 __isl_take isl_pw_aff *pwaff2);
6583 __isl_give isl_set *isl_pw_aff_lt_set(
6584 __isl_take isl_pw_aff *pwaff1,
6585 __isl_take isl_pw_aff *pwaff2);
6586 __isl_give isl_set *isl_pw_aff_ge_set(
6587 __isl_take isl_pw_aff *pwaff1,
6588 __isl_take isl_pw_aff *pwaff2);
6589 __isl_give isl_set *isl_pw_aff_gt_set(
6590 __isl_take isl_pw_aff *pwaff1,
6591 __isl_take isl_pw_aff *pwaff2);
6593 __isl_give isl_set *isl_multi_aff_lex_le_set(
6594 __isl_take isl_multi_aff *ma1,
6595 __isl_take isl_multi_aff *ma2);
6596 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6597 __isl_take isl_multi_aff *ma1,
6598 __isl_take isl_multi_aff *ma2);
6599 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6600 __isl_take isl_multi_aff *ma1,
6601 __isl_take isl_multi_aff *ma2);
6602 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6603 __isl_take isl_multi_aff *ma1,
6604 __isl_take isl_multi_aff *ma2);
6606 __isl_give isl_set *isl_pw_aff_list_eq_set(
6607 __isl_take isl_pw_aff_list *list1,
6608 __isl_take isl_pw_aff_list *list2);
6609 __isl_give isl_set *isl_pw_aff_list_ne_set(
6610 __isl_take isl_pw_aff_list *list1,
6611 __isl_take isl_pw_aff_list *list2);
6612 __isl_give isl_set *isl_pw_aff_list_le_set(
6613 __isl_take isl_pw_aff_list *list1,
6614 __isl_take isl_pw_aff_list *list2);
6615 __isl_give isl_set *isl_pw_aff_list_lt_set(
6616 __isl_take isl_pw_aff_list *list1,
6617 __isl_take isl_pw_aff_list *list2);
6618 __isl_give isl_set *isl_pw_aff_list_ge_set(
6619 __isl_take isl_pw_aff_list *list1,
6620 __isl_take isl_pw_aff_list *list2);
6621 __isl_give isl_set *isl_pw_aff_list_gt_set(
6622 __isl_take isl_pw_aff_list *list1,
6623 __isl_take isl_pw_aff_list *list2);
6625 The function C<isl_aff_ge_basic_set> returns a basic set
6626 containing those elements in the shared space
6627 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6628 The function C<isl_pw_aff_ge_set> returns a set
6629 containing those elements in the shared domain
6630 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6631 greater than or equal to C<pwaff2>.
6632 The function C<isl_multi_aff_lex_le_set> returns a set
6633 containing those elements in the shared domain space
6634 where C<ma1> is lexicographically smaller than or
6636 The functions operating on C<isl_pw_aff_list> apply the corresponding
6637 C<isl_pw_aff> function to each pair of elements in the two lists.
6639 #include <isl/aff.h>
6640 __isl_give isl_map *isl_pw_aff_eq_map(
6641 __isl_take isl_pw_aff *pa1,
6642 __isl_take isl_pw_aff *pa2);
6643 __isl_give isl_map *isl_pw_aff_lt_map(
6644 __isl_take isl_pw_aff *pa1,
6645 __isl_take isl_pw_aff *pa2);
6646 __isl_give isl_map *isl_pw_aff_gt_map(
6647 __isl_take isl_pw_aff *pa1,
6648 __isl_take isl_pw_aff *pa2);
6650 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6651 __isl_take isl_multi_pw_aff *mpa1,
6652 __isl_take isl_multi_pw_aff *mpa2);
6653 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6654 __isl_take isl_multi_pw_aff *mpa1,
6655 __isl_take isl_multi_pw_aff *mpa2);
6656 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6657 __isl_take isl_multi_pw_aff *mpa1,
6658 __isl_take isl_multi_pw_aff *mpa2);
6660 These functions return a map between domain elements of the arguments
6661 where the function values satisfy the given relation.
6663 #include <isl/union_map.h>
6664 __isl_give isl_union_map *
6665 isl_union_map_eq_at_multi_union_pw_aff(
6666 __isl_take isl_union_map *umap,
6667 __isl_take isl_multi_union_pw_aff *mupa);
6668 __isl_give isl_union_map *
6669 isl_union_map_lex_lt_at_multi_union_pw_aff(
6670 __isl_take isl_union_map *umap,
6671 __isl_take isl_multi_union_pw_aff *mupa);
6672 __isl_give isl_union_map *
6673 isl_union_map_lex_gt_at_multi_union_pw_aff(
6674 __isl_take isl_union_map *umap,
6675 __isl_take isl_multi_union_pw_aff *mupa);
6677 These functions select the subset of elements in the union map
6678 that have an equal or lexicographically smaller function value.
6680 =item * Cartesian Product
6682 #include <isl/space.h>
6683 __isl_give isl_space *isl_space_product(
6684 __isl_take isl_space *space1,
6685 __isl_take isl_space *space2);
6686 __isl_give isl_space *isl_space_domain_product(
6687 __isl_take isl_space *space1,
6688 __isl_take isl_space *space2);
6689 __isl_give isl_space *isl_space_range_product(
6690 __isl_take isl_space *space1,
6691 __isl_take isl_space *space2);
6694 C<isl_space_product>, C<isl_space_domain_product>
6695 and C<isl_space_range_product> take pairs or relation spaces and
6696 produce a single relations space, where either the domain, the range
6697 or both domain and range are wrapped spaces of relations between
6698 the domains and/or ranges of the input spaces.
6699 If the product is only constructed over the domain or the range
6700 then the ranges or the domains of the inputs should be the same.
6701 The function C<isl_space_product> also accepts a pair of set spaces,
6702 in which case it returns a wrapped space of a relation between the
6705 #include <isl/set.h>
6706 __isl_give isl_set *isl_set_product(
6707 __isl_take isl_set *set1,
6708 __isl_take isl_set *set2);
6710 #include <isl/map.h>
6711 __isl_give isl_basic_map *isl_basic_map_domain_product(
6712 __isl_take isl_basic_map *bmap1,
6713 __isl_take isl_basic_map *bmap2);
6714 __isl_give isl_basic_map *isl_basic_map_range_product(
6715 __isl_take isl_basic_map *bmap1,
6716 __isl_take isl_basic_map *bmap2);
6717 __isl_give isl_basic_map *isl_basic_map_product(
6718 __isl_take isl_basic_map *bmap1,
6719 __isl_take isl_basic_map *bmap2);
6720 __isl_give isl_map *isl_map_domain_product(
6721 __isl_take isl_map *map1,
6722 __isl_take isl_map *map2);
6723 __isl_give isl_map *isl_map_range_product(
6724 __isl_take isl_map *map1,
6725 __isl_take isl_map *map2);
6726 __isl_give isl_map *isl_map_product(
6727 __isl_take isl_map *map1,
6728 __isl_take isl_map *map2);
6730 #include <isl/union_set.h>
6731 __isl_give isl_union_set *isl_union_set_product(
6732 __isl_take isl_union_set *uset1,
6733 __isl_take isl_union_set *uset2);
6735 #include <isl/union_map.h>
6736 __isl_give isl_union_map *isl_union_map_domain_product(
6737 __isl_take isl_union_map *umap1,
6738 __isl_take isl_union_map *umap2);
6739 __isl_give isl_union_map *isl_union_map_range_product(
6740 __isl_take isl_union_map *umap1,
6741 __isl_take isl_union_map *umap2);
6742 __isl_give isl_union_map *isl_union_map_product(
6743 __isl_take isl_union_map *umap1,
6744 __isl_take isl_union_map *umap2);
6746 #include <isl/val.h>
6747 __isl_give isl_multi_val *isl_multi_val_range_product(
6748 __isl_take isl_multi_val *mv1,
6749 __isl_take isl_multi_val *mv2);
6750 __isl_give isl_multi_val *isl_multi_val_product(
6751 __isl_take isl_multi_val *mv1,
6752 __isl_take isl_multi_val *mv2);
6754 #include <isl/aff.h>
6755 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6756 __isl_take isl_multi_aff *ma1,
6757 __isl_take isl_multi_aff *ma2);
6758 __isl_give isl_multi_aff *isl_multi_aff_product(
6759 __isl_take isl_multi_aff *ma1,
6760 __isl_take isl_multi_aff *ma2);
6761 __isl_give isl_multi_pw_aff *
6762 isl_multi_pw_aff_range_product(
6763 __isl_take isl_multi_pw_aff *mpa1,
6764 __isl_take isl_multi_pw_aff *mpa2);
6765 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6766 __isl_take isl_multi_pw_aff *mpa1,
6767 __isl_take isl_multi_pw_aff *mpa2);
6768 __isl_give isl_pw_multi_aff *
6769 isl_pw_multi_aff_range_product(
6770 __isl_take isl_pw_multi_aff *pma1,
6771 __isl_take isl_pw_multi_aff *pma2);
6772 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6773 __isl_take isl_pw_multi_aff *pma1,
6774 __isl_take isl_pw_multi_aff *pma2);
6775 __isl_give isl_multi_union_pw_aff *
6776 isl_multi_union_pw_aff_range_product(
6777 __isl_take isl_multi_union_pw_aff *mupa1,
6778 __isl_take isl_multi_union_pw_aff *mupa2);
6780 The above functions compute the cross product of the given
6781 sets, relations or functions. The domains and ranges of the results
6782 are wrapped maps between domains and ranges of the inputs.
6783 To obtain a ``flat'' product, use the following functions
6786 #include <isl/set.h>
6787 __isl_give isl_basic_set *isl_basic_set_flat_product(
6788 __isl_take isl_basic_set *bset1,
6789 __isl_take isl_basic_set *bset2);
6790 __isl_give isl_set *isl_set_flat_product(
6791 __isl_take isl_set *set1,
6792 __isl_take isl_set *set2);
6794 #include <isl/map.h>
6795 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6796 __isl_take isl_basic_map *bmap1,
6797 __isl_take isl_basic_map *bmap2);
6798 __isl_give isl_map *isl_map_flat_domain_product(
6799 __isl_take isl_map *map1,
6800 __isl_take isl_map *map2);
6801 __isl_give isl_map *isl_map_flat_range_product(
6802 __isl_take isl_map *map1,
6803 __isl_take isl_map *map2);
6804 __isl_give isl_basic_map *isl_basic_map_flat_product(
6805 __isl_take isl_basic_map *bmap1,
6806 __isl_take isl_basic_map *bmap2);
6807 __isl_give isl_map *isl_map_flat_product(
6808 __isl_take isl_map *map1,
6809 __isl_take isl_map *map2);
6811 #include <isl/union_map.h>
6812 __isl_give isl_union_map *
6813 isl_union_map_flat_domain_product(
6814 __isl_take isl_union_map *umap1,
6815 __isl_take isl_union_map *umap2);
6816 __isl_give isl_union_map *
6817 isl_union_map_flat_range_product(
6818 __isl_take isl_union_map *umap1,
6819 __isl_take isl_union_map *umap2);
6821 #include <isl/val.h>
6822 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6823 __isl_take isl_multi_val *mv1,
6824 __isl_take isl_multi_aff *mv2);
6826 #include <isl/aff.h>
6827 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6828 __isl_take isl_multi_aff *ma1,
6829 __isl_take isl_multi_aff *ma2);
6830 __isl_give isl_pw_multi_aff *
6831 isl_pw_multi_aff_flat_range_product(
6832 __isl_take isl_pw_multi_aff *pma1,
6833 __isl_take isl_pw_multi_aff *pma2);
6834 __isl_give isl_multi_pw_aff *
6835 isl_multi_pw_aff_flat_range_product(
6836 __isl_take isl_multi_pw_aff *mpa1,
6837 __isl_take isl_multi_pw_aff *mpa2);
6838 __isl_give isl_union_pw_multi_aff *
6839 isl_union_pw_multi_aff_flat_range_product(
6840 __isl_take isl_union_pw_multi_aff *upma1,
6841 __isl_take isl_union_pw_multi_aff *upma2);
6842 __isl_give isl_multi_union_pw_aff *
6843 isl_multi_union_pw_aff_flat_range_product(
6844 __isl_take isl_multi_union_pw_aff *mupa1,
6845 __isl_take isl_multi_union_pw_aff *mupa2);
6847 #include <isl/space.h>
6848 __isl_give isl_space *isl_space_factor_domain(
6849 __isl_take isl_space *space);
6850 __isl_give isl_space *isl_space_factor_range(
6851 __isl_take isl_space *space);
6852 __isl_give isl_space *isl_space_domain_factor_domain(
6853 __isl_take isl_space *space);
6854 __isl_give isl_space *isl_space_domain_factor_range(
6855 __isl_take isl_space *space);
6856 __isl_give isl_space *isl_space_range_factor_domain(
6857 __isl_take isl_space *space);
6858 __isl_give isl_space *isl_space_range_factor_range(
6859 __isl_take isl_space *space);
6861 The functions C<isl_space_range_factor_domain> and
6862 C<isl_space_range_factor_range> extract the two arguments from
6863 the result of a call to C<isl_space_range_product>.
6865 The arguments of a call to a product can be extracted
6866 from the result using the following functions.
6868 #include <isl/map.h>
6869 __isl_give isl_map *isl_map_factor_domain(
6870 __isl_take isl_map *map);
6871 __isl_give isl_map *isl_map_factor_range(
6872 __isl_take isl_map *map);
6873 __isl_give isl_map *isl_map_domain_factor_domain(
6874 __isl_take isl_map *map);
6875 __isl_give isl_map *isl_map_domain_factor_range(
6876 __isl_take isl_map *map);
6877 __isl_give isl_map *isl_map_range_factor_domain(
6878 __isl_take isl_map *map);
6879 __isl_give isl_map *isl_map_range_factor_range(
6880 __isl_take isl_map *map);
6882 #include <isl/union_map.h>
6883 __isl_give isl_union_map *isl_union_map_factor_domain(
6884 __isl_take isl_union_map *umap);
6885 __isl_give isl_union_map *isl_union_map_factor_range(
6886 __isl_take isl_union_map *umap);
6887 __isl_give isl_union_map *
6888 isl_union_map_domain_factor_domain(
6889 __isl_take isl_union_map *umap);
6890 __isl_give isl_union_map *
6891 isl_union_map_domain_factor_range(
6892 __isl_take isl_union_map *umap);
6893 __isl_give isl_union_map *
6894 isl_union_map_range_factor_domain(
6895 __isl_take isl_union_map *umap);
6896 __isl_give isl_union_map *
6897 isl_union_map_range_factor_range(
6898 __isl_take isl_union_map *umap);
6900 #include <isl/val.h>
6901 __isl_give isl_multi_val *isl_multi_val_factor_range(
6902 __isl_take isl_multi_val *mv);
6903 __isl_give isl_multi_val *
6904 isl_multi_val_range_factor_domain(
6905 __isl_take isl_multi_val *mv);
6906 __isl_give isl_multi_val *
6907 isl_multi_val_range_factor_range(
6908 __isl_take isl_multi_val *mv);
6910 #include <isl/aff.h>
6911 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6912 __isl_take isl_multi_aff *ma);
6913 __isl_give isl_multi_aff *
6914 isl_multi_aff_range_factor_domain(
6915 __isl_take isl_multi_aff *ma);
6916 __isl_give isl_multi_aff *
6917 isl_multi_aff_range_factor_range(
6918 __isl_take isl_multi_aff *ma);
6919 __isl_give isl_multi_pw_aff *
6920 isl_multi_pw_aff_factor_range(
6921 __isl_take isl_multi_pw_aff *mpa);
6922 __isl_give isl_multi_pw_aff *
6923 isl_multi_pw_aff_range_factor_domain(
6924 __isl_take isl_multi_pw_aff *mpa);
6925 __isl_give isl_multi_pw_aff *
6926 isl_multi_pw_aff_range_factor_range(
6927 __isl_take isl_multi_pw_aff *mpa);
6928 __isl_give isl_multi_union_pw_aff *
6929 isl_multi_union_pw_aff_factor_range(
6930 __isl_take isl_multi_union_pw_aff *mupa);
6931 __isl_give isl_multi_union_pw_aff *
6932 isl_multi_union_pw_aff_range_factor_domain(
6933 __isl_take isl_multi_union_pw_aff *mupa);
6934 __isl_give isl_multi_union_pw_aff *
6935 isl_multi_union_pw_aff_range_factor_range(
6936 __isl_take isl_multi_union_pw_aff *mupa);
6938 The splice functions are a generalization of the flat product functions,
6939 where the second argument may be inserted at any position inside
6940 the first argument rather than being placed at the end.
6941 The functions C<isl_multi_val_factor_range>,
6942 C<isl_multi_aff_factor_range>,
6943 C<isl_multi_pw_aff_factor_range> and
6944 C<isl_multi_union_pw_aff_factor_range>
6945 take functions that live in a set space.
6947 #include <isl/val.h>
6948 __isl_give isl_multi_val *isl_multi_val_range_splice(
6949 __isl_take isl_multi_val *mv1, unsigned pos,
6950 __isl_take isl_multi_val *mv2);
6952 #include <isl/aff.h>
6953 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6954 __isl_take isl_multi_aff *ma1, unsigned pos,
6955 __isl_take isl_multi_aff *ma2);
6956 __isl_give isl_multi_aff *isl_multi_aff_splice(
6957 __isl_take isl_multi_aff *ma1,
6958 unsigned in_pos, unsigned out_pos,
6959 __isl_take isl_multi_aff *ma2);
6960 __isl_give isl_multi_pw_aff *
6961 isl_multi_pw_aff_range_splice(
6962 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6963 __isl_take isl_multi_pw_aff *mpa2);
6964 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6965 __isl_take isl_multi_pw_aff *mpa1,
6966 unsigned in_pos, unsigned out_pos,
6967 __isl_take isl_multi_pw_aff *mpa2);
6968 __isl_give isl_multi_union_pw_aff *
6969 isl_multi_union_pw_aff_range_splice(
6970 __isl_take isl_multi_union_pw_aff *mupa1,
6972 __isl_take isl_multi_union_pw_aff *mupa2);
6974 =item * Simplification
6976 When applied to a set or relation,
6977 the gist operation returns a set or relation that has the
6978 same intersection with the context as the input set or relation.
6979 Any implicit equality in the intersection is made explicit in the result,
6980 while all inequalities that are redundant with respect to the intersection
6982 In case of union sets and relations, the gist operation is performed
6985 When applied to a function,
6986 the gist operation applies the set gist operation to each of
6987 the cells in the domain of the input piecewise expression.
6988 The context is also exploited
6989 to simplify the expression associated to each cell.
6991 #include <isl/set.h>
6992 __isl_give isl_basic_set *isl_basic_set_gist(
6993 __isl_take isl_basic_set *bset,
6994 __isl_take isl_basic_set *context);
6995 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6996 __isl_take isl_set *context);
6997 __isl_give isl_set *isl_set_gist_params(
6998 __isl_take isl_set *set,
6999 __isl_take isl_set *context);
7001 #include <isl/map.h>
7002 __isl_give isl_basic_map *isl_basic_map_gist(
7003 __isl_take isl_basic_map *bmap,
7004 __isl_take isl_basic_map *context);
7005 __isl_give isl_basic_map *isl_basic_map_gist_domain(
7006 __isl_take isl_basic_map *bmap,
7007 __isl_take isl_basic_set *context);
7008 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
7009 __isl_take isl_map *context);
7010 __isl_give isl_map *isl_map_gist_params(
7011 __isl_take isl_map *map,
7012 __isl_take isl_set *context);
7013 __isl_give isl_map *isl_map_gist_domain(
7014 __isl_take isl_map *map,
7015 __isl_take isl_set *context);
7016 __isl_give isl_map *isl_map_gist_range(
7017 __isl_take isl_map *map,
7018 __isl_take isl_set *context);
7020 #include <isl/union_set.h>
7021 __isl_give isl_union_set *isl_union_set_gist(
7022 __isl_take isl_union_set *uset,
7023 __isl_take isl_union_set *context);
7024 __isl_give isl_union_set *isl_union_set_gist_params(
7025 __isl_take isl_union_set *uset,
7026 __isl_take isl_set *set);
7028 #include <isl/union_map.h>
7029 __isl_give isl_union_map *isl_union_map_gist(
7030 __isl_take isl_union_map *umap,
7031 __isl_take isl_union_map *context);
7032 __isl_give isl_union_map *isl_union_map_gist_params(
7033 __isl_take isl_union_map *umap,
7034 __isl_take isl_set *set);
7035 __isl_give isl_union_map *isl_union_map_gist_domain(
7036 __isl_take isl_union_map *umap,
7037 __isl_take isl_union_set *uset);
7038 __isl_give isl_union_map *isl_union_map_gist_range(
7039 __isl_take isl_union_map *umap,
7040 __isl_take isl_union_set *uset);
7042 #include <isl/aff.h>
7043 __isl_give isl_aff *isl_aff_gist_params(
7044 __isl_take isl_aff *aff,
7045 __isl_take isl_set *context);
7046 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
7047 __isl_take isl_set *context);
7048 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
7049 __isl_take isl_multi_aff *maff,
7050 __isl_take isl_set *context);
7051 __isl_give isl_multi_aff *isl_multi_aff_gist(
7052 __isl_take isl_multi_aff *maff,
7053 __isl_take isl_set *context);
7054 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
7055 __isl_take isl_pw_aff *pwaff,
7056 __isl_take isl_set *context);
7057 __isl_give isl_pw_aff *isl_pw_aff_gist(
7058 __isl_take isl_pw_aff *pwaff,
7059 __isl_take isl_set *context);
7060 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
7061 __isl_take isl_pw_multi_aff *pma,
7062 __isl_take isl_set *set);
7063 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
7064 __isl_take isl_pw_multi_aff *pma,
7065 __isl_take isl_set *set);
7066 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
7067 __isl_take isl_multi_pw_aff *mpa,
7068 __isl_take isl_set *set);
7069 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
7070 __isl_take isl_multi_pw_aff *mpa,
7071 __isl_take isl_set *set);
7072 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
7073 __isl_take isl_union_pw_aff *upa,
7074 __isl_take isl_union_set *context);
7075 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
7076 __isl_take isl_union_pw_aff *upa,
7077 __isl_take isl_set *context);
7078 __isl_give isl_union_pw_multi_aff *
7079 isl_union_pw_multi_aff_gist_params(
7080 __isl_take isl_union_pw_multi_aff *upma,
7081 __isl_take isl_set *context);
7082 __isl_give isl_union_pw_multi_aff *
7083 isl_union_pw_multi_aff_gist(
7084 __isl_take isl_union_pw_multi_aff *upma,
7085 __isl_take isl_union_set *context);
7086 __isl_give isl_multi_union_pw_aff *
7087 isl_multi_union_pw_aff_gist_params(
7088 __isl_take isl_multi_union_pw_aff *aff,
7089 __isl_take isl_set *context);
7090 __isl_give isl_multi_union_pw_aff *
7091 isl_multi_union_pw_aff_gist(
7092 __isl_take isl_multi_union_pw_aff *aff,
7093 __isl_take isl_union_set *context);
7095 #include <isl/polynomial.h>
7096 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
7097 __isl_take isl_qpolynomial *qp,
7098 __isl_take isl_set *context);
7099 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
7100 __isl_take isl_qpolynomial *qp,
7101 __isl_take isl_set *context);
7102 __isl_give isl_qpolynomial_fold *
7103 isl_qpolynomial_fold_gist_params(
7104 __isl_take isl_qpolynomial_fold *fold,
7105 __isl_take isl_set *context);
7106 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7107 __isl_take isl_qpolynomial_fold *fold,
7108 __isl_take isl_set *context);
7109 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7110 __isl_take isl_pw_qpolynomial *pwqp,
7111 __isl_take isl_set *context);
7112 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7113 __isl_take isl_pw_qpolynomial *pwqp,
7114 __isl_take isl_set *context);
7115 __isl_give isl_pw_qpolynomial_fold *
7116 isl_pw_qpolynomial_fold_gist(
7117 __isl_take isl_pw_qpolynomial_fold *pwf,
7118 __isl_take isl_set *context);
7119 __isl_give isl_pw_qpolynomial_fold *
7120 isl_pw_qpolynomial_fold_gist_params(
7121 __isl_take isl_pw_qpolynomial_fold *pwf,
7122 __isl_take isl_set *context);
7123 __isl_give isl_union_pw_qpolynomial *
7124 isl_union_pw_qpolynomial_gist_params(
7125 __isl_take isl_union_pw_qpolynomial *upwqp,
7126 __isl_take isl_set *context);
7127 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7128 __isl_take isl_union_pw_qpolynomial *upwqp,
7129 __isl_take isl_union_set *context);
7130 __isl_give isl_union_pw_qpolynomial_fold *
7131 isl_union_pw_qpolynomial_fold_gist(
7132 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7133 __isl_take isl_union_set *context);
7134 __isl_give isl_union_pw_qpolynomial_fold *
7135 isl_union_pw_qpolynomial_fold_gist_params(
7136 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7137 __isl_take isl_set *context);
7139 =item * Binary Arithmetic Operations
7141 #include <isl/set.h>
7142 __isl_give isl_set *isl_set_sum(
7143 __isl_take isl_set *set1,
7144 __isl_take isl_set *set2);
7145 #include <isl/map.h>
7146 __isl_give isl_map *isl_map_sum(
7147 __isl_take isl_map *map1,
7148 __isl_take isl_map *map2);
7150 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7151 i.e., the set containing the sums of pairs of elements from
7152 C<set1> and C<set2>.
7153 The domain of the result of C<isl_map_sum> is the intersection
7154 of the domains of its two arguments. The corresponding range
7155 elements are the sums of the corresponding range elements
7156 in the two arguments.
7158 #include <isl/val.h>
7159 __isl_give isl_multi_val *isl_multi_val_add(
7160 __isl_take isl_multi_val *mv1,
7161 __isl_take isl_multi_val *mv2);
7162 __isl_give isl_multi_val *isl_multi_val_sub(
7163 __isl_take isl_multi_val *mv1,
7164 __isl_take isl_multi_val *mv2);
7166 #include <isl/aff.h>
7167 __isl_give isl_aff *isl_aff_add(
7168 __isl_take isl_aff *aff1,
7169 __isl_take isl_aff *aff2);
7170 __isl_give isl_multi_aff *isl_multi_aff_add(
7171 __isl_take isl_multi_aff *maff1,
7172 __isl_take isl_multi_aff *maff2);
7173 __isl_give isl_pw_aff *isl_pw_aff_add(
7174 __isl_take isl_pw_aff *pwaff1,
7175 __isl_take isl_pw_aff *pwaff2);
7176 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7177 __isl_take isl_multi_pw_aff *mpa1,
7178 __isl_take isl_multi_pw_aff *mpa2);
7179 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7180 __isl_take isl_pw_multi_aff *pma1,
7181 __isl_take isl_pw_multi_aff *pma2);
7182 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7183 __isl_take isl_union_pw_aff *upa1,
7184 __isl_take isl_union_pw_aff *upa2);
7185 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7186 __isl_take isl_union_pw_multi_aff *upma1,
7187 __isl_take isl_union_pw_multi_aff *upma2);
7188 __isl_give isl_multi_union_pw_aff *
7189 isl_multi_union_pw_aff_add(
7190 __isl_take isl_multi_union_pw_aff *mupa1,
7191 __isl_take isl_multi_union_pw_aff *mupa2);
7192 __isl_give isl_pw_aff *isl_pw_aff_min(
7193 __isl_take isl_pw_aff *pwaff1,
7194 __isl_take isl_pw_aff *pwaff2);
7195 __isl_give isl_pw_aff *isl_pw_aff_max(
7196 __isl_take isl_pw_aff *pwaff1,
7197 __isl_take isl_pw_aff *pwaff2);
7198 __isl_give isl_aff *isl_aff_sub(
7199 __isl_take isl_aff *aff1,
7200 __isl_take isl_aff *aff2);
7201 __isl_give isl_multi_aff *isl_multi_aff_sub(
7202 __isl_take isl_multi_aff *ma1,
7203 __isl_take isl_multi_aff *ma2);
7204 __isl_give isl_pw_aff *isl_pw_aff_sub(
7205 __isl_take isl_pw_aff *pwaff1,
7206 __isl_take isl_pw_aff *pwaff2);
7207 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7208 __isl_take isl_multi_pw_aff *mpa1,
7209 __isl_take isl_multi_pw_aff *mpa2);
7210 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7211 __isl_take isl_pw_multi_aff *pma1,
7212 __isl_take isl_pw_multi_aff *pma2);
7213 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7214 __isl_take isl_union_pw_aff *upa1,
7215 __isl_take isl_union_pw_aff *upa2);
7216 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7217 __isl_take isl_union_pw_multi_aff *upma1,
7218 __isl_take isl_union_pw_multi_aff *upma2);
7219 __isl_give isl_multi_union_pw_aff *
7220 isl_multi_union_pw_aff_sub(
7221 __isl_take isl_multi_union_pw_aff *mupa1,
7222 __isl_take isl_multi_union_pw_aff *mupa2);
7224 C<isl_aff_sub> subtracts the second argument from the first.
7226 #include <isl/polynomial.h>
7227 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7228 __isl_take isl_qpolynomial *qp1,
7229 __isl_take isl_qpolynomial *qp2);
7230 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7231 __isl_take isl_pw_qpolynomial *pwqp1,
7232 __isl_take isl_pw_qpolynomial *pwqp2);
7233 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7234 __isl_take isl_pw_qpolynomial *pwqp1,
7235 __isl_take isl_pw_qpolynomial *pwqp2);
7236 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7237 __isl_take isl_pw_qpolynomial_fold *pwf1,
7238 __isl_take isl_pw_qpolynomial_fold *pwf2);
7239 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7240 __isl_take isl_union_pw_qpolynomial *upwqp1,
7241 __isl_take isl_union_pw_qpolynomial *upwqp2);
7242 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7243 __isl_take isl_qpolynomial *qp1,
7244 __isl_take isl_qpolynomial *qp2);
7245 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7246 __isl_take isl_pw_qpolynomial *pwqp1,
7247 __isl_take isl_pw_qpolynomial *pwqp2);
7248 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7249 __isl_take isl_union_pw_qpolynomial *upwqp1,
7250 __isl_take isl_union_pw_qpolynomial *upwqp2);
7251 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7252 __isl_take isl_pw_qpolynomial_fold *pwf1,
7253 __isl_take isl_pw_qpolynomial_fold *pwf2);
7254 __isl_give isl_union_pw_qpolynomial_fold *
7255 isl_union_pw_qpolynomial_fold_fold(
7256 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7257 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7259 #include <isl/aff.h>
7260 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7261 __isl_take isl_pw_aff *pwaff1,
7262 __isl_take isl_pw_aff *pwaff2);
7263 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7264 __isl_take isl_pw_multi_aff *pma1,
7265 __isl_take isl_pw_multi_aff *pma2);
7266 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7267 __isl_take isl_union_pw_aff *upa1,
7268 __isl_take isl_union_pw_aff *upa2);
7269 __isl_give isl_union_pw_multi_aff *
7270 isl_union_pw_multi_aff_union_add(
7271 __isl_take isl_union_pw_multi_aff *upma1,
7272 __isl_take isl_union_pw_multi_aff *upma2);
7273 __isl_give isl_multi_union_pw_aff *
7274 isl_multi_union_pw_aff_union_add(
7275 __isl_take isl_multi_union_pw_aff *mupa1,
7276 __isl_take isl_multi_union_pw_aff *mupa2);
7277 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7278 __isl_take isl_pw_aff *pwaff1,
7279 __isl_take isl_pw_aff *pwaff2);
7280 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7281 __isl_take isl_pw_aff *pwaff1,
7282 __isl_take isl_pw_aff *pwaff2);
7284 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7285 expression with a domain that is the union of those of C<pwaff1> and
7286 C<pwaff2> and such that on each cell, the quasi-affine expression is
7287 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7288 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7289 associated expression is the defined one.
7290 This in contrast to the C<isl_pw_aff_max> function, which is
7291 only defined on the shared definition domain of the arguments.
7293 #include <isl/val.h>
7294 __isl_give isl_multi_val *isl_multi_val_add_val(
7295 __isl_take isl_multi_val *mv,
7296 __isl_take isl_val *v);
7297 __isl_give isl_multi_val *isl_multi_val_mod_val(
7298 __isl_take isl_multi_val *mv,
7299 __isl_take isl_val *v);
7300 __isl_give isl_multi_val *isl_multi_val_scale_val(
7301 __isl_take isl_multi_val *mv,
7302 __isl_take isl_val *v);
7303 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7304 __isl_take isl_multi_val *mv,
7305 __isl_take isl_val *v);
7307 #include <isl/aff.h>
7308 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7309 __isl_take isl_val *mod);
7310 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7311 __isl_take isl_pw_aff *pa,
7312 __isl_take isl_val *mod);
7313 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7314 __isl_take isl_union_pw_aff *upa,
7315 __isl_take isl_val *f);
7316 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7317 __isl_take isl_val *v);
7318 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7319 __isl_take isl_multi_aff *ma,
7320 __isl_take isl_val *v);
7321 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7322 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7323 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7324 __isl_take isl_multi_pw_aff *mpa,
7325 __isl_take isl_val *v);
7326 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7327 __isl_take isl_pw_multi_aff *pma,
7328 __isl_take isl_val *v);
7329 __isl_give isl_union_pw_multi_aff *
7330 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7331 __isl_take isl_union_pw_aff *upa,
7332 __isl_take isl_val *f);
7333 isl_union_pw_multi_aff_scale_val(
7334 __isl_take isl_union_pw_multi_aff *upma,
7335 __isl_take isl_val *val);
7336 __isl_give isl_multi_union_pw_aff *
7337 isl_multi_union_pw_aff_scale_val(
7338 __isl_take isl_multi_union_pw_aff *mupa,
7339 __isl_take isl_val *v);
7340 __isl_give isl_aff *isl_aff_scale_down_ui(
7341 __isl_take isl_aff *aff, unsigned f);
7342 __isl_give isl_aff *isl_aff_scale_down_val(
7343 __isl_take isl_aff *aff, __isl_take isl_val *v);
7344 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7345 __isl_take isl_multi_aff *ma,
7346 __isl_take isl_val *v);
7347 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7348 __isl_take isl_pw_aff *pa,
7349 __isl_take isl_val *f);
7350 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7351 __isl_take isl_multi_pw_aff *mpa,
7352 __isl_take isl_val *v);
7353 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7354 __isl_take isl_pw_multi_aff *pma,
7355 __isl_take isl_val *v);
7356 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7357 __isl_take isl_union_pw_aff *upa,
7358 __isl_take isl_val *v);
7359 __isl_give isl_union_pw_multi_aff *
7360 isl_union_pw_multi_aff_scale_down_val(
7361 __isl_take isl_union_pw_multi_aff *upma,
7362 __isl_take isl_val *val);
7363 __isl_give isl_multi_union_pw_aff *
7364 isl_multi_union_pw_aff_scale_down_val(
7365 __isl_take isl_multi_union_pw_aff *mupa,
7366 __isl_take isl_val *v);
7368 #include <isl/polynomial.h>
7369 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7370 __isl_take isl_qpolynomial *qp,
7371 __isl_take isl_val *v);
7372 __isl_give isl_qpolynomial_fold *
7373 isl_qpolynomial_fold_scale_val(
7374 __isl_take isl_qpolynomial_fold *fold,
7375 __isl_take isl_val *v);
7376 __isl_give isl_pw_qpolynomial *
7377 isl_pw_qpolynomial_scale_val(
7378 __isl_take isl_pw_qpolynomial *pwqp,
7379 __isl_take isl_val *v);
7380 __isl_give isl_pw_qpolynomial_fold *
7381 isl_pw_qpolynomial_fold_scale_val(
7382 __isl_take isl_pw_qpolynomial_fold *pwf,
7383 __isl_take isl_val *v);
7384 __isl_give isl_union_pw_qpolynomial *
7385 isl_union_pw_qpolynomial_scale_val(
7386 __isl_take isl_union_pw_qpolynomial *upwqp,
7387 __isl_take isl_val *v);
7388 __isl_give isl_union_pw_qpolynomial_fold *
7389 isl_union_pw_qpolynomial_fold_scale_val(
7390 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7391 __isl_take isl_val *v);
7392 __isl_give isl_qpolynomial *
7393 isl_qpolynomial_scale_down_val(
7394 __isl_take isl_qpolynomial *qp,
7395 __isl_take isl_val *v);
7396 __isl_give isl_qpolynomial_fold *
7397 isl_qpolynomial_fold_scale_down_val(
7398 __isl_take isl_qpolynomial_fold *fold,
7399 __isl_take isl_val *v);
7400 __isl_give isl_pw_qpolynomial *
7401 isl_pw_qpolynomial_scale_down_val(
7402 __isl_take isl_pw_qpolynomial *pwqp,
7403 __isl_take isl_val *v);
7404 __isl_give isl_pw_qpolynomial_fold *
7405 isl_pw_qpolynomial_fold_scale_down_val(
7406 __isl_take isl_pw_qpolynomial_fold *pwf,
7407 __isl_take isl_val *v);
7408 __isl_give isl_union_pw_qpolynomial *
7409 isl_union_pw_qpolynomial_scale_down_val(
7410 __isl_take isl_union_pw_qpolynomial *upwqp,
7411 __isl_take isl_val *v);
7412 __isl_give isl_union_pw_qpolynomial_fold *
7413 isl_union_pw_qpolynomial_fold_scale_down_val(
7414 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7415 __isl_take isl_val *v);
7417 #include <isl/val.h>
7418 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7419 __isl_take isl_multi_val *mv1,
7420 __isl_take isl_multi_val *mv2);
7421 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7422 __isl_take isl_multi_val *mv1,
7423 __isl_take isl_multi_val *mv2);
7424 __isl_give isl_multi_val *
7425 isl_multi_val_scale_down_multi_val(
7426 __isl_take isl_multi_val *mv1,
7427 __isl_take isl_multi_val *mv2);
7429 #include <isl/aff.h>
7430 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7431 __isl_take isl_multi_aff *ma,
7432 __isl_take isl_multi_val *mv);
7433 __isl_give isl_multi_union_pw_aff *
7434 isl_multi_union_pw_aff_mod_multi_val(
7435 __isl_take isl_multi_union_pw_aff *upma,
7436 __isl_take isl_multi_val *mv);
7437 __isl_give isl_multi_pw_aff *
7438 isl_multi_pw_aff_mod_multi_val(
7439 __isl_take isl_multi_pw_aff *mpa,
7440 __isl_take isl_multi_val *mv);
7441 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7442 __isl_take isl_multi_aff *ma,
7443 __isl_take isl_multi_val *mv);
7444 __isl_give isl_pw_multi_aff *
7445 isl_pw_multi_aff_scale_multi_val(
7446 __isl_take isl_pw_multi_aff *pma,
7447 __isl_take isl_multi_val *mv);
7448 __isl_give isl_multi_pw_aff *
7449 isl_multi_pw_aff_scale_multi_val(
7450 __isl_take isl_multi_pw_aff *mpa,
7451 __isl_take isl_multi_val *mv);
7452 __isl_give isl_multi_union_pw_aff *
7453 isl_multi_union_pw_aff_scale_multi_val(
7454 __isl_take isl_multi_union_pw_aff *mupa,
7455 __isl_take isl_multi_val *mv);
7456 __isl_give isl_union_pw_multi_aff *
7457 isl_union_pw_multi_aff_scale_multi_val(
7458 __isl_take isl_union_pw_multi_aff *upma,
7459 __isl_take isl_multi_val *mv);
7460 __isl_give isl_multi_aff *
7461 isl_multi_aff_scale_down_multi_val(
7462 __isl_take isl_multi_aff *ma,
7463 __isl_take isl_multi_val *mv);
7464 __isl_give isl_multi_pw_aff *
7465 isl_multi_pw_aff_scale_down_multi_val(
7466 __isl_take isl_multi_pw_aff *mpa,
7467 __isl_take isl_multi_val *mv);
7468 __isl_give isl_multi_union_pw_aff *
7469 isl_multi_union_pw_aff_scale_down_multi_val(
7470 __isl_take isl_multi_union_pw_aff *mupa,
7471 __isl_take isl_multi_val *mv);
7473 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7474 by the corresponding elements of C<mv>.
7476 #include <isl/aff.h>
7477 __isl_give isl_aff *isl_aff_mul(
7478 __isl_take isl_aff *aff1,
7479 __isl_take isl_aff *aff2);
7480 __isl_give isl_aff *isl_aff_div(
7481 __isl_take isl_aff *aff1,
7482 __isl_take isl_aff *aff2);
7483 __isl_give isl_pw_aff *isl_pw_aff_mul(
7484 __isl_take isl_pw_aff *pwaff1,
7485 __isl_take isl_pw_aff *pwaff2);
7486 __isl_give isl_pw_aff *isl_pw_aff_div(
7487 __isl_take isl_pw_aff *pa1,
7488 __isl_take isl_pw_aff *pa2);
7489 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7490 __isl_take isl_pw_aff *pa1,
7491 __isl_take isl_pw_aff *pa2);
7492 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7493 __isl_take isl_pw_aff *pa1,
7494 __isl_take isl_pw_aff *pa2);
7496 When multiplying two affine expressions, at least one of the two needs
7497 to be a constant. Similarly, when dividing an affine expression by another,
7498 the second expression needs to be a constant.
7499 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7500 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7503 #include <isl/polynomial.h>
7504 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7505 __isl_take isl_qpolynomial *qp1,
7506 __isl_take isl_qpolynomial *qp2);
7507 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7508 __isl_take isl_pw_qpolynomial *pwqp1,
7509 __isl_take isl_pw_qpolynomial *pwqp2);
7510 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7511 __isl_take isl_union_pw_qpolynomial *upwqp1,
7512 __isl_take isl_union_pw_qpolynomial *upwqp2);
7516 =head3 Lexicographic Optimization
7518 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7519 the following functions
7520 compute a set that contains the lexicographic minimum or maximum
7521 of the elements in C<set> (or C<bset>) for those values of the parameters
7522 that satisfy C<dom>.
7523 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7524 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7526 In other words, the union of the parameter values
7527 for which the result is non-empty and of C<*empty>
7530 #include <isl/set.h>
7531 __isl_give isl_set *isl_basic_set_partial_lexmin(
7532 __isl_take isl_basic_set *bset,
7533 __isl_take isl_basic_set *dom,
7534 __isl_give isl_set **empty);
7535 __isl_give isl_set *isl_basic_set_partial_lexmax(
7536 __isl_take isl_basic_set *bset,
7537 __isl_take isl_basic_set *dom,
7538 __isl_give isl_set **empty);
7539 __isl_give isl_set *isl_set_partial_lexmin(
7540 __isl_take isl_set *set, __isl_take isl_set *dom,
7541 __isl_give isl_set **empty);
7542 __isl_give isl_set *isl_set_partial_lexmax(
7543 __isl_take isl_set *set, __isl_take isl_set *dom,
7544 __isl_give isl_set **empty);
7546 Given a (basic) set C<set> (or C<bset>), the following functions simply
7547 return a set containing the lexicographic minimum or maximum
7548 of the elements in C<set> (or C<bset>).
7549 In case of union sets, the optimum is computed per space.
7551 #include <isl/set.h>
7552 __isl_give isl_set *isl_basic_set_lexmin(
7553 __isl_take isl_basic_set *bset);
7554 __isl_give isl_set *isl_basic_set_lexmax(
7555 __isl_take isl_basic_set *bset);
7556 __isl_give isl_set *isl_set_lexmin(
7557 __isl_take isl_set *set);
7558 __isl_give isl_set *isl_set_lexmax(
7559 __isl_take isl_set *set);
7560 __isl_give isl_union_set *isl_union_set_lexmin(
7561 __isl_take isl_union_set *uset);
7562 __isl_give isl_union_set *isl_union_set_lexmax(
7563 __isl_take isl_union_set *uset);
7565 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7566 the following functions
7567 compute a relation that maps each element of C<dom>
7568 to the single lexicographic minimum or maximum
7569 of the elements that are associated to that same
7570 element in C<map> (or C<bmap>).
7571 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7572 that contains the elements in C<dom> that do not map
7573 to any elements in C<map> (or C<bmap>).
7574 In other words, the union of the domain of the result and of C<*empty>
7577 #include <isl/map.h>
7578 __isl_give isl_map *isl_basic_map_partial_lexmax(
7579 __isl_take isl_basic_map *bmap,
7580 __isl_take isl_basic_set *dom,
7581 __isl_give isl_set **empty);
7582 __isl_give isl_map *isl_basic_map_partial_lexmin(
7583 __isl_take isl_basic_map *bmap,
7584 __isl_take isl_basic_set *dom,
7585 __isl_give isl_set **empty);
7586 __isl_give isl_map *isl_map_partial_lexmax(
7587 __isl_take isl_map *map, __isl_take isl_set *dom,
7588 __isl_give isl_set **empty);
7589 __isl_give isl_map *isl_map_partial_lexmin(
7590 __isl_take isl_map *map, __isl_take isl_set *dom,
7591 __isl_give isl_set **empty);
7593 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7594 return a map mapping each element in the domain of
7595 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7596 of all elements associated to that element.
7597 In case of union relations, the optimum is computed per space.
7599 #include <isl/map.h>
7600 __isl_give isl_map *isl_basic_map_lexmin(
7601 __isl_take isl_basic_map *bmap);
7602 __isl_give isl_map *isl_basic_map_lexmax(
7603 __isl_take isl_basic_map *bmap);
7604 __isl_give isl_map *isl_map_lexmin(
7605 __isl_take isl_map *map);
7606 __isl_give isl_map *isl_map_lexmax(
7607 __isl_take isl_map *map);
7608 __isl_give isl_union_map *isl_union_map_lexmin(
7609 __isl_take isl_union_map *umap);
7610 __isl_give isl_union_map *isl_union_map_lexmax(
7611 __isl_take isl_union_map *umap);
7613 The following functions return their result in the form of
7614 a piecewise multi-affine expression,
7615 but are otherwise equivalent to the corresponding functions
7616 returning a basic set or relation.
7618 #include <isl/set.h>
7619 __isl_give isl_pw_multi_aff *
7620 isl_basic_set_partial_lexmin_pw_multi_aff(
7621 __isl_take isl_basic_set *bset,
7622 __isl_take isl_basic_set *dom,
7623 __isl_give isl_set **empty);
7624 __isl_give isl_pw_multi_aff *
7625 isl_basic_set_partial_lexmax_pw_multi_aff(
7626 __isl_take isl_basic_set *bset,
7627 __isl_take isl_basic_set *dom,
7628 __isl_give isl_set **empty);
7629 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7630 __isl_take isl_set *set);
7631 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7632 __isl_take isl_set *set);
7634 #include <isl/map.h>
7635 __isl_give isl_pw_multi_aff *
7636 isl_basic_map_lexmin_pw_multi_aff(
7637 __isl_take isl_basic_map *bmap);
7638 __isl_give isl_pw_multi_aff *
7639 isl_basic_map_partial_lexmin_pw_multi_aff(
7640 __isl_take isl_basic_map *bmap,
7641 __isl_take isl_basic_set *dom,
7642 __isl_give isl_set **empty);
7643 __isl_give isl_pw_multi_aff *
7644 isl_basic_map_partial_lexmax_pw_multi_aff(
7645 __isl_take isl_basic_map *bmap,
7646 __isl_take isl_basic_set *dom,
7647 __isl_give isl_set **empty);
7648 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7649 __isl_take isl_map *map);
7650 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7651 __isl_take isl_map *map);
7653 The following functions return the lexicographic minimum or maximum
7654 on the shared domain of the inputs and the single defined function
7655 on those parts of the domain where only a single function is defined.
7657 #include <isl/aff.h>
7658 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7659 __isl_take isl_pw_multi_aff *pma1,
7660 __isl_take isl_pw_multi_aff *pma2);
7661 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7662 __isl_take isl_pw_multi_aff *pma1,
7663 __isl_take isl_pw_multi_aff *pma2);
7665 If the input to a lexicographic optimization problem has
7666 multiple constraints with the same coefficients for the optimized
7667 variables, then, by default, this symmetry is exploited by
7668 replacing those constraints by a single constraint with
7669 an abstract bound, which is in turn bounded by the corresponding terms
7670 in the original constraints.
7671 Without this optimization, the solver would typically consider
7672 all possible orderings of those original bounds, resulting in a needless
7673 decomposition of the domain.
7674 However, the optimization can also result in slowdowns since
7675 an extra parameter is introduced that may get used in additional
7677 The following option determines whether symmetry detection is applied
7678 during lexicographic optimization.
7680 #include <isl/options.h>
7681 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7683 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7687 See also \autoref{s:offline}.
7691 =head2 Ternary Operations
7693 #include <isl/aff.h>
7694 __isl_give isl_pw_aff *isl_pw_aff_cond(
7695 __isl_take isl_pw_aff *cond,
7696 __isl_take isl_pw_aff *pwaff_true,
7697 __isl_take isl_pw_aff *pwaff_false);
7699 The function C<isl_pw_aff_cond> performs a conditional operator
7700 and returns an expression that is equal to C<pwaff_true>
7701 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7702 where C<cond> is zero.
7706 Lists are defined over several element types, including
7707 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7708 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7709 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7710 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7711 Here we take lists of C<isl_set>s as an example.
7712 Lists can be created, copied, modified and freed using the following functions.
7714 #include <isl/set.h>
7715 __isl_give isl_set_list *isl_set_list_from_set(
7716 __isl_take isl_set *el);
7717 __isl_give isl_set_list *isl_set_list_alloc(
7718 isl_ctx *ctx, int n);
7719 __isl_give isl_set_list *isl_set_list_copy(
7720 __isl_keep isl_set_list *list);
7721 __isl_give isl_set_list *isl_set_list_insert(
7722 __isl_take isl_set_list *list, unsigned pos,
7723 __isl_take isl_set *el);
7724 __isl_give isl_set_list *isl_set_list_add(
7725 __isl_take isl_set_list *list,
7726 __isl_take isl_set *el);
7727 __isl_give isl_set_list *isl_set_list_drop(
7728 __isl_take isl_set_list *list,
7729 unsigned first, unsigned n);
7730 __isl_give isl_set_list *isl_set_list_set_set(
7731 __isl_take isl_set_list *list, int index,
7732 __isl_take isl_set *set);
7733 __isl_give isl_set_list *isl_set_list_concat(
7734 __isl_take isl_set_list *list1,
7735 __isl_take isl_set_list *list2);
7736 __isl_give isl_set_list *isl_set_list_map(
7737 __isl_take isl_set_list *list,
7738 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7741 __isl_give isl_set_list *isl_set_list_sort(
7742 __isl_take isl_set_list *list,
7743 int (*cmp)(__isl_keep isl_set *a,
7744 __isl_keep isl_set *b, void *user),
7746 __isl_null isl_set_list *isl_set_list_free(
7747 __isl_take isl_set_list *list);
7749 C<isl_set_list_alloc> creates an empty list with an initial capacity
7750 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7751 add elements to a list, increasing its capacity as needed.
7752 C<isl_set_list_from_set> creates a list with a single element.
7754 Lists can be inspected using the following functions.
7756 #include <isl/set.h>
7757 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7758 __isl_give isl_set *isl_set_list_get_set(
7759 __isl_keep isl_set_list *list, int index);
7760 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7761 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7763 isl_stat isl_set_list_foreach_scc(
7764 __isl_keep isl_set_list *list,
7765 isl_bool (*follows)(__isl_keep isl_set *a,
7766 __isl_keep isl_set *b, void *user),
7768 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7771 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7772 strongly connected components of the graph with as vertices the elements
7773 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7774 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7775 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7777 Lists can be printed using
7779 #include <isl/set.h>
7780 __isl_give isl_printer *isl_printer_print_set_list(
7781 __isl_take isl_printer *p,
7782 __isl_keep isl_set_list *list);
7784 =head2 Associative arrays
7786 Associative arrays map isl objects of a specific type to isl objects
7787 of some (other) specific type. They are defined for several pairs
7788 of types, including (C<isl_map>, C<isl_basic_set>),
7789 (C<isl_id>, C<isl_ast_expr>),
7790 (C<isl_id>, C<isl_id>) and
7791 (C<isl_id>, C<isl_pw_aff>).
7792 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7795 Associative arrays can be created, copied and freed using
7796 the following functions.
7798 #include <isl/id_to_ast_expr.h>
7799 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7800 isl_ctx *ctx, int min_size);
7801 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7802 __isl_keep isl_id_to_ast_expr *id2expr);
7803 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7804 __isl_take isl_id_to_ast_expr *id2expr);
7806 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7807 to specify the expected size of the associative array.
7808 The associative array will be grown automatically as needed.
7810 Associative arrays can be inspected using the following functions.
7812 #include <isl/id_to_ast_expr.h>
7813 __isl_give isl_maybe_isl_ast_expr
7814 isl_id_to_ast_expr_try_get(
7815 __isl_keep isl_id_to_ast_expr *id2expr,
7816 __isl_keep isl_id *key);
7817 isl_bool isl_id_to_ast_expr_has(
7818 __isl_keep isl_id_to_ast_expr *id2expr,
7819 __isl_keep isl_id *key);
7820 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7821 __isl_keep isl_id_to_ast_expr *id2expr,
7822 __isl_take isl_id *key);
7823 isl_stat isl_id_to_ast_expr_foreach(
7824 __isl_keep isl_id_to_ast_expr *id2expr,
7825 isl_stat (*fn)(__isl_take isl_id *key,
7826 __isl_take isl_ast_expr *val, void *user),
7829 The function C<isl_id_to_ast_expr_try_get> returns a structure
7830 containing two elements, C<valid> and C<value>.
7831 If there is a value associated to the key, then C<valid>
7832 is set to C<isl_bool_true> and C<value> contains a copy of
7833 the associated value. Otherwise C<value> is C<NULL> and
7834 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7835 on whether some error has occurred or there simply is no associated value.
7836 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7837 in the structure and
7838 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7840 Associative arrays can be modified using the following functions.
7842 #include <isl/id_to_ast_expr.h>
7843 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7844 __isl_take isl_id_to_ast_expr *id2expr,
7845 __isl_take isl_id *key,
7846 __isl_take isl_ast_expr *val);
7847 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7848 __isl_take isl_id_to_ast_expr *id2expr,
7849 __isl_take isl_id *key);
7851 Associative arrays can be printed using the following function.
7853 #include <isl/id_to_ast_expr.h>
7854 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7855 __isl_take isl_printer *p,
7856 __isl_keep isl_id_to_ast_expr *id2expr);
7860 Vectors can be created, copied and freed using the following functions.
7862 #include <isl/vec.h>
7863 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7865 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
7867 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7868 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7870 Note that the elements of a vector created by C<isl_vec_alloc>
7871 may have arbitrary values.
7872 A vector created by C<isl_vec_zero> has elements with value zero.
7873 The elements can be changed and inspected using the following functions.
7875 int isl_vec_size(__isl_keep isl_vec *vec);
7876 __isl_give isl_val *isl_vec_get_element_val(
7877 __isl_keep isl_vec *vec, int pos);
7878 __isl_give isl_vec *isl_vec_set_element_si(
7879 __isl_take isl_vec *vec, int pos, int v);
7880 __isl_give isl_vec *isl_vec_set_element_val(
7881 __isl_take isl_vec *vec, int pos,
7882 __isl_take isl_val *v);
7883 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7885 __isl_give isl_vec *isl_vec_set_val(
7886 __isl_take isl_vec *vec, __isl_take isl_val *v);
7887 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7888 __isl_keep isl_vec *vec2, int pos);
7890 C<isl_vec_get_element> will return a negative value if anything went wrong.
7891 In that case, the value of C<*v> is undefined.
7893 The following function can be used to concatenate two vectors.
7895 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7896 __isl_take isl_vec *vec2);
7900 Matrices can be created, copied and freed using the following functions.
7902 #include <isl/mat.h>
7903 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7904 unsigned n_row, unsigned n_col);
7905 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7906 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7908 Note that the elements of a newly created matrix may have arbitrary values.
7909 The elements can be changed and inspected using the following functions.
7911 int isl_mat_rows(__isl_keep isl_mat *mat);
7912 int isl_mat_cols(__isl_keep isl_mat *mat);
7913 __isl_give isl_val *isl_mat_get_element_val(
7914 __isl_keep isl_mat *mat, int row, int col);
7915 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7916 int row, int col, int v);
7917 __isl_give isl_mat *isl_mat_set_element_val(
7918 __isl_take isl_mat *mat, int row, int col,
7919 __isl_take isl_val *v);
7921 The following function computes the rank of a matrix.
7922 The return value may be -1 if some error occurred.
7924 #include <isl/mat.h>
7925 int isl_mat_rank(__isl_keep isl_mat *mat);
7927 The following function can be used to compute the (right) inverse
7928 of a matrix, i.e., a matrix such that the product of the original
7929 and the inverse (in that order) is a multiple of the identity matrix.
7930 The input matrix is assumed to be of full row-rank.
7932 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7934 The following function can be used to compute the (right) kernel
7935 (or null space) of a matrix, i.e., a matrix such that the product of
7936 the original and the kernel (in that order) is the zero matrix.
7938 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7940 The following function computes a basis for the space spanned
7941 by the rows of a matrix.
7943 __isl_give isl_mat *isl_mat_row_basis(
7944 __isl_take isl_mat *mat);
7946 The following function computes rows that extend a basis of C<mat1>
7947 to a basis that also covers C<mat2>.
7949 __isl_give isl_mat *isl_mat_row_basis_extension(
7950 __isl_take isl_mat *mat1,
7951 __isl_take isl_mat *mat2);
7953 The following function checks whether there is no linear dependence
7954 among the combined rows of "mat1" and "mat2" that is not already present
7955 in "mat1" or "mat2" individually.
7956 If "mat1" and "mat2" have linearly independent rows by themselves,
7957 then this means that there is no linear dependence among all rows together.
7959 isl_bool isl_mat_has_linearly_independent_rows(
7960 __isl_keep isl_mat *mat1,
7961 __isl_keep isl_mat *mat2);
7963 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7965 The following functions determine
7966 an upper or lower bound on a quasipolynomial over its domain.
7968 __isl_give isl_pw_qpolynomial_fold *
7969 isl_pw_qpolynomial_bound(
7970 __isl_take isl_pw_qpolynomial *pwqp,
7971 enum isl_fold type, int *tight);
7973 __isl_give isl_union_pw_qpolynomial_fold *
7974 isl_union_pw_qpolynomial_bound(
7975 __isl_take isl_union_pw_qpolynomial *upwqp,
7976 enum isl_fold type, int *tight);
7978 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7979 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7980 is the returned bound is known be tight, i.e., for each value
7981 of the parameters there is at least
7982 one element in the domain that reaches the bound.
7983 If the domain of C<pwqp> is not wrapping, then the bound is computed
7984 over all elements in that domain and the result has a purely parametric
7985 domain. If the domain of C<pwqp> is wrapping, then the bound is
7986 computed over the range of the wrapped relation. The domain of the
7987 wrapped relation becomes the domain of the result.
7989 =head2 Parametric Vertex Enumeration
7991 The parametric vertex enumeration described in this section
7992 is mainly intended to be used internally and by the C<barvinok>
7995 #include <isl/vertices.h>
7996 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7997 __isl_keep isl_basic_set *bset);
7999 The function C<isl_basic_set_compute_vertices> performs the
8000 actual computation of the parametric vertices and the chamber
8001 decomposition and stores the result in an C<isl_vertices> object.
8002 This information can be queried by either iterating over all
8003 the vertices or iterating over all the chambers or cells
8004 and then iterating over all vertices that are active on the chamber.
8006 isl_stat isl_vertices_foreach_vertex(
8007 __isl_keep isl_vertices *vertices,
8008 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8009 void *user), void *user);
8011 isl_stat isl_vertices_foreach_cell(
8012 __isl_keep isl_vertices *vertices,
8013 isl_stat (*fn)(__isl_take isl_cell *cell,
8014 void *user), void *user);
8015 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
8016 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8017 void *user), void *user);
8019 Other operations that can be performed on an C<isl_vertices> object are
8022 int isl_vertices_get_n_vertices(
8023 __isl_keep isl_vertices *vertices);
8024 __isl_null isl_vertices *isl_vertices_free(
8025 __isl_take isl_vertices *vertices);
8027 Vertices can be inspected and destroyed using the following functions.
8029 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
8030 __isl_give isl_basic_set *isl_vertex_get_domain(
8031 __isl_keep isl_vertex *vertex);
8032 __isl_give isl_multi_aff *isl_vertex_get_expr(
8033 __isl_keep isl_vertex *vertex);
8034 void isl_vertex_free(__isl_take isl_vertex *vertex);
8036 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
8037 describing the vertex in terms of the parameters,
8038 while C<isl_vertex_get_domain> returns the activity domain
8041 Chambers can be inspected and destroyed using the following functions.
8043 __isl_give isl_basic_set *isl_cell_get_domain(
8044 __isl_keep isl_cell *cell);
8045 void isl_cell_free(__isl_take isl_cell *cell);
8047 =head1 Polyhedral Compilation Library
8049 This section collects functionality in C<isl> that has been specifically
8050 designed for use during polyhedral compilation.
8052 =head2 Schedule Trees
8054 A schedule tree is a structured representation of a schedule,
8055 assigning a relative order to a set of domain elements.
8056 The relative order expressed by the schedule tree is
8057 defined recursively. In particular, the order between
8058 two domain elements is determined by the node that is closest
8059 to the root that refers to both elements and that orders them apart.
8060 Each node in the tree is of one of several types.
8061 The root node is always of type C<isl_schedule_node_domain>
8062 (or C<isl_schedule_node_extension>)
8063 and it describes the (extra) domain elements to which the schedule applies.
8064 The other types of nodes are as follows.
8068 =item C<isl_schedule_node_band>
8070 A band of schedule dimensions. Each schedule dimension is represented
8071 by a union piecewise quasi-affine expression. If this expression
8072 assigns a different value to two domain elements, while all previous
8073 schedule dimensions in the same band assign them the same value,
8074 then the two domain elements are ordered according to these two
8076 Each expression is required to be total in the domain elements
8077 that reach the band node.
8079 =item C<isl_schedule_node_expansion>
8081 An expansion node maps each of the domain elements that reach the node
8082 to one or more domain elements. The image of this mapping forms
8083 the set of domain elements that reach the child of the expansion node.
8084 The function that maps each of the expanded domain elements
8085 to the original domain element from which it was expanded
8086 is called the contraction.
8088 =item C<isl_schedule_node_filter>
8090 A filter node does not impose any ordering, but rather intersects
8091 the set of domain elements that the current subtree refers to
8092 with a given union set. The subtree of the filter node only
8093 refers to domain elements in the intersection.
8094 A filter node is typically only used as a child of a sequence or
8097 =item C<isl_schedule_node_leaf>
8099 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
8101 =item C<isl_schedule_node_mark>
8103 A mark node can be used to attach any kind of information to a subtree
8104 of the schedule tree.
8106 =item C<isl_schedule_node_sequence>
8108 A sequence node has one or more children, each of which is a filter node.
8109 The filters on these filter nodes form a partition of
8110 the domain elements that the current subtree refers to.
8111 If two domain elements appear in distinct filters then the sequence
8112 node orders them according to the child positions of the corresponding
8115 =item C<isl_schedule_node_set>
8117 A set node is similar to a sequence node, except that
8118 it expresses that domain elements appearing in distinct filters
8119 may have any order. The order of the children of a set node
8120 is therefore also immaterial.
8124 The following node types are only supported by the AST generator.
8128 =item C<isl_schedule_node_context>
8130 The context describes constraints on the parameters and
8131 the schedule dimensions of outer
8132 bands that the AST generator may assume to hold. It is also the only
8133 kind of node that may introduce additional parameters.
8134 The space of the context is that of the flat product of the outer
8135 band nodes. In particular, if there are no outer band nodes, then
8136 this space is the unnamed zero-dimensional space.
8137 Since a context node references the outer band nodes, any tree
8138 containing a context node is considered to be anchored.
8140 =item C<isl_schedule_node_extension>
8142 An extension node instructs the AST generator to add additional
8143 domain elements that need to be scheduled.
8144 The additional domain elements are described by the range of
8145 the extension map in terms of the outer schedule dimensions,
8146 i.e., the flat product of the outer band nodes.
8147 Note that domain elements are added whenever the AST generator
8148 reaches the extension node, meaning that there are still some
8149 active domain elements for which an AST needs to be generated.
8150 The conditions under which some domain elements are still active
8151 may however not be completely described by the outer AST nodes
8152 generated at that point.
8153 Since an extension node references the outer band nodes, any tree
8154 containing an extension node is considered to be anchored.
8156 An extension node may also appear as the root of a schedule tree,
8157 when it is intended to be inserted into another tree
8158 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8159 In this case, the domain of the extension node should
8160 correspond to the flat product of the outer band nodes
8161 in this other schedule tree at the point where the extension tree
8164 =item C<isl_schedule_node_guard>
8166 The guard describes constraints on the parameters and
8167 the schedule dimensions of outer
8168 bands that need to be enforced by the outer nodes
8169 in the generated AST.
8170 That is, the part of the AST that is generated from descendants
8171 of the guard node can assume that these constraints are satisfied.
8172 The space of the guard is that of the flat product of the outer
8173 band nodes. In particular, if there are no outer band nodes, then
8174 this space is the unnamed zero-dimensional space.
8175 Since a guard node references the outer band nodes, any tree
8176 containing a guard node is considered to be anchored.
8180 Except for the C<isl_schedule_node_context> nodes,
8181 none of the nodes may introduce any parameters that were not
8182 already present in the root domain node.
8184 A schedule tree is encapsulated in an C<isl_schedule> object.
8185 The simplest such objects, those with a tree consisting of single domain node,
8186 can be created using the following functions with either an empty
8187 domain or a given domain.
8189 #include <isl/schedule.h>
8190 __isl_give isl_schedule *isl_schedule_empty(
8191 __isl_take isl_space *space);
8192 __isl_give isl_schedule *isl_schedule_from_domain(
8193 __isl_take isl_union_set *domain);
8195 The function C<isl_schedule_constraints_compute_schedule> described
8196 in L</"Scheduling"> can also be used to construct schedules.
8198 C<isl_schedule> objects may be copied and freed using the following functions.
8200 #include <isl/schedule.h>
8201 __isl_give isl_schedule *isl_schedule_copy(
8202 __isl_keep isl_schedule *sched);
8203 __isl_null isl_schedule *isl_schedule_free(
8204 __isl_take isl_schedule *sched);
8206 The following functions checks whether two C<isl_schedule> objects
8207 are obviously the same.
8209 #include <isl/schedule.h>
8210 isl_bool isl_schedule_plain_is_equal(
8211 __isl_keep isl_schedule *schedule1,
8212 __isl_keep isl_schedule *schedule2);
8214 The domain of the schedule, i.e., the domain described by the root node,
8215 can be obtained using the following function.
8217 #include <isl/schedule.h>
8218 __isl_give isl_union_set *isl_schedule_get_domain(
8219 __isl_keep isl_schedule *schedule);
8221 An extra top-level band node (right underneath the domain node) can
8222 be introduced into the schedule using the following function.
8223 The schedule tree is assumed not to have any anchored nodes.
8225 #include <isl/schedule.h>
8226 __isl_give isl_schedule *
8227 isl_schedule_insert_partial_schedule(
8228 __isl_take isl_schedule *schedule,
8229 __isl_take isl_multi_union_pw_aff *partial);
8231 A top-level context node (right underneath the domain node) can
8232 be introduced into the schedule using the following function.
8234 #include <isl/schedule.h>
8235 __isl_give isl_schedule *isl_schedule_insert_context(
8236 __isl_take isl_schedule *schedule,
8237 __isl_take isl_set *context)
8239 A top-level guard node (right underneath the domain node) can
8240 be introduced into the schedule using the following function.
8242 #include <isl/schedule.h>
8243 __isl_give isl_schedule *isl_schedule_insert_guard(
8244 __isl_take isl_schedule *schedule,
8245 __isl_take isl_set *guard)
8247 A schedule that combines two schedules either in the given
8248 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8249 or an C<isl_schedule_node_set> node,
8250 can be created using the following functions.
8252 #include <isl/schedule.h>
8253 __isl_give isl_schedule *isl_schedule_sequence(
8254 __isl_take isl_schedule *schedule1,
8255 __isl_take isl_schedule *schedule2);
8256 __isl_give isl_schedule *isl_schedule_set(
8257 __isl_take isl_schedule *schedule1,
8258 __isl_take isl_schedule *schedule2);
8260 The domains of the two input schedules need to be disjoint.
8262 The following function can be used to restrict the domain
8263 of a schedule with a domain node as root to be a subset of the given union set.
8264 This operation may remove nodes in the tree that have become
8267 #include <isl/schedule.h>
8268 __isl_give isl_schedule *isl_schedule_intersect_domain(
8269 __isl_take isl_schedule *schedule,
8270 __isl_take isl_union_set *domain);
8272 The following function can be used to simplify the domain
8273 of a schedule with a domain node as root with respect to the given
8276 #include <isl/schedule.h>
8277 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8278 __isl_take isl_schedule *schedule,
8279 __isl_take isl_set *context);
8281 The following function resets the user pointers on all parameter
8282 and tuple identifiers referenced by the nodes of the given schedule.
8284 #include <isl/schedule.h>
8285 __isl_give isl_schedule *isl_schedule_reset_user(
8286 __isl_take isl_schedule *schedule);
8288 The following function aligns the parameters of all nodes
8289 in the given schedule to the given space.
8291 #include <isl/schedule.h>
8292 __isl_give isl_schedule *isl_schedule_align_params(
8293 __isl_take isl_schedule *schedule,
8294 __isl_take isl_space *space);
8296 The following function allows the user to plug in a given function
8297 in the iteration domains. The input schedule is not allowed to contain
8298 any expansion nodes.
8300 #include <isl/schedule.h>
8301 __isl_give isl_schedule *
8302 isl_schedule_pullback_union_pw_multi_aff(
8303 __isl_take isl_schedule *schedule,
8304 __isl_take isl_union_pw_multi_aff *upma);
8306 The following function can be used to plug in the schedule C<expansion>
8307 in the leaves of C<schedule>, where C<contraction> describes how
8308 the domain elements of C<expansion> map to the domain elements
8309 at the original leaves of C<schedule>.
8310 The resulting schedule will contain expansion nodes, unless
8311 C<contraction> is an identity function.
8313 #include <isl/schedule.h>
8314 __isl_give isl_schedule *isl_schedule_expand(
8315 __isl_take isl_schedule *schedule,
8316 __isl_take isl_union_pw_multi_aff *contraction,
8317 __isl_take isl_schedule *expansion);
8319 An C<isl_union_map> representation of the schedule can be obtained
8320 from an C<isl_schedule> using the following function.
8322 #include <isl/schedule.h>
8323 __isl_give isl_union_map *isl_schedule_get_map(
8324 __isl_keep isl_schedule *sched);
8326 The resulting relation encodes the same relative ordering as
8327 the schedule by mapping the domain elements to a common schedule space.
8328 If the schedule_separate_components option is set, then the order
8329 of the children of a set node is explicitly encoded in the result.
8330 If the tree contains any expansion nodes, then the relation
8331 is formulated in terms of the expanded domain elements.
8333 Schedules can be read from input using the following functions.
8335 #include <isl/schedule.h>
8336 __isl_give isl_schedule *isl_schedule_read_from_file(
8337 isl_ctx *ctx, FILE *input);
8338 __isl_give isl_schedule *isl_schedule_read_from_str(
8339 isl_ctx *ctx, const char *str);
8341 A representation of the schedule can be printed using
8343 #include <isl/schedule.h>
8344 __isl_give isl_printer *isl_printer_print_schedule(
8345 __isl_take isl_printer *p,
8346 __isl_keep isl_schedule *schedule);
8347 __isl_give char *isl_schedule_to_str(
8348 __isl_keep isl_schedule *schedule);
8350 C<isl_schedule_to_str> prints the schedule in flow format.
8352 The schedule tree can be traversed through the use of
8353 C<isl_schedule_node> objects that point to a particular
8354 position in the schedule tree. Whenever a C<isl_schedule_node>
8355 is used to modify a node in the schedule tree, the original schedule
8356 tree is left untouched and the modifications are performed to a copy
8357 of the tree. The returned C<isl_schedule_node> then points to
8358 this modified copy of the tree.
8360 The root of the schedule tree can be obtained using the following function.
8362 #include <isl/schedule.h>
8363 __isl_give isl_schedule_node *isl_schedule_get_root(
8364 __isl_keep isl_schedule *schedule);
8366 A pointer to a newly created schedule tree with a single domain
8367 node can be created using the following functions.
8369 #include <isl/schedule_node.h>
8370 __isl_give isl_schedule_node *
8371 isl_schedule_node_from_domain(
8372 __isl_take isl_union_set *domain);
8373 __isl_give isl_schedule_node *
8374 isl_schedule_node_from_extension(
8375 __isl_take isl_union_map *extension);
8377 C<isl_schedule_node_from_extension> creates a tree with an extension
8380 Schedule nodes can be copied and freed using the following functions.
8382 #include <isl/schedule_node.h>
8383 __isl_give isl_schedule_node *isl_schedule_node_copy(
8384 __isl_keep isl_schedule_node *node);
8385 __isl_null isl_schedule_node *isl_schedule_node_free(
8386 __isl_take isl_schedule_node *node);
8388 The following functions can be used to check if two schedule
8389 nodes point to the same position in the same schedule.
8391 #include <isl/schedule_node.h>
8392 isl_bool isl_schedule_node_is_equal(
8393 __isl_keep isl_schedule_node *node1,
8394 __isl_keep isl_schedule_node *node2);
8396 The following properties can be obtained from a schedule node.
8398 #include <isl/schedule_node.h>
8399 enum isl_schedule_node_type isl_schedule_node_get_type(
8400 __isl_keep isl_schedule_node *node);
8401 enum isl_schedule_node_type
8402 isl_schedule_node_get_parent_type(
8403 __isl_keep isl_schedule_node *node);
8404 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8405 __isl_keep isl_schedule_node *node);
8407 The function C<isl_schedule_node_get_type> returns the type of
8408 the node, while C<isl_schedule_node_get_parent_type> returns
8409 type of the parent of the node, which is required to exist.
8410 The function C<isl_schedule_node_get_schedule> returns a copy
8411 to the schedule to which the node belongs.
8413 The following functions can be used to move the schedule node
8414 to a different position in the tree or to check if such a position
8417 #include <isl/schedule_node.h>
8418 isl_bool isl_schedule_node_has_parent(
8419 __isl_keep isl_schedule_node *node);
8420 __isl_give isl_schedule_node *isl_schedule_node_parent(
8421 __isl_take isl_schedule_node *node);
8422 __isl_give isl_schedule_node *isl_schedule_node_root(
8423 __isl_take isl_schedule_node *node);
8424 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8425 __isl_take isl_schedule_node *node,
8427 int isl_schedule_node_n_children(
8428 __isl_keep isl_schedule_node *node);
8429 __isl_give isl_schedule_node *isl_schedule_node_child(
8430 __isl_take isl_schedule_node *node, int pos);
8431 isl_bool isl_schedule_node_has_children(
8432 __isl_keep isl_schedule_node *node);
8433 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8434 __isl_take isl_schedule_node *node);
8435 isl_bool isl_schedule_node_has_previous_sibling(
8436 __isl_keep isl_schedule_node *node);
8437 __isl_give isl_schedule_node *
8438 isl_schedule_node_previous_sibling(
8439 __isl_take isl_schedule_node *node);
8440 isl_bool isl_schedule_node_has_next_sibling(
8441 __isl_keep isl_schedule_node *node);
8442 __isl_give isl_schedule_node *
8443 isl_schedule_node_next_sibling(
8444 __isl_take isl_schedule_node *node);
8446 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8447 is the node itself, the ancestor of generation 1 is its parent and so on.
8449 It is also possible to query the number of ancestors of a node,
8450 the position of the current node
8451 within the children of its parent, the position of the subtree
8452 containing a node within the children of an ancestor
8453 or to obtain a copy of a given
8454 child without destroying the current node.
8455 Given two nodes that point to the same schedule, their closest
8456 shared ancestor can be obtained using
8457 C<isl_schedule_node_get_shared_ancestor>.
8459 #include <isl/schedule_node.h>
8460 int isl_schedule_node_get_tree_depth(
8461 __isl_keep isl_schedule_node *node);
8462 int isl_schedule_node_get_child_position(
8463 __isl_keep isl_schedule_node *node);
8464 int isl_schedule_node_get_ancestor_child_position(
8465 __isl_keep isl_schedule_node *node,
8466 __isl_keep isl_schedule_node *ancestor);
8467 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8468 __isl_keep isl_schedule_node *node, int pos);
8469 __isl_give isl_schedule_node *
8470 isl_schedule_node_get_shared_ancestor(
8471 __isl_keep isl_schedule_node *node1,
8472 __isl_keep isl_schedule_node *node2);
8474 All nodes in a schedule tree or
8475 all descendants of a specific node (including the node) can be visited
8476 in depth-first pre-order using the following functions.
8478 #include <isl/schedule.h>
8479 isl_stat isl_schedule_foreach_schedule_node_top_down(
8480 __isl_keep isl_schedule *sched,
8481 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8482 void *user), void *user);
8484 #include <isl/schedule_node.h>
8485 isl_stat isl_schedule_node_foreach_descendant_top_down(
8486 __isl_keep isl_schedule_node *node,
8487 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8488 void *user), void *user);
8490 The callback function is slightly different from the usual
8491 callbacks in that it not only indicates success (non-negative result)
8492 or failure (negative result), but also indicates whether the children
8493 of the given node should be visited. In particular, if the callback
8494 returns a positive value, then the children are visited, but if
8495 the callback returns zero, then the children are not visited.
8497 The following functions checks whether
8498 all descendants of a specific node (including the node itself)
8499 satisfy a user-specified test.
8501 #include <isl/schedule_node.h>
8502 isl_bool isl_schedule_node_every_descendant(
8503 __isl_keep isl_schedule_node *node,
8504 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8505 void *user), void *user)
8507 The ancestors of a node in a schedule tree can be visited from
8508 the root down to and including the parent of the node using
8509 the following function.
8511 #include <isl/schedule_node.h>
8512 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8513 __isl_keep isl_schedule_node *node,
8514 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8515 void *user), void *user);
8517 The following functions allows for a depth-first post-order
8518 traversal of the nodes in a schedule tree or
8519 of the descendants of a specific node (including the node
8520 itself), where the user callback is allowed to modify the
8523 #include <isl/schedule.h>
8524 __isl_give isl_schedule *
8525 isl_schedule_map_schedule_node_bottom_up(
8526 __isl_take isl_schedule *schedule,
8527 __isl_give isl_schedule_node *(*fn)(
8528 __isl_take isl_schedule_node *node,
8529 void *user), void *user);
8531 #include <isl/schedule_node.h>
8532 __isl_give isl_schedule_node *
8533 isl_schedule_node_map_descendant_bottom_up(
8534 __isl_take isl_schedule_node *node,
8535 __isl_give isl_schedule_node *(*fn)(
8536 __isl_take isl_schedule_node *node,
8537 void *user), void *user);
8539 The traversal continues from the node returned by the callback function.
8540 It is the responsibility of the user to ensure that this does not
8541 lead to an infinite loop. It is safest to always return a pointer
8542 to the same position (same ancestors and child positions) as the input node.
8544 The following function removes a node (along with its descendants)
8545 from a schedule tree and returns a pointer to the leaf at the
8546 same position in the updated tree.
8547 It is not allowed to remove the root of a schedule tree or
8548 a child of a set or sequence node.
8550 #include <isl/schedule_node.h>
8551 __isl_give isl_schedule_node *isl_schedule_node_cut(
8552 __isl_take isl_schedule_node *node);
8554 The following function removes a single node
8555 from a schedule tree and returns a pointer to the child
8556 of the node, now located at the position of the original node
8557 or to a leaf node at that position if there was no child.
8558 It is not allowed to remove the root of a schedule tree,
8559 a set or sequence node, a child of a set or sequence node or
8560 a band node with an anchored subtree.
8562 #include <isl/schedule_node.h>
8563 __isl_give isl_schedule_node *isl_schedule_node_delete(
8564 __isl_take isl_schedule_node *node);
8566 Most nodes in a schedule tree only contain local information.
8567 In some cases, however, a node may also refer to the schedule dimensions
8568 of its outer band nodes.
8569 This means that the position of the node within the tree should
8570 not be changed, or at least that no changes are performed to the
8571 outer band nodes. The following function can be used to test
8572 whether the subtree rooted at a given node contains any such nodes.
8574 #include <isl/schedule_node.h>
8575 isl_bool isl_schedule_node_is_subtree_anchored(
8576 __isl_keep isl_schedule_node *node);
8578 The following function resets the user pointers on all parameter
8579 and tuple identifiers referenced by the given schedule node.
8581 #include <isl/schedule_node.h>
8582 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8583 __isl_take isl_schedule_node *node);
8585 The following function aligns the parameters of the given schedule
8586 node to the given space.
8588 #include <isl/schedule_node.h>
8589 __isl_give isl_schedule_node *
8590 isl_schedule_node_align_params(
8591 __isl_take isl_schedule_node *node,
8592 __isl_take isl_space *space);
8594 Several node types have their own functions for querying
8595 (and in some cases setting) some node type specific properties.
8597 #include <isl/schedule_node.h>
8598 __isl_give isl_space *isl_schedule_node_band_get_space(
8599 __isl_keep isl_schedule_node *node);
8600 __isl_give isl_multi_union_pw_aff *
8601 isl_schedule_node_band_get_partial_schedule(
8602 __isl_keep isl_schedule_node *node);
8603 __isl_give isl_union_map *
8604 isl_schedule_node_band_get_partial_schedule_union_map(
8605 __isl_keep isl_schedule_node *node);
8606 unsigned isl_schedule_node_band_n_member(
8607 __isl_keep isl_schedule_node *node);
8608 isl_bool isl_schedule_node_band_member_get_coincident(
8609 __isl_keep isl_schedule_node *node, int pos);
8610 __isl_give isl_schedule_node *
8611 isl_schedule_node_band_member_set_coincident(
8612 __isl_take isl_schedule_node *node, int pos,
8614 isl_bool isl_schedule_node_band_get_permutable(
8615 __isl_keep isl_schedule_node *node);
8616 __isl_give isl_schedule_node *
8617 isl_schedule_node_band_set_permutable(
8618 __isl_take isl_schedule_node *node, int permutable);
8619 enum isl_ast_loop_type
8620 isl_schedule_node_band_member_get_ast_loop_type(
8621 __isl_keep isl_schedule_node *node, int pos);
8622 __isl_give isl_schedule_node *
8623 isl_schedule_node_band_member_set_ast_loop_type(
8624 __isl_take isl_schedule_node *node, int pos,
8625 enum isl_ast_loop_type type);
8626 __isl_give isl_union_set *
8627 enum isl_ast_loop_type
8628 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8629 __isl_keep isl_schedule_node *node, int pos);
8630 __isl_give isl_schedule_node *
8631 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8632 __isl_take isl_schedule_node *node, int pos,
8633 enum isl_ast_loop_type type);
8634 isl_schedule_node_band_get_ast_build_options(
8635 __isl_keep isl_schedule_node *node);
8636 __isl_give isl_schedule_node *
8637 isl_schedule_node_band_set_ast_build_options(
8638 __isl_take isl_schedule_node *node,
8639 __isl_take isl_union_set *options);
8640 __isl_give isl_set *
8641 isl_schedule_node_band_get_ast_isolate_option(
8642 __isl_keep isl_schedule_node *node);
8644 The function C<isl_schedule_node_band_get_space> returns the space
8645 of the partial schedule of the band.
8646 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8647 returns a representation of the partial schedule of the band node
8648 in the form of an C<isl_union_map>.
8649 The coincident and permutable properties are set by
8650 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8652 A scheduling dimension is considered to be ``coincident''
8653 if it satisfies the coincidence constraints within its band.
8654 That is, if the dependence distances of the coincidence
8655 constraints are all zero in that direction (for fixed
8656 iterations of outer bands).
8657 A band is marked permutable if it was produced using the Pluto-like scheduler.
8658 Note that the scheduler may have to resort to a Feautrier style scheduling
8659 step even if the default scheduler is used.
8660 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8661 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8662 For the meaning of these loop AST generation types and the difference
8663 between the regular loop AST generation type and the isolate
8664 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8665 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8666 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8667 may return C<isl_ast_loop_error> if an error occurs.
8668 The AST build options govern how an AST is generated for
8669 the individual schedule dimensions during AST generation.
8670 See L</"AST Generation Options (Schedule Tree)">.
8671 The isolate option for the given node can be extracted from these
8672 AST build options using the function
8673 C<isl_schedule_node_band_get_ast_isolate_option>.
8675 #include <isl/schedule_node.h>
8676 __isl_give isl_set *
8677 isl_schedule_node_context_get_context(
8678 __isl_keep isl_schedule_node *node);
8680 #include <isl/schedule_node.h>
8681 __isl_give isl_union_set *
8682 isl_schedule_node_domain_get_domain(
8683 __isl_keep isl_schedule_node *node);
8685 #include <isl/schedule_node.h>
8686 __isl_give isl_union_map *
8687 isl_schedule_node_expansion_get_expansion(
8688 __isl_keep isl_schedule_node *node);
8689 __isl_give isl_union_pw_multi_aff *
8690 isl_schedule_node_expansion_get_contraction(
8691 __isl_keep isl_schedule_node *node);
8693 #include <isl/schedule_node.h>
8694 __isl_give isl_union_map *
8695 isl_schedule_node_extension_get_extension(
8696 __isl_keep isl_schedule_node *node);
8698 #include <isl/schedule_node.h>
8699 __isl_give isl_union_set *
8700 isl_schedule_node_filter_get_filter(
8701 __isl_keep isl_schedule_node *node);
8703 #include <isl/schedule_node.h>
8704 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8705 __isl_keep isl_schedule_node *node);
8707 #include <isl/schedule_node.h>
8708 __isl_give isl_id *isl_schedule_node_mark_get_id(
8709 __isl_keep isl_schedule_node *node);
8711 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8712 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8713 partial schedules related to the node.
8715 #include <isl/schedule_node.h>
8716 __isl_give isl_multi_union_pw_aff *
8717 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8718 __isl_keep isl_schedule_node *node);
8719 __isl_give isl_union_pw_multi_aff *
8720 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8721 __isl_keep isl_schedule_node *node);
8722 __isl_give isl_union_map *
8723 isl_schedule_node_get_prefix_schedule_union_map(
8724 __isl_keep isl_schedule_node *node);
8725 __isl_give isl_union_map *
8726 isl_schedule_node_get_prefix_schedule_relation(
8727 __isl_keep isl_schedule_node *node);
8728 __isl_give isl_union_map *
8729 isl_schedule_node_get_subtree_schedule_union_map(
8730 __isl_keep isl_schedule_node *node);
8732 In particular, the functions
8733 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8734 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8735 and C<isl_schedule_node_get_prefix_schedule_union_map>
8736 return a relative ordering on the domain elements that reach the given
8737 node determined by its ancestors.
8738 The function C<isl_schedule_node_get_prefix_schedule_relation>
8739 additionally includes the domain constraints in the result.
8740 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8741 returns a representation of the partial schedule defined by the
8742 subtree rooted at the given node.
8743 If the tree contains any expansion nodes, then the subtree schedule
8744 is formulated in terms of the expanded domain elements.
8745 The tree passed to functions returning a prefix schedule
8746 may only contain extension nodes if these would not affect
8747 the result of these functions. That is, if one of the ancestors
8748 is an extension node, then all of the domain elements that were
8749 added by the extension node need to have been filtered out
8750 by filter nodes between the extension node and the input node.
8751 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8752 may not contain in extension nodes in the selected subtree.
8754 The expansion/contraction defined by an entire subtree, combining
8755 the expansions/contractions
8756 on the expansion nodes in the subtree, can be obtained using
8757 the following functions.
8759 #include <isl/schedule_node.h>
8760 __isl_give isl_union_map *
8761 isl_schedule_node_get_subtree_expansion(
8762 __isl_keep isl_schedule_node *node);
8763 __isl_give isl_union_pw_multi_aff *
8764 isl_schedule_node_get_subtree_contraction(
8765 __isl_keep isl_schedule_node *node);
8767 The total number of outer band members of given node, i.e.,
8768 the shared output dimension of the maps in the result
8769 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8770 using the following function.
8772 #include <isl/schedule_node.h>
8773 int isl_schedule_node_get_schedule_depth(
8774 __isl_keep isl_schedule_node *node);
8776 The following functions return the elements that reach the given node
8777 or the union of universes in the spaces that contain these elements.
8779 #include <isl/schedule_node.h>
8780 __isl_give isl_union_set *
8781 isl_schedule_node_get_domain(
8782 __isl_keep isl_schedule_node *node);
8783 __isl_give isl_union_set *
8784 isl_schedule_node_get_universe_domain(
8785 __isl_keep isl_schedule_node *node);
8787 The input tree of C<isl_schedule_node_get_domain>
8788 may only contain extension nodes if these would not affect
8789 the result of this function. That is, if one of the ancestors
8790 is an extension node, then all of the domain elements that were
8791 added by the extension node need to have been filtered out
8792 by filter nodes between the extension node and the input node.
8794 The following functions can be used to introduce additional nodes
8795 in the schedule tree. The new node is introduced at the point
8796 in the tree where the C<isl_schedule_node> points to and
8797 the results points to the new node.
8799 #include <isl/schedule_node.h>
8800 __isl_give isl_schedule_node *
8801 isl_schedule_node_insert_partial_schedule(
8802 __isl_take isl_schedule_node *node,
8803 __isl_take isl_multi_union_pw_aff *schedule);
8805 This function inserts a new band node with (the greatest integer
8806 part of) the given partial schedule.
8807 The subtree rooted at the given node is assumed not to have
8810 #include <isl/schedule_node.h>
8811 __isl_give isl_schedule_node *
8812 isl_schedule_node_insert_context(
8813 __isl_take isl_schedule_node *node,
8814 __isl_take isl_set *context);
8816 This function inserts a new context node with the given context constraints.
8818 #include <isl/schedule_node.h>
8819 __isl_give isl_schedule_node *
8820 isl_schedule_node_insert_filter(
8821 __isl_take isl_schedule_node *node,
8822 __isl_take isl_union_set *filter);
8824 This function inserts a new filter node with the given filter.
8825 If the original node already pointed to a filter node, then the
8826 two filter nodes are merged into one.
8828 #include <isl/schedule_node.h>
8829 __isl_give isl_schedule_node *
8830 isl_schedule_node_insert_guard(
8831 __isl_take isl_schedule_node *node,
8832 __isl_take isl_set *guard);
8834 This function inserts a new guard node with the given guard constraints.
8836 #include <isl/schedule_node.h>
8837 __isl_give isl_schedule_node *
8838 isl_schedule_node_insert_mark(
8839 __isl_take isl_schedule_node *node,
8840 __isl_take isl_id *mark);
8842 This function inserts a new mark node with the give mark identifier.
8844 #include <isl/schedule_node.h>
8845 __isl_give isl_schedule_node *
8846 isl_schedule_node_insert_sequence(
8847 __isl_take isl_schedule_node *node,
8848 __isl_take isl_union_set_list *filters);
8849 __isl_give isl_schedule_node *
8850 isl_schedule_node_insert_set(
8851 __isl_take isl_schedule_node *node,
8852 __isl_take isl_union_set_list *filters);
8854 These functions insert a new sequence or set node with the given
8855 filters as children.
8857 #include <isl/schedule_node.h>
8858 __isl_give isl_schedule_node *isl_schedule_node_group(
8859 __isl_take isl_schedule_node *node,
8860 __isl_take isl_id *group_id);
8862 This function introduces an expansion node in between the current
8863 node and its parent that expands instances of a space with tuple
8864 identifier C<group_id> to the original domain elements that reach
8865 the node. The group instances are identified by the prefix schedule
8866 of those domain elements. The ancestors of the node are adjusted
8867 to refer to the group instances instead of the original domain
8868 elements. The return value points to the same node in the updated
8869 schedule tree as the input node, i.e., to the child of the newly
8870 introduced expansion node. Grouping instances of different statements
8871 ensures that they will be treated as a single statement by the
8872 AST generator up to the point of the expansion node.
8874 The following function can be used to flatten a nested
8877 #include <isl/schedule_node.h>
8878 __isl_give isl_schedule_node *
8879 isl_schedule_node_sequence_splice_child(
8880 __isl_take isl_schedule_node *node, int pos);
8882 That is, given a sequence node C<node> that has another sequence node
8883 in its child at position C<pos> (in particular, the child of that filter
8884 node is a sequence node), attach the children of that other sequence
8885 node as children of C<node>, replacing the original child at position
8888 The partial schedule of a band node can be scaled (down) or reduced using
8889 the following functions.
8891 #include <isl/schedule_node.h>
8892 __isl_give isl_schedule_node *
8893 isl_schedule_node_band_scale(
8894 __isl_take isl_schedule_node *node,
8895 __isl_take isl_multi_val *mv);
8896 __isl_give isl_schedule_node *
8897 isl_schedule_node_band_scale_down(
8898 __isl_take isl_schedule_node *node,
8899 __isl_take isl_multi_val *mv);
8900 __isl_give isl_schedule_node *
8901 isl_schedule_node_band_mod(
8902 __isl_take isl_schedule_node *node,
8903 __isl_take isl_multi_val *mv);
8905 The spaces of the two arguments need to match.
8906 After scaling, the partial schedule is replaced by its greatest
8907 integer part to ensure that the schedule remains integral.
8909 The partial schedule of a band node can be shifted by an
8910 C<isl_multi_union_pw_aff> with a domain that is a superset
8911 of the domain of the partial schedule using
8912 the following function.
8914 #include <isl/schedule_node.h>
8915 __isl_give isl_schedule_node *
8916 isl_schedule_node_band_shift(
8917 __isl_take isl_schedule_node *node,
8918 __isl_take isl_multi_union_pw_aff *shift);
8920 A band node can be tiled using the following function.
8922 #include <isl/schedule_node.h>
8923 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8924 __isl_take isl_schedule_node *node,
8925 __isl_take isl_multi_val *sizes);
8927 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8929 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8930 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8932 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8934 The C<isl_schedule_node_band_tile> function tiles
8935 the band using the given tile sizes inside its schedule.
8936 A new child band node is created to represent the point loops and it is
8937 inserted between the modified band and its children.
8938 The subtree rooted at the given node is assumed not to have
8940 The C<tile_scale_tile_loops> option specifies whether the tile
8941 loops iterators should be scaled by the tile sizes.
8942 If the C<tile_shift_point_loops> option is set, then the point loops
8943 are shifted to start at zero.
8945 A band node can be split into two nested band nodes
8946 using the following function.
8948 #include <isl/schedule_node.h>
8949 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8950 __isl_take isl_schedule_node *node, int pos);
8952 The resulting outer band node contains the first C<pos> dimensions of
8953 the schedule of C<node> while the inner band contains the remaining dimensions.
8954 The schedules of the two band nodes live in anonymous spaces.
8955 The loop AST generation type options and the isolate option
8956 are split over the two band nodes.
8958 A band node can be moved down to the leaves of the subtree rooted
8959 at the band node using the following function.
8961 #include <isl/schedule_node.h>
8962 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8963 __isl_take isl_schedule_node *node);
8965 The subtree rooted at the given node is assumed not to have
8967 The result points to the node in the resulting tree that is in the same
8968 position as the node pointed to by C<node> in the original tree.
8970 #include <isl/schedule_node.h>
8971 __isl_give isl_schedule_node *
8972 isl_schedule_node_order_before(
8973 __isl_take isl_schedule_node *node,
8974 __isl_take isl_union_set *filter);
8975 __isl_give isl_schedule_node *
8976 isl_schedule_node_order_after(
8977 __isl_take isl_schedule_node *node,
8978 __isl_take isl_union_set *filter);
8980 These functions split the domain elements that reach C<node>
8981 into those that satisfy C<filter> and those that do not and
8982 arranges for the elements that do satisfy the filter to be
8983 executed before (in case of C<isl_schedule_node_order_before>)
8984 or after (in case of C<isl_schedule_node_order_after>)
8985 those that do not. The order is imposed by
8986 a sequence node, possibly reusing the grandparent of C<node>
8987 on two copies of the subtree attached to the original C<node>.
8988 Both copies are simplified with respect to their filter.
8990 Return a pointer to the copy of the subtree that does not
8991 satisfy C<filter>. If there is no such copy (because all
8992 reaching domain elements satisfy the filter), then return
8993 the original pointer.
8995 #include <isl/schedule_node.h>
8996 __isl_give isl_schedule_node *
8997 isl_schedule_node_graft_before(
8998 __isl_take isl_schedule_node *node,
8999 __isl_take isl_schedule_node *graft);
9000 __isl_give isl_schedule_node *
9001 isl_schedule_node_graft_after(
9002 __isl_take isl_schedule_node *node,
9003 __isl_take isl_schedule_node *graft);
9005 This function inserts the C<graft> tree into the tree containing C<node>
9006 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
9007 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
9008 The root node of C<graft>
9009 should be an extension node where the domain of the extension
9010 is the flat product of all outer band nodes of C<node>.
9011 The root node may also be a domain node.
9012 The elements of the domain or the range of the extension may not
9013 intersect with the domain elements that reach "node".
9014 The schedule tree of C<graft> may not be anchored.
9016 The schedule tree of C<node> is modified to include an extension node
9017 corresponding to the root node of C<graft> as a child of the original
9018 parent of C<node>. The original node that C<node> points to and the
9019 child of the root node of C<graft> are attached to this extension node
9020 through a sequence, with appropriate filters and with the child
9021 of C<graft> appearing before or after the original C<node>.
9023 If C<node> already appears inside a sequence that is the child of
9024 an extension node and if the spaces of the new domain elements
9025 do not overlap with those of the original domain elements,
9026 then that extension node is extended with the new extension
9027 rather than introducing a new segment of extension and sequence nodes.
9029 Return a pointer to the same node in the modified tree that
9030 C<node> pointed to in the original tree.
9032 A representation of the schedule node can be printed using
9034 #include <isl/schedule_node.h>
9035 __isl_give isl_printer *isl_printer_print_schedule_node(
9036 __isl_take isl_printer *p,
9037 __isl_keep isl_schedule_node *node);
9038 __isl_give char *isl_schedule_node_to_str(
9039 __isl_keep isl_schedule_node *node);
9041 C<isl_schedule_node_to_str> prints the schedule node in block format.
9043 =head2 Dependence Analysis
9045 C<isl> contains specialized functionality for performing
9046 array dataflow analysis. That is, given a I<sink> access relation,
9047 a collection of possible I<source> accesses and
9048 a collection of I<kill> accesses,
9049 C<isl> can compute relations that describe
9050 for each iteration of the sink access, which iterations
9051 of which of the source access relations may have
9052 accessed the same data element before the given iteration
9053 of the sink access without any intermediate kill of that data element.
9054 The resulting dependence relations map source iterations
9055 to either the corresponding sink iterations or
9056 pairs of corresponding sink iterations and accessed data elements.
9057 To compute standard flow dependences, the sink should be
9058 a read, while the sources should be writes.
9059 If no kills are specified,
9060 then memory based dependence analysis is performed.
9061 If, on the other hand, all sources are also kills,
9062 then value based dependence analysis is performed.
9063 If any of the source accesses are marked as being I<must>
9064 accesses, then they are also treated as kills.
9065 Furthermore, the specification of must-sources results
9066 in the computation of must-dependences.
9067 Only dependences originating in a must access not coscheduled
9068 with any other access to the same element and without
9069 any may accesses between the must access and the sink access
9070 are considered to be must dependences.
9072 =head3 High-level Interface
9074 A high-level interface to dependence analysis is provided
9075 by the following function.
9077 #include <isl/flow.h>
9078 __isl_give isl_union_flow *
9079 isl_union_access_info_compute_flow(
9080 __isl_take isl_union_access_info *access);
9082 The input C<isl_union_access_info> object describes the sink
9083 access relations, the source access relations and a schedule,
9084 while the output C<isl_union_flow> object describes
9085 the resulting dependence relations and the subsets of the
9086 sink relations for which no source was found.
9088 An C<isl_union_access_info> is created, modified, copied and freed using
9089 the following functions.
9091 #include <isl/flow.h>
9092 __isl_give isl_union_access_info *
9093 isl_union_access_info_from_sink(
9094 __isl_take isl_union_map *sink);
9095 __isl_give isl_union_access_info *
9096 isl_union_access_info_set_kill(
9097 __isl_take isl_union_access_info *access,
9098 __isl_take isl_union_map *kill);
9099 __isl_give isl_union_access_info *
9100 isl_union_access_info_set_may_source(
9101 __isl_take isl_union_access_info *access,
9102 __isl_take isl_union_map *may_source);
9103 __isl_give isl_union_access_info *
9104 isl_union_access_info_set_must_source(
9105 __isl_take isl_union_access_info *access,
9106 __isl_take isl_union_map *must_source);
9107 __isl_give isl_union_access_info *
9108 isl_union_access_info_set_schedule(
9109 __isl_take isl_union_access_info *access,
9110 __isl_take isl_schedule *schedule);
9111 __isl_give isl_union_access_info *
9112 isl_union_access_info_set_schedule_map(
9113 __isl_take isl_union_access_info *access,
9114 __isl_take isl_union_map *schedule_map);
9115 __isl_give isl_union_access_info *
9116 isl_union_access_info_copy(
9117 __isl_keep isl_union_access_info *access);
9118 __isl_null isl_union_access_info *
9119 isl_union_access_info_free(
9120 __isl_take isl_union_access_info *access);
9122 The may sources set by C<isl_union_access_info_set_may_source>
9123 do not need to include the must sources set by
9124 C<isl_union_access_info_set_must_source> as a subset.
9125 The kills set by C<isl_union_access_info_set_kill> may overlap
9126 with the may-sources and/or must-sources.
9127 The user is free not to call one (or more) of these functions,
9128 in which case the corresponding set is kept to its empty default.
9129 Similarly, the default schedule initialized by
9130 C<isl_union_access_info_from_sink> is empty.
9131 The current schedule is determined by the last call to either
9132 C<isl_union_access_info_set_schedule> or
9133 C<isl_union_access_info_set_schedule_map>.
9134 The domain of the schedule corresponds to the domains of
9135 the access relations. In particular, the domains of the access
9136 relations are effectively intersected with the domain of the schedule
9137 and only the resulting accesses are considered by the dependence analysis.
9139 An C<isl_union_access_info> object can be read from input
9140 using the following function.
9142 #include <isl/flow.h>
9143 __isl_give isl_union_access_info *
9144 isl_union_access_info_read_from_file(isl_ctx *ctx,
9147 A representation of the information contained in an object
9148 of type C<isl_union_access_info> can be obtained using
9150 #include <isl/flow.h>
9151 __isl_give isl_printer *
9152 isl_printer_print_union_access_info(
9153 __isl_take isl_printer *p,
9154 __isl_keep isl_union_access_info *access);
9155 __isl_give char *isl_union_access_info_to_str(
9156 __isl_keep isl_union_access_info *access);
9158 C<isl_union_access_info_to_str> prints the information in flow format.
9160 The output of C<isl_union_access_info_compute_flow> can be examined,
9161 copied, and freed using the following functions.
9163 #include <isl/flow.h>
9164 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9165 __isl_keep isl_union_flow *flow);
9166 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9167 __isl_keep isl_union_flow *flow);
9168 __isl_give isl_union_map *
9169 isl_union_flow_get_full_must_dependence(
9170 __isl_keep isl_union_flow *flow);
9171 __isl_give isl_union_map *
9172 isl_union_flow_get_full_may_dependence(
9173 __isl_keep isl_union_flow *flow);
9174 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9175 __isl_keep isl_union_flow *flow);
9176 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9177 __isl_keep isl_union_flow *flow);
9178 __isl_give isl_union_flow *isl_union_flow_copy(
9179 __isl_keep isl_union_flow *flow);
9180 __isl_null isl_union_flow *isl_union_flow_free(
9181 __isl_take isl_union_flow *flow);
9183 The relation returned by C<isl_union_flow_get_must_dependence>
9184 relates domain elements of must sources to domain elements of the sink.
9185 The relation returned by C<isl_union_flow_get_may_dependence>
9186 relates domain elements of must or may sources to domain elements of the sink
9187 and includes the previous relation as a subset.
9188 The relation returned by C<isl_union_flow_get_full_must_dependence>
9189 relates domain elements of must sources to pairs of domain elements of the sink
9190 and accessed data elements.
9191 The relation returned by C<isl_union_flow_get_full_may_dependence>
9192 relates domain elements of must or may sources to pairs of
9193 domain elements of the sink and accessed data elements.
9194 This relation includes the previous relation as a subset.
9195 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9196 of the sink relation for which no dependences have been found.
9197 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9198 of the sink relation for which no definite dependences have been found.
9199 That is, it contains those sink access that do not contribute to any
9200 of the elements in the relation returned
9201 by C<isl_union_flow_get_must_dependence>.
9203 A representation of the information contained in an object
9204 of type C<isl_union_flow> can be obtained using
9206 #include <isl/flow.h>
9207 __isl_give isl_printer *isl_printer_print_union_flow(
9208 __isl_take isl_printer *p,
9209 __isl_keep isl_union_flow *flow);
9210 __isl_give char *isl_union_flow_to_str(
9211 __isl_keep isl_union_flow *flow);
9213 C<isl_union_flow_to_str> prints the information in flow format.
9215 =head3 Low-level Interface
9217 A lower-level interface is provided by the following functions.
9219 #include <isl/flow.h>
9221 typedef int (*isl_access_level_before)(void *first, void *second);
9223 __isl_give isl_access_info *isl_access_info_alloc(
9224 __isl_take isl_map *sink,
9225 void *sink_user, isl_access_level_before fn,
9227 __isl_give isl_access_info *isl_access_info_add_source(
9228 __isl_take isl_access_info *acc,
9229 __isl_take isl_map *source, int must,
9231 __isl_null isl_access_info *isl_access_info_free(
9232 __isl_take isl_access_info *acc);
9234 __isl_give isl_flow *isl_access_info_compute_flow(
9235 __isl_take isl_access_info *acc);
9237 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9238 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9239 void *dep_user, void *user),
9241 __isl_give isl_map *isl_flow_get_no_source(
9242 __isl_keep isl_flow *deps, int must);
9243 void isl_flow_free(__isl_take isl_flow *deps);
9245 The function C<isl_access_info_compute_flow> performs the actual
9246 dependence analysis. The other functions are used to construct
9247 the input for this function or to read off the output.
9249 The input is collected in an C<isl_access_info>, which can
9250 be created through a call to C<isl_access_info_alloc>.
9251 The arguments to this functions are the sink access relation
9252 C<sink>, a token C<sink_user> used to identify the sink
9253 access to the user, a callback function for specifying the
9254 relative order of source and sink accesses, and the number
9255 of source access relations that will be added.
9257 The callback function has type C<int (*)(void *first, void *second)>.
9258 The function is called with two user supplied tokens identifying
9259 either a source or the sink and it should return the shared nesting
9260 level and the relative order of the two accesses.
9261 In particular, let I<n> be the number of loops shared by
9262 the two accesses. If C<first> precedes C<second> textually,
9263 then the function should return I<2 * n + 1>; otherwise,
9264 it should return I<2 * n>.
9265 The low-level interface assumes that no sources are coscheduled.
9266 If the information returned by the callback does not allow
9267 the relative order to be determined, then one of the sources
9268 is arbitrarily taken to be executed after the other(s).
9270 The sources can be added to the C<isl_access_info> object by performing
9271 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9272 C<must> indicates whether the source is a I<must> access
9273 or a I<may> access. Note that a multi-valued access relation
9274 should only be marked I<must> if every iteration in the domain
9275 of the relation accesses I<all> elements in its image.
9276 The C<source_user> token is again used to identify
9277 the source access. The range of the source access relation
9278 C<source> should have the same dimension as the range
9279 of the sink access relation.
9280 The C<isl_access_info_free> function should usually not be
9281 called explicitly, because it is already called implicitly by
9282 C<isl_access_info_compute_flow>.
9284 The result of the dependence analysis is collected in an
9285 C<isl_flow>. There may be elements of
9286 the sink access for which no preceding source access could be
9287 found or for which all preceding sources are I<may> accesses.
9288 The relations containing these elements can be obtained through
9289 calls to C<isl_flow_get_no_source>, the first with C<must> set
9290 and the second with C<must> unset.
9291 In the case of standard flow dependence analysis,
9292 with the sink a read and the sources I<must> writes,
9293 the first relation corresponds to the reads from uninitialized
9294 array elements and the second relation is empty.
9295 The actual flow dependences can be extracted using
9296 C<isl_flow_foreach>. This function will call the user-specified
9297 callback function C<fn> for each B<non-empty> dependence between
9298 a source and the sink. The callback function is called
9299 with four arguments, the actual flow dependence relation
9300 mapping source iterations to sink iterations, a boolean that
9301 indicates whether it is a I<must> or I<may> dependence, a token
9302 identifying the source and an additional C<void *> with value
9303 equal to the third argument of the C<isl_flow_foreach> call.
9304 A dependence is marked I<must> if it originates from a I<must>
9305 source and if it is not followed by any I<may> sources.
9307 After finishing with an C<isl_flow>, the user should call
9308 C<isl_flow_free> to free all associated memory.
9310 =head3 Interaction with the Low-level Interface
9312 During the dependence analysis, we frequently need to perform
9313 the following operation. Given a relation between sink iterations
9314 and potential source iterations from a particular source domain,
9315 what is the last potential source iteration corresponding to each
9316 sink iteration. It can sometimes be convenient to adjust
9317 the set of potential source iterations before or after each such operation.
9318 The prototypical example is fuzzy array dataflow analysis,
9319 where we need to analyze if, based on data-dependent constraints,
9320 the sink iteration can ever be executed without one or more of
9321 the corresponding potential source iterations being executed.
9322 If so, we can introduce extra parameters and select an unknown
9323 but fixed source iteration from the potential source iterations.
9324 To be able to perform such manipulations, C<isl> provides the following
9327 #include <isl/flow.h>
9329 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9330 __isl_keep isl_map *source_map,
9331 __isl_keep isl_set *sink, void *source_user,
9333 __isl_give isl_access_info *isl_access_info_set_restrict(
9334 __isl_take isl_access_info *acc,
9335 isl_access_restrict fn, void *user);
9337 The function C<isl_access_info_set_restrict> should be called
9338 before calling C<isl_access_info_compute_flow> and registers a callback function
9339 that will be called any time C<isl> is about to compute the last
9340 potential source. The first argument is the (reverse) proto-dependence,
9341 mapping sink iterations to potential source iterations.
9342 The second argument represents the sink iterations for which
9343 we want to compute the last source iteration.
9344 The third argument is the token corresponding to the source
9345 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9346 The callback is expected to return a restriction on either the input or
9347 the output of the operation computing the last potential source.
9348 If the input needs to be restricted then restrictions are needed
9349 for both the source and the sink iterations. The sink iterations
9350 and the potential source iterations will be intersected with these sets.
9351 If the output needs to be restricted then only a restriction on the source
9352 iterations is required.
9353 If any error occurs, the callback should return C<NULL>.
9354 An C<isl_restriction> object can be created, freed and inspected
9355 using the following functions.
9357 #include <isl/flow.h>
9359 __isl_give isl_restriction *isl_restriction_input(
9360 __isl_take isl_set *source_restr,
9361 __isl_take isl_set *sink_restr);
9362 __isl_give isl_restriction *isl_restriction_output(
9363 __isl_take isl_set *source_restr);
9364 __isl_give isl_restriction *isl_restriction_none(
9365 __isl_take isl_map *source_map);
9366 __isl_give isl_restriction *isl_restriction_empty(
9367 __isl_take isl_map *source_map);
9368 __isl_null isl_restriction *isl_restriction_free(
9369 __isl_take isl_restriction *restr);
9371 C<isl_restriction_none> and C<isl_restriction_empty> are special
9372 cases of C<isl_restriction_input>. C<isl_restriction_none>
9373 is essentially equivalent to
9375 isl_restriction_input(isl_set_universe(
9376 isl_space_range(isl_map_get_space(source_map))),
9378 isl_space_domain(isl_map_get_space(source_map))));
9380 whereas C<isl_restriction_empty> is essentially equivalent to
9382 isl_restriction_input(isl_set_empty(
9383 isl_space_range(isl_map_get_space(source_map))),
9385 isl_space_domain(isl_map_get_space(source_map))));
9389 #include <isl/schedule.h>
9390 __isl_give isl_schedule *
9391 isl_schedule_constraints_compute_schedule(
9392 __isl_take isl_schedule_constraints *sc);
9394 The function C<isl_schedule_constraints_compute_schedule> can be
9395 used to compute a schedule that satisfies the given schedule constraints.
9396 These schedule constraints include the iteration domain for which
9397 a schedule should be computed and dependences between pairs of
9398 iterations. In particular, these dependences include
9399 I<validity> dependences and I<proximity> dependences.
9400 By default, the algorithm used to construct the schedule is similar
9401 to that of C<Pluto>.
9402 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9404 The generated schedule respects all validity dependences.
9405 That is, all dependence distances over these dependences in the
9406 scheduled space are lexicographically positive.
9408 The default algorithm tries to ensure that the dependence distances
9409 over coincidence constraints are zero and to minimize the
9410 dependence distances over proximity dependences.
9411 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9412 for groups of domains where the dependence distances over validity
9413 dependences have only non-negative values.
9414 Note that when minimizing the maximal dependence distance
9415 over proximity dependences, a single affine expression in the parameters
9416 is constructed that bounds all dependence distances. If no such expression
9417 exists, then the algorithm will fail and resort to an alternative
9418 scheduling algorithm. In particular, this means that adding proximity
9419 dependences may eliminate valid solutions. A typical example where this
9420 phenomenon may occur is when some subset of the proximity dependences
9421 has no restriction on some parameter, forcing the coefficient of that
9422 parameter to be zero, while some other subset forces the dependence
9423 distance to depend on that parameter, requiring the same coefficient
9425 When using Feautrier's algorithm, the coincidence and proximity constraints
9426 are only taken into account during the extension to a
9427 full-dimensional schedule.
9429 An C<isl_schedule_constraints> object can be constructed
9430 and manipulated using the following functions.
9432 #include <isl/schedule.h>
9433 __isl_give isl_schedule_constraints *
9434 isl_schedule_constraints_copy(
9435 __isl_keep isl_schedule_constraints *sc);
9436 __isl_give isl_schedule_constraints *
9437 isl_schedule_constraints_on_domain(
9438 __isl_take isl_union_set *domain);
9439 __isl_give isl_schedule_constraints *
9440 isl_schedule_constraints_set_context(
9441 __isl_take isl_schedule_constraints *sc,
9442 __isl_take isl_set *context);
9443 __isl_give isl_schedule_constraints *
9444 isl_schedule_constraints_set_validity(
9445 __isl_take isl_schedule_constraints *sc,
9446 __isl_take isl_union_map *validity);
9447 __isl_give isl_schedule_constraints *
9448 isl_schedule_constraints_set_coincidence(
9449 __isl_take isl_schedule_constraints *sc,
9450 __isl_take isl_union_map *coincidence);
9451 __isl_give isl_schedule_constraints *
9452 isl_schedule_constraints_set_proximity(
9453 __isl_take isl_schedule_constraints *sc,
9454 __isl_take isl_union_map *proximity);
9455 __isl_give isl_schedule_constraints *
9456 isl_schedule_constraints_set_conditional_validity(
9457 __isl_take isl_schedule_constraints *sc,
9458 __isl_take isl_union_map *condition,
9459 __isl_take isl_union_map *validity);
9460 __isl_give isl_schedule_constraints *
9461 isl_schedule_constraints_apply(
9462 __isl_take isl_schedule_constraints *sc,
9463 __isl_take isl_union_map *umap);
9464 __isl_null isl_schedule_constraints *
9465 isl_schedule_constraints_free(
9466 __isl_take isl_schedule_constraints *sc);
9468 The initial C<isl_schedule_constraints> object created by
9469 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9470 That is, it has an empty set of dependences.
9471 The function C<isl_schedule_constraints_set_context> allows the user
9472 to specify additional constraints on the parameters that may
9473 be assumed to hold during the construction of the schedule.
9474 The function C<isl_schedule_constraints_set_validity> replaces the
9475 validity dependences, mapping domain elements I<i> to domain
9476 elements that should be scheduled after I<i>.
9477 The function C<isl_schedule_constraints_set_coincidence> replaces the
9478 coincidence dependences, mapping domain elements I<i> to domain
9479 elements that should be scheduled together with I<I>, if possible.
9480 The function C<isl_schedule_constraints_set_proximity> replaces the
9481 proximity dependences, mapping domain elements I<i> to domain
9482 elements that should be scheduled either before I<I>
9483 or as early as possible after I<i>.
9485 The function C<isl_schedule_constraints_set_conditional_validity>
9486 replaces the conditional validity constraints.
9487 A conditional validity constraint is only imposed when any of the corresponding
9488 conditions is satisfied, i.e., when any of them is non-zero.
9489 That is, the scheduler ensures that within each band if the dependence
9490 distances over the condition constraints are not all zero
9491 then all corresponding conditional validity constraints are respected.
9492 A conditional validity constraint corresponds to a condition
9493 if the two are adjacent, i.e., if the domain of one relation intersect
9494 the range of the other relation.
9495 The typical use case of conditional validity constraints is
9496 to allow order constraints between live ranges to be violated
9497 as long as the live ranges themselves are local to the band.
9498 To allow more fine-grained control over which conditions correspond
9499 to which conditional validity constraints, the domains and ranges
9500 of these relations may include I<tags>. That is, the domains and
9501 ranges of those relation may themselves be wrapped relations
9502 where the iteration domain appears in the domain of those wrapped relations
9503 and the range of the wrapped relations can be arbitrarily chosen
9504 by the user. Conditions and conditional validity constraints are only
9505 considered adjacent to each other if the entire wrapped relation matches.
9506 In particular, a relation with a tag will never be considered adjacent
9507 to a relation without a tag.
9509 The function C<isl_schedule_constraints_apply> takes
9510 schedule constraints that are defined on some set of domain elements
9511 and transforms them to schedule constraints on the elements
9512 to which these domain elements are mapped by the given transformation.
9514 An C<isl_schedule_constraints> object can be inspected
9515 using the following functions.
9517 #include <isl/schedule.h>
9518 __isl_give isl_union_set *
9519 isl_schedule_constraints_get_domain(
9520 __isl_keep isl_schedule_constraints *sc);
9521 __isl_give isl_set *isl_schedule_constraints_get_context(
9522 __isl_keep isl_schedule_constraints *sc);
9523 __isl_give isl_union_map *
9524 isl_schedule_constraints_get_validity(
9525 __isl_keep isl_schedule_constraints *sc);
9526 __isl_give isl_union_map *
9527 isl_schedule_constraints_get_coincidence(
9528 __isl_keep isl_schedule_constraints *sc);
9529 __isl_give isl_union_map *
9530 isl_schedule_constraints_get_proximity(
9531 __isl_keep isl_schedule_constraints *sc);
9532 __isl_give isl_union_map *
9533 isl_schedule_constraints_get_conditional_validity(
9534 __isl_keep isl_schedule_constraints *sc);
9535 __isl_give isl_union_map *
9536 isl_schedule_constraints_get_conditional_validity_condition(
9537 __isl_keep isl_schedule_constraints *sc);
9539 An C<isl_schedule_constraints> object can be read from input
9540 using the following functions.
9542 #include <isl/schedule.h>
9543 __isl_give isl_schedule_constraints *
9544 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9546 __isl_give isl_schedule_constraints *
9547 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9550 The contents of an C<isl_schedule_constraints> object can be printed
9551 using the following functions.
9553 #include <isl/schedule.h>
9554 __isl_give isl_printer *
9555 isl_printer_print_schedule_constraints(
9556 __isl_take isl_printer *p,
9557 __isl_keep isl_schedule_constraints *sc);
9558 __isl_give char *isl_schedule_constraints_to_str(
9559 __isl_keep isl_schedule_constraints *sc);
9561 The following function computes a schedule directly from
9562 an iteration domain and validity and proximity dependences
9563 and is implemented in terms of the functions described above.
9564 The use of C<isl_union_set_compute_schedule> is discouraged.
9566 #include <isl/schedule.h>
9567 __isl_give isl_schedule *isl_union_set_compute_schedule(
9568 __isl_take isl_union_set *domain,
9569 __isl_take isl_union_map *validity,
9570 __isl_take isl_union_map *proximity);
9572 The generated schedule represents a schedule tree.
9573 For more information on schedule trees, see
9574 L</"Schedule Trees">.
9578 #include <isl/schedule.h>
9579 isl_stat isl_options_set_schedule_max_coefficient(
9580 isl_ctx *ctx, int val);
9581 int isl_options_get_schedule_max_coefficient(
9583 isl_stat isl_options_set_schedule_max_constant_term(
9584 isl_ctx *ctx, int val);
9585 int isl_options_get_schedule_max_constant_term(
9587 isl_stat isl_options_set_schedule_serialize_sccs(
9588 isl_ctx *ctx, int val);
9589 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9590 isl_stat isl_options_set_schedule_whole_component(
9591 isl_ctx *ctx, int val);
9592 int isl_options_get_schedule_whole_component(
9594 isl_stat isl_options_set_schedule_maximize_band_depth(
9595 isl_ctx *ctx, int val);
9596 int isl_options_get_schedule_maximize_band_depth(
9598 isl_stat isl_options_set_schedule_maximize_coincidence(
9599 isl_ctx *ctx, int val);
9600 int isl_options_get_schedule_maximize_coincidence(
9602 isl_stat isl_options_set_schedule_outer_coincidence(
9603 isl_ctx *ctx, int val);
9604 int isl_options_get_schedule_outer_coincidence(
9606 isl_stat isl_options_set_schedule_split_scaled(
9607 isl_ctx *ctx, int val);
9608 int isl_options_get_schedule_split_scaled(
9610 isl_stat isl_options_set_schedule_treat_coalescing(
9611 isl_ctx *ctx, int val);
9612 int isl_options_get_schedule_treat_coalescing(
9614 isl_stat isl_options_set_schedule_algorithm(
9615 isl_ctx *ctx, int val);
9616 int isl_options_get_schedule_algorithm(
9618 isl_stat isl_options_set_schedule_carry_self_first(
9619 isl_ctx *ctx, int val);
9620 int isl_options_get_schedule_carry_self_first(
9622 isl_stat isl_options_set_schedule_separate_components(
9623 isl_ctx *ctx, int val);
9624 int isl_options_get_schedule_separate_components(
9629 =item * schedule_max_coefficient
9631 This option enforces that the coefficients for variable and parameter
9632 dimensions in the calculated schedule are not larger than the specified value.
9633 This option can significantly increase the speed of the scheduling calculation
9634 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9635 this option does not introduce bounds on the variable or parameter
9638 =item * schedule_max_constant_term
9640 This option enforces that the constant coefficients in the calculated schedule
9641 are not larger than the maximal constant term. This option can significantly
9642 increase the speed of the scheduling calculation and may also prevent fusing of
9643 unrelated dimensions. A value of -1 means that this option does not introduce
9644 bounds on the constant coefficients.
9646 =item * schedule_serialize_sccs
9648 If this option is set, then all strongly connected components
9649 in the dependence graph are serialized as soon as they are detected.
9650 This means in particular that instances of statements will only
9651 appear in the same band node if these statements belong
9652 to the same strongly connected component at the point where
9653 the band node is constructed.
9655 =item * schedule_whole_component
9657 If this option is set, then entire (weakly) connected
9658 components in the dependence graph are scheduled together
9660 Otherwise, each strongly connected component within
9661 such a weakly connected component is first scheduled separately
9662 and then combined with other strongly connected components.
9663 This option has no effect if C<schedule_serialize_sccs> is set.
9665 =item * schedule_maximize_band_depth
9667 If this option is set, then the scheduler tries to maximize
9668 the width of the bands. Wider bands give more possibilities for tiling.
9669 In particular, if the C<schedule_whole_component> option is set,
9670 then bands are split if this might result in wider bands.
9671 Otherwise, the effect of this option is to only allow
9672 strongly connected components to be combined if this does
9673 not reduce the width of the bands.
9674 Note that if the C<schedule_serialize_sccs> options is set, then
9675 the C<schedule_maximize_band_depth> option therefore has no effect.
9677 =item * schedule_maximize_coincidence
9679 This option is only effective if the C<schedule_whole_component>
9680 option is turned off.
9681 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9682 strongly connected components are only combined with each other
9683 if this does not reduce the number of coincident band members.
9685 =item * schedule_outer_coincidence
9687 If this option is set, then we try to construct schedules
9688 where the outermost scheduling dimension in each band
9689 satisfies the coincidence constraints.
9691 =item * schedule_algorithm
9693 Selects the scheduling algorithm to be used.
9694 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9695 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9697 =item * schedule_split_scaled
9699 If this option is set, then we try to construct schedules in which the
9700 constant term is split off from the linear part if the linear parts of
9701 the scheduling rows for all nodes in the graph have a common non-trivial
9703 The constant term is then dropped and the linear
9705 This option is only effective when the Feautrier style scheduler is
9706 being used, either as the main scheduler or as a fallback for the
9707 Pluto-like scheduler.
9709 =item * schedule_treat_coalescing
9711 If this option is set, then the scheduler will try and avoid
9712 producing schedules that perform loop coalescing.
9713 In particular, for the Pluto-like scheduler, this option places
9714 bounds on the schedule coefficients based on the sizes of the instance sets.
9715 For the Feautrier style scheduler, this option detects potentially
9716 coalescing schedules and then tries to adjust the schedule to avoid
9719 =item * schedule_carry_self_first
9721 If this option is set, then the Feautrier style scheduler
9722 (when used as a fallback for the Pluto-like scheduler) will
9723 first try to only carry self-dependences.
9725 =item * schedule_separate_components
9727 If this option is set then the function C<isl_schedule_get_map>
9728 will treat set nodes in the same way as sequence nodes.
9732 =head2 AST Generation
9734 This section describes the C<isl> functionality for generating
9735 ASTs that visit all the elements
9736 in a domain in an order specified by a schedule tree or
9738 In case the schedule given as a C<isl_union_map>, an AST is generated
9739 that visits all the elements in the domain of the C<isl_union_map>
9740 according to the lexicographic order of the corresponding image
9741 element(s). If the range of the C<isl_union_map> consists of
9742 elements in more than one space, then each of these spaces is handled
9743 separately in an arbitrary order.
9744 It should be noted that the schedule tree or the image elements
9745 in a schedule map only specify the I<order>
9746 in which the corresponding domain elements should be visited.
9747 No direct relation between the partial schedule values
9748 or the image elements on the one hand and the loop iterators
9749 in the generated AST on the other hand should be assumed.
9751 Each AST is generated within a build. The initial build
9752 simply specifies the constraints on the parameters (if any)
9753 and can be created, inspected, copied and freed using the following functions.
9755 #include <isl/ast_build.h>
9756 __isl_give isl_ast_build *isl_ast_build_alloc(
9758 __isl_give isl_ast_build *isl_ast_build_from_context(
9759 __isl_take isl_set *set);
9760 __isl_give isl_ast_build *isl_ast_build_copy(
9761 __isl_keep isl_ast_build *build);
9762 __isl_null isl_ast_build *isl_ast_build_free(
9763 __isl_take isl_ast_build *build);
9765 The C<set> argument is usually a parameter set with zero or more parameters.
9766 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9767 this set is required to be a parameter set.
9768 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9769 specify any parameter constraints.
9770 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9771 and L</"Fine-grained Control over AST Generation">.
9772 Finally, the AST itself can be constructed using one of the following
9775 #include <isl/ast_build.h>
9776 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9777 __isl_keep isl_ast_build *build,
9778 __isl_take isl_schedule *schedule);
9779 __isl_give isl_ast_node *
9780 isl_ast_build_node_from_schedule_map(
9781 __isl_keep isl_ast_build *build,
9782 __isl_take isl_union_map *schedule);
9784 =head3 Inspecting the AST
9786 The basic properties of an AST node can be obtained as follows.
9788 #include <isl/ast.h>
9789 enum isl_ast_node_type isl_ast_node_get_type(
9790 __isl_keep isl_ast_node *node);
9792 The type of an AST node is one of
9793 C<isl_ast_node_for>,
9795 C<isl_ast_node_block>,
9796 C<isl_ast_node_mark> or
9797 C<isl_ast_node_user>.
9798 An C<isl_ast_node_for> represents a for node.
9799 An C<isl_ast_node_if> represents an if node.
9800 An C<isl_ast_node_block> represents a compound node.
9801 An C<isl_ast_node_mark> introduces a mark in the AST.
9802 An C<isl_ast_node_user> represents an expression statement.
9803 An expression statement typically corresponds to a domain element, i.e.,
9804 one of the elements that is visited by the AST.
9806 Each type of node has its own additional properties.
9808 #include <isl/ast.h>
9809 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9810 __isl_keep isl_ast_node *node);
9811 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9812 __isl_keep isl_ast_node *node);
9813 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9814 __isl_keep isl_ast_node *node);
9815 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9816 __isl_keep isl_ast_node *node);
9817 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9818 __isl_keep isl_ast_node *node);
9819 isl_bool isl_ast_node_for_is_degenerate(
9820 __isl_keep isl_ast_node *node);
9822 An C<isl_ast_for> is considered degenerate if it is known to execute
9825 #include <isl/ast.h>
9826 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9827 __isl_keep isl_ast_node *node);
9828 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9829 __isl_keep isl_ast_node *node);
9830 isl_bool isl_ast_node_if_has_else(
9831 __isl_keep isl_ast_node *node);
9832 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9833 __isl_keep isl_ast_node *node);
9835 __isl_give isl_ast_node_list *
9836 isl_ast_node_block_get_children(
9837 __isl_keep isl_ast_node *node);
9839 __isl_give isl_id *isl_ast_node_mark_get_id(
9840 __isl_keep isl_ast_node *node);
9841 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9842 __isl_keep isl_ast_node *node);
9844 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9845 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9847 #include <isl/ast.h>
9848 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9849 __isl_keep isl_ast_node *node);
9851 All descendants of a specific node in the AST (including the node itself)
9853 in depth-first pre-order using the following function.
9855 #include <isl/ast.h>
9856 isl_stat isl_ast_node_foreach_descendant_top_down(
9857 __isl_keep isl_ast_node *node,
9858 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9859 void *user), void *user);
9861 The callback function should return C<isl_bool_true> if the children
9862 of the given node should be visited and C<isl_bool_false> if they should not.
9863 It should return C<isl_bool_error> in case of failure, in which case
9864 the entire traversal is aborted.
9866 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9867 the following functions.
9869 #include <isl/ast.h>
9870 enum isl_ast_expr_type isl_ast_expr_get_type(
9871 __isl_keep isl_ast_expr *expr);
9873 The type of an AST expression is one of
9875 C<isl_ast_expr_id> or
9876 C<isl_ast_expr_int>.
9877 An C<isl_ast_expr_op> represents the result of an operation.
9878 An C<isl_ast_expr_id> represents an identifier.
9879 An C<isl_ast_expr_int> represents an integer value.
9881 Each type of expression has its own additional properties.
9883 #include <isl/ast.h>
9884 enum isl_ast_op_type isl_ast_expr_get_op_type(
9885 __isl_keep isl_ast_expr *expr);
9886 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9887 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9888 __isl_keep isl_ast_expr *expr, int pos);
9889 isl_stat isl_ast_expr_foreach_ast_op_type(
9890 __isl_keep isl_ast_expr *expr,
9891 isl_stat (*fn)(enum isl_ast_op_type type,
9892 void *user), void *user);
9893 isl_stat isl_ast_node_foreach_ast_op_type(
9894 __isl_keep isl_ast_node *node,
9895 isl_stat (*fn)(enum isl_ast_op_type type,
9896 void *user), void *user);
9898 C<isl_ast_expr_get_op_type> returns the type of the operation
9899 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9900 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9902 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9903 C<isl_ast_op_type> that appears in C<expr>.
9904 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9905 C<isl_ast_op_type> that appears in C<node>.
9906 The operation type is one of the following.
9910 =item C<isl_ast_op_and>
9912 Logical I<and> of two arguments.
9913 Both arguments can be evaluated.
9915 =item C<isl_ast_op_and_then>
9917 Logical I<and> of two arguments.
9918 The second argument can only be evaluated if the first evaluates to true.
9920 =item C<isl_ast_op_or>
9922 Logical I<or> of two arguments.
9923 Both arguments can be evaluated.
9925 =item C<isl_ast_op_or_else>
9927 Logical I<or> of two arguments.
9928 The second argument can only be evaluated if the first evaluates to false.
9930 =item C<isl_ast_op_max>
9932 Maximum of two or more arguments.
9934 =item C<isl_ast_op_min>
9936 Minimum of two or more arguments.
9938 =item C<isl_ast_op_minus>
9942 =item C<isl_ast_op_add>
9944 Sum of two arguments.
9946 =item C<isl_ast_op_sub>
9948 Difference of two arguments.
9950 =item C<isl_ast_op_mul>
9952 Product of two arguments.
9954 =item C<isl_ast_op_div>
9956 Exact division. That is, the result is known to be an integer.
9958 =item C<isl_ast_op_fdiv_q>
9960 Result of integer division, rounded towards negative
9962 The divisor is known to be positive.
9964 =item C<isl_ast_op_pdiv_q>
9966 Result of integer division, where dividend is known to be non-negative.
9967 The divisor is known to be positive.
9969 =item C<isl_ast_op_pdiv_r>
9971 Remainder of integer division, where dividend is known to be non-negative.
9972 The divisor is known to be positive.
9974 =item C<isl_ast_op_zdiv_r>
9976 Equal to zero iff the remainder on integer division is zero.
9977 The divisor is known to be positive.
9979 =item C<isl_ast_op_cond>
9981 Conditional operator defined on three arguments.
9982 If the first argument evaluates to true, then the result
9983 is equal to the second argument. Otherwise, the result
9984 is equal to the third argument.
9985 The second and third argument may only be evaluated if
9986 the first argument evaluates to true and false, respectively.
9987 Corresponds to C<a ? b : c> in C.
9989 =item C<isl_ast_op_select>
9991 Conditional operator defined on three arguments.
9992 If the first argument evaluates to true, then the result
9993 is equal to the second argument. Otherwise, the result
9994 is equal to the third argument.
9995 The second and third argument may be evaluated independently
9996 of the value of the first argument.
9997 Corresponds to C<a * b + (1 - a) * c> in C.
9999 =item C<isl_ast_op_eq>
10003 =item C<isl_ast_op_le>
10005 Less than or equal relation.
10007 =item C<isl_ast_op_lt>
10009 Less than relation.
10011 =item C<isl_ast_op_ge>
10013 Greater than or equal relation.
10015 =item C<isl_ast_op_gt>
10017 Greater than relation.
10019 =item C<isl_ast_op_call>
10022 The number of arguments of the C<isl_ast_expr> is one more than
10023 the number of arguments in the function call, the first argument
10024 representing the function being called.
10026 =item C<isl_ast_op_access>
10029 The number of arguments of the C<isl_ast_expr> is one more than
10030 the number of index expressions in the array access, the first argument
10031 representing the array being accessed.
10033 =item C<isl_ast_op_member>
10036 This operation has two arguments, a structure and the name of
10037 the member of the structure being accessed.
10041 #include <isl/ast.h>
10042 __isl_give isl_id *isl_ast_expr_get_id(
10043 __isl_keep isl_ast_expr *expr);
10045 Return the identifier represented by the AST expression.
10047 #include <isl/ast.h>
10048 __isl_give isl_val *isl_ast_expr_get_val(
10049 __isl_keep isl_ast_expr *expr);
10051 Return the integer represented by the AST expression.
10053 =head3 Properties of ASTs
10055 #include <isl/ast.h>
10056 isl_bool isl_ast_expr_is_equal(
10057 __isl_keep isl_ast_expr *expr1,
10058 __isl_keep isl_ast_expr *expr2);
10060 Check if two C<isl_ast_expr>s are equal to each other.
10062 =head3 Manipulating and printing the AST
10064 AST nodes can be copied and freed using the following functions.
10066 #include <isl/ast.h>
10067 __isl_give isl_ast_node *isl_ast_node_copy(
10068 __isl_keep isl_ast_node *node);
10069 __isl_null isl_ast_node *isl_ast_node_free(
10070 __isl_take isl_ast_node *node);
10072 AST expressions can be copied and freed using the following functions.
10074 #include <isl/ast.h>
10075 __isl_give isl_ast_expr *isl_ast_expr_copy(
10076 __isl_keep isl_ast_expr *expr);
10077 __isl_null isl_ast_expr *isl_ast_expr_free(
10078 __isl_take isl_ast_expr *expr);
10080 New AST expressions can be created either directly or within
10081 the context of an C<isl_ast_build>.
10083 #include <isl/ast.h>
10084 __isl_give isl_ast_expr *isl_ast_expr_from_val(
10085 __isl_take isl_val *v);
10086 __isl_give isl_ast_expr *isl_ast_expr_from_id(
10087 __isl_take isl_id *id);
10088 __isl_give isl_ast_expr *isl_ast_expr_neg(
10089 __isl_take isl_ast_expr *expr);
10090 __isl_give isl_ast_expr *isl_ast_expr_address_of(
10091 __isl_take isl_ast_expr *expr);
10092 __isl_give isl_ast_expr *isl_ast_expr_add(
10093 __isl_take isl_ast_expr *expr1,
10094 __isl_take isl_ast_expr *expr2);
10095 __isl_give isl_ast_expr *isl_ast_expr_sub(
10096 __isl_take isl_ast_expr *expr1,
10097 __isl_take isl_ast_expr *expr2);
10098 __isl_give isl_ast_expr *isl_ast_expr_mul(
10099 __isl_take isl_ast_expr *expr1,
10100 __isl_take isl_ast_expr *expr2);
10101 __isl_give isl_ast_expr *isl_ast_expr_div(
10102 __isl_take isl_ast_expr *expr1,
10103 __isl_take isl_ast_expr *expr2);
10104 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
10105 __isl_take isl_ast_expr *expr1,
10106 __isl_take isl_ast_expr *expr2);
10107 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
10108 __isl_take isl_ast_expr *expr1,
10109 __isl_take isl_ast_expr *expr2);
10110 __isl_give isl_ast_expr *isl_ast_expr_and(
10111 __isl_take isl_ast_expr *expr1,
10112 __isl_take isl_ast_expr *expr2)
10113 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10114 __isl_take isl_ast_expr *expr1,
10115 __isl_take isl_ast_expr *expr2)
10116 __isl_give isl_ast_expr *isl_ast_expr_or(
10117 __isl_take isl_ast_expr *expr1,
10118 __isl_take isl_ast_expr *expr2)
10119 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10120 __isl_take isl_ast_expr *expr1,
10121 __isl_take isl_ast_expr *expr2)
10122 __isl_give isl_ast_expr *isl_ast_expr_eq(
10123 __isl_take isl_ast_expr *expr1,
10124 __isl_take isl_ast_expr *expr2);
10125 __isl_give isl_ast_expr *isl_ast_expr_le(
10126 __isl_take isl_ast_expr *expr1,
10127 __isl_take isl_ast_expr *expr2);
10128 __isl_give isl_ast_expr *isl_ast_expr_lt(
10129 __isl_take isl_ast_expr *expr1,
10130 __isl_take isl_ast_expr *expr2);
10131 __isl_give isl_ast_expr *isl_ast_expr_ge(
10132 __isl_take isl_ast_expr *expr1,
10133 __isl_take isl_ast_expr *expr2);
10134 __isl_give isl_ast_expr *isl_ast_expr_gt(
10135 __isl_take isl_ast_expr *expr1,
10136 __isl_take isl_ast_expr *expr2);
10137 __isl_give isl_ast_expr *isl_ast_expr_access(
10138 __isl_take isl_ast_expr *array,
10139 __isl_take isl_ast_expr_list *indices);
10140 __isl_give isl_ast_expr *isl_ast_expr_call(
10141 __isl_take isl_ast_expr *function,
10142 __isl_take isl_ast_expr_list *arguments);
10144 The function C<isl_ast_expr_address_of> can be applied to an
10145 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10146 to represent the address of the C<isl_ast_expr_access>.
10147 The second argument of the functions C<isl_ast_expr_pdiv_q> and
10148 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
10150 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10151 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10153 #include <isl/ast_build.h>
10154 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10155 __isl_keep isl_ast_build *build,
10156 __isl_take isl_set *set);
10157 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10158 __isl_keep isl_ast_build *build,
10159 __isl_take isl_pw_aff *pa);
10160 __isl_give isl_ast_expr *
10161 isl_ast_build_access_from_pw_multi_aff(
10162 __isl_keep isl_ast_build *build,
10163 __isl_take isl_pw_multi_aff *pma);
10164 __isl_give isl_ast_expr *
10165 isl_ast_build_access_from_multi_pw_aff(
10166 __isl_keep isl_ast_build *build,
10167 __isl_take isl_multi_pw_aff *mpa);
10168 __isl_give isl_ast_expr *
10169 isl_ast_build_call_from_pw_multi_aff(
10170 __isl_keep isl_ast_build *build,
10171 __isl_take isl_pw_multi_aff *pma);
10172 __isl_give isl_ast_expr *
10173 isl_ast_build_call_from_multi_pw_aff(
10174 __isl_keep isl_ast_build *build,
10175 __isl_take isl_multi_pw_aff *mpa);
10178 the domains of C<pa>, C<mpa> and C<pma> should correspond
10179 to the schedule space of C<build>.
10180 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10181 the function being called.
10182 If the accessed space is a nested relation, then it is taken
10183 to represent an access of the member specified by the range
10184 of this nested relation of the structure specified by the domain
10185 of the nested relation.
10187 The following functions can be used to modify an C<isl_ast_expr>.
10189 #include <isl/ast.h>
10190 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10191 __isl_take isl_ast_expr *expr, int pos,
10192 __isl_take isl_ast_expr *arg);
10194 Replace the argument of C<expr> at position C<pos> by C<arg>.
10196 #include <isl/ast.h>
10197 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10198 __isl_take isl_ast_expr *expr,
10199 __isl_take isl_id_to_ast_expr *id2expr);
10201 The function C<isl_ast_expr_substitute_ids> replaces the
10202 subexpressions of C<expr> of type C<isl_ast_expr_id>
10203 by the corresponding expression in C<id2expr>, if there is any.
10206 User specified data can be attached to an C<isl_ast_node> and obtained
10207 from the same C<isl_ast_node> using the following functions.
10209 #include <isl/ast.h>
10210 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10211 __isl_take isl_ast_node *node,
10212 __isl_take isl_id *annotation);
10213 __isl_give isl_id *isl_ast_node_get_annotation(
10214 __isl_keep isl_ast_node *node);
10216 Basic printing can be performed using the following functions.
10218 #include <isl/ast.h>
10219 __isl_give isl_printer *isl_printer_print_ast_expr(
10220 __isl_take isl_printer *p,
10221 __isl_keep isl_ast_expr *expr);
10222 __isl_give isl_printer *isl_printer_print_ast_node(
10223 __isl_take isl_printer *p,
10224 __isl_keep isl_ast_node *node);
10225 __isl_give char *isl_ast_expr_to_str(
10226 __isl_keep isl_ast_expr *expr);
10227 __isl_give char *isl_ast_node_to_str(
10228 __isl_keep isl_ast_node *node);
10229 __isl_give char *isl_ast_expr_to_C_str(
10230 __isl_keep isl_ast_expr *expr);
10231 __isl_give char *isl_ast_node_to_C_str(
10232 __isl_keep isl_ast_node *node);
10234 The functions C<isl_ast_expr_to_C_str> and
10235 C<isl_ast_node_to_C_str> are convenience functions
10236 that return a string representation of the input in C format.
10238 More advanced printing can be performed using the following functions.
10240 #include <isl/ast.h>
10241 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10242 __isl_take isl_printer *p,
10243 enum isl_ast_op_type type,
10244 __isl_keep const char *name);
10245 isl_stat isl_options_set_ast_print_macro_once(
10246 isl_ctx *ctx, int val);
10247 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10248 __isl_give isl_printer *isl_ast_op_type_print_macro(
10249 enum isl_ast_op_type type,
10250 __isl_take isl_printer *p);
10251 __isl_give isl_printer *isl_ast_expr_print_macros(
10252 __isl_keep isl_ast_expr *expr,
10253 __isl_take isl_printer *p);
10254 __isl_give isl_printer *isl_ast_node_print_macros(
10255 __isl_keep isl_ast_node *node,
10256 __isl_take isl_printer *p);
10257 __isl_give isl_printer *isl_ast_node_print(
10258 __isl_keep isl_ast_node *node,
10259 __isl_take isl_printer *p,
10260 __isl_take isl_ast_print_options *options);
10261 __isl_give isl_printer *isl_ast_node_for_print(
10262 __isl_keep isl_ast_node *node,
10263 __isl_take isl_printer *p,
10264 __isl_take isl_ast_print_options *options);
10265 __isl_give isl_printer *isl_ast_node_if_print(
10266 __isl_keep isl_ast_node *node,
10267 __isl_take isl_printer *p,
10268 __isl_take isl_ast_print_options *options);
10270 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10271 C<isl> may print out an AST that makes use of macros such
10272 as C<floord>, C<min> and C<max>.
10273 The names of these macros may be modified by a call
10274 to C<isl_ast_op_type_set_print_name>. The user-specified
10275 names are associated to the printer object.
10276 C<isl_ast_op_type_print_macro> prints out the macro
10277 corresponding to a specific C<isl_ast_op_type>.
10278 If the print-macro-once option is set, then a given macro definition
10279 is only printed once to any given printer object.
10280 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10281 for subexpressions where these macros would be used and prints
10282 out the required macro definitions.
10283 Essentially, C<isl_ast_expr_print_macros> calls
10284 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10285 as function argument.
10286 C<isl_ast_node_print_macros> does the same
10287 for expressions in its C<isl_ast_node> argument.
10288 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10289 C<isl_ast_node_if_print> print an C<isl_ast_node>
10290 in C<ISL_FORMAT_C>, but allow for some extra control
10291 through an C<isl_ast_print_options> object.
10292 This object can be created using the following functions.
10294 #include <isl/ast.h>
10295 __isl_give isl_ast_print_options *
10296 isl_ast_print_options_alloc(isl_ctx *ctx);
10297 __isl_give isl_ast_print_options *
10298 isl_ast_print_options_copy(
10299 __isl_keep isl_ast_print_options *options);
10300 __isl_null isl_ast_print_options *
10301 isl_ast_print_options_free(
10302 __isl_take isl_ast_print_options *options);
10304 __isl_give isl_ast_print_options *
10305 isl_ast_print_options_set_print_user(
10306 __isl_take isl_ast_print_options *options,
10307 __isl_give isl_printer *(*print_user)(
10308 __isl_take isl_printer *p,
10309 __isl_take isl_ast_print_options *options,
10310 __isl_keep isl_ast_node *node, void *user),
10312 __isl_give isl_ast_print_options *
10313 isl_ast_print_options_set_print_for(
10314 __isl_take isl_ast_print_options *options,
10315 __isl_give isl_printer *(*print_for)(
10316 __isl_take isl_printer *p,
10317 __isl_take isl_ast_print_options *options,
10318 __isl_keep isl_ast_node *node, void *user),
10321 The callback set by C<isl_ast_print_options_set_print_user>
10322 is called whenever a node of type C<isl_ast_node_user> needs to
10324 The callback set by C<isl_ast_print_options_set_print_for>
10325 is called whenever a node of type C<isl_ast_node_for> needs to
10327 Note that C<isl_ast_node_for_print> will I<not> call the
10328 callback set by C<isl_ast_print_options_set_print_for> on the node
10329 on which C<isl_ast_node_for_print> is called, but only on nested
10330 nodes of type C<isl_ast_node_for>. It is therefore safe to
10331 call C<isl_ast_node_for_print> from within the callback set by
10332 C<isl_ast_print_options_set_print_for>.
10334 The following option determines the type to be used for iterators
10335 while printing the AST.
10337 isl_stat isl_options_set_ast_iterator_type(
10338 isl_ctx *ctx, const char *val);
10339 const char *isl_options_get_ast_iterator_type(
10342 The AST printer only prints body nodes as blocks if these
10343 blocks cannot be safely omitted.
10344 For example, a C<for> node with one body node will not be
10345 surrounded with braces in C<ISL_FORMAT_C>.
10346 A block will always be printed by setting the following option.
10348 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10350 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10354 #include <isl/ast_build.h>
10355 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10356 isl_ctx *ctx, int val);
10357 int isl_options_get_ast_build_atomic_upper_bound(
10359 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10361 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10362 isl_stat isl_options_set_ast_build_detect_min_max(
10363 isl_ctx *ctx, int val);
10364 int isl_options_get_ast_build_detect_min_max(
10366 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10367 isl_ctx *ctx, int val);
10368 int isl_options_get_ast_build_exploit_nested_bounds(
10370 isl_stat isl_options_set_ast_build_group_coscheduled(
10371 isl_ctx *ctx, int val);
10372 int isl_options_get_ast_build_group_coscheduled(
10374 isl_stat isl_options_set_ast_build_separation_bounds(
10375 isl_ctx *ctx, int val);
10376 int isl_options_get_ast_build_separation_bounds(
10378 isl_stat isl_options_set_ast_build_scale_strides(
10379 isl_ctx *ctx, int val);
10380 int isl_options_get_ast_build_scale_strides(
10382 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10384 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10385 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10387 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10391 =item * ast_build_atomic_upper_bound
10393 Generate loop upper bounds that consist of the current loop iterator,
10394 an operator and an expression not involving the iterator.
10395 If this option is not set, then the current loop iterator may appear
10396 several times in the upper bound.
10397 For example, when this option is turned off, AST generation
10400 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10404 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10407 When the option is turned on, the following AST is generated
10409 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10412 =item * ast_build_prefer_pdiv
10414 If this option is turned off, then the AST generation will
10415 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10416 operators, but no C<isl_ast_op_pdiv_q> or
10417 C<isl_ast_op_pdiv_r> operators.
10418 If this option is turned on, then C<isl> will try to convert
10419 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10420 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10422 =item * ast_build_detect_min_max
10424 If this option is turned on, then C<isl> will try and detect
10425 min or max-expressions when building AST expressions from
10426 piecewise affine expressions.
10428 =item * ast_build_exploit_nested_bounds
10430 Simplify conditions based on bounds of nested for loops.
10431 In particular, remove conditions that are implied by the fact
10432 that one or more nested loops have at least one iteration,
10433 meaning that the upper bound is at least as large as the lower bound.
10434 For example, when this option is turned off, AST generation
10437 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10443 for (int c0 = 0; c0 <= N; c0 += 1)
10444 for (int c1 = 0; c1 <= M; c1 += 1)
10447 When the option is turned on, the following AST is generated
10449 for (int c0 = 0; c0 <= N; c0 += 1)
10450 for (int c1 = 0; c1 <= M; c1 += 1)
10453 =item * ast_build_group_coscheduled
10455 If two domain elements are assigned the same schedule point, then
10456 they may be executed in any order and they may even appear in different
10457 loops. If this options is set, then the AST generator will make
10458 sure that coscheduled domain elements do not appear in separate parts
10459 of the AST. This is useful in case of nested AST generation
10460 if the outer AST generation is given only part of a schedule
10461 and the inner AST generation should handle the domains that are
10462 coscheduled by this initial part of the schedule together.
10463 For example if an AST is generated for a schedule
10465 { A[i] -> [0]; B[i] -> [0] }
10467 then the C<isl_ast_build_set_create_leaf> callback described
10468 below may get called twice, once for each domain.
10469 Setting this option ensures that the callback is only called once
10470 on both domains together.
10472 =item * ast_build_separation_bounds
10474 This option specifies which bounds to use during separation.
10475 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10476 then all (possibly implicit) bounds on the current dimension will
10477 be used during separation.
10478 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10479 then only those bounds that are explicitly available will
10480 be used during separation.
10482 =item * ast_build_scale_strides
10484 This option specifies whether the AST generator is allowed
10485 to scale down iterators of strided loops.
10487 =item * ast_build_allow_else
10489 This option specifies whether the AST generator is allowed
10490 to construct if statements with else branches.
10492 =item * ast_build_allow_or
10494 This option specifies whether the AST generator is allowed
10495 to construct if conditions with disjunctions.
10499 =head3 AST Generation Options (Schedule Tree)
10501 In case of AST construction from a schedule tree, the options
10502 that control how an AST is created from the individual schedule
10503 dimensions are stored in the band nodes of the tree
10504 (see L</"Schedule Trees">).
10506 In particular, a schedule dimension can be handled in four
10507 different ways, atomic, separate, unroll or the default.
10508 This loop AST generation type can be set using
10509 C<isl_schedule_node_band_member_set_ast_loop_type>.
10511 the first three can be selected by including a one-dimensional
10512 element with as value the position of the schedule dimension
10513 within the band and as name one of C<atomic>, C<separate>
10514 or C<unroll> in the options
10515 set by C<isl_schedule_node_band_set_ast_build_options>.
10516 Only one of these three may be specified for
10517 any given schedule dimension within a band node.
10518 If none of these is specified, then the default
10519 is used. The meaning of the options is as follows.
10525 When this option is specified, the AST generator will make
10526 sure that a given domains space only appears in a single
10527 loop at the specified level.
10529 For example, for the schedule tree
10531 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10533 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10534 options: "{ atomic[x] }"
10536 the following AST will be generated
10538 for (int c0 = 0; c0 <= 10; c0 += 1) {
10545 On the other hand, for the schedule tree
10547 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10549 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10550 options: "{ separate[x] }"
10552 the following AST will be generated
10556 for (int c0 = 1; c0 <= 9; c0 += 1) {
10563 If neither C<atomic> nor C<separate> is specified, then the AST generator
10564 may produce either of these two results or some intermediate form.
10568 When this option is specified, the AST generator will
10569 split the domain of the specified schedule dimension
10570 into pieces with a fixed set of statements for which
10571 instances need to be executed by the iterations in
10572 the schedule domain part. This option tends to avoid
10573 the generation of guards inside the corresponding loops.
10574 See also the C<atomic> option.
10578 When this option is specified, the AST generator will
10579 I<completely> unroll the corresponding schedule dimension.
10580 It is the responsibility of the user to ensure that such
10581 unrolling is possible.
10582 To obtain a partial unrolling, the user should apply an additional
10583 strip-mining to the schedule and fully unroll the inner schedule
10588 The C<isolate> option is a bit more involved. It allows the user
10589 to isolate a range of schedule dimension values from smaller and
10590 greater values. Additionally, the user may specify a different
10591 atomic/separate/unroll choice for the isolated part and the remaining
10592 parts. The typical use case of the C<isolate> option is to isolate
10593 full tiles from partial tiles.
10594 The part that needs to be isolated may depend on outer schedule dimensions.
10595 The option therefore needs to be able to reference those outer schedule
10596 dimensions. In particular, the space of the C<isolate> option is that
10597 of a wrapped map with as domain the flat product of all outer band nodes
10598 and as range the space of the current band node.
10599 The atomic/separate/unroll choice for the isolated part is determined
10600 by an option that lives in an unnamed wrapped space with as domain
10601 a zero-dimensional C<isolate> space and as range the regular
10602 C<atomic>, C<separate> or C<unroll> space.
10603 This option may also be set directly using
10604 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10605 The atomic/separate/unroll choice for the remaining part is determined
10606 by the regular C<atomic>, C<separate> or C<unroll> option.
10607 Since the C<isolate> option references outer schedule dimensions,
10608 its use in a band node causes any tree containing the node
10609 to be considered anchored.
10611 As an example, consider the isolation of full tiles from partial tiles
10612 in a tiling of a triangular domain. The original schedule is as follows.
10614 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10616 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10617 { A[i,j] -> [floor(j/10)] }, \
10618 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10622 for (int c0 = 0; c0 <= 10; c0 += 1)
10623 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10624 for (int c2 = 10 * c0;
10625 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10626 for (int c3 = 10 * c1;
10627 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10630 Isolating the full tiles, we have the following input
10632 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10634 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10635 { A[i,j] -> [floor(j/10)] }, \
10636 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10637 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10638 10a+9+10b+9 <= 100 }"
10643 for (int c0 = 0; c0 <= 8; c0 += 1) {
10644 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10645 for (int c2 = 10 * c0;
10646 c2 <= 10 * c0 + 9; c2 += 1)
10647 for (int c3 = 10 * c1;
10648 c3 <= 10 * c1 + 9; c3 += 1)
10650 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10651 for (int c2 = 10 * c0;
10652 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10653 for (int c3 = 10 * c1;
10654 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10657 for (int c0 = 9; c0 <= 10; c0 += 1)
10658 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10659 for (int c2 = 10 * c0;
10660 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10661 for (int c3 = 10 * c1;
10662 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10666 We may then additionally unroll the innermost loop of the isolated part
10668 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10670 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10671 { A[i,j] -> [floor(j/10)] }, \
10672 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10673 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10674 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10679 for (int c0 = 0; c0 <= 8; c0 += 1) {
10680 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10681 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10683 A(c2, 10 * c1 + 1);
10684 A(c2, 10 * c1 + 2);
10685 A(c2, 10 * c1 + 3);
10686 A(c2, 10 * c1 + 4);
10687 A(c2, 10 * c1 + 5);
10688 A(c2, 10 * c1 + 6);
10689 A(c2, 10 * c1 + 7);
10690 A(c2, 10 * c1 + 8);
10691 A(c2, 10 * c1 + 9);
10693 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10694 for (int c2 = 10 * c0;
10695 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10696 for (int c3 = 10 * c1;
10697 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10700 for (int c0 = 9; c0 <= 10; c0 += 1)
10701 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10702 for (int c2 = 10 * c0;
10703 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10704 for (int c3 = 10 * c1;
10705 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10710 =head3 AST Generation Options (Schedule Map)
10712 In case of AST construction using
10713 C<isl_ast_build_node_from_schedule_map>, the options
10714 that control how an AST is created from the individual schedule
10715 dimensions are stored in the C<isl_ast_build>.
10716 They can be set using the following function.
10718 #include <isl/ast_build.h>
10719 __isl_give isl_ast_build *
10720 isl_ast_build_set_options(
10721 __isl_take isl_ast_build *build,
10722 __isl_take isl_union_map *options);
10724 The options are encoded in an C<isl_union_map>.
10725 The domain of this union relation refers to the schedule domain,
10726 i.e., the range of the schedule passed
10727 to C<isl_ast_build_node_from_schedule_map>.
10728 In the case of nested AST generation (see L</"Nested AST Generation">),
10729 the domain of C<options> should refer to the extra piece of the schedule.
10730 That is, it should be equal to the range of the wrapped relation in the
10731 range of the schedule.
10732 The range of the options can consist of elements in one or more spaces,
10733 the names of which determine the effect of the option.
10734 The values of the range typically also refer to the schedule dimension
10735 to which the option applies, with value C<0> representing
10736 the outermost schedule dimension. In case of nested AST generation
10737 (see L</"Nested AST Generation">), these values refer to the position
10738 of the schedule dimension within the innermost AST generation.
10739 The constraints on the domain elements of
10740 the option should only refer to this dimension and earlier dimensions.
10741 We consider the following spaces.
10745 =item C<separation_class>
10747 B<This option has been deprecated. Use the isolate option on
10748 schedule trees instead.>
10750 This space is a wrapped relation between two one dimensional spaces.
10751 The input space represents the schedule dimension to which the option
10752 applies and the output space represents the separation class.
10753 While constructing a loop corresponding to the specified schedule
10754 dimension(s), the AST generator will try to generate separate loops
10755 for domain elements that are assigned different classes.
10756 If only some of the elements are assigned a class, then those elements
10757 that are not assigned any class will be treated as belonging to a class
10758 that is separate from the explicitly assigned classes.
10759 The typical use case for this option is to separate full tiles from
10761 The other options, described below, are applied after the separation
10764 As an example, consider the separation into full and partial tiles
10765 of a tiling of a triangular domain.
10766 Take, for example, the domain
10768 { A[i,j] : 0 <= i,j and i + j <= 100 }
10770 and a tiling into tiles of 10 by 10. The input to the AST generator
10771 is then the schedule
10773 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10776 Without any options, the following AST is generated
10778 for (int c0 = 0; c0 <= 10; c0 += 1)
10779 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10780 for (int c2 = 10 * c0;
10781 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10783 for (int c3 = 10 * c1;
10784 c3 <= min(10 * c1 + 9, -c2 + 100);
10788 Separation into full and partial tiles can be obtained by assigning
10789 a class, say C<0>, to the full tiles. The full tiles are represented by those
10790 values of the first and second schedule dimensions for which there are
10791 values of the third and fourth dimensions to cover an entire tile.
10792 That is, we need to specify the following option
10794 { [a,b,c,d] -> separation_class[[0]->[0]] :
10795 exists b': 0 <= 10a,10b' and
10796 10a+9+10b'+9 <= 100;
10797 [a,b,c,d] -> separation_class[[1]->[0]] :
10798 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10800 which simplifies to
10802 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10803 a >= 0 and b >= 0 and b <= 8 - a;
10804 [a, b, c, d] -> separation_class[[0] -> [0]] :
10805 a >= 0 and a <= 8 }
10807 With this option, the generated AST is as follows
10810 for (int c0 = 0; c0 <= 8; c0 += 1) {
10811 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10812 for (int c2 = 10 * c0;
10813 c2 <= 10 * c0 + 9; c2 += 1)
10814 for (int c3 = 10 * c1;
10815 c3 <= 10 * c1 + 9; c3 += 1)
10817 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10818 for (int c2 = 10 * c0;
10819 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10821 for (int c3 = 10 * c1;
10822 c3 <= min(-c2 + 100, 10 * c1 + 9);
10826 for (int c0 = 9; c0 <= 10; c0 += 1)
10827 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10828 for (int c2 = 10 * c0;
10829 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10831 for (int c3 = 10 * c1;
10832 c3 <= min(10 * c1 + 9, -c2 + 100);
10839 This is a single-dimensional space representing the schedule dimension(s)
10840 to which ``separation'' should be applied. Separation tries to split
10841 a loop into several pieces if this can avoid the generation of guards
10843 See also the C<atomic> option.
10847 This is a single-dimensional space representing the schedule dimension(s)
10848 for which the domains should be considered ``atomic''. That is, the
10849 AST generator will make sure that any given domain space will only appear
10850 in a single loop at the specified level.
10852 Consider the following schedule
10854 { a[i] -> [i] : 0 <= i < 10;
10855 b[i] -> [i+1] : 0 <= i < 10 }
10857 If the following option is specified
10859 { [i] -> separate[x] }
10861 then the following AST will be generated
10865 for (int c0 = 1; c0 <= 9; c0 += 1) {
10872 If, on the other hand, the following option is specified
10874 { [i] -> atomic[x] }
10876 then the following AST will be generated
10878 for (int c0 = 0; c0 <= 10; c0 += 1) {
10885 If neither C<atomic> nor C<separate> is specified, then the AST generator
10886 may produce either of these two results or some intermediate form.
10890 This is a single-dimensional space representing the schedule dimension(s)
10891 that should be I<completely> unrolled.
10892 To obtain a partial unrolling, the user should apply an additional
10893 strip-mining to the schedule and fully unroll the inner loop.
10897 =head3 Fine-grained Control over AST Generation
10899 Besides specifying the constraints on the parameters,
10900 an C<isl_ast_build> object can be used to control
10901 various aspects of the AST generation process.
10902 In case of AST construction using
10903 C<isl_ast_build_node_from_schedule_map>,
10904 the most prominent way of control is through ``options'',
10905 as explained above.
10907 Additional control is available through the following functions.
10909 #include <isl/ast_build.h>
10910 __isl_give isl_ast_build *
10911 isl_ast_build_set_iterators(
10912 __isl_take isl_ast_build *build,
10913 __isl_take isl_id_list *iterators);
10915 The function C<isl_ast_build_set_iterators> allows the user to
10916 specify a list of iterator C<isl_id>s to be used as iterators.
10917 If the input schedule is injective, then
10918 the number of elements in this list should be as large as the dimension
10919 of the schedule space, but no direct correspondence should be assumed
10920 between dimensions and elements.
10921 If the input schedule is not injective, then an additional number
10922 of C<isl_id>s equal to the largest dimension of the input domains
10924 If the number of provided C<isl_id>s is insufficient, then additional
10925 names are automatically generated.
10927 #include <isl/ast_build.h>
10928 __isl_give isl_ast_build *
10929 isl_ast_build_set_create_leaf(
10930 __isl_take isl_ast_build *build,
10931 __isl_give isl_ast_node *(*fn)(
10932 __isl_take isl_ast_build *build,
10933 void *user), void *user);
10936 C<isl_ast_build_set_create_leaf> function allows for the
10937 specification of a callback that should be called whenever the AST
10938 generator arrives at an element of the schedule domain.
10939 The callback should return an AST node that should be inserted
10940 at the corresponding position of the AST. The default action (when
10941 the callback is not set) is to continue generating parts of the AST to scan
10942 all the domain elements associated to the schedule domain element
10943 and to insert user nodes, ``calling'' the domain element, for each of them.
10944 The C<build> argument contains the current state of the C<isl_ast_build>.
10945 To ease nested AST generation (see L</"Nested AST Generation">),
10946 all control information that is
10947 specific to the current AST generation such as the options and
10948 the callbacks has been removed from this C<isl_ast_build>.
10949 The callback would typically return the result of a nested
10950 AST generation or a
10951 user defined node created using the following function.
10953 #include <isl/ast.h>
10954 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10955 __isl_take isl_ast_expr *expr);
10957 #include <isl/ast_build.h>
10958 __isl_give isl_ast_build *
10959 isl_ast_build_set_at_each_domain(
10960 __isl_take isl_ast_build *build,
10961 __isl_give isl_ast_node *(*fn)(
10962 __isl_take isl_ast_node *node,
10963 __isl_keep isl_ast_build *build,
10964 void *user), void *user);
10965 __isl_give isl_ast_build *
10966 isl_ast_build_set_before_each_for(
10967 __isl_take isl_ast_build *build,
10968 __isl_give isl_id *(*fn)(
10969 __isl_keep isl_ast_build *build,
10970 void *user), void *user);
10971 __isl_give isl_ast_build *
10972 isl_ast_build_set_after_each_for(
10973 __isl_take isl_ast_build *build,
10974 __isl_give isl_ast_node *(*fn)(
10975 __isl_take isl_ast_node *node,
10976 __isl_keep isl_ast_build *build,
10977 void *user), void *user);
10978 __isl_give isl_ast_build *
10979 isl_ast_build_set_before_each_mark(
10980 __isl_take isl_ast_build *build,
10981 isl_stat (*fn)(__isl_keep isl_id *mark,
10982 __isl_keep isl_ast_build *build,
10983 void *user), void *user);
10984 __isl_give isl_ast_build *
10985 isl_ast_build_set_after_each_mark(
10986 __isl_take isl_ast_build *build,
10987 __isl_give isl_ast_node *(*fn)(
10988 __isl_take isl_ast_node *node,
10989 __isl_keep isl_ast_build *build,
10990 void *user), void *user);
10992 The callback set by C<isl_ast_build_set_at_each_domain> will
10993 be called for each domain AST node.
10994 The callbacks set by C<isl_ast_build_set_before_each_for>
10995 and C<isl_ast_build_set_after_each_for> will be called
10996 for each for AST node. The first will be called in depth-first
10997 pre-order, while the second will be called in depth-first post-order.
10998 Since C<isl_ast_build_set_before_each_for> is called before the for
10999 node is actually constructed, it is only passed an C<isl_ast_build>.
11000 The returned C<isl_id> will be added as an annotation (using
11001 C<isl_ast_node_set_annotation>) to the constructed for node.
11002 In particular, if the user has also specified an C<after_each_for>
11003 callback, then the annotation can be retrieved from the node passed to
11004 that callback using C<isl_ast_node_get_annotation>.
11005 The callbacks set by C<isl_ast_build_set_before_each_mark>
11006 and C<isl_ast_build_set_after_each_mark> will be called for each
11007 mark AST node that is created, i.e., for each mark schedule node
11008 in the input schedule tree. The first will be called in depth-first
11009 pre-order, while the second will be called in depth-first post-order.
11010 Since the callback set by C<isl_ast_build_set_before_each_mark>
11011 is called before the mark AST node is actually constructed, it is passed
11012 the identifier of the mark node.
11013 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
11014 The given C<isl_ast_build> can be used to create new
11015 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
11016 or C<isl_ast_build_call_from_pw_multi_aff>.
11018 =head3 Nested AST Generation
11020 C<isl> allows the user to create an AST within the context
11021 of another AST. These nested ASTs are created using the
11022 same C<isl_ast_build_node_from_schedule_map> function that is used to create
11023 the outer AST. The C<build> argument should be an C<isl_ast_build>
11024 passed to a callback set by
11025 C<isl_ast_build_set_create_leaf>.
11026 The space of the range of the C<schedule> argument should refer
11027 to this build. In particular, the space should be a wrapped
11028 relation and the domain of this wrapped relation should be the
11029 same as that of the range of the schedule returned by
11030 C<isl_ast_build_get_schedule> below.
11031 In practice, the new schedule is typically
11032 created by calling C<isl_union_map_range_product> on the old schedule
11033 and some extra piece of the schedule.
11034 The space of the schedule domain is also available from
11035 the C<isl_ast_build>.
11037 #include <isl/ast_build.h>
11038 __isl_give isl_union_map *isl_ast_build_get_schedule(
11039 __isl_keep isl_ast_build *build);
11040 __isl_give isl_space *isl_ast_build_get_schedule_space(
11041 __isl_keep isl_ast_build *build);
11042 __isl_give isl_ast_build *isl_ast_build_restrict(
11043 __isl_take isl_ast_build *build,
11044 __isl_take isl_set *set);
11046 The C<isl_ast_build_get_schedule> function returns a (partial)
11047 schedule for the domains elements for which part of the AST still needs to
11048 be generated in the current build.
11049 In particular, the domain elements are mapped to those iterations of the loops
11050 enclosing the current point of the AST generation inside which
11051 the domain elements are executed.
11052 No direct correspondence between
11053 the input schedule and this schedule should be assumed.
11054 The space obtained from C<isl_ast_build_get_schedule_space> can be used
11055 to create a set for C<isl_ast_build_restrict> to intersect
11056 with the current build. In particular, the set passed to
11057 C<isl_ast_build_restrict> can have additional parameters.
11058 The ids of the set dimensions in the space returned by
11059 C<isl_ast_build_get_schedule_space> correspond to the
11060 iterators of the already generated loops.
11061 The user should not rely on the ids of the output dimensions
11062 of the relations in the union relation returned by
11063 C<isl_ast_build_get_schedule> having any particular value.
11065 =head1 Applications
11067 Although C<isl> is mainly meant to be used as a library,
11068 it also contains some basic applications that use some
11069 of the functionality of C<isl>.
11070 For applications that take one or more polytopes or polyhedra
11071 as input, this input may be specified in either the L<isl format>
11072 or the L<PolyLib format>.
11074 =head2 C<isl_polyhedron_sample>
11076 C<isl_polyhedron_sample> takes a polyhedron as input and prints
11077 an integer element of the polyhedron, if there is any.
11078 The first column in the output is the denominator and is always
11079 equal to 1. If the polyhedron contains no integer points,
11080 then a vector of length zero is printed.
11084 C<isl_pip> takes the same input as the C<example> program
11085 from the C<piplib> distribution, i.e., a set of constraints
11086 on the parameters, a line containing only -1 and finally a set
11087 of constraints on a parametric polyhedron.
11088 The coefficients of the parameters appear in the last columns
11089 (but before the final constant column).
11090 The output is the lexicographic minimum of the parametric polyhedron.
11091 As C<isl> currently does not have its own output format, the output
11092 is just a dump of the internal state.
11094 =head2 C<isl_polyhedron_minimize>
11096 C<isl_polyhedron_minimize> computes the minimum of some linear
11097 or affine objective function over the integer points in a polyhedron.
11098 If an affine objective function
11099 is given, then the constant should appear in the last column.
11101 =head2 C<isl_polytope_scan>
11103 Given a polytope, C<isl_polytope_scan> prints
11104 all integer points in the polytope.
11108 Given an C<isl_union_access_info> object as input,
11109 C<isl_flow> prints out the corresponding dependences,
11110 as computed by C<isl_union_access_info_compute_flow>.
11112 =head2 C<isl_codegen>
11114 Given either a schedule tree or a sequence consisting of
11115 a schedule map, a context set and an options relation,
11116 C<isl_codegen> prints out an AST that scans the domain elements
11117 of the schedule in the order of their image(s) taking into account
11118 the constraints in the context set.
11120 =head2 C<isl_schedule>
11122 Given an C<isl_schedule_constraints> object as input,
11123 C<isl_schedule> prints out a schedule that satisfies the given