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.
284 =head3 Changes since isl-0.20
288 =item * Several functions that used to return C<unsigned>
289 now return C<isl_size>. This means that these functions may
290 now return a negative value in case an error occurred.
291 The same holds for functions that used to return C<int>,
292 although some of those were already returning
293 a negative value in case of error.
295 =item * The C<isl_ast_op_type> enumeration type has been
296 renamed to C<isl_ast_expr_op_type>. The corresponding
297 enumeration constants have been similarly renamed.
298 The old names are defined to the new names for backward
301 =item * Several functions returning an extra boolean value
302 through an C<int *> argument now do so through an C<isl_bool *>
303 argument. The returned values are the same, only the type
304 of the pointer has been changed.
310 C<isl> is released under the MIT license.
314 Permission is hereby granted, free of charge, to any person obtaining a copy of
315 this software and associated documentation files (the "Software"), to deal in
316 the Software without restriction, including without limitation the rights to
317 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
318 of the Software, and to permit persons to whom the Software is furnished to do
319 so, subject to the following conditions:
321 The above copyright notice and this permission notice shall be included in all
322 copies or substantial portions of the Software.
324 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
325 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
326 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
327 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
328 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
329 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
334 Note that by default C<isl> requires C<GMP>, which is released
335 under the GNU Lesser General Public License (LGPL). This means
336 that code linked against C<isl> is also linked against LGPL code.
338 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
339 will link against C<imath>, a library for exact integer arithmetic released
340 under the MIT license.
344 The source of C<isl> can be obtained either as a tarball
345 or from the git repository. Both are available from
346 L<http://isl.gforge.inria.fr/>.
347 The installation process depends on how you obtained
350 =head2 Installation from the git repository
354 =item 1 Clone or update the repository
356 The first time the source is obtained, you need to clone
359 git clone git://repo.or.cz/isl.git
361 To obtain updates, you need to pull in the latest changes
365 =item 2 Optionally get C<imath> submodule
367 To build C<isl> with C<imath>, you need to obtain the C<imath>
368 submodule by running in the git source tree of C<isl>
373 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
375 =item 2 Generate C<configure>
381 After performing the above steps, continue
382 with the L<Common installation instructions>.
384 =head2 Common installation instructions
388 =item 1 Obtain C<GMP>
390 By default, building C<isl> requires C<GMP>, including its headers files.
391 Your distribution may not provide these header files by default
392 and you may need to install a package called C<gmp-devel> or something
393 similar. Alternatively, C<GMP> can be built from
394 source, available from L<http://gmplib.org/>.
395 C<GMP> is not needed if you build C<isl> with C<imath>.
399 C<isl> uses the standard C<autoconf> C<configure> script.
404 optionally followed by some configure options.
405 A complete list of options can be obtained by running
409 Below we discuss some of the more common options.
415 Installation prefix for C<isl>
417 =item C<--with-int=[gmp|imath|imath-32]>
419 Select the integer library to be used by C<isl>, the default is C<gmp>.
420 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
421 for values out of the 32 bit range. In most applications, C<isl> will run
422 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
425 =item C<--with-gmp-prefix>
427 Installation prefix for C<GMP> (architecture-independent files).
429 =item C<--with-gmp-exec-prefix>
431 Installation prefix for C<GMP> (architecture-dependent files).
439 =item 4 Install (optional)
445 =head1 Integer Set Library
447 =head2 Memory Management
449 Since a high-level operation on isl objects usually involves
450 several substeps and since the user is usually not interested in
451 the intermediate results, most functions that return a new object
452 will also release all the objects passed as arguments.
453 If the user still wants to use one or more of these arguments
454 after the function call, she should pass along a copy of the
455 object rather than the object itself.
456 The user is then responsible for making sure that the original
457 object gets used somewhere else or is explicitly freed.
459 The arguments and return values of all documented functions are
460 annotated to make clear which arguments are released and which
461 arguments are preserved. In particular, the following annotations
468 C<__isl_give> means that a new object is returned.
469 The user should make sure that the returned pointer is
470 used exactly once as a value for an C<__isl_take> argument.
471 In between, it can be used as a value for as many
472 C<__isl_keep> arguments as the user likes.
473 There is one exception, and that is the case where the
474 pointer returned is C<NULL>. In this case, the user
475 is free to use it as an C<__isl_take> argument or not.
476 When applied to a C<char *>, the returned pointer needs to be
481 C<__isl_null> means that a C<NULL> value is returned.
485 C<__isl_take> means that the object the argument points to
486 is taken over by the function and may no longer be used
487 by the user as an argument to any other function.
488 The pointer value must be one returned by a function
489 returning an C<__isl_give> pointer.
490 If the user passes in a C<NULL> value, then this will
491 be treated as an error in the sense that the function will
492 not perform its usual operation. However, it will still
493 make sure that all the other C<__isl_take> arguments
498 C<__isl_keep> means that the function will only use the object
499 temporarily. After the function has finished, the user
500 can still use it as an argument to other functions.
501 A C<NULL> value will be treated in the same way as
502 a C<NULL> value for an C<__isl_take> argument.
503 This annotation may also be used on return values of
504 type C<const char *>, in which case the returned pointer should
505 not be freed by the user and is only valid until the object
506 from which it was derived is updated or freed.
510 =head2 Initialization
512 All manipulations of integer sets and relations occur within
513 the context of an C<isl_ctx>.
514 A given C<isl_ctx> can only be used within a single thread.
515 All arguments of a function are required to have been allocated
516 within the same context.
517 There are currently no functions available for moving an object
518 from one C<isl_ctx> to another C<isl_ctx>. This means that
519 there is currently no way of safely moving an object from one
520 thread to another, unless the whole C<isl_ctx> is moved.
522 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
523 freed using C<isl_ctx_free>.
524 All objects allocated within an C<isl_ctx> should be freed
525 before the C<isl_ctx> itself is freed.
527 isl_ctx *isl_ctx_alloc();
528 void isl_ctx_free(isl_ctx *ctx);
530 The user can impose a bound on the number of low-level I<operations>
531 that can be performed by an C<isl_ctx>. This bound can be set and
532 retrieved using the following functions. A bound of zero means that
533 no bound is imposed. The number of operations performed can be
534 reset using C<isl_ctx_reset_operations>. Note that the number
535 of low-level operations needed to perform a high-level computation
536 may differ significantly across different versions
537 of C<isl>, but it should be the same across different platforms
538 for the same version of C<isl>.
540 Warning: This feature is experimental. C<isl> has good support to abort and
541 bail out during the computation, but this feature may exercise error code paths
542 that are normally not used that much. Consequently, it is not unlikely that
543 hidden bugs will be exposed.
545 void isl_ctx_set_max_operations(isl_ctx *ctx,
546 unsigned long max_operations);
547 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
548 void isl_ctx_reset_operations(isl_ctx *ctx);
550 In order to be able to create an object in the same context
551 as another object, most object types (described later in
552 this document) provide a function to obtain the context
553 in which the object was created.
556 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
557 isl_ctx *isl_multi_val_get_ctx(
558 __isl_keep isl_multi_val *mv);
561 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
562 isl_ctx *isl_multi_id_get_ctx(
563 __isl_keep isl_multi_id *mi);
565 #include <isl/local_space.h>
566 isl_ctx *isl_local_space_get_ctx(
567 __isl_keep isl_local_space *ls);
570 isl_ctx *isl_set_list_get_ctx(
571 __isl_keep isl_set_list *list);
574 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
575 isl_ctx *isl_multi_aff_get_ctx(
576 __isl_keep isl_multi_aff *maff);
577 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
578 isl_ctx *isl_pw_multi_aff_get_ctx(
579 __isl_keep isl_pw_multi_aff *pma);
580 isl_ctx *isl_multi_pw_aff_get_ctx(
581 __isl_keep isl_multi_pw_aff *mpa);
582 isl_ctx *isl_union_pw_aff_get_ctx(
583 __isl_keep isl_union_pw_aff *upa);
584 isl_ctx *isl_union_pw_multi_aff_get_ctx(
585 __isl_keep isl_union_pw_multi_aff *upma);
586 isl_ctx *isl_multi_union_pw_aff_get_ctx(
587 __isl_keep isl_multi_union_pw_aff *mupa);
589 #include <isl/id_to_ast_expr.h>
590 isl_ctx *isl_id_to_ast_expr_get_ctx(
591 __isl_keep isl_id_to_ast_expr *id2expr);
593 #include <isl/point.h>
594 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
597 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
600 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
602 #include <isl/vertices.h>
603 isl_ctx *isl_vertices_get_ctx(
604 __isl_keep isl_vertices *vertices);
605 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
606 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
608 #include <isl/flow.h>
609 isl_ctx *isl_restriction_get_ctx(
610 __isl_keep isl_restriction *restr);
611 isl_ctx *isl_union_access_info_get_ctx(
612 __isl_keep isl_union_access_info *access);
613 isl_ctx *isl_union_flow_get_ctx(
614 __isl_keep isl_union_flow *flow);
616 #include <isl/schedule.h>
617 isl_ctx *isl_schedule_get_ctx(
618 __isl_keep isl_schedule *sched);
619 isl_ctx *isl_schedule_constraints_get_ctx(
620 __isl_keep isl_schedule_constraints *sc);
622 #include <isl/schedule_node.h>
623 isl_ctx *isl_schedule_node_get_ctx(
624 __isl_keep isl_schedule_node *node);
626 #include <isl/ast_build.h>
627 isl_ctx *isl_ast_build_get_ctx(
628 __isl_keep isl_ast_build *build);
631 isl_ctx *isl_ast_expr_get_ctx(
632 __isl_keep isl_ast_expr *expr);
633 isl_ctx *isl_ast_node_get_ctx(
634 __isl_keep isl_ast_node *node);
636 #include <isl/stride_info.h>
637 isl_ctx *isl_stride_info_get_ctx(
638 __isl_keep isl_stride_info *si);
640 #include <isl/fixed_box.h>
641 isl_ctx *isl_fixed_box_get_ctx(
642 __isl_keep isl_fixed_box *box);
646 C<isl> uses the special return type C<isl_size> for functions
647 that return a non-negative value, typically a number or a position.
648 Besides the regular non-negative return values, a special (negative)
649 value C<isl_size_error> may be returned, indicating that something
652 C<isl> also uses two special return types for functions that either return
653 a boolean or that in principle do not return anything.
654 In particular, the C<isl_bool> type has three possible values:
655 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
656 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
657 C<isl_bool_error> (a negative integer value), indicating that something
658 went wrong. The following operations are defined on C<isl_bool>. The function
659 C<isl_bool_not> can be used to negate an C<isl_bool>, where the negation of
660 C<isl_bool_error> is C<isl_bool_error> again. The function C<isl_bool_ok>
661 converts an integer to an C<isl_bool>. Any non-zero values yields
662 C<isl_bool_true> and zero yields C<isl_bool_false>.
665 isl_bool isl_bool_not(isl_bool b);
666 isl_bool isl_bool_ok(int b);
668 The C<isl_stat> type has two possible values:
669 C<isl_stat_ok> (the integer value zero), indicating a successful
671 C<isl_stat_error> (a negative integer value), indicating that something
673 The function C<isl_stat_non_null> converts an isl object pointer
674 to an C<isl_stat>, returning C<isl_stat_ok> if the object pointer is valid and
675 C<isl_stat_error> if it is C<NULL>.
678 isl_stat isl_stat_non_null(void *obj);
680 See L</"Error Handling"> for more information on
681 C<isl_size_error>, C<isl_bool_error> and C<isl_stat_error>.
685 An C<isl_val> represents an integer value, a rational value
686 or one of three special values, infinity, negative infinity and NaN.
687 Some predefined values can be created using the following functions.
690 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
691 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
692 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
693 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
694 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
695 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
697 Specific integer values can be created using the following functions.
700 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
702 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
704 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
705 size_t n, size_t size, const void *chunks);
707 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
708 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
709 The least significant digit is assumed to be stored first.
711 Value objects can be copied and freed using the following functions.
714 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
715 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
717 They can be inspected using the following functions.
720 long isl_val_get_num_si(__isl_keep isl_val *v);
721 long isl_val_get_den_si(__isl_keep isl_val *v);
722 __isl_give isl_val *isl_val_get_den_val(
723 __isl_keep isl_val *v);
724 double isl_val_get_d(__isl_keep isl_val *v);
725 isl_size isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
727 isl_stat isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
728 size_t size, void *chunks);
730 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
731 of C<size> bytes needed to store the absolute value of the
733 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
734 which is assumed to have been preallocated by the caller.
735 The least significant digit is stored first.
736 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
737 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
738 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
740 An C<isl_val> can be modified using the following function.
743 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
746 The following unary properties are defined on C<isl_val>s.
749 int isl_val_sgn(__isl_keep isl_val *v);
750 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
751 isl_bool isl_val_is_one(__isl_keep isl_val *v);
752 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
753 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
754 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
755 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
756 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
757 isl_bool isl_val_is_int(__isl_keep isl_val *v);
758 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
759 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
760 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
761 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
763 Note that the sign of NaN is undefined.
765 The following binary properties are defined on pairs of C<isl_val>s.
768 isl_bool isl_val_lt(__isl_keep isl_val *v1,
769 __isl_keep isl_val *v2);
770 isl_bool isl_val_le(__isl_keep isl_val *v1,
771 __isl_keep isl_val *v2);
772 isl_bool isl_val_gt(__isl_keep isl_val *v1,
773 __isl_keep isl_val *v2);
774 isl_bool isl_val_ge(__isl_keep isl_val *v1,
775 __isl_keep isl_val *v2);
776 isl_bool isl_val_eq(__isl_keep isl_val *v1,
777 __isl_keep isl_val *v2);
778 isl_bool isl_val_ne(__isl_keep isl_val *v1,
779 __isl_keep isl_val *v2);
780 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
781 __isl_keep isl_val *v2);
783 Comparisons to NaN always return false.
784 That is, a NaN is not considered to hold any relative position
785 with respect to any value. In particular, a NaN
786 is neither considered to be equal to nor to be different from
787 any value (including another NaN).
788 The function C<isl_val_abs_eq> checks whether its two arguments
789 are equal in absolute value.
791 For integer C<isl_val>s we additionally have the following binary property.
794 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
795 __isl_keep isl_val *v2);
797 An C<isl_val> can also be compared to an integer using the following
798 functions. The result of C<isl_val_cmp_si> is undefined for NaN.
801 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
802 isl_bool isl_val_eq_si(__isl_keep isl_val *v, long i);
803 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
805 The following unary operations are available on C<isl_val>s.
808 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
809 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
810 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
811 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
812 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
813 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
815 The following binary operations are available on C<isl_val>s.
818 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
819 __isl_take isl_val *v2);
820 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
821 __isl_take isl_val *v2);
822 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
823 __isl_take isl_val *v2);
824 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
826 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
827 __isl_take isl_val *v2);
828 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
830 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
831 __isl_take isl_val *v2);
832 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
834 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
835 __isl_take isl_val *v2);
836 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
839 On integer values, we additionally have the following operations.
842 __isl_give isl_val *isl_val_pow2(__isl_take isl_val *v);
843 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
844 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
845 __isl_take isl_val *v2);
846 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
847 __isl_take isl_val *v2);
848 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
849 __isl_take isl_val *v2, __isl_give isl_val **x,
850 __isl_give isl_val **y);
852 C<isl_val_2exp> is an alternative name for C<isl_val_pow2>.
853 The function C<isl_val_gcdext> returns the greatest common divisor g
854 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
855 that C<*x> * C<v1> + C<*y> * C<v2> = g.
857 =head3 GMP specific functions
859 These functions are only available if C<isl> has been compiled with C<GMP>
862 Specific integer and rational values can be created from C<GMP> values using
863 the following functions.
865 #include <isl/val_gmp.h>
866 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
868 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
869 const mpz_t n, const mpz_t d);
871 The numerator and denominator of a rational value can be extracted as
872 C<GMP> values using the following functions.
874 #include <isl/val_gmp.h>
875 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
876 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
878 =head2 Sets and Relations
880 C<isl> uses six types of objects for representing sets and relations,
881 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
882 C<isl_union_set> and C<isl_union_map>.
883 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
884 can be described as a conjunction of affine constraints, while
885 C<isl_set> and C<isl_map> represent unions of
886 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
887 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
888 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
889 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
890 where spaces are considered different if they have a different number
891 of dimensions and/or different names (see L<"Spaces">).
892 The difference between sets and relations (maps) is that sets have
893 one set of variables, while relations have two sets of variables,
894 input variables and output variables.
896 =head2 Error Handling
898 C<isl> supports different ways to react in case a runtime error is triggered.
899 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
900 with two maps that have incompatible spaces. There are three possible ways
901 to react on error: to warn, to continue or to abort.
903 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
904 the last error in the corresponding C<isl_ctx> and the function in which the
905 error was triggered returns a value indicating that some error has
906 occurred. In case of functions returning a pointer, this value is
907 C<NULL>. In case of functions returning an C<isl_size>, C<isl_bool> or an
908 C<isl_stat>, this value is C<isl_size_error>,
909 C<isl_bool_error> or C<isl_stat_error>.
910 An error does not corrupt internal state,
911 such that isl can continue to be used. C<isl> also provides functions to
912 read the last error, including the specific error message,
913 the isl source file where the error occurred and the line number,
914 and to reset all information about the last error. The
915 last error is only stored for information purposes. Its presence does not
916 change the behavior of C<isl>. Hence, resetting an error is not required to
917 continue to use isl, but only to observe new errors.
920 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
921 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
922 const char *isl_ctx_last_error_file(isl_ctx *ctx);
923 int isl_ctx_last_error_line(isl_ctx *ctx);
924 void isl_ctx_reset_error(isl_ctx *ctx);
926 If no error has occurred since the last call to C<isl_ctx_reset_error>,
927 then the functions C<isl_ctx_last_error_msg> and
928 C<isl_ctx_last_error_file> return C<NULL>.
930 Another option is to continue on error. This is similar to warn on error mode,
931 except that C<isl> does not print any warning. This allows a program to
932 implement its own error reporting.
934 The last option is to directly abort the execution of the program from within
935 the isl library. This makes it obviously impossible to recover from an error,
936 but it allows to directly spot the error location. By aborting on error,
937 debuggers break at the location the error occurred and can provide a stack
938 trace. Other tools that automatically provide stack traces on abort or that do
939 not want to continue execution after an error was triggered may also prefer to
942 The on error behavior of isl can be specified by calling
943 C<isl_options_set_on_error> or by setting the command line option
944 C<--isl-on-error>. Valid arguments for the function call are
945 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
946 choices for the command line option are C<warn>, C<continue> and C<abort>.
947 It is also possible to query the current error mode.
949 #include <isl/options.h>
950 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
951 int isl_options_get_on_error(isl_ctx *ctx);
955 Identifiers are used to identify both individual dimensions
956 and tuples of dimensions. They consist of an optional name and an optional
957 user pointer. The name and the user pointer cannot both be C<NULL>, however.
958 Identifiers with the same name but different pointer values
959 are considered to be distinct.
960 Similarly, identifiers with different names but the same pointer value
961 are also considered to be distinct.
962 Equal identifiers are represented using the same object.
963 Pairs of identifiers can therefore be tested for equality using the
965 Identifiers can be constructed, copied, freed, inspected and printed
966 using the following functions.
969 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
970 __isl_keep const char *name, void *user);
971 __isl_give isl_id *isl_id_set_free_user(
972 __isl_take isl_id *id,
973 void (*free_user)(void *user));
974 __isl_give isl_id *isl_id_copy(isl_id *id);
975 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
977 void *isl_id_get_user(__isl_keep isl_id *id);
978 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
980 __isl_give isl_printer *isl_printer_print_id(
981 __isl_take isl_printer *p, __isl_keep isl_id *id);
983 The callback set by C<isl_id_set_free_user> is called on the user
984 pointer when the last reference to the C<isl_id> is freed.
985 Note that C<isl_id_get_name> returns a pointer to some internal
986 data structure, so the result can only be used while the
987 corresponding C<isl_id> is alive.
991 Whenever a new set, relation or similar object is created from scratch,
992 the space in which it lives needs to be specified using an C<isl_space>.
993 Each space involves zero or more parameters and zero, one or two
994 tuples of set or input/output dimensions. The parameters and dimensions
995 are identified by an C<isl_dim_type> and a position.
996 The type C<isl_dim_param> refers to parameters,
997 the type C<isl_dim_set> refers to set dimensions (for spaces
998 with a single tuple of dimensions) and the types C<isl_dim_in>
999 and C<isl_dim_out> refer to input and output dimensions
1000 (for spaces with two tuples of dimensions).
1001 Local spaces (see L</"Local Spaces">) also contain dimensions
1002 of type C<isl_dim_div>.
1003 Note that parameters are only identified by their position within
1004 a given object. Across different objects, parameters are (usually)
1005 identified by their names or identifiers. Only unnamed parameters
1006 are identified by their positions across objects. The use of unnamed
1007 parameters is discouraged.
1009 #include <isl/space.h>
1010 __isl_give isl_space *isl_space_unit(isl_ctx *ctx);
1011 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
1012 unsigned nparam, unsigned n_in, unsigned n_out);
1013 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
1015 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
1016 unsigned nparam, unsigned dim);
1017 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
1018 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
1020 The space used for creating a parameter domain
1021 needs to be created using C<isl_space_unit> or C<isl_space_params_alloc>.
1022 For other sets, the space
1023 needs to be created using C<isl_space_set_alloc>, while
1024 for a relation, the space
1025 needs to be created using C<isl_space_alloc>.
1026 The use of C<isl_space_params_alloc>,
1027 C<isl_space_set_alloc> and C<isl_space_alloc> is discouraged as they allow
1028 for the introduction of unnamed parameters.
1030 To check whether a given space is that of a set or a map
1031 or whether it is a parameter space, use these functions:
1033 #include <isl/space.h>
1034 isl_bool isl_space_is_params(__isl_keep isl_space *space);
1035 isl_bool isl_space_is_set(__isl_keep isl_space *space);
1036 isl_bool isl_space_is_map(__isl_keep isl_space *space);
1038 Spaces can be compared using the following functions:
1040 #include <isl/space.h>
1041 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
1042 __isl_keep isl_space *space2);
1043 isl_bool isl_space_has_equal_params(
1044 __isl_keep isl_space *space1,
1045 __isl_keep isl_space *space2);
1046 isl_bool isl_space_has_equal_tuples(
1047 __isl_keep isl_space *space1,
1048 __isl_keep isl_space *space2);
1049 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
1050 __isl_keep isl_space *space2);
1051 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
1052 __isl_keep isl_space *space2);
1053 isl_bool isl_space_tuple_is_equal(
1054 __isl_keep isl_space *space1,
1055 enum isl_dim_type type1,
1056 __isl_keep isl_space *space2,
1057 enum isl_dim_type type2);
1059 C<isl_space_is_domain> checks whether the first argument is equal
1060 to the domain of the second argument. This requires in particular that
1061 the first argument is a set space and that the second argument
1062 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1063 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1064 spaces are the same. That is, it checks if they have the same
1065 identifier (if any), the same dimension and the same internal structure
1068 C<isl_space_has_equal_params> checks whether two spaces
1069 have the same parameters in the same order.
1070 C<isl_space_has_equal_tuples> check whether two spaces have
1071 the same tuples. In contrast to C<isl_space_is_equal> below,
1072 it does not check the
1073 parameters. This is useful because many C<isl> functions align the
1074 parameters before they perform their operations, such that equivalence
1076 C<isl_space_is_equal> checks whether two spaces are identical,
1077 meaning that they have the same parameters and the same tuples.
1078 That is, it checks whether both C<isl_space_has_equal_params> and
1079 C<isl_space_has_equal_tuples> hold.
1081 It is often useful to create objects that live in the
1082 same space as some other object. This can be accomplished
1083 by creating the new objects
1084 (see L</"Creating New Sets and Relations"> or
1085 L</"Functions">) based on the space
1086 of the original object.
1088 #include <isl/set.h>
1089 __isl_give isl_space *isl_basic_set_get_space(
1090 __isl_keep isl_basic_set *bset);
1091 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1093 #include <isl/union_set.h>
1094 __isl_give isl_space *isl_union_set_get_space(
1095 __isl_keep isl_union_set *uset);
1097 #include <isl/map.h>
1098 __isl_give isl_space *isl_basic_map_get_space(
1099 __isl_keep isl_basic_map *bmap);
1100 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1102 #include <isl/union_map.h>
1103 __isl_give isl_space *isl_union_map_get_space(
1104 __isl_keep isl_union_map *umap);
1106 #include <isl/constraint.h>
1107 __isl_give isl_space *isl_constraint_get_space(
1108 __isl_keep isl_constraint *constraint);
1110 #include <isl/polynomial.h>
1111 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1112 __isl_keep isl_qpolynomial *qp);
1113 __isl_give isl_space *isl_qpolynomial_get_space(
1114 __isl_keep isl_qpolynomial *qp);
1115 __isl_give isl_space *
1116 isl_qpolynomial_fold_get_domain_space(
1117 __isl_keep isl_qpolynomial_fold *fold);
1118 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1119 __isl_keep isl_qpolynomial_fold *fold);
1120 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1121 __isl_keep isl_pw_qpolynomial *pwqp);
1122 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1123 __isl_keep isl_pw_qpolynomial *pwqp);
1124 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1125 __isl_keep isl_pw_qpolynomial_fold *pwf);
1126 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1127 __isl_keep isl_pw_qpolynomial_fold *pwf);
1128 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1129 __isl_keep isl_union_pw_qpolynomial *upwqp);
1130 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1131 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1134 __isl_give isl_space *isl_multi_id_get_space(
1135 __isl_keep isl_multi_id *mi);
1137 #include <isl/val.h>
1138 __isl_give isl_space *isl_multi_val_get_space(
1139 __isl_keep isl_multi_val *mv);
1141 #include <isl/aff.h>
1142 __isl_give isl_space *isl_aff_get_domain_space(
1143 __isl_keep isl_aff *aff);
1144 __isl_give isl_space *isl_aff_get_space(
1145 __isl_keep isl_aff *aff);
1146 __isl_give isl_space *isl_pw_aff_get_domain_space(
1147 __isl_keep isl_pw_aff *pwaff);
1148 __isl_give isl_space *isl_pw_aff_get_space(
1149 __isl_keep isl_pw_aff *pwaff);
1150 __isl_give isl_space *isl_multi_aff_get_domain_space(
1151 __isl_keep isl_multi_aff *maff);
1152 __isl_give isl_space *isl_multi_aff_get_space(
1153 __isl_keep isl_multi_aff *maff);
1154 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1155 __isl_keep isl_pw_multi_aff *pma);
1156 __isl_give isl_space *isl_pw_multi_aff_get_space(
1157 __isl_keep isl_pw_multi_aff *pma);
1158 __isl_give isl_space *isl_union_pw_aff_get_space(
1159 __isl_keep isl_union_pw_aff *upa);
1160 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1161 __isl_keep isl_union_pw_multi_aff *upma);
1162 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1163 __isl_keep isl_multi_pw_aff *mpa);
1164 __isl_give isl_space *isl_multi_pw_aff_get_space(
1165 __isl_keep isl_multi_pw_aff *mpa);
1166 __isl_give isl_space *
1167 isl_multi_union_pw_aff_get_domain_space(
1168 __isl_keep isl_multi_union_pw_aff *mupa);
1169 __isl_give isl_space *
1170 isl_multi_union_pw_aff_get_space(
1171 __isl_keep isl_multi_union_pw_aff *mupa);
1173 #include <isl/point.h>
1174 __isl_give isl_space *isl_point_get_space(
1175 __isl_keep isl_point *pnt);
1177 #include <isl/fixed_box.h>
1178 __isl_give isl_space *isl_fixed_box_get_space(
1179 __isl_keep isl_fixed_box *box);
1181 The number of dimensions of a given type of space
1182 may be read off from a space or an object that lives
1183 in a space using the following functions.
1184 In case of C<isl_space_dim>, type may be
1185 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1186 C<isl_dim_out> (only for relations), C<isl_dim_set>
1187 (only for sets) or C<isl_dim_all>.
1189 #include <isl/space.h>
1190 isl_size isl_space_dim(__isl_keep isl_space *space,
1191 enum isl_dim_type type);
1193 #include <isl/local_space.h>
1194 isl_size isl_local_space_dim(__isl_keep isl_local_space *ls,
1195 enum isl_dim_type type);
1197 #include <isl/set.h>
1198 isl_size isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1199 enum isl_dim_type type);
1200 isl_size isl_set_tuple_dim(__isl_keep isl_set *set);
1201 isl_size isl_set_dim(__isl_keep isl_set *set,
1202 enum isl_dim_type type);
1204 #include <isl/union_set.h>
1205 isl_size isl_union_set_dim(__isl_keep isl_union_set *uset,
1206 enum isl_dim_type type);
1208 #include <isl/map.h>
1209 isl_size isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1210 enum isl_dim_type type);
1211 isl_size isl_map_domain_tuple_dim(
1212 __isl_keep isl_map *map);
1213 isl_size isl_map_range_tuple_dim(
1214 __isl_keep isl_map *map);
1215 isl_size isl_map_dim(__isl_keep isl_map *map,
1216 enum isl_dim_type type);
1218 #include <isl/union_map.h>
1219 isl_size isl_union_map_dim(__isl_keep isl_union_map *umap,
1220 enum isl_dim_type type);
1222 #include <isl/val.h>
1223 isl_size isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1224 enum isl_dim_type type);
1226 #include <isl/aff.h>
1227 isl_size isl_aff_dim(__isl_keep isl_aff *aff,
1228 enum isl_dim_type type);
1229 isl_size isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1230 enum isl_dim_type type);
1231 isl_size isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1232 enum isl_dim_type type);
1233 isl_size isl_pw_multi_aff_dim(
1234 __isl_keep isl_pw_multi_aff *pma,
1235 enum isl_dim_type type);
1236 isl_size isl_multi_pw_aff_dim(
1237 __isl_keep isl_multi_pw_aff *mpa,
1238 enum isl_dim_type type);
1239 isl_size isl_union_pw_aff_dim(
1240 __isl_keep isl_union_pw_aff *upa,
1241 enum isl_dim_type type);
1242 isl_size isl_union_pw_multi_aff_dim(
1243 __isl_keep isl_union_pw_multi_aff *upma,
1244 enum isl_dim_type type);
1245 isl_size isl_multi_union_pw_aff_dim(
1246 __isl_keep isl_multi_union_pw_aff *mupa,
1247 enum isl_dim_type type);
1249 #include <isl/polynomial.h>
1250 isl_size isl_union_pw_qpolynomial_dim(
1251 __isl_keep isl_union_pw_qpolynomial *upwqp,
1252 enum isl_dim_type type);
1253 isl_size isl_union_pw_qpolynomial_fold_dim(
1254 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1255 enum isl_dim_type type);
1257 Note that an C<isl_union_set>, an C<isl_union_map>,
1258 an C<isl_union_pw_multi_aff>,
1259 an C<isl_union_pw_qpolynomial> and
1260 an C<isl_union_pw_qpolynomial_fold>
1261 only have parameters.
1263 Additional parameters can be added to a space using the following function.
1265 #include <isl/space.h>
1266 __isl_give isl_space *isl_space_add_param_id(
1267 __isl_take isl_space *space,
1268 __isl_take isl_id *id);
1270 If a parameter with the given identifier already appears in the space,
1271 then it is not added again.
1273 Conversely, all parameters can be removed from a space
1274 using the following function.
1276 #include <isl/space.h>
1277 __isl_give isl_space *isl_space_drop_all_params(
1278 __isl_take isl_space *space);
1280 The identifiers or names of the individual dimensions of spaces
1281 may be set or read off using the following functions on spaces
1282 or objects that live in spaces.
1283 These functions are mostly useful to obtain the identifiers, positions
1284 or names of the parameters. Identifiers of individual dimensions are
1285 essentially only useful for printing. They are ignored by all other
1286 operations and may not be preserved across those operations.
1287 To keep track of a space along with names/identifiers of
1288 the set dimensions, use an C<isl_multi_id> as described in
1291 #include <isl/space.h>
1292 __isl_give isl_space *isl_space_set_dim_id(
1293 __isl_take isl_space *space,
1294 enum isl_dim_type type, unsigned pos,
1295 __isl_take isl_id *id);
1296 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1297 enum isl_dim_type type, unsigned pos);
1298 __isl_give isl_id *isl_space_get_dim_id(
1299 __isl_keep isl_space *space,
1300 enum isl_dim_type type, unsigned pos);
1301 __isl_give isl_space *isl_space_set_dim_name(
1302 __isl_take isl_space *space,
1303 enum isl_dim_type type, unsigned pos,
1304 __isl_keep const char *name);
1305 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1306 enum isl_dim_type type, unsigned pos);
1307 __isl_keep const char *isl_space_get_dim_name(
1308 __isl_keep isl_space *space,
1309 enum isl_dim_type type, unsigned pos);
1311 #include <isl/local_space.h>
1312 __isl_give isl_local_space *isl_local_space_set_dim_id(
1313 __isl_take isl_local_space *ls,
1314 enum isl_dim_type type, unsigned pos,
1315 __isl_take isl_id *id);
1316 isl_bool isl_local_space_has_dim_id(
1317 __isl_keep isl_local_space *ls,
1318 enum isl_dim_type type, unsigned pos);
1319 __isl_give isl_id *isl_local_space_get_dim_id(
1320 __isl_keep isl_local_space *ls,
1321 enum isl_dim_type type, unsigned pos);
1322 __isl_give isl_local_space *isl_local_space_set_dim_name(
1323 __isl_take isl_local_space *ls,
1324 enum isl_dim_type type, unsigned pos, const char *s);
1325 isl_bool isl_local_space_has_dim_name(
1326 __isl_keep isl_local_space *ls,
1327 enum isl_dim_type type, unsigned pos)
1328 const char *isl_local_space_get_dim_name(
1329 __isl_keep isl_local_space *ls,
1330 enum isl_dim_type type, unsigned pos);
1332 #include <isl/constraint.h>
1333 const char *isl_constraint_get_dim_name(
1334 __isl_keep isl_constraint *constraint,
1335 enum isl_dim_type type, unsigned pos);
1337 #include <isl/set.h>
1338 __isl_give isl_id *isl_basic_set_get_dim_id(
1339 __isl_keep isl_basic_set *bset,
1340 enum isl_dim_type type, unsigned pos);
1341 __isl_give isl_set *isl_set_set_dim_id(
1342 __isl_take isl_set *set, enum isl_dim_type type,
1343 unsigned pos, __isl_take isl_id *id);
1344 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1345 enum isl_dim_type type, unsigned pos);
1346 __isl_give isl_id *isl_set_get_dim_id(
1347 __isl_keep isl_set *set, enum isl_dim_type type,
1349 const char *isl_basic_set_get_dim_name(
1350 __isl_keep isl_basic_set *bset,
1351 enum isl_dim_type type, unsigned pos);
1352 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1353 enum isl_dim_type type, unsigned pos);
1354 const char *isl_set_get_dim_name(
1355 __isl_keep isl_set *set,
1356 enum isl_dim_type type, unsigned pos);
1358 #include <isl/map.h>
1359 __isl_give isl_map *isl_map_set_dim_id(
1360 __isl_take isl_map *map, enum isl_dim_type type,
1361 unsigned pos, __isl_take isl_id *id);
1362 isl_bool isl_basic_map_has_dim_id(
1363 __isl_keep isl_basic_map *bmap,
1364 enum isl_dim_type type, unsigned pos);
1365 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1366 enum isl_dim_type type, unsigned pos);
1367 __isl_give isl_id *isl_map_get_dim_id(
1368 __isl_keep isl_map *map, enum isl_dim_type type,
1370 __isl_give isl_id *isl_union_map_get_dim_id(
1371 __isl_keep isl_union_map *umap,
1372 enum isl_dim_type type, unsigned pos);
1373 const char *isl_basic_map_get_dim_name(
1374 __isl_keep isl_basic_map *bmap,
1375 enum isl_dim_type type, unsigned pos);
1376 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1377 enum isl_dim_type type, unsigned pos);
1378 const char *isl_map_get_dim_name(
1379 __isl_keep isl_map *map,
1380 enum isl_dim_type type, unsigned pos);
1382 #include <isl/val.h>
1383 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1384 __isl_take isl_multi_val *mv,
1385 enum isl_dim_type type, unsigned pos,
1386 __isl_take isl_id *id);
1387 __isl_give isl_id *isl_multi_val_get_dim_id(
1388 __isl_keep isl_multi_val *mv,
1389 enum isl_dim_type type, unsigned pos);
1390 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1391 __isl_take isl_multi_val *mv,
1392 enum isl_dim_type type, unsigned pos, const char *s);
1394 #include <isl/aff.h>
1395 __isl_give isl_aff *isl_aff_set_dim_id(
1396 __isl_take isl_aff *aff, enum isl_dim_type type,
1397 unsigned pos, __isl_take isl_id *id);
1398 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1399 __isl_take isl_multi_aff *maff,
1400 enum isl_dim_type type, unsigned pos,
1401 __isl_take isl_id *id);
1402 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1403 __isl_take isl_pw_aff *pma,
1404 enum isl_dim_type type, unsigned pos,
1405 __isl_take isl_id *id);
1406 __isl_give isl_multi_pw_aff *
1407 isl_multi_pw_aff_set_dim_id(
1408 __isl_take isl_multi_pw_aff *mpa,
1409 enum isl_dim_type type, unsigned pos,
1410 __isl_take isl_id *id);
1411 __isl_give isl_multi_union_pw_aff *
1412 isl_multi_union_pw_aff_set_dim_id(
1413 __isl_take isl_multi_union_pw_aff *mupa,
1414 enum isl_dim_type type, unsigned pos,
1415 __isl_take isl_id *id);
1416 __isl_give isl_id *isl_multi_aff_get_dim_id(
1417 __isl_keep isl_multi_aff *ma,
1418 enum isl_dim_type type, unsigned pos);
1419 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1420 enum isl_dim_type type, unsigned pos);
1421 __isl_give isl_id *isl_pw_aff_get_dim_id(
1422 __isl_keep isl_pw_aff *pa,
1423 enum isl_dim_type type, unsigned pos);
1424 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1425 __isl_keep isl_pw_multi_aff *pma,
1426 enum isl_dim_type type, unsigned pos);
1427 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1428 __isl_keep isl_multi_pw_aff *mpa,
1429 enum isl_dim_type type, unsigned pos);
1430 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1431 __isl_keep isl_multi_union_pw_aff *mupa,
1432 enum isl_dim_type type, unsigned pos);
1433 __isl_give isl_aff *isl_aff_set_dim_name(
1434 __isl_take isl_aff *aff, enum isl_dim_type type,
1435 unsigned pos, const char *s);
1436 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1437 __isl_take isl_multi_aff *maff,
1438 enum isl_dim_type type, unsigned pos, const char *s);
1439 __isl_give isl_multi_pw_aff *
1440 isl_multi_pw_aff_set_dim_name(
1441 __isl_take isl_multi_pw_aff *mpa,
1442 enum isl_dim_type type, unsigned pos, const char *s);
1443 __isl_give isl_union_pw_aff *
1444 isl_union_pw_aff_set_dim_name(
1445 __isl_take isl_union_pw_aff *upa,
1446 enum isl_dim_type type, unsigned pos,
1448 __isl_give isl_union_pw_multi_aff *
1449 isl_union_pw_multi_aff_set_dim_name(
1450 __isl_take isl_union_pw_multi_aff *upma,
1451 enum isl_dim_type type, unsigned pos,
1453 __isl_give isl_multi_union_pw_aff *
1454 isl_multi_union_pw_aff_set_dim_name(
1455 __isl_take isl_multi_union_pw_aff *mupa,
1456 enum isl_dim_type type, unsigned pos,
1458 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1459 enum isl_dim_type type, unsigned pos);
1460 const char *isl_pw_aff_get_dim_name(
1461 __isl_keep isl_pw_aff *pa,
1462 enum isl_dim_type type, unsigned pos);
1463 const char *isl_pw_multi_aff_get_dim_name(
1464 __isl_keep isl_pw_multi_aff *pma,
1465 enum isl_dim_type type, unsigned pos);
1467 #include <isl/polynomial.h>
1468 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1469 __isl_take isl_qpolynomial *qp,
1470 enum isl_dim_type type, unsigned pos,
1472 __isl_give isl_pw_qpolynomial *
1473 isl_pw_qpolynomial_set_dim_name(
1474 __isl_take isl_pw_qpolynomial *pwqp,
1475 enum isl_dim_type type, unsigned pos,
1477 __isl_give isl_pw_qpolynomial_fold *
1478 isl_pw_qpolynomial_fold_set_dim_name(
1479 __isl_take isl_pw_qpolynomial_fold *pwf,
1480 enum isl_dim_type type, unsigned pos,
1482 __isl_give isl_union_pw_qpolynomial *
1483 isl_union_pw_qpolynomial_set_dim_name(
1484 __isl_take isl_union_pw_qpolynomial *upwqp,
1485 enum isl_dim_type type, unsigned pos,
1487 __isl_give isl_union_pw_qpolynomial_fold *
1488 isl_union_pw_qpolynomial_fold_set_dim_name(
1489 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1490 enum isl_dim_type type, unsigned pos,
1493 Note that C<isl_space_get_name> returns a pointer to some internal
1494 data structure, so the result can only be used while the
1495 corresponding C<isl_space> is alive.
1496 Also note that every function that operates on two sets or relations
1497 requires that both arguments have the same parameters. This also
1498 means that if one of the arguments has named parameters, then the
1499 other needs to have named parameters too and the names need to match.
1500 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1501 arguments may have different parameters (as long as they are named),
1502 in which case the result will have as parameters the union of the parameters of
1505 Given the identifier or name of a dimension (typically a parameter),
1506 its position can be obtained from the following functions.
1508 #include <isl/space.h>
1509 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1510 enum isl_dim_type type, __isl_keep isl_id *id);
1511 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1512 enum isl_dim_type type, const char *name);
1514 #include <isl/local_space.h>
1515 int isl_local_space_find_dim_by_name(
1516 __isl_keep isl_local_space *ls,
1517 enum isl_dim_type type, const char *name);
1519 #include <isl/val.h>
1520 int isl_multi_val_find_dim_by_id(
1521 __isl_keep isl_multi_val *mv,
1522 enum isl_dim_type type, __isl_keep isl_id *id);
1523 int isl_multi_val_find_dim_by_name(
1524 __isl_keep isl_multi_val *mv,
1525 enum isl_dim_type type, const char *name);
1527 #include <isl/set.h>
1528 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1529 enum isl_dim_type type, __isl_keep isl_id *id);
1530 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1531 enum isl_dim_type type, const char *name);
1533 #include <isl/map.h>
1534 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1535 enum isl_dim_type type, __isl_keep isl_id *id);
1536 int isl_basic_map_find_dim_by_name(
1537 __isl_keep isl_basic_map *bmap,
1538 enum isl_dim_type type, const char *name);
1539 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1540 enum isl_dim_type type, const char *name);
1541 int isl_union_map_find_dim_by_name(
1542 __isl_keep isl_union_map *umap,
1543 enum isl_dim_type type, const char *name);
1545 #include <isl/aff.h>
1546 int isl_multi_aff_find_dim_by_id(
1547 __isl_keep isl_multi_aff *ma,
1548 enum isl_dim_type type, __isl_keep isl_id *id);
1549 int isl_multi_pw_aff_find_dim_by_id(
1550 __isl_keep isl_multi_pw_aff *mpa,
1551 enum isl_dim_type type, __isl_keep isl_id *id);
1552 int isl_multi_union_pw_aff_find_dim_by_id(
1553 __isl_keep isl_multi_union_pw_aff *mupa,
1554 enum isl_dim_type type, __isl_keep isl_id *id);
1555 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1556 enum isl_dim_type type, const char *name);
1557 int isl_multi_aff_find_dim_by_name(
1558 __isl_keep isl_multi_aff *ma,
1559 enum isl_dim_type type, const char *name);
1560 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1561 enum isl_dim_type type, const char *name);
1562 int isl_multi_pw_aff_find_dim_by_name(
1563 __isl_keep isl_multi_pw_aff *mpa,
1564 enum isl_dim_type type, const char *name);
1565 int isl_pw_multi_aff_find_dim_by_name(
1566 __isl_keep isl_pw_multi_aff *pma,
1567 enum isl_dim_type type, const char *name);
1568 int isl_union_pw_aff_find_dim_by_name(
1569 __isl_keep isl_union_pw_aff *upa,
1570 enum isl_dim_type type, const char *name);
1571 int isl_union_pw_multi_aff_find_dim_by_name(
1572 __isl_keep isl_union_pw_multi_aff *upma,
1573 enum isl_dim_type type, const char *name);
1574 int isl_multi_union_pw_aff_find_dim_by_name(
1575 __isl_keep isl_multi_union_pw_aff *mupa,
1576 enum isl_dim_type type, const char *name);
1578 #include <isl/polynomial.h>
1579 int isl_pw_qpolynomial_find_dim_by_name(
1580 __isl_keep isl_pw_qpolynomial *pwqp,
1581 enum isl_dim_type type, const char *name);
1582 int isl_pw_qpolynomial_fold_find_dim_by_name(
1583 __isl_keep isl_pw_qpolynomial_fold *pwf,
1584 enum isl_dim_type type, const char *name);
1585 int isl_union_pw_qpolynomial_find_dim_by_name(
1586 __isl_keep isl_union_pw_qpolynomial *upwqp,
1587 enum isl_dim_type type, const char *name);
1588 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1589 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1590 enum isl_dim_type type, const char *name);
1592 The identifiers or names of entire spaces may be set or read off
1593 using the following functions.
1595 #include <isl/space.h>
1596 __isl_give isl_space *isl_space_set_domain_tuple_id(
1597 __isl_take isl_space *space,
1598 __isl_take isl_id *id);
1599 __isl_give isl_space *isl_space_set_range_tuple_id(
1600 __isl_take isl_space *space,
1601 __isl_take isl_id *id);
1602 __isl_give isl_space *isl_space_set_tuple_id(
1603 __isl_take isl_space *space,
1604 enum isl_dim_type type, __isl_take isl_id *id);
1605 __isl_give isl_space *isl_space_reset_tuple_id(
1606 __isl_take isl_space *space, enum isl_dim_type type);
1607 isl_bool isl_space_has_domain_tuple_id(
1608 __isl_keep isl_space *space);
1609 isl_bool isl_space_has_range_tuple_id(
1610 __isl_keep isl_space *space);
1611 isl_bool isl_space_has_tuple_id(
1612 __isl_keep isl_space *space,
1613 enum isl_dim_type type);
1614 __isl_give isl_id *isl_space_get_domain_tuple_id(
1615 __isl_keep isl_space *space);
1616 __isl_give isl_id *isl_space_get_range_tuple_id(
1617 __isl_keep isl_space *space);
1618 __isl_give isl_id *isl_space_get_tuple_id(
1619 __isl_keep isl_space *space, enum isl_dim_type type);
1620 __isl_give isl_space *isl_space_set_tuple_name(
1621 __isl_take isl_space *space,
1622 enum isl_dim_type type, const char *s);
1623 isl_bool isl_space_has_tuple_name(
1624 __isl_keep isl_space *space,
1625 enum isl_dim_type type);
1626 __isl_keep const char *isl_space_get_tuple_name(
1627 __isl_keep isl_space *space,
1628 enum isl_dim_type type);
1630 #include <isl/local_space.h>
1631 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1632 __isl_take isl_local_space *ls,
1633 enum isl_dim_type type, __isl_take isl_id *id);
1635 #include <isl/set.h>
1636 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1637 __isl_take isl_basic_set *bset,
1638 __isl_take isl_id *id);
1639 __isl_give isl_set *isl_set_set_tuple_id(
1640 __isl_take isl_set *set, __isl_take isl_id *id);
1641 __isl_give isl_set *isl_set_reset_tuple_id(
1642 __isl_take isl_set *set);
1643 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1644 __isl_give isl_id *isl_set_get_tuple_id(
1645 __isl_keep isl_set *set);
1646 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1647 __isl_take isl_basic_set *set, const char *s);
1648 __isl_give isl_set *isl_set_set_tuple_name(
1649 __isl_take isl_set *set, const char *s);
1650 const char *isl_basic_set_get_tuple_name(
1651 __isl_keep isl_basic_set *bset);
1652 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1653 const char *isl_set_get_tuple_name(
1654 __isl_keep isl_set *set);
1656 #include <isl/map.h>
1657 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1658 __isl_take isl_basic_map *bmap,
1659 enum isl_dim_type type, __isl_take isl_id *id);
1660 __isl_give isl_map *isl_map_set_domain_tuple_id(
1661 __isl_take isl_map *map, __isl_take isl_id *id);
1662 __isl_give isl_map *isl_map_set_range_tuple_id(
1663 __isl_take isl_map *map, __isl_take isl_id *id);
1664 __isl_give isl_map *isl_map_set_tuple_id(
1665 __isl_take isl_map *map, enum isl_dim_type type,
1666 __isl_take isl_id *id);
1667 __isl_give isl_map *isl_map_reset_tuple_id(
1668 __isl_take isl_map *map, enum isl_dim_type type);
1669 isl_bool isl_map_has_domain_tuple_id(
1670 __isl_keep isl_map *map);
1671 isl_bool isl_map_has_range_tuple_id(
1672 __isl_keep isl_map *map);
1673 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1674 enum isl_dim_type type);
1675 __isl_give isl_id *isl_map_get_domain_tuple_id(
1676 __isl_keep isl_map *map);
1677 __isl_give isl_id *isl_map_get_range_tuple_id(
1678 __isl_keep isl_map *map);
1679 __isl_give isl_id *isl_map_get_tuple_id(
1680 __isl_keep isl_map *map, enum isl_dim_type type);
1681 __isl_give isl_map *isl_map_set_tuple_name(
1682 __isl_take isl_map *map,
1683 enum isl_dim_type type, const char *s);
1684 const char *isl_basic_map_get_tuple_name(
1685 __isl_keep isl_basic_map *bmap,
1686 enum isl_dim_type type);
1687 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1688 __isl_take isl_basic_map *bmap,
1689 enum isl_dim_type type, const char *s);
1690 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1691 enum isl_dim_type type);
1692 const char *isl_map_get_tuple_name(
1693 __isl_keep isl_map *map,
1694 enum isl_dim_type type);
1696 #include <isl/val.h>
1697 __isl_give isl_multi_val *isl_multi_val_set_range_tuple_id(
1698 __isl_take isl_multi_val *mv,
1699 __isl_take isl_id *id);
1700 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1701 __isl_take isl_multi_val *mv,
1702 enum isl_dim_type type, __isl_take isl_id *id);
1703 __isl_give isl_multi_val *
1704 isl_multi_val_reset_range_tuple_id(
1705 __isl_take isl_multi_val *mv);
1706 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1707 __isl_take isl_multi_val *mv,
1708 enum isl_dim_type type);
1709 isl_bool isl_multi_val_has_range_tuple_id(
1710 __isl_keep isl_multi_val *mv);
1711 __isl_give isl_id *isl_multi_val_get_range_tuple_id(
1712 __isl_keep isl_multi_val *mv);
1713 isl_bool isl_multi_val_has_tuple_id(
1714 __isl_keep isl_multi_val *mv,
1715 enum isl_dim_type type);
1716 __isl_give isl_id *isl_multi_val_get_tuple_id(
1717 __isl_keep isl_multi_val *mv,
1718 enum isl_dim_type type);
1719 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1720 __isl_take isl_multi_val *mv,
1721 enum isl_dim_type type, const char *s);
1722 const char *isl_multi_val_get_tuple_name(
1723 __isl_keep isl_multi_val *mv,
1724 enum isl_dim_type type);
1726 #include <isl/aff.h>
1727 __isl_give isl_aff *isl_aff_set_tuple_id(
1728 __isl_take isl_aff *aff,
1729 enum isl_dim_type type, __isl_take isl_id *id);
1730 __isl_give isl_multi_aff *isl_multi_aff_set_range_tuple_id(
1731 __isl_take isl_multi_aff *ma,
1732 __isl_take isl_id *id);
1733 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1734 __isl_take isl_multi_aff *maff,
1735 enum isl_dim_type type, __isl_take isl_id *id);
1736 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1737 __isl_take isl_pw_aff *pwaff,
1738 enum isl_dim_type type, __isl_take isl_id *id);
1739 __isl_give isl_pw_multi_aff *
1740 isl_pw_multi_aff_set_range_tuple_id(
1741 __isl_take isl_pw_multi_aff *pma,
1742 __isl_take isl_id *id);
1743 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1744 __isl_take isl_pw_multi_aff *pma,
1745 enum isl_dim_type type, __isl_take isl_id *id);
1746 __isl_give isl_multi_pw_aff *
1747 isl_multi_pw_aff_set_range_tuple_id(
1748 __isl_take isl_multi_pw_aff *mpa,
1749 __isl_take isl_id *id);
1750 __isl_give isl_multi_union_pw_aff *
1751 isl_multi_union_pw_aff_set_range_tuple_id(
1752 __isl_take isl_multi_union_pw_aff *mupa,
1753 __isl_take isl_id *id);
1754 __isl_give isl_multi_union_pw_aff *
1755 isl_multi_union_pw_aff_set_tuple_id(
1756 __isl_take isl_multi_union_pw_aff *mupa,
1757 enum isl_dim_type type, __isl_take isl_id *id);
1758 __isl_give isl_multi_aff *
1759 isl_multi_aff_reset_range_tuple_id(
1760 __isl_take isl_multi_aff *ma);
1761 __isl_give isl_multi_pw_aff *
1762 isl_multi_pw_aff_reset_range_tuple_id(
1763 __isl_take isl_multi_pw_aff *mpa);
1764 __isl_give isl_multi_union_pw_aff *
1765 isl_multi_union_pw_aff_reset_range_tuple_id(
1766 __isl_take isl_multi_union_pw_aff *mupa);
1767 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1768 __isl_take isl_multi_aff *ma,
1769 enum isl_dim_type type);
1770 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1771 __isl_take isl_pw_aff *pa,
1772 enum isl_dim_type type);
1773 __isl_give isl_multi_pw_aff *
1774 isl_multi_pw_aff_reset_tuple_id(
1775 __isl_take isl_multi_pw_aff *mpa,
1776 enum isl_dim_type type);
1777 __isl_give isl_pw_multi_aff *
1778 isl_pw_multi_aff_reset_tuple_id(
1779 __isl_take isl_pw_multi_aff *pma,
1780 enum isl_dim_type type);
1781 __isl_give isl_multi_union_pw_aff *
1782 isl_multi_union_pw_aff_reset_tuple_id(
1783 __isl_take isl_multi_union_pw_aff *mupa,
1784 enum isl_dim_type type);
1785 isl_bool isl_multi_aff_has_range_tuple_id(
1786 __isl_keep isl_multi_aff *ma);
1787 __isl_give isl_id *isl_multi_aff_get_range_tuple_id(
1788 __isl_keep isl_multi_aff *ma);
1789 isl_bool isl_multi_aff_has_tuple_id(
1790 __isl_keep isl_multi_aff *ma,
1791 enum isl_dim_type type);
1792 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1793 __isl_keep isl_multi_aff *ma,
1794 enum isl_dim_type type);
1795 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1796 enum isl_dim_type type);
1797 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1798 __isl_keep isl_pw_aff *pa,
1799 enum isl_dim_type type);
1800 isl_bool isl_pw_multi_aff_has_range_tuple_id(
1801 __isl_keep isl_pw_multi_aff *pma);
1802 isl_bool isl_pw_multi_aff_has_tuple_id(
1803 __isl_keep isl_pw_multi_aff *pma,
1804 enum isl_dim_type type);
1805 __isl_give isl_id *isl_pw_multi_aff_get_range_tuple_id(
1806 __isl_keep isl_pw_multi_aff *pma);
1807 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1808 __isl_keep isl_pw_multi_aff *pma,
1809 enum isl_dim_type type);
1810 isl_bool isl_multi_pw_aff_has_range_tuple_id(
1811 __isl_keep isl_multi_pw_aff *mpa);
1812 __isl_give isl_id *isl_multi_pw_aff_get_range_tuple_id(
1813 __isl_keep isl_multi_pw_aff *mpa);
1814 isl_bool isl_multi_pw_aff_has_tuple_id(
1815 __isl_keep isl_multi_pw_aff *mpa,
1816 enum isl_dim_type type);
1817 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1818 __isl_keep isl_multi_pw_aff *mpa,
1819 enum isl_dim_type type);
1820 isl_bool isl_multi_union_pw_aff_has_range_tuple_id(
1821 __isl_keep isl_multi_union_pw_aff *mupa);
1823 isl_multi_union_pw_aff_get_range_tuple_id(
1824 __isl_keep isl_multi_union_pw_aff *mupa);
1825 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1826 __isl_keep isl_multi_union_pw_aff *mupa,
1827 enum isl_dim_type type);
1828 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1829 __isl_keep isl_multi_union_pw_aff *mupa,
1830 enum isl_dim_type type);
1831 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1832 __isl_take isl_multi_aff *maff,
1833 enum isl_dim_type type, const char *s);
1834 __isl_give isl_multi_pw_aff *
1835 isl_multi_pw_aff_set_tuple_name(
1836 __isl_take isl_multi_pw_aff *mpa,
1837 enum isl_dim_type type, const char *s);
1838 __isl_give isl_multi_union_pw_aff *
1839 isl_multi_union_pw_aff_set_tuple_name(
1840 __isl_take isl_multi_union_pw_aff *mupa,
1841 enum isl_dim_type type, const char *s);
1842 const char *isl_multi_aff_get_tuple_name(
1843 __isl_keep isl_multi_aff *multi,
1844 enum isl_dim_type type);
1845 isl_bool isl_pw_multi_aff_has_tuple_name(
1846 __isl_keep isl_pw_multi_aff *pma,
1847 enum isl_dim_type type);
1848 const char *isl_pw_multi_aff_get_tuple_name(
1849 __isl_keep isl_pw_multi_aff *pma,
1850 enum isl_dim_type type);
1851 const char *isl_multi_union_pw_aff_get_tuple_name(
1852 __isl_keep isl_multi_union_pw_aff *mupa,
1853 enum isl_dim_type type);
1855 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1856 or C<isl_dim_set>. As with C<isl_space_get_name>,
1857 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1859 Binary operations require the corresponding spaces of their arguments
1860 to have the same name.
1862 To keep the names of all parameters and tuples, but reset the user pointers
1863 of all the corresponding identifiers, use the following function.
1865 #include <isl/space.h>
1866 __isl_give isl_space *isl_space_reset_user(
1867 __isl_take isl_space *space);
1869 #include <isl/set.h>
1870 __isl_give isl_set *isl_set_reset_user(
1871 __isl_take isl_set *set);
1873 #include <isl/map.h>
1874 __isl_give isl_map *isl_map_reset_user(
1875 __isl_take isl_map *map);
1877 #include <isl/union_set.h>
1878 __isl_give isl_union_set *isl_union_set_reset_user(
1879 __isl_take isl_union_set *uset);
1881 #include <isl/union_map.h>
1882 __isl_give isl_union_map *isl_union_map_reset_user(
1883 __isl_take isl_union_map *umap);
1886 __isl_give isl_multi_id *isl_multi_id_reset_user(
1887 __isl_take isl_multi_id *mi);
1889 #include <isl/val.h>
1890 __isl_give isl_multi_val *isl_multi_val_reset_user(
1891 __isl_take isl_multi_val *mv);
1893 #include <isl/aff.h>
1894 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1895 __isl_take isl_multi_aff *ma);
1896 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1897 __isl_take isl_pw_aff *pa);
1898 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1899 __isl_take isl_multi_pw_aff *mpa);
1900 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1901 __isl_take isl_pw_multi_aff *pma);
1902 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1903 __isl_take isl_union_pw_aff *upa);
1904 __isl_give isl_multi_union_pw_aff *
1905 isl_multi_union_pw_aff_reset_user(
1906 __isl_take isl_multi_union_pw_aff *mupa);
1907 __isl_give isl_union_pw_multi_aff *
1908 isl_union_pw_multi_aff_reset_user(
1909 __isl_take isl_union_pw_multi_aff *upma);
1911 #include <isl/polynomial.h>
1912 __isl_give isl_pw_qpolynomial *
1913 isl_pw_qpolynomial_reset_user(
1914 __isl_take isl_pw_qpolynomial *pwqp);
1915 __isl_give isl_union_pw_qpolynomial *
1916 isl_union_pw_qpolynomial_reset_user(
1917 __isl_take isl_union_pw_qpolynomial *upwqp);
1918 __isl_give isl_pw_qpolynomial_fold *
1919 isl_pw_qpolynomial_fold_reset_user(
1920 __isl_take isl_pw_qpolynomial_fold *pwf);
1921 __isl_give isl_union_pw_qpolynomial_fold *
1922 isl_union_pw_qpolynomial_fold_reset_user(
1923 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1925 Spaces can be nested. In particular, the domain of a set or
1926 the domain or range of a relation can be a nested relation.
1927 This process is also called I<wrapping>.
1928 The functions for detecting, constructing and deconstructing
1929 such nested spaces can be found in the wrapping properties
1930 of L</"Unary Properties">, the wrapping operations
1931 of L</"Unary Operations"> and the Cartesian product operations
1932 of L</"Basic Operations">.
1934 Spaces can be created from other spaces
1935 using the functions described in L</"Unary Operations">
1936 and L</"Binary Operations">.
1940 A local space is essentially a space with
1941 zero or more existentially quantified variables.
1942 The local space of various objects can be obtained
1943 using the following functions.
1945 #include <isl/constraint.h>
1946 __isl_give isl_local_space *isl_constraint_get_local_space(
1947 __isl_keep isl_constraint *constraint);
1949 #include <isl/set.h>
1950 __isl_give isl_local_space *isl_basic_set_get_local_space(
1951 __isl_keep isl_basic_set *bset);
1953 #include <isl/map.h>
1954 __isl_give isl_local_space *isl_basic_map_get_local_space(
1955 __isl_keep isl_basic_map *bmap);
1957 #include <isl/aff.h>
1958 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1959 __isl_keep isl_aff *aff);
1960 __isl_give isl_local_space *isl_aff_get_local_space(
1961 __isl_keep isl_aff *aff);
1963 A new local space can be created from a space using
1965 #include <isl/local_space.h>
1966 __isl_give isl_local_space *isl_local_space_from_space(
1967 __isl_take isl_space *space);
1969 They can be inspected, modified, copied and freed using the following functions.
1971 #include <isl/local_space.h>
1972 isl_bool isl_local_space_is_params(
1973 __isl_keep isl_local_space *ls);
1974 isl_bool isl_local_space_is_set(
1975 __isl_keep isl_local_space *ls);
1976 __isl_give isl_space *isl_local_space_get_space(
1977 __isl_keep isl_local_space *ls);
1978 __isl_give isl_aff *isl_local_space_get_div(
1979 __isl_keep isl_local_space *ls, int pos);
1980 __isl_give isl_local_space *isl_local_space_copy(
1981 __isl_keep isl_local_space *ls);
1982 __isl_null isl_local_space *isl_local_space_free(
1983 __isl_take isl_local_space *ls);
1985 Note that C<isl_local_space_get_div> can only be used on local spaces
1988 Two local spaces can be compared using
1990 isl_bool isl_local_space_is_equal(
1991 __isl_keep isl_local_space *ls1,
1992 __isl_keep isl_local_space *ls2);
1994 Local spaces can be created from other local spaces
1995 using the functions described in L</"Unary Operations">
1996 and L</"Binary Operations">.
1998 =head2 Creating New Sets and Relations
2000 C<isl> has functions for creating some standard sets and relations.
2004 =item * Empty sets and relations
2006 __isl_give isl_basic_set *isl_basic_set_empty(
2007 __isl_take isl_space *space);
2008 __isl_give isl_basic_map *isl_basic_map_empty(
2009 __isl_take isl_space *space);
2010 __isl_give isl_set *isl_set_empty(
2011 __isl_take isl_space *space);
2012 __isl_give isl_map *isl_map_empty(
2013 __isl_take isl_space *space);
2014 __isl_give isl_union_set *isl_union_set_empty_ctx(
2016 __isl_give isl_union_set *isl_union_set_empty_space(
2017 __isl_take isl_space *space);
2018 __isl_give isl_union_set *isl_union_set_empty(
2019 __isl_take isl_space *space);
2020 __isl_give isl_union_map *isl_union_map_empty_ctx(
2022 __isl_give isl_union_map *isl_union_map_empty_space(
2023 __isl_take isl_space *space);
2024 __isl_give isl_union_map *isl_union_map_empty(
2025 __isl_take isl_space *space);
2027 For C<isl_union_set>s and C<isl_union_map>s, the space
2028 is only used to specify the parameters.
2029 C<isl_union_set_empty> is an alternative name for
2030 C<isl_union_set_empty_space>.
2031 Similarly for the other pair of functions.
2033 =item * Universe sets and relations
2035 #include <isl/set.h>
2036 __isl_give isl_basic_set *isl_basic_set_universe(
2037 __isl_take isl_space *space);
2038 __isl_give isl_set *isl_set_universe(
2039 __isl_take isl_space *space);
2040 __isl_give isl_set *isl_space_universe_set(
2041 __isl_take isl_space *space);
2043 #include <isl/map.h>
2044 __isl_give isl_basic_map *isl_basic_map_universe(
2045 __isl_take isl_space *space);
2046 __isl_give isl_map *isl_map_universe(
2047 __isl_take isl_space *space);
2048 __isl_give isl_map *isl_space_universe_map(
2049 __isl_take isl_space *space);
2051 #include <isl/union_set.h>
2052 __isl_give isl_union_set *isl_union_set_universe(
2053 __isl_take isl_union_set *uset);
2055 #include <isl/union_map.h>
2056 __isl_give isl_union_map *isl_union_map_universe(
2057 __isl_take isl_union_map *umap);
2059 C<isl_set_universe> and C<isl_space_universe_set>
2060 perform the same operation.
2062 for the pair C<isl_map_universe> and C<isl_space_universe_map>.
2064 The sets and relations constructed by the functions above
2065 contain all integer values, while those constructed by the
2066 functions below only contain non-negative values.
2068 __isl_give isl_basic_set *isl_basic_set_nat_universe(
2069 __isl_take isl_space *space);
2070 __isl_give isl_basic_map *isl_basic_map_nat_universe(
2071 __isl_take isl_space *space);
2072 __isl_give isl_set *isl_set_nat_universe(
2073 __isl_take isl_space *space);
2074 __isl_give isl_map *isl_map_nat_universe(
2075 __isl_take isl_space *space);
2077 =item * Identity relations
2079 __isl_give isl_basic_map *isl_basic_map_identity(
2080 __isl_take isl_space *space);
2081 __isl_give isl_map *isl_map_identity(
2082 __isl_take isl_space *space);
2084 The number of input and output dimensions in C<space> needs
2087 =item * Lexicographic order
2089 __isl_give isl_map *isl_map_lex_lt(
2090 __isl_take isl_space *set_space);
2091 __isl_give isl_map *isl_map_lex_le(
2092 __isl_take isl_space *set_space);
2093 __isl_give isl_map *isl_map_lex_gt(
2094 __isl_take isl_space *set_space);
2095 __isl_give isl_map *isl_map_lex_ge(
2096 __isl_take isl_space *set_space);
2097 __isl_give isl_map *isl_map_lex_lt_first(
2098 __isl_take isl_space *space, unsigned n);
2099 __isl_give isl_map *isl_map_lex_le_first(
2100 __isl_take isl_space *space, unsigned n);
2101 __isl_give isl_map *isl_map_lex_gt_first(
2102 __isl_take isl_space *space, unsigned n);
2103 __isl_give isl_map *isl_map_lex_ge_first(
2104 __isl_take isl_space *space, unsigned n);
2106 The first four functions take a space for a B<set>
2107 and return relations that express that the elements in the domain
2108 are lexicographically less
2109 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
2110 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
2111 than the elements in the range.
2112 The last four functions take a space for a map
2113 and return relations that express that the first C<n> dimensions
2114 in the domain are lexicographically less
2115 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
2116 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
2117 than the first C<n> dimensions in the range.
2121 A basic set or relation can be converted to a set or relation
2122 using the following functions.
2124 __isl_give isl_set *isl_basic_set_to_set(
2125 __isl_take isl_basic_set *bset);
2126 __isl_give isl_set *isl_set_from_basic_set(
2127 __isl_take isl_basic_set *bset);
2128 __isl_give isl_map *isl_map_from_basic_map(
2129 __isl_take isl_basic_map *bmap);
2131 C<isl_basic_set_to_set> and C<isl_set_from_basic_set> perform
2134 Sets and relations can be converted to union sets and relations
2135 using the following functions.
2137 __isl_give isl_union_set *isl_union_set_from_basic_set(
2138 __isl_take isl_basic_set *bset);
2139 __isl_give isl_union_map *isl_union_map_from_basic_map(
2140 __isl_take isl_basic_map *bmap);
2141 __isl_give isl_union_set *isl_set_to_union_set(
2142 __isl_take isl_set *set);
2143 __isl_give isl_union_set *isl_union_set_from_set(
2144 __isl_take isl_set *set);
2145 __isl_give isl_union_map *isl_map_to_union_map(
2146 __isl_take isl_map *map);
2147 __isl_give isl_union_map *isl_union_map_from_map(
2148 __isl_take isl_map *map);
2150 C<isl_map_to_union_map> and C<isl_union_map_from_map> perform
2152 Similarly for C<isl_set_to_union_set> and C<isl_union_set_from_set>.
2154 The inverse conversions below can only be used if the input
2155 union set or relation is known to contain elements in exactly one
2158 #include <isl/union_set.h>
2159 isl_bool isl_union_set_isa_set(
2160 __isl_keep isl_union_set *uset);
2161 __isl_give isl_set *isl_union_set_as_set(
2162 __isl_take isl_union_set *uset);
2163 __isl_give isl_set *isl_set_from_union_set(
2164 __isl_take isl_union_set *uset);
2166 #include <isl/union_map.h>
2167 isl_bool isl_union_map_isa_map(
2168 __isl_keep isl_union_map *umap);
2169 __isl_give isl_map *isl_union_map_as_map(
2170 __isl_take isl_union_map *umap);
2171 __isl_give isl_map *isl_map_from_union_map(
2172 __isl_take isl_union_map *umap);
2174 C<isl_union_map_as_map> and C<isl_map_from_union_map> perform
2176 Similarly for C<isl_union_set_as_set> and C<isl_set_from_union_set>.
2178 Sets and relations can be copied and freed again using the following
2181 __isl_give isl_basic_set *isl_basic_set_copy(
2182 __isl_keep isl_basic_set *bset);
2183 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
2184 __isl_give isl_union_set *isl_union_set_copy(
2185 __isl_keep isl_union_set *uset);
2186 __isl_give isl_basic_map *isl_basic_map_copy(
2187 __isl_keep isl_basic_map *bmap);
2188 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
2189 __isl_give isl_union_map *isl_union_map_copy(
2190 __isl_keep isl_union_map *umap);
2191 __isl_null isl_basic_set *isl_basic_set_free(
2192 __isl_take isl_basic_set *bset);
2193 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
2194 __isl_null isl_union_set *isl_union_set_free(
2195 __isl_take isl_union_set *uset);
2196 __isl_null isl_basic_map *isl_basic_map_free(
2197 __isl_take isl_basic_map *bmap);
2198 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
2199 __isl_null isl_union_map *isl_union_map_free(
2200 __isl_take isl_union_map *umap);
2202 Other sets and relations can be constructed by starting
2203 from a universe set or relation, adding equality and/or
2204 inequality constraints and then projecting out the
2205 existentially quantified variables, if any.
2206 Constraints can be constructed, manipulated and
2207 added to (or removed from) (basic) sets and relations
2208 using the following functions.
2210 #include <isl/constraint.h>
2211 __isl_give isl_constraint *isl_constraint_alloc_equality(
2212 __isl_take isl_local_space *ls);
2213 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2214 __isl_take isl_local_space *ls);
2215 __isl_give isl_constraint *isl_constraint_set_constant_si(
2216 __isl_take isl_constraint *constraint, int v);
2217 __isl_give isl_constraint *isl_constraint_set_constant_val(
2218 __isl_take isl_constraint *constraint,
2219 __isl_take isl_val *v);
2220 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2221 __isl_take isl_constraint *constraint,
2222 enum isl_dim_type type, int pos, int v);
2223 __isl_give isl_constraint *
2224 isl_constraint_set_coefficient_val(
2225 __isl_take isl_constraint *constraint,
2226 enum isl_dim_type type, int pos,
2227 __isl_take isl_val *v);
2228 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2229 __isl_take isl_basic_map *bmap,
2230 __isl_take isl_constraint *constraint);
2231 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2232 __isl_take isl_basic_set *bset,
2233 __isl_take isl_constraint *constraint);
2234 __isl_give isl_map *isl_map_add_constraint(
2235 __isl_take isl_map *map,
2236 __isl_take isl_constraint *constraint);
2237 __isl_give isl_set *isl_set_add_constraint(
2238 __isl_take isl_set *set,
2239 __isl_take isl_constraint *constraint);
2241 For example, to create a set containing the even integers
2242 between 10 and 42, you could use the following code.
2245 isl_local_space *ls;
2247 isl_basic_set *bset;
2249 space = isl_space_set_alloc(ctx, 0, 2);
2250 bset = isl_basic_set_universe(isl_space_copy(space));
2251 ls = isl_local_space_from_space(space);
2253 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2254 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2255 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2256 bset = isl_basic_set_add_constraint(bset, c);
2258 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2259 c = isl_constraint_set_constant_si(c, -10);
2260 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2261 bset = isl_basic_set_add_constraint(bset, c);
2263 c = isl_constraint_alloc_inequality(ls);
2264 c = isl_constraint_set_constant_si(c, 42);
2265 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2266 bset = isl_basic_set_add_constraint(bset, c);
2268 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2270 However, this is considered to be a fairly low-level approach.
2271 It is more appropriate to construct a (basic) set by means
2272 of affine expressions (defined below in L</"Functions">).
2273 For example, the same set could be constructed as follows.
2279 isl_basic_set *bset;
2281 space = isl_space_unit(ctx);
2282 space = isl_space_add_unnamed_tuple_ui(space, 1);
2283 ma = isl_multi_aff_identity_on_domain_space(
2284 isl_space_copy(space));
2285 var = isl_multi_aff_get_at(ma, 0);
2286 v = isl_val_int_from_si(ctx, 10);
2287 cst = isl_aff_val_on_domain_space(isl_space_copy(space), v);
2288 bset = isl_aff_ge_basic_set(isl_aff_copy(var), cst);
2290 v = isl_val_int_from_si(ctx, 42);
2291 cst = isl_aff_val_on_domain_space(space, v);
2292 bset = isl_basic_set_intersect(bset,
2293 isl_aff_le_basic_set(var, cst));
2295 two = isl_val_int_from_si(ctx, 2);
2296 ma = isl_multi_aff_scale_val(ma, isl_val_copy(two));
2297 bset = isl_basic_set_preimage_multi_aff(bset,
2298 isl_multi_aff_copy(ma));
2299 ma = isl_multi_aff_scale_down_val(ma, isl_val_copy(two));
2300 ma = isl_multi_aff_scale_down_val(ma, two);
2301 bset = isl_basic_set_preimage_multi_aff(bset, ma);
2303 Alternatively, the set can be parsed from a string representation.
2305 isl_basic_set *bset;
2306 bset = isl_basic_set_read_from_str(ctx,
2307 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2309 A basic set or relation can also be constructed from two matrices
2310 describing the equalities and the inequalities.
2312 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2313 __isl_take isl_space *space,
2314 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2315 enum isl_dim_type c1,
2316 enum isl_dim_type c2, enum isl_dim_type c3,
2317 enum isl_dim_type c4);
2318 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2319 __isl_take isl_space *space,
2320 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2321 enum isl_dim_type c1,
2322 enum isl_dim_type c2, enum isl_dim_type c3,
2323 enum isl_dim_type c4, enum isl_dim_type c5);
2325 The C<isl_dim_type> arguments indicate the order in which
2326 different kinds of variables appear in the input matrices
2327 and should be a permutation of C<isl_dim_cst> (the constant term),
2328 C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div> for sets and
2329 of C<isl_dim_cst>, C<isl_dim_param>,
2330 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2332 A (basic or union) set or relation can also be constructed from a
2333 (union) (piecewise) (multiple) affine expression
2334 or a list of affine expressions
2335 (See L</"Functions">), provided these affine expressions do not
2338 #include <isl/set.h>
2339 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2340 __isl_take isl_multi_aff *ma);
2341 __isl_give isl_set *isl_multi_aff_as_set(
2342 __isl_take isl_multi_aff *ma);
2343 __isl_give isl_set *isl_set_from_multi_aff(
2344 __isl_take isl_multi_aff *ma);
2346 #include <isl/map.h>
2347 __isl_give isl_basic_map *isl_basic_map_from_aff(
2348 __isl_take isl_aff *aff);
2349 __isl_give isl_map *isl_map_from_aff(
2350 __isl_take isl_aff *aff);
2351 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2352 __isl_take isl_space *domain_space,
2353 __isl_take isl_aff_list *list);
2354 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2355 __isl_take isl_multi_aff *maff)
2356 __isl_give isl_map *isl_multi_aff_as_map(
2357 __isl_take isl_multi_aff *ma);
2358 __isl_give isl_map *isl_map_from_multi_aff(
2359 __isl_take isl_multi_aff *maff)
2361 #include <isl/aff.h>
2362 __isl_give isl_set *isl_set_from_pw_aff(
2363 __isl_take isl_pw_aff *pwaff);
2364 __isl_give isl_map *isl_pw_aff_as_map(
2365 __isl_take isl_pw_aff *pa);
2366 __isl_give isl_map *isl_map_from_pw_aff(
2367 __isl_take isl_pw_aff *pwaff);
2368 __isl_give isl_set *isl_pw_multi_aff_as_set(
2369 __isl_take isl_pw_multi_aff *pma);
2370 __isl_give isl_set *isl_set_from_pw_multi_aff(
2371 __isl_take isl_pw_multi_aff *pma);
2372 __isl_give isl_map *isl_pw_multi_aff_as_map(
2373 __isl_take isl_pw_multi_aff *pma);
2374 __isl_give isl_map *isl_map_from_pw_multi_aff(
2375 __isl_take isl_pw_multi_aff *pma);
2376 __isl_give isl_set *isl_multi_pw_aff_as_set(
2377 __isl_take isl_multi_pw_aff *mpa);
2378 __isl_give isl_set *isl_set_from_multi_pw_aff(
2379 __isl_take isl_multi_pw_aff *mpa);
2380 __isl_give isl_map *isl_multi_pw_aff_as_map(
2381 __isl_take isl_multi_pw_aff *mpa);
2382 __isl_give isl_map *isl_map_from_multi_pw_aff(
2383 __isl_take isl_multi_pw_aff *mpa);
2384 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2385 __isl_take isl_union_pw_aff *upa);
2386 __isl_give isl_union_map *
2387 isl_union_pw_multi_aff_as_union_map(
2388 __isl_take isl_union_pw_multi_aff *upma);
2389 __isl_give isl_union_map *
2390 isl_union_map_from_union_pw_multi_aff(
2391 __isl_take isl_union_pw_multi_aff *upma);
2392 __isl_give isl_union_map *
2393 isl_union_map_from_multi_union_pw_aff(
2394 __isl_take isl_multi_union_pw_aff *mupa);
2396 The C<domain_space> argument describes the domain of the resulting
2397 basic relation. It is required because the C<list> may consist
2398 of zero affine expressions.
2399 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2400 is not allowed to be zero-dimensional. The domain of the result
2401 is the shared domain of the union piecewise affine elements.
2402 C<isl_multi_aff_as_set> and C<isl_set_from_multi_aff> perform
2404 Similarly for the pair C<isl_multi_aff_as_map> and C<isl_map_from_multi_aff>,
2405 for the pair C<isl_pw_aff_as_map> and C<isl_map_from_pw_aff>,
2406 for the pair C<isl_pw_multi_aff_as_set> and C<isl_set_from_pw_multi_aff>,
2407 for the pair C<isl_pw_multi_aff_as_map> and C<isl_map_from_pw_multi_aff>,
2408 the pair C<isl_multi_pw_aff_as_set> and C<isl_set_from_multi_pw_aff>,
2409 the pair C<isl_multi_pw_aff_as_map> and C<isl_map_from_multi_pw_aff>,
2411 C<isl_union_pw_multi_aff_as_union_map> and
2412 C<isl_union_map_from_union_pw_multi_aff>.
2414 =head2 Inspecting Sets and Relations
2416 Usually, the user should not have to care about the actual constraints
2417 of the sets and maps, but should instead apply the abstract operations
2418 explained in the following sections.
2419 Occasionally, however, it may be required to inspect the individual
2420 coefficients of the constraints. This section explains how to do so.
2421 In these cases, it may also be useful to have C<isl> compute
2422 an explicit representation of the existentially quantified variables.
2424 __isl_give isl_set *isl_set_compute_divs(
2425 __isl_take isl_set *set);
2426 __isl_give isl_map *isl_map_compute_divs(
2427 __isl_take isl_map *map);
2428 __isl_give isl_union_set *isl_union_set_compute_divs(
2429 __isl_take isl_union_set *uset);
2430 __isl_give isl_union_map *isl_union_map_compute_divs(
2431 __isl_take isl_union_map *umap);
2433 This explicit representation defines the existentially quantified
2434 variables as integer divisions of the other variables, possibly
2435 including earlier existentially quantified variables.
2436 An explicitly represented existentially quantified variable therefore
2437 has a unique value when the values of the other variables are known.
2439 Alternatively, the existentially quantified variables can be removed
2440 using the following functions, which compute an overapproximation.
2442 #include <isl/set.h>
2443 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2444 __isl_take isl_basic_set *bset);
2445 __isl_give isl_set *isl_set_remove_divs(
2446 __isl_take isl_set *set);
2448 #include <isl/map.h>
2449 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2450 __isl_take isl_basic_map *bmap);
2451 __isl_give isl_map *isl_map_remove_divs(
2452 __isl_take isl_map *map);
2454 #include <isl/union_set.h>
2455 __isl_give isl_union_set *isl_union_set_remove_divs(
2456 __isl_take isl_union_set *bset);
2458 #include <isl/union_map.h>
2459 __isl_give isl_union_map *isl_union_map_remove_divs(
2460 __isl_take isl_union_map *bmap);
2462 It is also possible to only remove those divs that are defined
2463 in terms of a given range of dimensions or only those for which
2464 no explicit representation is known.
2466 __isl_give isl_basic_set *
2467 isl_basic_set_remove_divs_involving_dims(
2468 __isl_take isl_basic_set *bset,
2469 enum isl_dim_type type,
2470 unsigned first, unsigned n);
2471 __isl_give isl_basic_map *
2472 isl_basic_map_remove_divs_involving_dims(
2473 __isl_take isl_basic_map *bmap,
2474 enum isl_dim_type type,
2475 unsigned first, unsigned n);
2476 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2477 __isl_take isl_set *set, enum isl_dim_type type,
2478 unsigned first, unsigned n);
2479 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2480 __isl_take isl_map *map, enum isl_dim_type type,
2481 unsigned first, unsigned n);
2483 __isl_give isl_basic_set *
2484 isl_basic_set_remove_unknown_divs(
2485 __isl_take isl_basic_set *bset);
2486 __isl_give isl_set *isl_set_remove_unknown_divs(
2487 __isl_take isl_set *set);
2488 __isl_give isl_map *isl_map_remove_unknown_divs(
2489 __isl_take isl_map *map);
2491 To iterate over all the sets or maps in a union set or map, use
2493 #include <isl/union_set.h>
2494 isl_stat isl_union_set_foreach_set(
2495 __isl_keep isl_union_set *uset,
2496 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2498 isl_bool isl_union_set_every_set(
2499 __isl_keep isl_union_set *uset,
2500 isl_bool (*test)(__isl_keep isl_set *set,
2504 #include <isl/union_map.h>
2505 isl_stat isl_union_map_foreach_map(
2506 __isl_keep isl_union_map *umap,
2507 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2509 isl_bool isl_union_map_every_map(
2510 __isl_keep isl_union_map *umap,
2511 isl_bool (*test)(__isl_keep isl_map *map,
2515 These functions call the callback function once for each
2516 (pair of) space(s) for which there are elements in the input.
2517 The argument to the callback contains all elements in the input
2518 with that (pair of) space(s).
2519 The C<isl_union_set_every_set> and
2520 C<isl_union_map_every_map> variants check whether each
2521 call to the callback returns true and stops checking as soon as one
2522 of these calls returns false.
2524 The number of sets or maps in a union set or map can be obtained
2527 isl_size isl_union_set_n_set(__isl_keep isl_union_set *uset);
2528 isl_size isl_union_map_n_map(__isl_keep isl_union_map *umap);
2530 To extract the set or map in a given space from a union, use
2532 __isl_give isl_set *isl_union_set_extract_set(
2533 __isl_keep isl_union_set *uset,
2534 __isl_take isl_space *space);
2535 __isl_give isl_map *isl_union_map_extract_map(
2536 __isl_keep isl_union_map *umap,
2537 __isl_take isl_space *space);
2539 To iterate over all the basic sets or maps in a set or map, use
2541 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2542 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2545 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2546 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2550 The callback function C<fn> should return C<isl_stat_ok> if successful and
2551 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2552 occurs, the above functions will return C<isl_stat_error>.
2554 It should be noted that C<isl> does not guarantee that
2555 the basic sets or maps passed to C<fn> are disjoint.
2556 If this is required, then the user should call one of
2557 the following functions first.
2559 __isl_give isl_set *isl_set_make_disjoint(
2560 __isl_take isl_set *set);
2561 __isl_give isl_map *isl_map_make_disjoint(
2562 __isl_take isl_map *map);
2564 The number of basic sets in a set can be obtained
2565 or the number of basic maps in a map can be obtained
2568 #include <isl/set.h>
2569 isl_size isl_set_n_basic_set(__isl_keep isl_set *set);
2571 #include <isl/map.h>
2572 isl_size isl_map_n_basic_map(__isl_keep isl_map *map);
2574 It is also possible to obtain a list of (basic) sets from a set
2575 or union set, a list of basic maps from a map and a list of maps from a union
2578 #include <isl/set.h>
2579 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2580 __isl_keep isl_set *set);
2582 #include <isl/union_set.h>
2583 __isl_give isl_basic_set_list *
2584 isl_union_set_get_basic_set_list(
2585 __isl_keep isl_union_set *uset);
2586 __isl_give isl_set_list *isl_union_set_get_set_list(
2587 __isl_keep isl_union_set *uset);
2589 #include <isl/map.h>
2590 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2591 __isl_keep isl_map *map);
2593 #include <isl/union_map.h>
2594 __isl_give isl_map_list *isl_union_map_get_map_list(
2595 __isl_keep isl_union_map *umap);
2597 The returned list can be manipulated using the functions in L<"Lists">.
2599 To iterate over the constraints of a basic set or map, use
2601 #include <isl/constraint.h>
2603 isl_size isl_basic_set_n_constraint(
2604 __isl_keep isl_basic_set *bset);
2605 isl_stat isl_basic_set_foreach_constraint(
2606 __isl_keep isl_basic_set *bset,
2607 isl_stat (*fn)(__isl_take isl_constraint *c,
2610 isl_size isl_basic_map_n_constraint(
2611 __isl_keep isl_basic_map *bmap);
2612 isl_stat isl_basic_map_foreach_constraint(
2613 __isl_keep isl_basic_map *bmap,
2614 isl_stat (*fn)(__isl_take isl_constraint *c,
2617 __isl_null isl_constraint *isl_constraint_free(
2618 __isl_take isl_constraint *c);
2620 Again, the callback function C<fn> should return C<isl_stat_ok>
2622 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2623 occurs, the above functions will return C<isl_stat_error>.
2624 The constraint C<c> represents either an equality or an inequality.
2625 Use the following function to find out whether a constraint
2626 represents an equality. If not, it represents an inequality.
2628 isl_bool isl_constraint_is_equality(
2629 __isl_keep isl_constraint *constraint);
2631 It is also possible to obtain a list of constraints from a basic
2634 #include <isl/constraint.h>
2635 __isl_give isl_constraint_list *
2636 isl_basic_map_get_constraint_list(
2637 __isl_keep isl_basic_map *bmap);
2638 __isl_give isl_constraint_list *
2639 isl_basic_set_get_constraint_list(
2640 __isl_keep isl_basic_set *bset);
2642 These functions require that all existentially quantified variables
2643 have an explicit representation.
2644 The returned list can be manipulated using the functions in L<"Lists">.
2646 The coefficients of the constraints can be inspected using
2647 the following functions.
2649 isl_bool isl_constraint_is_lower_bound(
2650 __isl_keep isl_constraint *constraint,
2651 enum isl_dim_type type, unsigned pos);
2652 isl_bool isl_constraint_is_upper_bound(
2653 __isl_keep isl_constraint *constraint,
2654 enum isl_dim_type type, unsigned pos);
2655 __isl_give isl_val *isl_constraint_get_constant_val(
2656 __isl_keep isl_constraint *constraint);
2657 __isl_give isl_val *isl_constraint_get_coefficient_val(
2658 __isl_keep isl_constraint *constraint,
2659 enum isl_dim_type type, int pos);
2661 The explicit representations of the existentially quantified
2662 variables can be inspected using the following function.
2663 Note that the user is only allowed to use this function
2664 if the inspected set or map is the result of a call
2665 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2666 The existentially quantified variable is equal to the floor
2667 of the returned affine expression. The affine expression
2668 itself can be inspected using the functions in
2671 __isl_give isl_aff *isl_constraint_get_div(
2672 __isl_keep isl_constraint *constraint, int pos);
2674 To obtain the constraints of a basic set or map in matrix
2675 form, use the following functions.
2677 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2678 __isl_keep isl_basic_set *bset,
2679 enum isl_dim_type c1, enum isl_dim_type c2,
2680 enum isl_dim_type c3, enum isl_dim_type c4);
2681 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2682 __isl_keep isl_basic_set *bset,
2683 enum isl_dim_type c1, enum isl_dim_type c2,
2684 enum isl_dim_type c3, enum isl_dim_type c4);
2685 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2686 __isl_keep isl_basic_map *bmap,
2687 enum isl_dim_type c1,
2688 enum isl_dim_type c2, enum isl_dim_type c3,
2689 enum isl_dim_type c4, enum isl_dim_type c5);
2690 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2691 __isl_keep isl_basic_map *bmap,
2692 enum isl_dim_type c1,
2693 enum isl_dim_type c2, enum isl_dim_type c3,
2694 enum isl_dim_type c4, enum isl_dim_type c5);
2696 The C<isl_dim_type> arguments dictate the order in which
2697 different kinds of variables appear in the resulting matrix.
2698 For set inputs, they should be a permutation of
2699 C<isl_dim_cst> (the constant term), C<isl_dim_param>, C<isl_dim_set> and
2701 For map inputs, they should be a permutation of
2702 C<isl_dim_cst>, C<isl_dim_param>,
2703 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2707 Points are elements of a set. They can be used to construct
2708 simple sets (boxes) or they can be used to represent the
2709 individual elements of a set.
2710 The zero point (the origin) can be created using
2712 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2714 The coordinates of a point can be inspected, set and changed
2717 #include <isl/point.h>
2718 __isl_give isl_multi_val *isl_point_get_multi_val(
2719 __isl_keep isl_point *pnt);
2720 __isl_give isl_val *isl_point_get_coordinate_val(
2721 __isl_keep isl_point *pnt,
2722 enum isl_dim_type type, int pos);
2723 __isl_give isl_point *isl_point_set_coordinate_val(
2724 __isl_take isl_point *pnt,
2725 enum isl_dim_type type, int pos,
2726 __isl_take isl_val *v);
2728 __isl_give isl_point *isl_point_add_ui(
2729 __isl_take isl_point *pnt,
2730 enum isl_dim_type type, int pos, unsigned val);
2731 __isl_give isl_point *isl_point_sub_ui(
2732 __isl_take isl_point *pnt,
2733 enum isl_dim_type type, int pos, unsigned val);
2735 Points can be copied or freed using
2737 __isl_give isl_point *isl_point_copy(
2738 __isl_keep isl_point *pnt);
2739 __isl_null isl_point *isl_point_free(
2740 __isl_take isl_point *pnt);
2742 A singleton set can be created from a point using the following functions.
2744 __isl_give isl_basic_set *isl_basic_set_from_point(
2745 __isl_take isl_point *pnt);
2746 __isl_give isl_set *isl_point_to_set(
2747 __isl_take isl_point *pnt);
2748 __isl_give isl_set *isl_set_from_point(
2749 __isl_take isl_point *pnt);
2750 __isl_give isl_union_set *isl_union_set_from_point(
2751 __isl_take isl_point *pnt);
2753 C<isl_point_to_set> and C<isl_set_from_point> perform
2756 A box can be created from two opposite extremal points using
2758 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2759 __isl_take isl_point *pnt1,
2760 __isl_take isl_point *pnt2);
2761 __isl_give isl_set *isl_set_box_from_points(
2762 __isl_take isl_point *pnt1,
2763 __isl_take isl_point *pnt2);
2765 All elements of a B<bounded> (union) set can be enumerated using
2766 the following functions.
2768 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2769 isl_stat (*fn)(__isl_take isl_point *pnt,
2772 isl_stat isl_union_set_foreach_point(
2773 __isl_keep isl_union_set *uset,
2774 isl_stat (*fn)(__isl_take isl_point *pnt,
2778 The function C<fn> is called for each integer point in
2779 C<set> with as second argument the last argument of
2780 the C<isl_set_foreach_point> call. The function C<fn>
2781 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2782 In the latter case, C<isl_set_foreach_point> will stop
2783 enumerating and return C<isl_stat_error> as well.
2784 If the enumeration is performed successfully and to completion,
2785 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2787 To obtain a single point of a (basic or union) set, use
2789 __isl_give isl_point *isl_basic_set_sample_point(
2790 __isl_take isl_basic_set *bset);
2791 __isl_give isl_point *isl_set_sample_point(
2792 __isl_take isl_set *set);
2793 __isl_give isl_point *isl_union_set_sample_point(
2794 __isl_take isl_union_set *uset);
2796 If C<set> does not contain any (integer) points, then the
2797 resulting point will be ``void'', a property that can be
2800 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2804 Besides sets and relation, C<isl> also supports various types of functions.
2805 Each of these types is derived from the value type (see L</"Values">)
2806 or from one of two primitive function types
2807 through the application of zero or more type constructors.
2808 As a special case, a multiple expression can also be derived
2809 from an identifier (see L</"Identifiers">) although the result
2810 is not really a function.
2811 We first describe the primitive type and then we describe
2812 the types derived from these primitive types.
2814 =head3 Primitive Functions
2816 C<isl> support two primitive function types, quasi-affine
2817 expressions and quasipolynomials.
2818 A quasi-affine expression is defined either over a parameter
2819 space or over a set and is composed of integer constants,
2820 parameters and set variables, addition, subtraction and
2821 integer division by an integer constant.
2822 For example, the quasi-affine expression
2824 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2826 maps C<x> to C<2*floor((4 n + x)/9>.
2827 A quasipolynomial is a polynomial expression in quasi-affine
2828 expression. That is, it additionally allows for multiplication.
2829 Note, though, that it is not allowed to construct an integer
2830 division of an expression involving multiplications.
2831 Here is an example of a quasipolynomial that is not
2832 quasi-affine expression
2834 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2836 Note that the external representations of quasi-affine expressions
2837 and quasipolynomials are different. Quasi-affine expressions
2838 use a notation with square brackets just like binary relations,
2839 while quasipolynomials do not. This might change at some point.
2841 If a primitive function is defined over a parameter space,
2842 then the space of the function itself is that of a set.
2843 If it is defined over a set, then the space of the function
2844 is that of a relation. In both cases, the set space (or
2845 the output space) is single-dimensional, anonymous and unstructured.
2846 To create functions with multiple dimensions or with other kinds
2847 of set or output spaces, use multiple expressions
2848 (see L</"Multiple Expressions">).
2852 =item * Quasi-affine Expressions
2854 Besides the expressions described above, a quasi-affine
2855 expression can also be set to NaN. Such expressions
2856 typically represent a failure to represent a result
2857 as a quasi-affine expression.
2859 The zero quasi affine expression or the quasi affine expression
2860 that is equal to a given value, parameter or
2861 a specified dimension on a given domain can be created using
2863 #include <isl/aff.h>
2864 __isl_give isl_aff *isl_aff_zero_on_domain_space(
2865 __isl_take isl_space *space);
2866 __isl_give isl_aff *isl_space_zero_aff_on_domain(
2867 __isl_take isl_space *space);
2868 __isl_give isl_aff *isl_aff_zero_on_domain(
2869 __isl_take isl_local_space *ls);
2870 __isl_give isl_aff *isl_aff_val_on_domain_space(
2871 __isl_take isl_space *space,
2872 __isl_take isl_val *val);
2873 __isl_give isl_aff *isl_aff_val_on_domain(
2874 __isl_take isl_local_space *ls,
2875 __isl_take isl_val *val);
2876 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2877 __isl_take isl_space *space,
2878 __isl_take isl_id *id);
2879 __isl_give isl_aff *isl_space_param_aff_on_domain_id(
2880 __isl_take isl_space *space,
2881 __isl_take isl_id *id);
2882 __isl_give isl_aff *isl_aff_var_on_domain(
2883 __isl_take isl_local_space *ls,
2884 enum isl_dim_type type, unsigned pos);
2885 __isl_give isl_aff *isl_aff_nan_on_domain_space(
2886 __isl_take isl_space *space);
2887 __isl_give isl_aff *isl_aff_nan_on_domain(
2888 __isl_take isl_local_space *ls);
2890 The space passed to C<isl_aff_param_on_domain_space_id>
2891 is required to have a parameter with the given identifier.
2892 C<isl_aff_param_on_domain_space_id> and
2893 C<isl_space_param_aff_on_domain_id> perform the same operation.
2895 C<isl_aff_zero_on_domain_space> and C<isl_space_zero_aff_on_domain>
2896 perform the same operation.
2898 Quasi affine expressions can be copied and freed using
2900 #include <isl/aff.h>
2901 __isl_give isl_aff *isl_aff_copy(
2902 __isl_keep isl_aff *aff);
2903 __isl_null isl_aff *isl_aff_free(
2904 __isl_take isl_aff *aff);
2906 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2907 using the following function. The constraint is required to have
2908 a non-zero coefficient for the specified dimension.
2910 #include <isl/constraint.h>
2911 __isl_give isl_aff *isl_constraint_get_bound(
2912 __isl_keep isl_constraint *constraint,
2913 enum isl_dim_type type, int pos);
2915 The entire affine expression of the constraint can also be extracted
2916 using the following function.
2918 #include <isl/constraint.h>
2919 __isl_give isl_aff *isl_constraint_get_aff(
2920 __isl_keep isl_constraint *constraint);
2922 Conversely, an equality constraint equating
2923 the affine expression to zero or an inequality constraint enforcing
2924 the affine expression to be non-negative, can be constructed using
2926 __isl_give isl_constraint *isl_equality_from_aff(
2927 __isl_take isl_aff *aff);
2928 __isl_give isl_constraint *isl_inequality_from_aff(
2929 __isl_take isl_aff *aff);
2931 The coefficients and the integer divisions of an affine expression
2932 can be inspected using the following functions.
2934 #include <isl/aff.h>
2935 __isl_give isl_val *isl_aff_get_constant_val(
2936 __isl_keep isl_aff *aff);
2937 __isl_give isl_val *isl_aff_get_coefficient_val(
2938 __isl_keep isl_aff *aff,
2939 enum isl_dim_type type, int pos);
2940 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2941 enum isl_dim_type type, int pos);
2942 __isl_give isl_val *isl_aff_get_denominator_val(
2943 __isl_keep isl_aff *aff);
2944 __isl_give isl_aff *isl_aff_get_div(
2945 __isl_keep isl_aff *aff, int pos);
2947 They can be modified using the following functions.
2949 #include <isl/aff.h>
2950 __isl_give isl_aff *isl_aff_set_constant_si(
2951 __isl_take isl_aff *aff, int v);
2952 __isl_give isl_aff *isl_aff_set_constant_val(
2953 __isl_take isl_aff *aff, __isl_take isl_val *v);
2954 __isl_give isl_aff *isl_aff_set_coefficient_si(
2955 __isl_take isl_aff *aff,
2956 enum isl_dim_type type, int pos, int v);
2957 __isl_give isl_aff *isl_aff_set_coefficient_val(
2958 __isl_take isl_aff *aff,
2959 enum isl_dim_type type, int pos,
2960 __isl_take isl_val *v);
2962 __isl_give isl_aff *isl_aff_add_constant_si(
2963 __isl_take isl_aff *aff, int v);
2964 __isl_give isl_aff *isl_aff_add_constant_val(
2965 __isl_take isl_aff *aff, __isl_take isl_val *v);
2966 __isl_give isl_aff *isl_aff_add_constant_num_si(
2967 __isl_take isl_aff *aff, int v);
2968 __isl_give isl_aff *isl_aff_add_coefficient_si(
2969 __isl_take isl_aff *aff,
2970 enum isl_dim_type type, int pos, int v);
2971 __isl_give isl_aff *isl_aff_add_coefficient_val(
2972 __isl_take isl_aff *aff,
2973 enum isl_dim_type type, int pos,
2974 __isl_take isl_val *v);
2976 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2977 set the I<numerator> of the constant or coefficient, while
2978 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2979 the constant or coefficient as a whole.
2980 The C<add_constant> and C<add_coefficient> functions add an integer
2981 or rational value to
2982 the possibly rational constant or coefficient.
2983 The C<add_constant_num> functions add an integer value to
2986 =item * Quasipolynomials
2988 Some simple quasipolynomials can be created using the following functions.
2990 #include <isl/polynomial.h>
2991 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2992 __isl_take isl_space *domain);
2993 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2994 __isl_take isl_space *domain);
2995 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2996 __isl_take isl_space *domain);
2997 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2998 __isl_take isl_space *domain);
2999 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3000 __isl_take isl_space *domain);
3001 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
3002 __isl_take isl_space *domain,
3003 __isl_take isl_val *val);
3004 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3005 __isl_take isl_space *domain,
3006 enum isl_dim_type type, unsigned pos);
3007 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3008 __isl_take isl_aff *aff);
3010 Recall that the space in which a quasipolynomial lives is a map space
3011 with a one-dimensional range. The C<domain> argument in some of
3012 the functions above corresponds to the domain of this map space.
3014 Quasipolynomials can be copied and freed again using the following
3017 #include <isl/polynomial.h>
3018 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3019 __isl_keep isl_qpolynomial *qp);
3020 __isl_null isl_qpolynomial *isl_qpolynomial_free(
3021 __isl_take isl_qpolynomial *qp);
3023 The constant term of a quasipolynomial can be extracted using
3025 __isl_give isl_val *isl_qpolynomial_get_constant_val(
3026 __isl_keep isl_qpolynomial *qp);
3028 To iterate over all terms in a quasipolynomial,
3031 isl_stat isl_qpolynomial_foreach_term(
3032 __isl_keep isl_qpolynomial *qp,
3033 isl_stat (*fn)(__isl_take isl_term *term,
3034 void *user), void *user);
3036 The terms themselves can be inspected and freed using
3039 isl_size isl_term_dim(__isl_keep isl_term *term,
3040 enum isl_dim_type type);
3041 __isl_give isl_val *isl_term_get_coefficient_val(
3042 __isl_keep isl_term *term);
3043 isl_size isl_term_get_exp(__isl_keep isl_term *term,
3044 enum isl_dim_type type, unsigned pos);
3045 __isl_give isl_aff *isl_term_get_div(
3046 __isl_keep isl_term *term, unsigned pos);
3047 __isl_null isl_term *isl_term_free(
3048 __isl_take isl_term *term);
3050 Each term is a product of parameters, set variables and
3051 integer divisions. The function C<isl_term_get_exp>
3052 returns the exponent of a given dimensions in the given term.
3058 A reduction represents a maximum or a minimum of its
3060 The only reduction type defined by C<isl> is
3061 C<isl_qpolynomial_fold>.
3063 There are currently no functions to directly create such
3064 objects, but they do appear in the piecewise quasipolynomial
3065 reductions returned by the C<isl_pw_qpolynomial_bound> function.
3067 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
3069 Reductions can be copied and freed using
3070 the following functions.
3072 #include <isl/polynomial.h>
3073 __isl_give isl_qpolynomial_fold *
3074 isl_qpolynomial_fold_copy(
3075 __isl_keep isl_qpolynomial_fold *fold);
3076 __isl_null isl_qpolynomial_fold *
3077 isl_qpolynomial_fold_free(
3078 __isl_take isl_qpolynomial_fold *fold);
3080 The type of a (union piecewise) reduction
3081 can be obtained using the following functions.
3083 #include <isl/polynomial.h>
3084 enum isl_fold isl_qpolynomial_fold_get_type(
3085 __isl_keep isl_qpolynomial_fold *fold);
3086 enum isl_fold isl_pw_qpolynomial_fold_get_type(
3087 __isl_keep isl_pw_qpolynomial_fold *pwf);
3088 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
3089 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3091 The type may be either C<isl_fold_min> or C<isl_fold_max>
3092 (or C<isl_fold_error> in case of error).
3094 To iterate over all quasipolynomials in a reduction, use
3096 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
3097 __isl_keep isl_qpolynomial_fold *fold,
3098 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
3099 void *user), void *user);
3101 =head3 Multiple Expressions
3103 A multiple expression represents a sequence of zero or
3104 more base expressions, all defined on the same domain space.
3105 The domain space of the multiple expression is the same
3106 as that of the base expressions, but the range space
3107 can be any space. In case the base expressions have
3108 a set space, the corresponding multiple expression
3109 also has a set space.
3110 Objects of the value or identifier type do not have an associated space.
3111 The space of a multiple value or
3112 multiple identifier is therefore always a set space.
3113 Similarly, the space of a multiple union piecewise
3114 affine expression is always a set space.
3115 If the base expressions are not total, then
3116 a corresponding zero-dimensional multiple expression may
3117 have an explicit domain that keeps track of the domain
3118 outside of any base expressions.
3120 The multiple expression types defined by C<isl>
3121 are C<isl_multi_val>, C<isl_multi_id>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
3122 C<isl_multi_union_pw_aff>.
3124 A multiple expression with the value zero for
3125 each output (or set) dimension can be created
3126 using the following functions.
3128 #include <isl/val.h>
3129 __isl_give isl_multi_val *isl_multi_val_zero(
3130 __isl_take isl_space *space);
3131 __isl_give isl_multi_val *isl_space_zero_multi_val(
3132 __isl_take isl_space *space);
3134 #include <isl/aff.h>
3135 __isl_give isl_multi_aff *isl_multi_aff_zero(
3136 __isl_take isl_space *space);
3137 __isl_give isl_multi_aff *isl_space_zero_multi_aff(
3138 __isl_take isl_space *space);
3139 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3140 __isl_take isl_space *space);
3141 __isl_give isl_multi_pw_aff *isl_space_zero_multi_pw_aff(
3142 __isl_take isl_space *space);
3143 __isl_give isl_multi_union_pw_aff *
3144 isl_multi_union_pw_aff_zero(
3145 __isl_take isl_space *space);
3146 __isl_give isl_multi_union_pw_aff *
3147 isl_space_zero_multi_union_pw_aff(
3148 __isl_take isl_space *space);
3150 Since there is no canonical way of representing a zero
3151 value of type C<isl_union_pw_aff>, the space passed
3152 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
3153 C<isl_multi_val_zero> and C<isl_space_zero_multi_val>
3154 perform the same operation.
3156 for the pair C<isl_multi_aff_zero> and C<isl_space_zero_multi_aff>,
3157 for the pair C<isl_multi_pw_aff_zero> and C<isl_space_zero_multi_pw_aff> and
3158 for the pair C<isl_multi_union_pw_aff_zero> and
3159 C<isl_space_zero_multi_union_pw_aff>.
3162 An identity function can be created using the following
3164 For the first group of functions, the space needs to be that of a set.
3165 For the second group,
3166 the space needs to be that of a relation
3167 with the same number of input and output dimensions.
3168 For the third group, the input function needs to live in a space
3169 with the same number of input and output dimensions and
3170 the identity function is created in that space.
3172 #include <isl/aff.h>
3173 __isl_give isl_multi_aff *
3174 isl_multi_aff_identity_on_domain_space(
3175 __isl_take isl_space *space);
3176 __isl_give isl_multi_aff *
3177 isl_space_identity_multi_aff_on_domain(
3178 __isl_take isl_space *space);
3179 __isl_give isl_multi_pw_aff *
3180 isl_multi_pw_aff_identity_on_domain_space(
3181 __isl_take isl_space *space);
3182 __isl_give isl_multi_pw_aff *
3183 isl_space_identity_multi_pw_aff_on_domain(
3184 __isl_take isl_space *space);
3185 __isl_give isl_multi_aff *isl_multi_aff_identity(
3186 __isl_take isl_space *space);
3187 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3188 __isl_take isl_space *space);
3189 __isl_give isl_multi_aff *
3190 isl_multi_aff_identity_multi_aff(
3191 __isl_take isl_multi_aff *ma);
3192 __isl_give isl_multi_pw_aff *
3193 isl_multi_pw_aff_identity_multi_pw_aff(
3194 __isl_take isl_multi_pw_aff *mpa);
3196 C<isl_multi_aff_identity_on_domain_space> and
3197 C<isl_space_identity_multi_aff_on_domain>
3198 perform the same operation.
3200 for the pair C<isl_multi_pw_aff_identity_on_domain_space> and
3201 C<isl_space_identity_multi_pw_aff_on_domain>.
3203 A function that performs a projection on a universe
3204 relation or set can be created using the following functions.
3205 See also the corresponding
3206 projection operations in L</"Unary Operations">.
3208 #include <isl/aff.h>
3209 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
3210 __isl_take isl_space *space);
3211 __isl_give isl_multi_aff *isl_space_domain_map_multi_aff(
3212 __isl_take isl_space *space);
3213 __isl_give isl_multi_aff *isl_multi_aff_range_map(
3214 __isl_take isl_space *space);
3215 __isl_give isl_multi_aff *isl_space_range_map_multi_aff(
3216 __isl_take isl_space *space);
3217 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
3218 __isl_take isl_space *space,
3219 enum isl_dim_type type,
3220 unsigned first, unsigned n);
3222 C<isl_multi_aff_domain_map> and C<isl_space_domain_map_multi_aff> perform
3225 for the pair C<isl_multi_aff_range_map> and C<isl_space_range_map_multi_aff>.
3227 A multiple expression can be created from a single
3228 base expression using the following functions.
3229 The space of the created multiple expression is the same
3230 as that of the base expression, except for
3231 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
3232 lives in a parameter space and the output lives
3233 in a single-dimensional set space.
3235 #include <isl/aff.h>
3236 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3237 __isl_take isl_aff *aff);
3238 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3239 __isl_take isl_pw_aff *pa);
3240 __isl_give isl_multi_union_pw_aff *
3241 isl_multi_union_pw_aff_from_union_pw_aff(
3242 __isl_take isl_union_pw_aff *upa);
3244 A multiple expression can be created from a list
3245 of base expression in a specified space.
3246 The domain of this space needs to be the same
3247 as the domains of the base expressions in the list.
3248 If the base expressions have a set space (or no associated space),
3249 then this space also needs to be a set space.
3252 __isl_give isl_multi_id *isl_multi_id_from_id_list(
3253 __isl_take isl_space *space,
3254 __isl_take isl_id_list *list);
3255 __isl_give isl_multi_id *isl_space_multi_id(
3256 __isl_take isl_space *space,
3257 __isl_take isl_id_list *list);
3259 #include <isl/val.h>
3260 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3261 __isl_take isl_space *space,
3262 __isl_take isl_val_list *list);
3263 __isl_give isl_multi_val *isl_space_multi_val(
3264 __isl_take isl_space *space,
3265 __isl_take isl_val_list *list);
3267 #include <isl/aff.h>
3268 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3269 __isl_take isl_space *space,
3270 __isl_take isl_aff_list *list);
3271 __isl_give isl_multi_aff *isl_space_multi_aff(
3272 __isl_take isl_space *space,
3273 __isl_take isl_aff_list *list);
3274 __isl_give isl_multi_pw_aff *
3275 isl_multi_pw_aff_from_pw_aff_list(
3276 __isl_take isl_space *space,
3277 __isl_take isl_pw_aff_list *list);
3278 __isl_give isl_multi_pw_aff *
3279 isl_space_multi_pw_aff(
3280 __isl_take isl_space *space,
3281 __isl_take isl_pw_aff_list *list);
3282 __isl_give isl_multi_union_pw_aff *
3283 isl_multi_union_pw_aff_from_union_pw_aff_list(
3284 __isl_take isl_space *space,
3285 __isl_take isl_union_pw_aff_list *list);
3286 __isl_give isl_multi_union_pw_aff *
3287 isl_space_multi_union_pw_aff(
3288 __isl_take isl_space *space,
3289 __isl_take isl_union_pw_aff_list *list);
3291 C<isl_multi_id_from_id_list> and C<isl_space_multi_id> perform
3293 Similarly for the pair C<isl_multi_val_from_val_list> and
3294 C<isl_space_multi_val>,
3295 for the pair C<isl_multi_aff_from_aff_list> and
3296 C<isl_space_multi_aff>,
3297 for the pair C<isl_multi_pw_aff_from_pw_aff_list> and
3298 C<isl_space_multi_pw_aff> and
3299 for the pair C<isl_multi_union_pw_aff_from_union_pw_aff_list> and
3300 C<isl_space_multi_union_pw_aff>.
3302 As a convenience, a multiple piecewise expression can
3303 also be created from a multiple expression,
3304 or even directly from a single base expression.
3305 Each piecewise expression in the result has a single
3308 #include <isl/aff.h>
3309 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_aff(
3310 __isl_take isl_aff *aff);
3311 __isl_give isl_multi_pw_aff *
3312 isl_multi_aff_to_multi_pw_aff(
3313 __isl_take isl_multi_aff *ma);
3314 __isl_give isl_multi_pw_aff *
3315 isl_multi_pw_aff_from_multi_aff(
3316 __isl_take isl_multi_aff *ma);
3318 C<isl_multi_aff_to_multi_pw_aff> and
3319 C<isl_multi_pw_aff_from_multi_aff> perform the same operation.
3321 Similarly, a multiple union expression can be
3322 created from a multiple expression.
3324 #include <isl/aff.h>
3325 __isl_give isl_multi_union_pw_aff *
3326 isl_multi_union_pw_aff_from_multi_aff(
3327 __isl_take isl_multi_aff *ma);
3328 __isl_give isl_multi_union_pw_aff *
3329 isl_multi_aff_to_multi_union_pw_aff(
3330 __isl_take isl_multi_aff *ma);
3331 __isl_give isl_multi_union_pw_aff *
3332 isl_multi_union_pw_aff_from_multi_pw_aff(
3333 __isl_take isl_multi_pw_aff *mpa);
3335 C<isl_multi_aff_to_multi_union_pw_aff> and
3336 C<isl_multi_union_pw_aff_from_multi_aff> perform the same operation.
3338 A multiple quasi-affine expression can be created from
3339 a multiple value with a given domain space using the following
3342 #include <isl/aff.h>
3343 __isl_give isl_multi_aff *
3344 isl_multi_aff_multi_val_on_domain_space(
3345 __isl_take isl_space *space,
3346 __isl_take isl_multi_val *mv);
3347 __isl_give isl_multi_aff *
3348 isl_space_multi_aff_on_domain_multi_val(
3349 __isl_take isl_space *space,
3350 __isl_take isl_multi_val *mv);
3351 __isl_give isl_multi_aff *
3352 isl_multi_aff_multi_val_on_space(
3353 __isl_take isl_space *space,
3354 __isl_take isl_multi_val *mv);
3356 C<isl_space_multi_aff_on_domain_multi_val> and
3357 C<isl_multi_aff_multi_val_on_space> are alternative names
3358 for C<isl_multi_aff_multi_val_on_domain_space>.
3361 a multiple union piecewise affine expression can be created from
3362 a multiple value with a given domain or
3363 a (piecewise) multiple affine expression with a given domain
3364 using the following functions.
3366 #include <isl/aff.h>
3367 __isl_give isl_multi_union_pw_aff *
3368 isl_multi_union_pw_aff_multi_val_on_domain(
3369 __isl_take isl_union_set *domain,
3370 __isl_take isl_multi_val *mv);
3371 __isl_give isl_multi_union_pw_aff *
3372 isl_multi_union_pw_aff_multi_aff_on_domain(
3373 __isl_take isl_union_set *domain,
3374 __isl_take isl_multi_aff *ma);
3375 __isl_give isl_multi_union_pw_aff *
3376 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
3377 __isl_take isl_union_set *domain,
3378 __isl_take isl_pw_multi_aff *pma);
3380 Multiple expressions can be copied and freed using
3381 the following functions.
3384 __isl_give isl_multi_id *isl_multi_id_copy(
3385 __isl_keep isl_multi_id *mi);
3386 __isl_null isl_multi_id *isl_multi_id_free(
3387 __isl_take isl_multi_id *mi);
3389 #include <isl/val.h>
3390 __isl_give isl_multi_val *isl_multi_val_copy(
3391 __isl_keep isl_multi_val *mv);
3392 __isl_null isl_multi_val *isl_multi_val_free(
3393 __isl_take isl_multi_val *mv);
3395 #include <isl/aff.h>
3396 __isl_give isl_multi_aff *isl_multi_aff_copy(
3397 __isl_keep isl_multi_aff *maff);
3398 __isl_null isl_multi_aff *isl_multi_aff_free(
3399 __isl_take isl_multi_aff *maff);
3400 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3401 __isl_keep isl_multi_pw_aff *mpa);
3402 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
3403 __isl_take isl_multi_pw_aff *mpa);
3404 __isl_give isl_multi_union_pw_aff *
3405 isl_multi_union_pw_aff_copy(
3406 __isl_keep isl_multi_union_pw_aff *mupa);
3407 __isl_null isl_multi_union_pw_aff *
3408 isl_multi_union_pw_aff_free(
3409 __isl_take isl_multi_union_pw_aff *mupa);
3411 The number of base expressions in a multiple
3412 expression can be obtained using the following functions.
3415 int isl_multi_id_size(__isl_keep isl_multi_id *mi);
3417 #include <isl/val.h>
3418 isl_size isl_multi_val_size(__isl_keep isl_multi_val *mv);
3420 #include <isl/aff.h>
3421 isl_size isl_multi_aff_size(
3422 __isl_keep isl_multi_aff *multi);
3423 isl_size isl_multi_pw_aff_size(
3424 __isl_keep isl_multi_pw_aff *mpa);
3425 isl_size isl_multi_union_pw_aff_size(
3426 __isl_keep isl_multi_union_pw_aff *mupa);
3428 The base expression at a given position of a multiple
3429 expression can be extracted using the following functions.
3432 __isl_give isl_id *isl_multi_id_get_at(
3433 __isl_keep isl_multi_id *mi, int pos);
3434 __isl_give isl_id *isl_multi_id_get_id(
3435 __isl_keep isl_multi_id *mi, int pos);
3437 #include <isl/val.h>
3438 __isl_give isl_val *isl_multi_val_get_at(
3439 __isl_keep isl_multi_val *mv, int pos);
3440 __isl_give isl_val *isl_multi_val_get_val(
3441 __isl_keep isl_multi_val *mv, int pos);
3443 #include <isl/aff.h>
3444 __isl_give isl_aff *isl_multi_aff_get_at(
3445 __isl_keep isl_multi_aff *ma, int pos);
3446 __isl_give isl_aff *isl_multi_aff_get_aff(
3447 __isl_keep isl_multi_aff *multi, int pos);
3448 __isl_give isl_pw_aff *isl_multi_pw_aff_get_at(
3449 __isl_keep isl_multi_pw_aff *mpa, int pos);
3450 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3451 __isl_keep isl_multi_pw_aff *mpa, int pos);
3452 __isl_give isl_union_pw_aff *
3453 isl_multi_union_pw_aff_get_at(
3454 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3455 __isl_give isl_union_pw_aff *
3456 isl_multi_union_pw_aff_get_union_pw_aff(
3457 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3459 C<isl_multi_id_get_id> is an alternative name for C<isl_multi_id_get_at>.
3460 Similarly for the other pairs of functions.
3462 The base expression can be replaced using the following functions.
3465 __isl_give isl_multi_id *isl_multi_id_set_at(
3466 __isl_take isl_multi_id *mi, int pos,
3467 __isl_take isl_id *id);
3468 __isl_give isl_multi_id *isl_multi_id_set_id(
3469 __isl_take isl_multi_id *mi, int pos,
3470 __isl_take isl_id *id);
3472 #include <isl/val.h>
3473 __isl_give isl_multi_val *isl_multi_val_set_at(
3474 __isl_take isl_multi_val *mv, int pos,
3475 __isl_take isl_val *val);
3476 __isl_give isl_multi_val *isl_multi_val_set_val(
3477 __isl_take isl_multi_val *mv, int pos,
3478 __isl_take isl_val *val);
3480 #include <isl/aff.h>
3481 __isl_give isl_multi_aff *isl_multi_aff_set_at(
3482 __isl_take isl_multi_aff *ma, int pos,
3483 __isl_take isl_aff *aff);
3484 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3485 __isl_take isl_multi_aff *multi, int pos,
3486 __isl_take isl_aff *aff);
3487 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_at(
3488 __isl_take isl_multi_pw_aff *mpa, int pos,
3489 __isl_take isl_pw_aff *pa);
3490 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_pw_aff(
3491 __isl_take isl_multi_pw_aff *mpa, int pos,
3492 __isl_take isl_pw_aff *pa);
3493 __isl_give isl_multi_union_pw_aff *
3494 isl_multi_union_pw_aff_set_at(
3495 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3496 __isl_take isl_union_pw_aff *upa);
3497 __isl_give isl_multi_union_pw_aff *
3498 isl_multi_union_pw_aff_set_union_pw_aff(
3499 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3500 __isl_take isl_union_pw_aff *upa);
3502 C<isl_multi_id_set_id> is an alternative name for C<isl_multi_id_set_at>.
3503 Similarly for the other pairs of functions.
3505 A list of all base expressions of a multiple
3506 expression can be extracted using the following functions.
3509 __isl_give isl_id_list *isl_multi_id_get_list(
3510 __isl_keep isl_multi_id *mi);
3512 #include <isl/val.h>
3513 __isl_give isl_val_list *isl_multi_val_get_list(
3514 __isl_keep isl_multi_val *mv);
3516 #include <isl/aff.h>
3517 __isl_give isl_aff_list *isl_multi_aff_get_list(
3518 __isl_keep isl_multi_aff *multi);
3519 __isl_give isl_pw_aff_list *isl_multi_pw_aff_get_list(
3520 __isl_keep isl_multi_pw_aff *mpa);
3521 __isl_give isl_union_pw_aff_list *
3522 isl_multi_union_pw_aff_list(
3523 __isl_keep isl_multi_union_pw_aff *mupa);
3525 The constant terms of the base expressions can be obtained using
3526 the following function.
3528 #include <isl/aff.h>
3529 __isl_give isl_multi_val *
3530 isl_multi_aff_get_constant_multi_val(
3531 __isl_keep isl_multi_aff *ma);
3533 As a convenience, a sequence of base expressions that have
3534 their domains in a given space can be extracted from a sequence
3535 of union expressions using the following function.
3537 #include <isl/aff.h>
3538 __isl_give isl_multi_pw_aff *
3539 isl_multi_union_pw_aff_extract_multi_pw_aff(
3540 __isl_keep isl_multi_union_pw_aff *mupa,
3541 __isl_take isl_space *space);
3543 Note that there is a difference between C<isl_multi_union_pw_aff>
3544 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3545 of unions of piecewise expressions, while the second is a union
3546 of piecewise sequences. In particular, multiple affine expressions
3547 in an C<isl_union_pw_multi_aff> may live in different spaces,
3548 while there is only a single multiple expression in
3549 an C<isl_multi_union_pw_aff>, which can therefore only live
3550 in a single space. This means that not every
3551 C<isl_union_pw_multi_aff> can be converted to
3552 an C<isl_multi_union_pw_aff>. Conversely, the elements
3553 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3554 while each multiple expression inside an C<isl_union_pw_multi_aff>
3555 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3556 of dimension greater than one may therefore not be exact.
3557 The following functions can
3558 be used to perform these conversions when they are possible.
3560 #include <isl/aff.h>
3561 __isl_give isl_multi_union_pw_aff *
3562 isl_union_pw_multi_aff_as_multi_union_pw_aff(
3563 __isl_take isl_union_pw_multi_aff *upma);
3564 __isl_give isl_multi_union_pw_aff *
3565 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3566 __isl_take isl_union_pw_multi_aff *upma);
3567 __isl_give isl_union_pw_multi_aff *
3568 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3569 __isl_take isl_multi_union_pw_aff *mupa);
3571 C<isl_union_pw_multi_aff_as_multi_union_pw_aff> and
3572 C<isl_multi_union_pw_aff_from_union_pw_multi_aff>
3573 perform the same operation.
3575 =head3 Piecewise Expressions
3577 A piecewise expression is an expression that is described
3578 using zero or more base expression defined over the same
3579 number of cells in the domain space of the base expressions.
3580 All base expressions are defined over the same
3581 domain space and the cells are disjoint.
3582 The space of a piecewise expression is the same as
3583 that of the base expressions.
3584 If the union of the cells is a strict subset of the domain
3585 space, then the value of the piecewise expression outside
3586 this union is different for types derived from quasi-affine
3587 expressions and those derived from quasipolynomials.
3588 Piecewise expressions derived from quasi-affine expressions
3589 are considered to be undefined outside the union of their cells.
3590 Piecewise expressions derived from quasipolynomials
3591 are considered to be zero outside the union of their cells.
3593 Piecewise quasipolynomials are mainly used by the C<barvinok>
3594 library for representing the number of elements in a parametric set or map.
3595 For example, the piecewise quasipolynomial
3597 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3599 represents the number of points in the map
3601 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3603 The piecewise expression types defined by C<isl>
3604 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3605 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3607 A piecewise expression with no cells can be created using
3608 the following functions.
3610 #include <isl/aff.h>
3611 __isl_give isl_pw_aff *isl_pw_aff_empty(
3612 __isl_take isl_space *space);
3613 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3614 __isl_take isl_space *space);
3616 A piecewise expression with a single universe cell can be
3617 created using the following functions.
3619 #include <isl/aff.h>
3620 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3621 __isl_take isl_aff *aff);
3622 __isl_give isl_pw_multi_aff *
3623 isl_multi_aff_to_pw_multi_aff(
3624 __isl_take isl_multi_aff *ma);
3625 __isl_give isl_pw_multi_aff *
3626 isl_pw_multi_aff_from_multi_aff(
3627 __isl_take isl_multi_aff *ma);
3629 #include <isl/polynomial.h>
3630 __isl_give isl_pw_qpolynomial *
3631 isl_pw_qpolynomial_from_qpolynomial(
3632 __isl_take isl_qpolynomial *qp);
3633 __isl_give isl_pw_qpolynomial_fold *
3634 isl_pw_qpolynomial_fold_from_qpolynomial_fold(
3635 __isl_take isl_qpolynomial_fold *fold);
3637 C<isl_multi_aff_to_pw_multi_aff> and C<isl_pw_multi_aff_from_multi_aff> perform
3640 The inverse conversions below can only be used if the input
3641 expression is known to be defined over a single universe domain.
3643 #include <isl/aff.h>
3644 isl_bool isl_pw_aff_isa_aff(__isl_keep isl_pw_aff *pa);
3645 __isl_give isl_aff *isl_pw_aff_as_aff(
3646 __isl_take isl_pw_aff *pa);
3647 isl_bool isl_multi_pw_aff_isa_multi_aff(
3648 __isl_keep isl_multi_pw_aff *mpa);
3649 __isl_give isl_multi_aff *isl_multi_pw_aff_as_multi_aff(
3650 __isl_take isl_multi_pw_aff *mpa);
3651 isl_bool isl_pw_multi_aff_isa_multi_aff(
3652 __isl_keep isl_pw_multi_aff *pma);
3653 __isl_give isl_multi_aff *isl_pw_multi_aff_as_multi_aff(
3654 __isl_take isl_pw_multi_aff *pma);
3656 #include <isl/polynomial.h>
3657 isl_bool isl_pw_qpolynomial_isa_qpolynomial(
3658 __isl_keep isl_pw_qpolynomial *pwqp);
3659 __isl_give isl_qpolynomial *
3660 isl_pw_qpolynomial_as_qpolynomial(
3661 __isl_take isl_pw_qpolynomial *pwqp);
3662 isl_bool isl_pw_qpolynomial_fold_isa_qpolynomial_fold(
3663 __isl_keep isl_pw_qpolynomial_fold *pwf);
3664 __isl_give isl_qpolynomial_fold *
3665 isl_pw_qpolynomial_fold_as_qpolynomial_fold(
3666 __isl_take isl_pw_qpolynomial_fold *pwf);
3668 A piecewise expression with a single specified cell can be
3669 created using the following functions.
3671 #include <isl/aff.h>
3672 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3673 __isl_take isl_set *set, __isl_take isl_aff *aff);
3674 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3675 __isl_take isl_set *set,
3676 __isl_take isl_multi_aff *maff);
3678 #include <isl/polynomial.h>
3679 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3680 __isl_take isl_set *set,
3681 __isl_take isl_qpolynomial *qp);
3683 The following convenience functions first create a base expression and
3684 then create a piecewise expression over a universe domain.
3686 #include <isl/aff.h>
3687 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3688 __isl_take isl_local_space *ls);
3689 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3690 __isl_take isl_local_space *ls,
3691 enum isl_dim_type type, unsigned pos);
3692 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain_space(
3693 __isl_take isl_space *space);
3694 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3695 __isl_take isl_local_space *ls);
3696 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3697 __isl_take isl_space *space);
3698 __isl_give isl_pw_multi_aff *
3699 isl_pw_multi_aff_identity_on_domain_space(
3700 __isl_take isl_space *space)
3701 __isl_give isl_pw_multi_aff *
3702 isl_space_identity_pw_multi_aff_on_domain(
3703 __isl_take isl_space *space)
3704 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3705 __isl_take isl_space *space);
3706 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_domain_map(
3707 __isl_take isl_space *space);
3708 __isl_give isl_pw_multi_aff *
3709 isl_space_domain_map_pw_multi_aff(
3710 __isl_take isl_space *space);
3711 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3712 __isl_take isl_space *space);
3713 __isl_give isl_pw_multi_aff *
3714 isl_space_range_map_pw_multi_aff(
3715 __isl_take isl_space *space);
3716 __isl_give isl_pw_multi_aff *
3717 isl_pw_multi_aff_project_out_map(
3718 __isl_take isl_space *space,
3719 enum isl_dim_type type,
3720 unsigned first, unsigned n);
3722 #include <isl/polynomial.h>
3723 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3724 __isl_take isl_space *space);
3726 C<isl_pw_multi_aff_identity_on_domain_space> and
3727 C<isl_space_identity_pw_multi_aff_on_domain>
3728 perform the same operation.
3730 for the pair C<isl_pw_multi_aff_domain_map> and
3731 C<isl_space_domain_map_pw_multi_aff> and
3732 for the pair C<isl_pw_multi_aff_range_map> and
3733 C<isl_space_range_map_pw_multi_aff>.
3735 The following convenience functions first create a base expression and
3736 then create a piecewise expression over a given domain.
3738 #include <isl/aff.h>
3739 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3740 __isl_take isl_set *domain,
3741 __isl_take isl_val *v);
3742 __isl_give isl_pw_multi_aff *
3743 isl_pw_multi_aff_multi_val_on_domain(
3744 __isl_take isl_set *domain,
3745 __isl_take isl_multi_val *mv);
3746 __isl_give isl_pw_multi_aff *
3747 isl_set_pw_multi_aff_on_domain_multi_val(
3748 __isl_take isl_set *domain,
3749 __isl_take isl_multi_val *mv);
3750 __isl_give isl_pw_aff *isl_pw_aff_param_on_domain_id(
3751 __isl_take isl_set *domain,
3752 __isl_take isl_id *id);
3754 C<isl_set_pw_multi_aff_on_domain_multi_val> is an alternative name
3755 for C<isl_pw_multi_aff_multi_val_on_domain>.
3757 As a convenience, a piecewise multiple expression can
3758 also be created from a piecewise expression.
3759 Each multiple expression in the result is derived
3760 from the corresponding base expression.
3762 #include <isl/aff.h>
3763 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3764 __isl_take isl_pw_aff *pa);
3766 Similarly, a piecewise quasipolynomial can be
3767 created from a piecewise quasi-affine expression using
3768 the following function.
3770 #include <isl/polynomial.h>
3771 __isl_give isl_pw_qpolynomial *
3772 isl_pw_qpolynomial_from_pw_aff(
3773 __isl_take isl_pw_aff *pwaff);
3775 Piecewise expressions can be copied and freed using the following functions.
3777 #include <isl/aff.h>
3778 __isl_give isl_pw_aff *isl_pw_aff_copy(
3779 __isl_keep isl_pw_aff *pwaff);
3780 __isl_null isl_pw_aff *isl_pw_aff_free(
3781 __isl_take isl_pw_aff *pwaff);
3782 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3783 __isl_keep isl_pw_multi_aff *pma);
3784 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3785 __isl_take isl_pw_multi_aff *pma);
3787 #include <isl/polynomial.h>
3788 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3789 __isl_keep isl_pw_qpolynomial *pwqp);
3790 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3791 __isl_take isl_pw_qpolynomial *pwqp);
3792 __isl_give isl_pw_qpolynomial_fold *
3793 isl_pw_qpolynomial_fold_copy(
3794 __isl_keep isl_pw_qpolynomial_fold *pwf);
3795 __isl_null isl_pw_qpolynomial_fold *
3796 isl_pw_qpolynomial_fold_free(
3797 __isl_take isl_pw_qpolynomial_fold *pwf);
3799 To iterate over the different cells of a piecewise expression,
3800 use the following functions.
3802 #include <isl/aff.h>
3803 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3804 isl_size isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3805 isl_stat isl_pw_aff_foreach_piece(
3806 __isl_keep isl_pw_aff *pwaff,
3807 isl_stat (*fn)(__isl_take isl_set *set,
3808 __isl_take isl_aff *aff,
3809 void *user), void *user);
3810 isl_bool isl_pw_aff_every_piece(__isl_keep isl_pw_aff *pa,
3811 isl_bool (*test)(__isl_keep isl_set *set,
3812 __isl_keep isl_aff *aff, void *user),
3814 isl_size isl_pw_multi_aff_n_piece(
3815 __isl_keep isl_pw_multi_aff *pma);
3816 isl_stat isl_pw_multi_aff_foreach_piece(
3817 __isl_keep isl_pw_multi_aff *pma,
3818 isl_stat (*fn)(__isl_take isl_set *set,
3819 __isl_take isl_multi_aff *maff,
3820 void *user), void *user);
3821 isl_bool isl_pw_multi_aff_every_piece(
3822 __isl_keep isl_pw_multi_aff *pma,
3823 isl_bool (*test)(__isl_keep isl_set *set,
3824 __isl_keep isl_multi_aff *ma, void *user),
3827 #include <isl/polynomial.h>
3828 isl_size isl_pw_qpolynomial_n_piece(
3829 __isl_keep isl_pw_qpolynomial *pwqp);
3830 isl_stat isl_pw_qpolynomial_foreach_piece(
3831 __isl_keep isl_pw_qpolynomial *pwqp,
3832 isl_stat (*fn)(__isl_take isl_set *set,
3833 __isl_take isl_qpolynomial *qp,
3834 void *user), void *user);
3835 isl_bool isl_pw_qpolynomial_every_piece(
3836 __isl_keep isl_pw_qpolynomial *pwqp,
3837 isl_bool (*test)(__isl_keep isl_set *set,
3838 __isl_keep isl_qpolynomial *qp,
3839 void *user), void *user);
3840 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3841 __isl_keep isl_pw_qpolynomial *pwqp,
3842 isl_stat (*fn)(__isl_take isl_set *set,
3843 __isl_take isl_qpolynomial *qp,
3844 void *user), void *user);
3845 isl_size isl_pw_qpolynomial_fold_n_piece(
3846 __isl_keep isl_pw_qpolynomial_fold *pwf);
3847 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3848 __isl_keep isl_pw_qpolynomial_fold *pwf,
3849 isl_stat (*fn)(__isl_take isl_set *set,
3850 __isl_take isl_qpolynomial_fold *fold,
3851 void *user), void *user);
3852 isl_bool isl_pw_qpolynomial_fold_every_piece(
3853 __isl_keep isl_pw_qpolynomial_fold *pwf,
3854 isl_bool (*test)(__isl_keep isl_set *set,
3855 __isl_keep isl_qpolynomial_fold *fold,
3856 void *user), void *user);
3857 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3858 __isl_keep isl_pw_qpolynomial_fold *pwf,
3859 isl_stat (*fn)(__isl_take isl_set *set,
3860 __isl_take isl_qpolynomial_fold *fold,
3861 void *user), void *user);
3863 As usual, the function C<fn> should return C<isl_stat_ok> on success
3864 and C<isl_stat_error> on failure. The difference between
3865 C<isl_pw_qpolynomial_foreach_piece> and
3866 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3867 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3868 compute unique representations for all existentially quantified
3869 variables and then turn these existentially quantified variables
3870 into extra set variables, adapting the associated quasipolynomial
3871 accordingly. This means that the C<set> passed to C<fn>
3872 will not have any existentially quantified variables, but that
3873 the dimensions of the sets may be different for different
3874 invocations of C<fn>.
3875 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3876 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3877 The function C<isl_pw_aff_every_piece> and its variants
3878 check whether each call to the callback returns true and
3879 stop checking as soon as one of these calls returns false (or error).
3881 A piecewise expression consisting of the expressions at a given
3882 position of a piecewise multiple expression can be extracted
3883 using the following function.
3885 #include <isl/aff.h>
3886 __isl_give isl_pw_aff *isl_pw_multi_aff_get_at(
3887 __isl_keep isl_pw_multi_aff *pma, int pos);
3888 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3889 __isl_keep isl_pw_multi_aff *pma, int pos);
3891 C<isl_pw_multi_aff_get_pw_aff> is an alternative name for
3892 C<isl_pw_multi_aff_get_at>.
3894 These expressions can be replaced using the following function.
3896 #include <isl/aff.h>
3897 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3898 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3899 __isl_take isl_pw_aff *pa);
3901 Note that there is a difference between C<isl_multi_pw_aff> and
3902 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3903 affine expressions, while the second is a piecewise sequence
3904 of affine expressions. In particular, each of the piecewise
3905 affine expressions in an C<isl_multi_pw_aff> may have a different
3906 domain, while all multiple expressions associated to a cell
3907 in an C<isl_pw_multi_aff> have the same domain.
3908 It is possible to convert between the two, but when converting
3909 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3910 of the result is the intersection of the domains of the input.
3911 The reverse conversion is exact.
3913 #include <isl/aff.h>
3914 __isl_give isl_pw_multi_aff *
3915 isl_pw_multi_aff_from_multi_pw_aff(
3916 __isl_take isl_multi_pw_aff *mpa);
3917 __isl_give isl_multi_pw_aff *
3918 isl_pw_multi_aff_to_multi_pw_aff(
3919 __isl_take isl_pw_multi_aff *pma);
3920 __isl_give isl_multi_pw_aff *
3921 isl_multi_pw_aff_from_pw_multi_aff(
3922 __isl_take isl_pw_multi_aff *pma);
3924 C<isl_pw_multi_aff_to_multi_pw_aff> and
3925 C<isl_multi_pw_aff_from_pw_multi_aff> perform the same operation.
3927 =head3 Union Expressions
3929 A union expression collects base expressions defined
3930 over different domains. The space of a union expression
3931 is that of the shared parameter space.
3933 The union expression types defined by C<isl>
3934 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3935 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3937 C<isl_union_pw_aff>,
3938 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3939 there can be at most one base expression for a given domain space.
3941 C<isl_union_pw_multi_aff>,
3942 there can be multiple such expressions for a given domain space,
3943 but the domains of these expressions need to be disjoint.
3945 An empty union expression can be created using the following functions.
3947 #include <isl/aff.h>
3948 __isl_give isl_union_pw_aff *
3949 isl_union_pw_aff_empty_ctx(
3951 __isl_give isl_union_pw_aff *
3952 isl_union_pw_aff_empty_space(
3953 __isl_take isl_space *space);
3954 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3955 __isl_take isl_space *space);
3956 __isl_give isl_union_pw_multi_aff *
3957 isl_union_pw_multi_aff_empty_ctx(
3959 __isl_give isl_union_pw_multi_aff *
3960 isl_union_pw_multi_aff_empty_space(
3961 __isl_take isl_space *space);
3962 __isl_give isl_union_pw_multi_aff *
3963 isl_union_pw_multi_aff_empty(
3964 __isl_take isl_space *space);
3966 #include <isl/polynomial.h>
3967 __isl_give isl_union_pw_qpolynomial *
3968 isl_union_pw_qpolynomial_zero_ctx(
3970 __isl_give isl_union_pw_qpolynomial *
3971 isl_union_pw_qpolynomial_zero_space(
3972 __isl_take isl_space *space);
3973 __isl_give isl_union_pw_qpolynomial *
3974 isl_union_pw_qpolynomial_zero(
3975 __isl_take isl_space *space);
3977 C<isl_union_pw_aff_empty> is an alternative name for
3978 C<isl_union_pw_aff_empty_space>.
3979 Similarly for the other pairs of functions.
3981 A union expression containing a single base expression
3982 can be created using the following functions.
3984 #include <isl/aff.h>
3985 __isl_give isl_union_pw_aff *
3986 isl_pw_aff_to_union_pw_aff(
3987 __isl_take isl_pw_aff *pa);
3988 __isl_give isl_union_pw_aff *
3989 isl_union_pw_aff_from_pw_aff(
3990 __isl_take isl_pw_aff *pa);
3991 __isl_give isl_union_pw_multi_aff *
3992 isl_union_pw_multi_aff_from_aff(
3993 __isl_take isl_aff *aff);
3994 __isl_give isl_union_pw_multi_aff *
3995 isl_pw_multi_aff_to_union_pw_multi_aff(
3996 __isl_take isl_pw_multi_aff *pma);
3997 __isl_give isl_union_pw_multi_aff *
3998 isl_union_pw_multi_aff_from_pw_multi_aff(
3999 __isl_take isl_pw_multi_aff *pma);
4001 #include <isl/polynomial.h>
4002 __isl_give isl_union_pw_qpolynomial *
4003 isl_pw_qpolynomial_to_union_pw_qpolynomial(
4004 __isl_take isl_pw_qpolynomial *pwqp);
4005 __isl_give isl_union_pw_qpolynomial *
4006 isl_union_pw_qpolynomial_from_pw_qpolynomial(
4007 __isl_take isl_pw_qpolynomial *pwqp);
4008 __isl_give isl_union_pw_qpolynomial_fold *
4009 isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold(
4010 __isl_take isl_pw_qpolynomial_fold *pwf);
4011 __isl_give isl_union_pw_qpolynomial_fold *
4012 isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold(
4013 __isl_take isl_pw_qpolynomial_fold *pwf);
4015 C<isl_pw_aff_to_union_pw_aff> and C<isl_union_pw_aff_from_pw_aff> perform
4017 Similarly for C<isl_pw_multi_aff_to_union_pw_multi_aff> and
4018 C<isl_union_pw_multi_aff_from_pw_multi_aff>,
4020 C<isl_pw_qpolynomial_to_union_pw_qpolynomial> and
4021 C<isl_union_pw_qpolynomial_from_pw_qpolynomial>, and
4023 C<isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold> and
4024 C<isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold>.
4026 The inverse conversions below can only be used if the input
4027 expression is known to live in exactly one space.
4029 #include <isl/aff.h>
4030 isl_bool isl_union_pw_multi_aff_isa_pw_multi_aff(
4031 __isl_keep isl_union_pw_multi_aff *upma);
4032 __isl_give isl_pw_multi_aff *
4033 isl_union_pw_multi_aff_as_pw_multi_aff(
4034 __isl_take isl_union_pw_multi_aff *upma);
4036 A union piecewise expression containing a single base expression
4037 on a universe domain can also be created directly from
4038 a base expression using the following functions.
4040 #include <isl/aff.h>
4041 __isl_give isl_union_pw_aff *isl_union_pw_aff_from_aff(
4042 __isl_take isl_aff *aff);
4043 __isl_give isl_union_pw_multi_aff *
4044 isl_union_pw_multi_aff_from_multi_aff(
4045 __isl_take isl_multi_aff *ma);
4047 The following functions create a base expression on each
4048 of the sets in the union set and collect the results.
4050 #include <isl/aff.h>
4051 __isl_give isl_union_pw_multi_aff *
4052 isl_union_pw_multi_aff_from_union_pw_aff(
4053 __isl_take isl_union_pw_aff *upa);
4054 __isl_give isl_union_pw_aff *
4055 isl_union_pw_multi_aff_get_union_pw_aff(
4056 __isl_keep isl_union_pw_multi_aff *upma, int pos);
4057 __isl_give isl_union_pw_aff *
4058 isl_union_pw_aff_val_on_domain(
4059 __isl_take isl_union_set *domain,
4060 __isl_take isl_val *v);
4061 __isl_give isl_union_pw_multi_aff *
4062 isl_union_pw_multi_aff_multi_val_on_domain(
4063 __isl_take isl_union_set *domain,
4064 __isl_take isl_multi_val *mv);
4065 __isl_give isl_union_pw_aff *
4066 isl_union_pw_aff_param_on_domain_id(
4067 __isl_take isl_union_set *domain,
4068 __isl_take isl_id *id);
4070 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
4071 is the identifier of a parameter that may or may not already
4072 be present in C<domain>.
4074 An C<isl_union_pw_aff> that is equal to a (parametric) affine
4076 expression on a given domain can be created using the following
4079 #include <isl/aff.h>
4080 __isl_give isl_union_pw_aff *
4081 isl_union_pw_aff_aff_on_domain(
4082 __isl_take isl_union_set *domain,
4083 __isl_take isl_aff *aff);
4084 __isl_give isl_union_pw_aff *
4085 isl_union_pw_aff_pw_aff_on_domain(
4086 __isl_take isl_union_set *domain,
4087 __isl_take isl_pw_aff *pa);
4089 A base expression can be added to a union expression using
4090 the following functions.
4092 #include <isl/aff.h>
4093 __isl_give isl_union_pw_aff *
4094 isl_union_pw_aff_add_pw_aff(
4095 __isl_take isl_union_pw_aff *upa,
4096 __isl_take isl_pw_aff *pa);
4097 __isl_give isl_union_pw_multi_aff *
4098 isl_union_pw_multi_aff_add_pw_multi_aff(
4099 __isl_take isl_union_pw_multi_aff *upma,
4100 __isl_take isl_pw_multi_aff *pma);
4102 #include <isl/polynomial.h>
4103 __isl_give isl_union_pw_qpolynomial *
4104 isl_union_pw_qpolynomial_add_pw_qpolynomial(
4105 __isl_take isl_union_pw_qpolynomial *upwqp,
4106 __isl_take isl_pw_qpolynomial *pwqp);
4108 Union expressions can be copied and freed using
4109 the following functions.
4111 #include <isl/aff.h>
4112 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
4113 __isl_keep isl_union_pw_aff *upa);
4114 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
4115 __isl_take isl_union_pw_aff *upa);
4116 __isl_give isl_union_pw_multi_aff *
4117 isl_union_pw_multi_aff_copy(
4118 __isl_keep isl_union_pw_multi_aff *upma);
4119 __isl_null isl_union_pw_multi_aff *
4120 isl_union_pw_multi_aff_free(
4121 __isl_take isl_union_pw_multi_aff *upma);
4123 #include <isl/polynomial.h>
4124 __isl_give isl_union_pw_qpolynomial *
4125 isl_union_pw_qpolynomial_copy(
4126 __isl_keep isl_union_pw_qpolynomial *upwqp);
4127 __isl_null isl_union_pw_qpolynomial *
4128 isl_union_pw_qpolynomial_free(
4129 __isl_take isl_union_pw_qpolynomial *upwqp);
4130 __isl_give isl_union_pw_qpolynomial_fold *
4131 isl_union_pw_qpolynomial_fold_copy(
4132 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4133 __isl_null isl_union_pw_qpolynomial_fold *
4134 isl_union_pw_qpolynomial_fold_free(
4135 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4137 To iterate over the base expressions in a union expression,
4138 use the following functions.
4140 #include <isl/aff.h>
4141 isl_size isl_union_pw_aff_n_pw_aff(
4142 __isl_keep isl_union_pw_aff *upa);
4143 isl_stat isl_union_pw_aff_foreach_pw_aff(
4144 __isl_keep isl_union_pw_aff *upa,
4145 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
4146 void *user), void *user);
4147 isl_bool isl_union_pw_aff_every_pw_aff(
4148 __isl_keep isl_union_pw_aff *upa,
4149 isl_bool (*test)(__isl_keep isl_pw_aff *pa,
4150 void *user), void *user);
4151 isl_size isl_union_pw_multi_aff_n_pw_multi_aff(
4152 __isl_keep isl_union_pw_multi_aff *upma);
4153 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
4154 __isl_keep isl_union_pw_multi_aff *upma,
4155 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
4156 void *user), void *user);
4157 isl_bool isl_union_pw_multi_aff_every_pw_multi_aff(
4158 __isl_keep isl_union_pw_multi_aff *upma,
4160 __isl_keep isl_pw_multi_aff *pma,
4161 void *user), void *user);
4163 #include <isl/polynomial.h>
4164 isl_size isl_union_pw_qpolynomial_n_pw_qpolynomial(
4165 __isl_keep isl_union_pw_qpolynomial *upwqp);
4166 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4167 __isl_keep isl_union_pw_qpolynomial *upwqp,
4168 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
4169 void *user), void *user);
4170 isl_bool isl_union_pw_qpolynomial_every_pw_qpolynomial(
4171 __isl_keep isl_union_pw_qpolynomial *upwqp,
4173 __isl_keep isl_pw_qpolynomial *pwqp,
4174 void *user), void *user);
4175 isl_size isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
4176 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4177 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4178 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4179 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4180 void *user), void *user);
4182 isl_union_pw_qpolynomial_fold_every_pw_qpolynomial_fold(
4183 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4185 __isl_keep isl_pw_qpolynomial_fold *pwf,
4186 void *user), void *user);
4188 To extract the base expression in a given space from a union, use
4189 the following functions.
4191 #include <isl/aff.h>
4192 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
4193 __isl_keep isl_union_pw_aff *upa,
4194 __isl_take isl_space *space);
4195 __isl_give isl_pw_multi_aff *
4196 isl_union_pw_multi_aff_extract_pw_multi_aff(
4197 __isl_keep isl_union_pw_multi_aff *upma,
4198 __isl_take isl_space *space);
4200 #include <isl/polynomial.h>
4201 __isl_give isl_pw_qpolynomial *
4202 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4203 __isl_keep isl_union_pw_qpolynomial *upwqp,
4204 __isl_take isl_space *space);
4206 It is also possible to obtain a list of the base expressions using
4207 the following functions.
4209 #include <isl/aff.h>
4210 __isl_give isl_pw_aff_list *
4211 isl_union_pw_aff_get_pw_aff_list(
4212 __isl_keep isl_union_pw_aff *upa);
4213 __isl_give isl_pw_multi_aff_list *
4214 isl_union_pw_multi_aff_get_pw_multi_aff_list(
4215 __isl_keep isl_union_pw_multi_aff *upma);
4217 #include <isl/polynomial.h>
4218 __isl_give isl_pw_qpolynomial_list *
4219 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
4220 __isl_keep isl_union_pw_qpolynomial *upwqp);
4221 __isl_give isl_pw_qpolynomial_fold_list *
4222 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
4223 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4225 The returned list can be manipulated using the functions in L<"Lists">.
4227 =head2 Input and Output
4229 For set and relation,
4230 C<isl> supports its own input/output format, which is similar
4231 to the C<Omega> format, but also supports the C<PolyLib> format
4233 For other object types, typically only an C<isl> format is supported.
4235 =head3 C<isl> format
4237 The C<isl> format is similar to that of C<Omega>, but has a different
4238 syntax for describing the parameters and allows for the definition
4239 of an existentially quantified variable as the integer division
4240 of an affine expression.
4241 For example, the set of integers C<i> between C<0> and C<n>
4242 such that C<i % 10 <= 6> can be described as
4244 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
4247 A set or relation can have several disjuncts, separated
4248 by the keyword C<or>. Each disjunct is either a conjunction
4249 of constraints or a projection (C<exists>) of a conjunction
4250 of constraints. The constraints are separated by the keyword
4253 =head3 C<PolyLib> format
4255 If the represented set is a union, then the first line
4256 contains a single number representing the number of disjuncts.
4257 Otherwise, a line containing the number C<1> is optional.
4259 Each disjunct is represented by a matrix of constraints.
4260 The first line contains two numbers representing
4261 the number of rows and columns,
4262 where the number of rows is equal to the number of constraints
4263 and the number of columns is equal to two plus the number of variables.
4264 The following lines contain the actual rows of the constraint matrix.
4265 In each row, the first column indicates whether the constraint
4266 is an equality (C<0>) or inequality (C<1>). The final column
4267 corresponds to the constant term.
4269 If the set is parametric, then the coefficients of the parameters
4270 appear in the last columns before the constant column.
4271 The coefficients of any existentially quantified variables appear
4272 between those of the set variables and those of the parameters.
4274 =head3 Extended C<PolyLib> format
4276 The extended C<PolyLib> format is nearly identical to the
4277 C<PolyLib> format. The only difference is that the line
4278 containing the number of rows and columns of a constraint matrix
4279 also contains four additional numbers:
4280 the number of output dimensions, the number of input dimensions,
4281 the number of local dimensions (i.e., the number of existentially
4282 quantified variables) and the number of parameters.
4283 For sets, the number of ``output'' dimensions is equal
4284 to the number of set dimensions, while the number of ``input''
4289 Objects can be read from input using the following functions.
4292 __isl_give isl_id *isl_id_read_from_str(isl_ctx *ctx,
4294 __isl_give isl_multi_id *isl_multi_id_read_from_str(
4295 isl_ctx *ctx, const char *str);
4297 #include <isl/val.h>
4298 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
4300 __isl_give isl_multi_val *isl_multi_val_read_from_str(
4301 isl_ctx *ctx, const char *str);
4303 #include <isl/set.h>
4304 __isl_give isl_basic_set *isl_basic_set_read_from_file(
4305 isl_ctx *ctx, FILE *input);
4306 __isl_give isl_basic_set *isl_basic_set_read_from_str(
4307 isl_ctx *ctx, const char *str);
4308 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
4310 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
4313 #include <isl/map.h>
4314 __isl_give isl_basic_map *isl_basic_map_read_from_file(
4315 isl_ctx *ctx, FILE *input);
4316 __isl_give isl_basic_map *isl_basic_map_read_from_str(
4317 isl_ctx *ctx, const char *str);
4318 __isl_give isl_map *isl_map_read_from_file(
4319 isl_ctx *ctx, FILE *input);
4320 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
4323 #include <isl/union_set.h>
4324 __isl_give isl_union_set *isl_union_set_read_from_file(
4325 isl_ctx *ctx, FILE *input);
4326 __isl_give isl_union_set *isl_union_set_read_from_str(
4327 isl_ctx *ctx, const char *str);
4329 #include <isl/union_map.h>
4330 __isl_give isl_union_map *isl_union_map_read_from_file(
4331 isl_ctx *ctx, FILE *input);
4332 __isl_give isl_union_map *isl_union_map_read_from_str(
4333 isl_ctx *ctx, const char *str);
4335 #include <isl/aff.h>
4336 __isl_give isl_aff *isl_aff_read_from_str(
4337 isl_ctx *ctx, const char *str);
4338 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4339 isl_ctx *ctx, const char *str);
4340 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4341 isl_ctx *ctx, const char *str);
4342 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4343 isl_ctx *ctx, const char *str);
4344 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4345 isl_ctx *ctx, const char *str);
4346 __isl_give isl_union_pw_aff *
4347 isl_union_pw_aff_read_from_str(
4348 isl_ctx *ctx, const char *str);
4349 __isl_give isl_union_pw_multi_aff *
4350 isl_union_pw_multi_aff_read_from_str(
4351 isl_ctx *ctx, const char *str);
4352 __isl_give isl_multi_union_pw_aff *
4353 isl_multi_union_pw_aff_read_from_str(
4354 isl_ctx *ctx, const char *str);
4356 #include <isl/polynomial.h>
4357 __isl_give isl_union_pw_qpolynomial *
4358 isl_union_pw_qpolynomial_read_from_str(
4359 isl_ctx *ctx, const char *str);
4361 __isl_give isl_pw_qpolynomial_fold *
4362 isl_pw_qpolynomial_fold_read_from_str(
4363 isl_ctx *ctx, const char *str);
4365 For sets and relations,
4366 the input format is autodetected and may be either the C<PolyLib> format
4367 or the C<isl> format.
4371 Before anything can be printed, an C<isl_printer> needs to
4374 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
4376 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
4377 __isl_null isl_printer *isl_printer_free(
4378 __isl_take isl_printer *printer);
4380 C<isl_printer_to_file> prints to the given file, while
4381 C<isl_printer_to_str> prints to a string that can be extracted
4382 using the following function.
4384 #include <isl/printer.h>
4385 __isl_give char *isl_printer_get_str(
4386 __isl_keep isl_printer *printer);
4388 The printer can be inspected using the following functions.
4390 FILE *isl_printer_get_file(
4391 __isl_keep isl_printer *printer);
4392 int isl_printer_get_output_format(
4393 __isl_keep isl_printer *p);
4394 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
4396 The behavior of the printer can be modified in various ways
4398 __isl_give isl_printer *isl_printer_set_output_format(
4399 __isl_take isl_printer *p, int output_format);
4400 __isl_give isl_printer *isl_printer_set_indent(
4401 __isl_take isl_printer *p, int indent);
4402 __isl_give isl_printer *isl_printer_set_indent_prefix(
4403 __isl_take isl_printer *p, const char *prefix);
4404 __isl_give isl_printer *isl_printer_indent(
4405 __isl_take isl_printer *p, int indent);
4406 __isl_give isl_printer *isl_printer_set_prefix(
4407 __isl_take isl_printer *p, const char *prefix);
4408 __isl_give isl_printer *isl_printer_set_suffix(
4409 __isl_take isl_printer *p, const char *suffix);
4410 __isl_give isl_printer *isl_printer_set_yaml_style(
4411 __isl_take isl_printer *p, int yaml_style);
4413 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
4414 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
4415 and defaults to C<ISL_FORMAT_ISL>.
4416 Each line in the output is prefixed by C<indent_prefix>,
4417 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
4418 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
4419 In the C<PolyLib> format output,
4420 the coefficients of the existentially quantified variables
4421 appear between those of the set variables and those
4423 The function C<isl_printer_indent> increases the indentation
4424 by the specified amount (which may be negative).
4425 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
4426 C<ISL_YAML_STYLE_FLOW> and when we are printing something
4429 To actually print something, use
4431 #include <isl/printer.h>
4432 __isl_give isl_printer *isl_printer_print_double(
4433 __isl_take isl_printer *p, double d);
4435 #include <isl/val.h>
4436 __isl_give isl_printer *isl_printer_print_val(
4437 __isl_take isl_printer *p, __isl_keep isl_val *v);
4439 #include <isl/set.h>
4440 __isl_give isl_printer *isl_printer_print_basic_set(
4441 __isl_take isl_printer *printer,
4442 __isl_keep isl_basic_set *bset);
4443 __isl_give isl_printer *isl_printer_print_set(
4444 __isl_take isl_printer *printer,
4445 __isl_keep isl_set *set);
4447 #include <isl/map.h>
4448 __isl_give isl_printer *isl_printer_print_basic_map(
4449 __isl_take isl_printer *printer,
4450 __isl_keep isl_basic_map *bmap);
4451 __isl_give isl_printer *isl_printer_print_map(
4452 __isl_take isl_printer *printer,
4453 __isl_keep isl_map *map);
4455 #include <isl/union_set.h>
4456 __isl_give isl_printer *isl_printer_print_union_set(
4457 __isl_take isl_printer *p,
4458 __isl_keep isl_union_set *uset);
4460 #include <isl/union_map.h>
4461 __isl_give isl_printer *isl_printer_print_union_map(
4462 __isl_take isl_printer *p,
4463 __isl_keep isl_union_map *umap);
4465 #include <isl/val.h>
4466 __isl_give isl_printer *isl_printer_print_multi_val(
4467 __isl_take isl_printer *p,
4468 __isl_keep isl_multi_val *mv);
4471 __isl_give isl_printer *isl_printer_print_multi_id(
4472 __isl_take isl_printer *p,
4473 __isl_keep isl_multi_id *mi);
4475 #include <isl/aff.h>
4476 __isl_give isl_printer *isl_printer_print_aff(
4477 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4478 __isl_give isl_printer *isl_printer_print_multi_aff(
4479 __isl_take isl_printer *p,
4480 __isl_keep isl_multi_aff *maff);
4481 __isl_give isl_printer *isl_printer_print_pw_aff(
4482 __isl_take isl_printer *p,
4483 __isl_keep isl_pw_aff *pwaff);
4484 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4485 __isl_take isl_printer *p,
4486 __isl_keep isl_pw_multi_aff *pma);
4487 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4488 __isl_take isl_printer *p,
4489 __isl_keep isl_multi_pw_aff *mpa);
4490 __isl_give isl_printer *isl_printer_print_union_pw_aff(
4491 __isl_take isl_printer *p,
4492 __isl_keep isl_union_pw_aff *upa);
4493 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4494 __isl_take isl_printer *p,
4495 __isl_keep isl_union_pw_multi_aff *upma);
4496 __isl_give isl_printer *
4497 isl_printer_print_multi_union_pw_aff(
4498 __isl_take isl_printer *p,
4499 __isl_keep isl_multi_union_pw_aff *mupa);
4501 #include <isl/polynomial.h>
4502 __isl_give isl_printer *isl_printer_print_qpolynomial(
4503 __isl_take isl_printer *p,
4504 __isl_keep isl_qpolynomial *qp);
4505 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4506 __isl_take isl_printer *p,
4507 __isl_keep isl_pw_qpolynomial *pwqp);
4508 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4509 __isl_take isl_printer *p,
4510 __isl_keep isl_union_pw_qpolynomial *upwqp);
4512 __isl_give isl_printer *
4513 isl_printer_print_pw_qpolynomial_fold(
4514 __isl_take isl_printer *p,
4515 __isl_keep isl_pw_qpolynomial_fold *pwf);
4516 __isl_give isl_printer *
4517 isl_printer_print_union_pw_qpolynomial_fold(
4518 __isl_take isl_printer *p,
4519 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4521 For C<isl_printer_print_qpolynomial>,
4522 C<isl_printer_print_pw_qpolynomial> and
4523 C<isl_printer_print_pw_qpolynomial_fold>,
4524 the output format of the printer
4525 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4526 For C<isl_printer_print_union_pw_qpolynomial> and
4527 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
4529 In case of printing in C<ISL_FORMAT_C>, the user may want
4530 to set the names of all dimensions first.
4532 C<isl> also provides limited support for printing YAML documents,
4533 just enough for the internal use for printing such documents.
4535 #include <isl/printer.h>
4536 __isl_give isl_printer *isl_printer_yaml_start_mapping(
4537 __isl_take isl_printer *p);
4538 __isl_give isl_printer *isl_printer_yaml_end_mapping(
4539 __isl_take isl_printer *p);
4540 __isl_give isl_printer *isl_printer_yaml_start_sequence(
4541 __isl_take isl_printer *p);
4542 __isl_give isl_printer *isl_printer_yaml_end_sequence(
4543 __isl_take isl_printer *p);
4544 __isl_give isl_printer *isl_printer_yaml_next(
4545 __isl_take isl_printer *p);
4547 A document is started by a call to either
4548 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4549 Anything printed to the printer after such a call belong to the
4550 first key of the mapping or the first element in the sequence.
4551 The function C<isl_printer_yaml_next> moves to the value if
4552 we are currently printing a mapping key, the next key if we
4553 are printing a value or the next element if we are printing
4554 an element in a sequence.
4555 Nested mappings and sequences are initiated by the same
4556 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4557 Each call to these functions needs to have a corresponding call to
4558 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
4560 When called on a file printer, the following function flushes
4561 the file. When called on a string printer, the buffer is cleared.
4563 __isl_give isl_printer *isl_printer_flush(
4564 __isl_take isl_printer *p);
4566 The following functions allow the user to attach
4567 notes to a printer in order to keep track of additional state.
4569 #include <isl/printer.h>
4570 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
4571 __isl_keep isl_id *id);
4572 __isl_give isl_id *isl_printer_get_note(
4573 __isl_keep isl_printer *p, __isl_take isl_id *id);
4574 __isl_give isl_printer *isl_printer_set_note(
4575 __isl_take isl_printer *p,
4576 __isl_take isl_id *id, __isl_take isl_id *note);
4578 C<isl_printer_set_note> associates the given note to the given
4579 identifier in the printer.
4580 C<isl_printer_get_note> retrieves a note associated to an
4582 C<isl_printer_has_note> checks if there is such a note.
4583 C<isl_printer_get_note> fails if the requested note does not exist.
4585 Alternatively, a string representation can be obtained
4586 directly using the following functions, which always print
4590 __isl_give char *isl_id_to_str(
4591 __isl_keep isl_id *id);
4592 __isl_give char *isl_multi_id_to_str(
4593 __isl_keep isl_multi_id *mi);
4595 #include <isl/space.h>
4596 __isl_give char *isl_space_to_str(
4597 __isl_keep isl_space *space);
4599 #include <isl/val.h>
4600 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
4601 __isl_give char *isl_multi_val_to_str(
4602 __isl_keep isl_multi_val *mv);
4604 #include <isl/set.h>
4605 __isl_give char *isl_basic_set_to_str(
4606 __isl_keep isl_basic_set *bset);
4607 __isl_give char *isl_set_to_str(
4608 __isl_keep isl_set *set);
4610 #include <isl/union_set.h>
4611 __isl_give char *isl_union_set_to_str(
4612 __isl_keep isl_union_set *uset);
4614 #include <isl/map.h>
4615 __isl_give char *isl_basic_map_to_str(
4616 __isl_keep isl_basic_map *bmap);
4617 __isl_give char *isl_map_to_str(
4618 __isl_keep isl_map *map);
4620 #include <isl/union_map.h>
4621 __isl_give char *isl_union_map_to_str(
4622 __isl_keep isl_union_map *umap);
4624 #include <isl/aff.h>
4625 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
4626 __isl_give char *isl_pw_aff_to_str(
4627 __isl_keep isl_pw_aff *pa);
4628 __isl_give char *isl_multi_aff_to_str(
4629 __isl_keep isl_multi_aff *ma);
4630 __isl_give char *isl_pw_multi_aff_to_str(
4631 __isl_keep isl_pw_multi_aff *pma);
4632 __isl_give char *isl_multi_pw_aff_to_str(
4633 __isl_keep isl_multi_pw_aff *mpa);
4634 __isl_give char *isl_union_pw_aff_to_str(
4635 __isl_keep isl_union_pw_aff *upa);
4636 __isl_give char *isl_union_pw_multi_aff_to_str(
4637 __isl_keep isl_union_pw_multi_aff *upma);
4638 __isl_give char *isl_multi_union_pw_aff_to_str(
4639 __isl_keep isl_multi_union_pw_aff *mupa);
4641 #include <isl/point.h>
4642 __isl_give char *isl_point_to_str(
4643 __isl_keep isl_point *pnt);
4645 #include <isl/polynomial.h>
4646 __isl_give char *isl_pw_qpolynomial_to_str(
4647 __isl_keep isl_pw_qpolynomial *pwqp);
4648 __isl_give char *isl_union_pw_qpolynomial_to_str(
4649 __isl_keep isl_union_pw_qpolynomial *upwqp);
4653 =head3 Unary Properties
4659 The following functions test whether the given set or relation
4660 contains any integer points. The ``plain'' variants do not perform
4661 any computations, but simply check if the given set or relation
4662 is already known to be empty.
4664 #include <isl/set.h>
4665 isl_bool isl_basic_set_plain_is_empty(
4666 __isl_keep isl_basic_set *bset);
4667 isl_bool isl_basic_set_is_empty(
4668 __isl_keep isl_basic_set *bset);
4669 isl_bool isl_set_plain_is_empty(
4670 __isl_keep isl_set *set);
4671 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
4673 #include <isl/union_set.h>
4674 isl_bool isl_union_set_is_empty(
4675 __isl_keep isl_union_set *uset);
4677 #include <isl/map.h>
4678 isl_bool isl_basic_map_plain_is_empty(
4679 __isl_keep isl_basic_map *bmap);
4680 isl_bool isl_basic_map_is_empty(
4681 __isl_keep isl_basic_map *bmap);
4682 isl_bool isl_map_plain_is_empty(
4683 __isl_keep isl_map *map);
4684 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
4686 #include <isl/union_map.h>
4687 isl_bool isl_union_map_plain_is_empty(
4688 __isl_keep isl_union_map *umap);
4689 isl_bool isl_union_map_is_empty(
4690 __isl_keep isl_union_map *umap);
4692 #include <isl/aff.h>
4693 isl_bool isl_union_pw_multi_aff_plain_is_empty(
4694 __isl_keep isl_union_pw_multi_aff *upma);
4696 =item * Universality
4698 isl_bool isl_basic_set_plain_is_universe(
4699 __isl_keep isl_basic_set *bset);
4700 isl_bool isl_basic_set_is_universe(
4701 __isl_keep isl_basic_set *bset);
4702 isl_bool isl_basic_map_plain_is_universe(
4703 __isl_keep isl_basic_map *bmap);
4704 isl_bool isl_basic_map_is_universe(
4705 __isl_keep isl_basic_map *bmap);
4706 isl_bool isl_set_plain_is_universe(
4707 __isl_keep isl_set *set);
4708 isl_bool isl_map_plain_is_universe(
4709 __isl_keep isl_map *map);
4711 =item * Single-valuedness
4713 #include <isl/set.h>
4714 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
4716 #include <isl/map.h>
4717 isl_bool isl_basic_map_is_single_valued(
4718 __isl_keep isl_basic_map *bmap);
4719 isl_bool isl_map_plain_is_single_valued(
4720 __isl_keep isl_map *map);
4721 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
4723 #include <isl/union_map.h>
4724 isl_bool isl_union_map_is_single_valued(
4725 __isl_keep isl_union_map *umap);
4729 isl_bool isl_map_plain_is_injective(
4730 __isl_keep isl_map *map);
4731 isl_bool isl_map_is_injective(
4732 __isl_keep isl_map *map);
4733 isl_bool isl_union_map_plain_is_injective(
4734 __isl_keep isl_union_map *umap);
4735 isl_bool isl_union_map_is_injective(
4736 __isl_keep isl_union_map *umap);
4740 isl_bool isl_map_is_bijective(
4741 __isl_keep isl_map *map);
4742 isl_bool isl_union_map_is_bijective(
4743 __isl_keep isl_union_map *umap);
4747 The following functions test whether the given relation
4748 only maps elements to themselves.
4750 #include <isl/map.h>
4751 isl_bool isl_map_is_identity(
4752 __isl_keep isl_map *map);
4754 #include <isl/union_map.h>
4755 isl_bool isl_union_map_is_identity(
4756 __isl_keep isl_union_map *umap);
4760 __isl_give isl_val *
4761 isl_basic_map_plain_get_val_if_fixed(
4762 __isl_keep isl_basic_map *bmap,
4763 enum isl_dim_type type, unsigned pos);
4764 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4765 __isl_keep isl_set *set,
4766 enum isl_dim_type type, unsigned pos);
4767 __isl_give isl_multi_val *
4768 isl_set_get_plain_multi_val_if_fixed(
4769 __isl_keep isl_set *set);
4770 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4771 __isl_keep isl_map *map,
4772 enum isl_dim_type type, unsigned pos);
4774 If the set or relation obviously lies on a hyperplane where the given dimension
4775 has a fixed value, then return that value.
4776 Otherwise return NaN.
4777 C<isl_set_get_plain_multi_val_if_fixed> collects the results over
4782 Stride detection is based on heuristics.
4783 The strides returned by the functions below are always valid,
4784 but there may be larger valid strides that are not detected.
4786 isl_stat isl_set_dim_residue_class_val(
4787 __isl_keep isl_set *set,
4788 int pos, __isl_give isl_val **modulo,
4789 __isl_give isl_val **residue);
4791 Check if the values of the given set dimension are equal to a fixed
4792 value modulo some integer value. If so, assign the modulo to C<*modulo>
4793 and the fixed value to C<*residue>. If the given dimension attains only
4794 a single value, then assign C<0> to C<*modulo> and the fixed value to
4796 If the dimension does not attain only a single value and if no modulo
4797 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4799 #include <isl/set.h>
4800 __isl_give isl_stride_info *isl_set_get_stride_info(
4801 __isl_keep isl_set *set, int pos);
4802 __isl_give isl_val *isl_set_get_stride(
4803 __isl_keep isl_set *set, int pos);
4805 #include <isl/map.h>
4806 __isl_give isl_stride_info *
4807 isl_map_get_range_stride_info(
4808 __isl_keep isl_map *map, int pos);
4809 __isl_give isl_fixed_box *
4810 isl_map_get_range_lattice_tile(
4811 __isl_keep isl_map *map);
4813 Check if the values of the given set dimension are equal to
4814 some affine expression of the other dimensions (the offset)
4815 modulo some integer stride or
4816 check if the values of the given output dimensions are equal to
4817 some affine expression of the input dimensions (the offset)
4818 modulo some integer stride.
4819 If no more specific information can be found, then the stride
4820 is taken to be one and the offset is taken to be the zero expression.
4821 The function C<isl_set_get_stride> performs the same
4822 computation as C<isl_set_get_stride_info> but only returns the stride.
4823 The function C<isl_map_get_range_lattice_tile> collects the stride
4824 information over all output dimensions.
4825 In particular, it returns a tile of a rectangular lattice
4826 (possibly of size 1 in all directions)
4827 containing the output in terms of the parameters and the input dimensions.
4828 The size and the offset of this tile correspond to
4829 the strides and the offsets of the stride information and
4830 can be extracted from the returned
4831 C<isl_fixed_box> using the functions described under "Box hull" in
4832 L</"Unary Operations">. Note that the C<isl_fixed_box> object returned by
4833 C<isl_map_get_range_lattice_tile> is always valid.
4834 For the other functions,
4835 the stride and offset can be extracted from the returned object
4836 using the following functions.
4838 #include <isl/stride_info.h>
4839 __isl_give isl_val *isl_stride_info_get_stride(
4840 __isl_keep isl_stride_info *si);
4841 __isl_give isl_aff *isl_stride_info_get_offset(
4842 __isl_keep isl_stride_info *si);
4844 The stride info object can be copied and released using the following
4847 #include <isl/stride_info.h>
4848 __isl_give isl_stride_info *isl_stride_info_copy(
4849 __isl_keep isl_stride_info *si);
4850 __isl_null isl_stride_info *isl_stride_info_free(
4851 __isl_take isl_stride_info *si);
4855 To check whether a function involves any local variables,
4856 i.e., integer divisions,
4857 the following functions can be used.
4859 #include <isl/set.h>
4860 isl_bool isl_set_involves_locals(
4861 __isl_keep isl_set *set);
4863 #include <isl/aff.h>
4864 isl_bool isl_aff_involves_locals(
4865 __isl_keep isl_aff *aff);
4866 isl_bool isl_multi_aff_involves_locals(
4867 __isl_keep isl_multi_aff *ma);
4868 isl_bool isl_pw_multi_aff_involves_locals(
4869 __isl_keep isl_pw_multi_aff *pma);
4870 isl_bool isl_union_pw_multi_aff_involves_locals(
4871 __isl_keep isl_union_pw_multi_aff *upma);
4873 To check whether the description of a set, relation or function depends
4874 on a parameter or one or more given dimensions,
4875 the following functions can be used.
4877 #include <isl/constraint.h>
4878 isl_bool isl_constraint_involves_dims(
4879 __isl_keep isl_constraint *constraint,
4880 enum isl_dim_type type, unsigned first, unsigned n);
4882 #include <isl/set.h>
4883 isl_bool isl_basic_set_involves_dims(
4884 __isl_keep isl_basic_set *bset,
4885 enum isl_dim_type type, unsigned first, unsigned n);
4886 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4887 enum isl_dim_type type, unsigned first, unsigned n);
4889 #include <isl/map.h>
4890 isl_bool isl_basic_map_involves_dims(
4891 __isl_keep isl_basic_map *bmap,
4892 enum isl_dim_type type, unsigned first, unsigned n);
4893 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4894 enum isl_dim_type type, unsigned first, unsigned n);
4896 #include <isl/union_map.h>
4897 isl_bool isl_union_map_involves_dims(
4898 __isl_keep isl_union_map *umap,
4899 enum isl_dim_type type, unsigned first, unsigned n);
4901 #include <isl/aff.h>
4902 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4903 enum isl_dim_type type, unsigned first, unsigned n);
4904 isl_bool isl_pw_aff_involves_param_id(
4905 __isl_keep isl_pw_aff *pa,
4906 __isl_keep isl_id *id);
4907 isl_bool isl_pw_aff_involves_dims(
4908 __isl_keep isl_pw_aff *pwaff,
4909 enum isl_dim_type type, unsigned first, unsigned n);
4910 isl_bool isl_multi_aff_involves_dims(
4911 __isl_keep isl_multi_aff *ma,
4912 enum isl_dim_type type, unsigned first, unsigned n);
4913 isl_bool isl_pw_multi_aff_involves_param_id(
4914 __isl_keep isl_pw_multi_aff *pma,
4915 __isl_keep isl_id *id);
4916 isl_bool isl_pw_multi_aff_involves_dims(
4917 __isl_keep isl_pw_multi_aff *pma,
4918 enum isl_dim_type type, unsigned first, unsigned n);
4919 isl_bool isl_multi_pw_aff_involves_dims(
4920 __isl_keep isl_multi_pw_aff *mpa,
4921 enum isl_dim_type type, unsigned first, unsigned n);
4922 isl_bool isl_multi_pw_aff_involves_param_id(
4923 __isl_keep isl_multi_pw_aff *mpa,
4924 __isl_keep isl_id *id);
4925 isl_bool isl_multi_pw_aff_involves_param_id_list(
4926 __isl_keep isl_multi_pw_aff *mpa,
4927 __isl_keep isl_id_list *list);
4929 #include <isl/polynomial.h>
4930 isl_bool isl_qpolynomial_involves_dims(
4931 __isl_keep isl_qpolynomial *qp,
4932 enum isl_dim_type type, unsigned first, unsigned n);
4933 isl_bool isl_pw_qpolynomial_involves_param_id(
4934 __isl_keep isl_pw_qpolynomial *pwqp,
4935 __isl_keep isl_id *id);
4936 isl_bool isl_pw_qpolynomial_fold_involves_param_id(
4937 __isl_keep isl_pw_qpolynomial_fold *pwf,
4938 __isl_keep isl_id *id);
4940 Similarly, the following functions can be used to check whether
4941 a given dimension is involved in any lower or upper bound.
4943 #include <isl/set.h>
4944 isl_bool isl_set_dim_has_any_lower_bound(
4945 __isl_keep isl_set *set,
4946 enum isl_dim_type type, unsigned pos);
4947 isl_bool isl_set_dim_has_any_upper_bound(
4948 __isl_keep isl_set *set,
4949 enum isl_dim_type type, unsigned pos);
4951 Note that these functions return true even if there is a bound on
4952 the dimension on only some of the basic sets of C<set>.
4953 To check if they have a bound for all of the basic sets in C<set>,
4954 use the following functions instead.
4956 #include <isl/set.h>
4957 isl_bool isl_set_dim_has_lower_bound(
4958 __isl_keep isl_set *set,
4959 enum isl_dim_type type, unsigned pos);
4960 isl_bool isl_set_dim_has_upper_bound(
4961 __isl_keep isl_set *set,
4962 enum isl_dim_type type, unsigned pos);
4966 To check whether a set is a parameter domain, use this function:
4968 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4969 isl_bool isl_union_set_is_params(
4970 __isl_keep isl_union_set *uset);
4974 The following functions check whether the space of the given
4975 (basic) set or relation domain and/or range is a wrapped relation.
4977 #include <isl/space.h>
4978 isl_bool isl_space_is_wrapping(
4979 __isl_keep isl_space *space);
4980 isl_bool isl_space_domain_is_wrapping(
4981 __isl_keep isl_space *space);
4982 isl_bool isl_space_range_is_wrapping(
4983 __isl_keep isl_space *space);
4984 isl_bool isl_space_is_product(
4985 __isl_keep isl_space *space);
4987 #include <isl/set.h>
4988 isl_bool isl_basic_set_is_wrapping(
4989 __isl_keep isl_basic_set *bset);
4990 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4992 #include <isl/map.h>
4993 isl_bool isl_map_domain_is_wrapping(
4994 __isl_keep isl_map *map);
4995 isl_bool isl_map_range_is_wrapping(
4996 __isl_keep isl_map *map);
4997 isl_bool isl_map_is_product(__isl_keep isl_map *map);
5000 isl_bool isl_multi_id_range_is_wrapping(
5001 __isl_keep isl_multi_id *mi);
5003 #include <isl/val.h>
5004 isl_bool isl_multi_val_range_is_wrapping(
5005 __isl_keep isl_multi_val *mv);
5007 #include <isl/aff.h>
5008 isl_bool isl_multi_aff_range_is_wrapping(
5009 __isl_keep isl_multi_aff *ma);
5010 isl_bool isl_multi_pw_aff_range_is_wrapping(
5011 __isl_keep isl_multi_pw_aff *mpa);
5012 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
5013 __isl_keep isl_multi_union_pw_aff *mupa);
5015 The input to C<isl_space_is_wrapping> should
5016 be the space of a set, while that of
5017 C<isl_space_domain_is_wrapping> and
5018 C<isl_space_range_is_wrapping> should be the space of a relation.
5019 The input to C<isl_space_is_product> can be either the space
5020 of a set or that of a binary relation.
5021 In case the input is the space of a binary relation, it checks
5022 whether both domain and range are wrapping.
5024 =item * Internal Product
5026 isl_bool isl_basic_map_can_zip(
5027 __isl_keep isl_basic_map *bmap);
5028 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
5030 Check whether the product of domain and range of the given relation
5032 i.e., whether both domain and range are nested relations.
5036 #include <isl/space.h>
5037 isl_bool isl_space_can_curry(
5038 __isl_keep isl_space *space);
5040 #include <isl/map.h>
5041 isl_bool isl_basic_map_can_curry(
5042 __isl_keep isl_basic_map *bmap);
5043 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
5045 Check whether the domain of the (basic) relation is a wrapped relation.
5047 #include <isl/space.h>
5048 isl_bool isl_space_can_uncurry(
5049 __isl_keep isl_space *space);
5051 #include <isl/map.h>
5052 isl_bool isl_basic_map_can_uncurry(
5053 __isl_keep isl_basic_map *bmap);
5054 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
5056 Check whether the range of the (basic) relation is a wrapped relation.
5058 #include <isl/space.h>
5059 isl_bool isl_space_can_range_curry(
5060 __isl_keep isl_space *space);
5062 #include <isl/map.h>
5063 isl_bool isl_map_can_range_curry(
5064 __isl_keep isl_map *map);
5066 Check whether the domain of the relation wrapped in the range of
5067 the input is itself a wrapped relation.
5069 =item * Special Values
5071 #include <isl/aff.h>
5072 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
5073 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
5074 isl_bool isl_multi_pw_aff_is_cst(
5075 __isl_keep isl_multi_pw_aff *mpa);
5077 Check whether the given expression is a constant.
5079 #include <isl/val.h>
5080 isl_bool isl_multi_val_involves_nan(
5081 __isl_keep isl_multi_val *mv);
5083 #include <isl/aff.h>
5084 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
5085 isl_bool isl_multi_aff_involves_nan(
5086 __isl_keep isl_multi_aff *ma);
5087 isl_bool isl_pw_aff_involves_nan(
5088 __isl_keep isl_pw_aff *pa);
5089 isl_bool isl_pw_multi_aff_involves_nan(
5090 __isl_keep isl_pw_multi_aff *pma);
5091 isl_bool isl_multi_pw_aff_involves_nan(
5092 __isl_keep isl_multi_pw_aff *mpa);
5093 isl_bool isl_union_pw_aff_involves_nan(
5094 __isl_keep isl_union_pw_aff *upa);
5095 isl_bool isl_union_pw_multi_aff_involves_nan(
5096 __isl_keep isl_union_pw_multi_aff *upma);
5097 isl_bool isl_multi_union_pw_aff_involves_nan(
5098 __isl_keep isl_multi_union_pw_aff *mupa);
5100 #include <isl/polynomial.h>
5101 isl_bool isl_qpolynomial_is_nan(
5102 __isl_keep isl_qpolynomial *qp);
5103 isl_bool isl_qpolynomial_fold_is_nan(
5104 __isl_keep isl_qpolynomial_fold *fold);
5105 isl_bool isl_pw_qpolynomial_involves_nan(
5106 __isl_keep isl_pw_qpolynomial *pwqp);
5107 isl_bool isl_pw_qpolynomial_fold_involves_nan(
5108 __isl_keep isl_pw_qpolynomial_fold *pwf);
5109 isl_bool isl_union_pw_qpolynomial_involves_nan(
5110 __isl_keep isl_union_pw_qpolynomial *upwqp);
5111 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
5112 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5114 Check whether the given expression is equal to or involves NaN.
5116 #include <isl/val.h>
5117 isl_bool isl_multi_val_is_zero(
5118 __isl_keep isl_multi_val *mv);
5120 Check whether the multiple value is zero.
5122 #include <isl/aff.h>
5123 isl_bool isl_aff_plain_is_zero(
5124 __isl_keep isl_aff *aff);
5126 Check whether the affine expression is obviously zero.
5130 =head3 Binary Properties
5136 The following functions check whether two objects
5137 represent the same set, relation or function.
5138 The C<plain> variants only return true if the objects
5139 are obviously the same. That is, they may return false
5140 even if the objects are the same, but they will never
5141 return true if the objects are not the same.
5143 #include <isl/set.h>
5144 isl_bool isl_basic_set_plain_is_equal(
5145 __isl_keep isl_basic_set *bset1,
5146 __isl_keep isl_basic_set *bset2);
5147 isl_bool isl_basic_set_is_equal(
5148 __isl_keep isl_basic_set *bset1,
5149 __isl_keep isl_basic_set *bset2);
5150 isl_bool isl_set_plain_is_equal(
5151 __isl_keep isl_set *set1,
5152 __isl_keep isl_set *set2);
5153 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
5154 __isl_keep isl_set *set2);
5156 #include <isl/map.h>
5157 isl_bool isl_basic_map_is_equal(
5158 __isl_keep isl_basic_map *bmap1,
5159 __isl_keep isl_basic_map *bmap2);
5160 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
5161 __isl_keep isl_map *map2);
5162 isl_bool isl_map_plain_is_equal(
5163 __isl_keep isl_map *map1,
5164 __isl_keep isl_map *map2);
5166 #include <isl/union_set.h>
5167 isl_bool isl_union_set_is_equal(
5168 __isl_keep isl_union_set *uset1,
5169 __isl_keep isl_union_set *uset2);
5171 #include <isl/union_map.h>
5172 isl_bool isl_union_map_is_equal(
5173 __isl_keep isl_union_map *umap1,
5174 __isl_keep isl_union_map *umap2);
5177 isl_bool isl_multi_id_plain_is_equal(
5178 __isl_keep isl_multi_id *mi1,
5179 __isl_keep isl_multi_id *mi2);
5181 #include <isl/val.h>
5182 isl_bool isl_multi_val_plain_is_equal(
5183 __isl_keep isl_multi_val *mv1,
5184 __isl_keep isl_multi_val *mv2);
5186 #include <isl/aff.h>
5187 isl_bool isl_aff_plain_is_equal(
5188 __isl_keep isl_aff *aff1,
5189 __isl_keep isl_aff *aff2);
5190 isl_bool isl_multi_aff_plain_is_equal(
5191 __isl_keep isl_multi_aff *maff1,
5192 __isl_keep isl_multi_aff *maff2);
5193 isl_bool isl_pw_aff_plain_is_equal(
5194 __isl_keep isl_pw_aff *pwaff1,
5195 __isl_keep isl_pw_aff *pwaff2);
5196 isl_bool isl_pw_aff_is_equal(
5197 __isl_keep isl_pw_aff *pa1,
5198 __isl_keep isl_pw_aff *pa2);
5199 isl_bool isl_pw_multi_aff_plain_is_equal(
5200 __isl_keep isl_pw_multi_aff *pma1,
5201 __isl_keep isl_pw_multi_aff *pma2);
5202 isl_bool isl_pw_multi_aff_is_equal(
5203 __isl_keep isl_pw_multi_aff *pma1,
5204 __isl_keep isl_pw_multi_aff *pma2);
5205 isl_bool isl_multi_pw_aff_plain_is_equal(
5206 __isl_keep isl_multi_pw_aff *mpa1,
5207 __isl_keep isl_multi_pw_aff *mpa2);
5208 isl_bool isl_multi_pw_aff_is_equal(
5209 __isl_keep isl_multi_pw_aff *mpa1,
5210 __isl_keep isl_multi_pw_aff *mpa2);
5211 isl_bool isl_union_pw_aff_plain_is_equal(
5212 __isl_keep isl_union_pw_aff *upa1,
5213 __isl_keep isl_union_pw_aff *upa2);
5214 isl_bool isl_union_pw_multi_aff_plain_is_equal(
5215 __isl_keep isl_union_pw_multi_aff *upma1,
5216 __isl_keep isl_union_pw_multi_aff *upma2);
5217 isl_bool isl_multi_union_pw_aff_plain_is_equal(
5218 __isl_keep isl_multi_union_pw_aff *mupa1,
5219 __isl_keep isl_multi_union_pw_aff *mupa2);
5221 #include <isl/polynomial.h>
5222 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
5223 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5224 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5225 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
5226 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5227 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5229 =item * Disjointness
5231 #include <isl/set.h>
5232 isl_bool isl_basic_set_is_disjoint(
5233 __isl_keep isl_basic_set *bset1,
5234 __isl_keep isl_basic_set *bset2);
5235 isl_bool isl_set_plain_is_disjoint(
5236 __isl_keep isl_set *set1,
5237 __isl_keep isl_set *set2);
5238 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
5239 __isl_keep isl_set *set2);
5241 #include <isl/map.h>
5242 isl_bool isl_basic_map_is_disjoint(
5243 __isl_keep isl_basic_map *bmap1,
5244 __isl_keep isl_basic_map *bmap2);
5245 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
5246 __isl_keep isl_map *map2);
5248 #include <isl/union_set.h>
5249 isl_bool isl_union_set_is_disjoint(
5250 __isl_keep isl_union_set *uset1,
5251 __isl_keep isl_union_set *uset2);
5253 #include <isl/union_map.h>
5254 isl_bool isl_union_map_is_disjoint(
5255 __isl_keep isl_union_map *umap1,
5256 __isl_keep isl_union_map *umap2);
5260 isl_bool isl_basic_set_is_subset(
5261 __isl_keep isl_basic_set *bset1,
5262 __isl_keep isl_basic_set *bset2);
5263 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
5264 __isl_keep isl_set *set2);
5265 isl_bool isl_set_is_strict_subset(
5266 __isl_keep isl_set *set1,
5267 __isl_keep isl_set *set2);
5268 isl_bool isl_union_set_is_subset(
5269 __isl_keep isl_union_set *uset1,
5270 __isl_keep isl_union_set *uset2);
5271 isl_bool isl_union_set_is_strict_subset(
5272 __isl_keep isl_union_set *uset1,
5273 __isl_keep isl_union_set *uset2);
5274 isl_bool isl_basic_map_is_subset(
5275 __isl_keep isl_basic_map *bmap1,
5276 __isl_keep isl_basic_map *bmap2);
5277 isl_bool isl_basic_map_is_strict_subset(
5278 __isl_keep isl_basic_map *bmap1,
5279 __isl_keep isl_basic_map *bmap2);
5280 isl_bool isl_map_is_subset(
5281 __isl_keep isl_map *map1,
5282 __isl_keep isl_map *map2);
5283 isl_bool isl_map_is_strict_subset(
5284 __isl_keep isl_map *map1,
5285 __isl_keep isl_map *map2);
5286 isl_bool isl_union_map_is_subset(
5287 __isl_keep isl_union_map *umap1,
5288 __isl_keep isl_union_map *umap2);
5289 isl_bool isl_union_map_is_strict_subset(
5290 __isl_keep isl_union_map *umap1,
5291 __isl_keep isl_union_map *umap2);
5293 Check whether the first argument is a (strict) subset of the
5298 Every comparison function returns a negative value if the first
5299 argument is considered smaller than the second, a positive value
5300 if the first argument is considered greater and zero if the two
5301 constraints are considered the same by the comparison criterion.
5303 #include <isl/constraint.h>
5304 int isl_constraint_plain_cmp(
5305 __isl_keep isl_constraint *c1,
5306 __isl_keep isl_constraint *c2);
5308 This function is useful for sorting C<isl_constraint>s.
5309 The order depends on the internal representation of the inputs.
5310 The order is fixed over different calls to the function (assuming
5311 the internal representation of the inputs has not changed), but may
5312 change over different versions of C<isl>.
5314 #include <isl/constraint.h>
5315 int isl_constraint_cmp_last_non_zero(
5316 __isl_keep isl_constraint *c1,
5317 __isl_keep isl_constraint *c2);
5319 This function can be used to sort constraints that live in the same
5320 local space. Constraints that involve ``earlier'' dimensions or
5321 that have a smaller coefficient for the shared latest dimension
5322 are considered smaller than other constraints.
5323 This function only defines a B<partial> order.
5325 #include <isl/set.h>
5326 int isl_set_plain_cmp(__isl_keep isl_set *set1,
5327 __isl_keep isl_set *set2);
5329 This function is useful for sorting C<isl_set>s.
5330 The order depends on the internal representation of the inputs.
5331 The order is fixed over different calls to the function (assuming
5332 the internal representation of the inputs has not changed), but may
5333 change over different versions of C<isl>.
5335 #include <isl/aff.h>
5336 int isl_multi_aff_plain_cmp(
5337 __isl_keep isl_multi_aff *ma1,
5338 __isl_keep isl_multi_aff *ma2);
5339 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
5340 __isl_keep isl_pw_aff *pa2);
5342 The functions C<isl_multi_aff_plain_cmp> and
5343 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
5344 C<isl_pw_aff>s. The order is not strictly defined.
5345 The current order sorts expressions that only involve
5346 earlier dimensions before those that involve later dimensions.
5350 =head2 Unary Operations
5356 __isl_give isl_set *isl_set_complement(
5357 __isl_take isl_set *set);
5358 __isl_give isl_map *isl_map_complement(
5359 __isl_take isl_map *map);
5363 #include <isl/space.h>
5364 __isl_give isl_space *isl_space_reverse(
5365 __isl_take isl_space *space);
5366 __isl_give isl_space *isl_space_range_reverse(
5367 __isl_take isl_space *space);
5369 #include <isl/map.h>
5370 __isl_give isl_basic_map *isl_basic_map_reverse(
5371 __isl_take isl_basic_map *bmap);
5372 __isl_give isl_map *isl_map_reverse(
5373 __isl_take isl_map *map);
5374 __isl_give isl_map *isl_map_range_reverse(
5375 __isl_take isl_map *map);
5377 #include <isl/union_map.h>
5378 __isl_give isl_union_map *isl_union_map_reverse(
5379 __isl_take isl_union_map *umap);
5380 __isl_give isl_union_map *isl_union_map_range_reverse(
5381 __isl_take isl_union_map *umap);
5383 The function C<isl_space_range_reverse> reverses the relation
5384 that is embedded in the range of the input map space.
5385 The identifier of the range, if any, is only preserved
5386 if this embedded relation has identical input and output tuples.
5388 =item * Tuple binding
5390 The following function binds
5391 a tuple to a sequence of parameter identifiers, equating
5392 the tuple dimensions to the parameters with those identifiers and
5393 subsequently projecting out the tuple.
5394 If the original object did not reference any such parameters,
5395 then this means that the tuple dimensions are reinterpreted
5397 The space of C<tuple> needs to match that of the bound tuple.
5399 #include <isl/set.h>
5400 __isl_give isl_set *isl_set_bind(
5401 __isl_take isl_set *set,
5402 __isl_take isl_multi_id *tuple);
5404 #include <isl/map.h>
5405 __isl_give isl_set *isl_map_bind_domain(
5406 __isl_take isl_map *map,
5407 __isl_take isl_multi_id *tuple);
5408 __isl_give isl_set *isl_map_bind_range(
5409 __isl_take isl_map *map,
5410 __isl_take isl_multi_id *tuple);
5412 #include <isl/union_map.h>
5413 __isl_give isl_union_set *isl_union_map_bind_range(
5414 __isl_take isl_union_map *umap,
5415 __isl_take isl_multi_id *tuple);
5417 #include <isl/aff.h>
5418 __isl_give isl_pw_aff *isl_pw_aff_bind_domain(
5419 __isl_take isl_pw_aff *pa,
5420 __isl_take isl_multi_id *tuple);
5421 __isl_give isl_multi_aff *isl_multi_aff_bind_domain(
5422 __isl_take isl_multi_aff *ma,
5423 __isl_take isl_multi_id *tuple);
5424 __isl_give isl_pw_multi_aff *
5425 isl_pw_multi_aff_bind_domain(
5426 __isl_take isl_pw_multi_aff *pma,
5427 __isl_take isl_multi_id *tuple);
5428 __isl_give isl_multi_pw_aff *
5429 isl_multi_pw_aff_bind_domain(
5430 __isl_take isl_multi_pw_aff *mpa,
5431 __isl_take isl_multi_id *tuple);
5432 __isl_give isl_pw_aff *
5433 isl_pw_aff_bind_domain_wrapped_domain(
5434 __isl_take isl_pw_aff *pa,
5435 __isl_take isl_multi_id *tuple);
5436 __isl_give isl_multi_aff *
5437 isl_multi_aff_bind_domain_wrapped_domain(
5438 __isl_take isl_multi_aff *ma,
5439 __isl_take isl_multi_id *tuple);
5440 __isl_give isl_pw_multi_aff *
5441 isl_pw_multi_aff_bind_domain_wrapped_domain(
5442 __isl_take isl_pw_multi_aff *pma,
5443 __isl_take isl_multi_id *tuple);
5444 __isl_give isl_multi_pw_aff *
5445 isl_multi_pw_aff_bind_domain_wrapped_domain(
5446 __isl_take isl_multi_pw_aff *mpa,
5447 __isl_take isl_multi_id *tuple);
5448 __isl_give isl_basic_set *isl_aff_bind_id(
5449 __isl_take isl_aff *aff,
5450 __isl_take isl_id *id);
5451 __isl_give isl_set *isl_pw_aff_bind_id(
5452 __isl_take isl_pw_aff *pa,
5453 __isl_take isl_id *id);
5454 __isl_give isl_basic_set *isl_multi_aff_bind(
5455 __isl_take isl_multi_aff *ma,
5456 __isl_take isl_multi_id *tuple);
5457 __isl_give isl_set *isl_multi_pw_aff_bind(
5458 __isl_take isl_multi_pw_aff *mpa,
5459 __isl_take isl_multi_id *tuple);
5460 __isl_give isl_union_set *isl_union_pw_aff_bind_id(
5461 __isl_take isl_union_pw_aff *upa,
5462 __isl_take isl_id *id);
5463 __isl_give isl_union_set *
5464 isl_multi_union_pw_aff_bind(
5465 __isl_take isl_multi_union_pw_aff *mupa,
5466 __isl_take isl_multi_id *tuple);
5468 Projecting out the domain of the wrapped relation in the domain
5469 of a function leaves the range of that wrapped relation
5470 in the domain of the resulting function.
5471 In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>,
5472 C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>,
5473 C<isl_union_pw_aff_bind_id> and
5474 C<isl_multi_union_pw_aff_bind>, the parameters
5475 are bound to the function values and the result lives
5476 in the domain of the input function.
5480 #include <isl/space.h>
5481 __isl_give isl_space *isl_space_domain(
5482 __isl_take isl_space *space);
5483 __isl_give isl_space *isl_space_range(
5484 __isl_take isl_space *space);
5485 __isl_give isl_space *isl_space_params(
5486 __isl_take isl_space *space);
5488 #include <isl/local_space.h>
5489 __isl_give isl_local_space *isl_local_space_domain(
5490 __isl_take isl_local_space *ls);
5491 __isl_give isl_local_space *isl_local_space_range(
5492 __isl_take isl_local_space *ls);
5494 #include <isl/set.h>
5495 __isl_give isl_basic_set *isl_basic_set_project_out(
5496 __isl_take isl_basic_set *bset,
5497 enum isl_dim_type type, unsigned first, unsigned n);
5498 __isl_give isl_set *isl_set_project_out_param_id(
5499 __isl_take isl_set *set,
5500 __isl_take isl_id *id);
5501 __isl_give isl_set *
5502 isl_set_project_out_param_id_list(
5503 __isl_take isl_set *set,
5504 __isl_take isl_id_list *list);
5505 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
5506 enum isl_dim_type type, unsigned first, unsigned n);
5507 __isl_give isl_set *isl_set_project_out_all_params(
5508 __isl_take isl_set *set);
5509 __isl_give isl_map *isl_set_project_onto_map(
5510 __isl_take isl_set *set,
5511 enum isl_dim_type type, unsigned first,
5513 __isl_give isl_basic_set *isl_basic_set_params(
5514 __isl_take isl_basic_set *bset);
5515 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
5517 The function C<isl_set_project_onto_map> returns a relation
5518 that projects the input set onto the given set dimensions.
5520 #include <isl/map.h>
5521 __isl_give isl_basic_map *isl_basic_map_project_out(
5522 __isl_take isl_basic_map *bmap,
5523 enum isl_dim_type type, unsigned first, unsigned n);
5524 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
5525 enum isl_dim_type type, unsigned first, unsigned n);
5526 __isl_give isl_map *isl_map_project_out_all_params(
5527 __isl_take isl_map *map);
5528 __isl_give isl_basic_set *isl_basic_map_domain(
5529 __isl_take isl_basic_map *bmap);
5530 __isl_give isl_basic_set *isl_basic_map_range(
5531 __isl_take isl_basic_map *bmap);
5532 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
5533 __isl_give isl_set *isl_map_domain(
5534 __isl_take isl_map *bmap);
5535 __isl_give isl_set *isl_map_range(
5536 __isl_take isl_map *map);
5538 #include <isl/union_set.h>
5539 __isl_give isl_union_set *isl_union_set_project_out(
5540 __isl_take isl_union_set *uset,
5541 enum isl_dim_type type,
5542 unsigned first, unsigned n);
5543 __isl_give isl_union_set *
5544 isl_union_set_project_out_all_params(
5545 __isl_take isl_union_set *uset);
5546 __isl_give isl_set *isl_union_set_params(
5547 __isl_take isl_union_set *uset);
5549 The function C<isl_union_set_project_out> can only project out
5552 #include <isl/union_map.h>
5553 __isl_give isl_union_map *isl_union_map_project_out(
5554 __isl_take isl_union_map *umap,
5555 enum isl_dim_type type, unsigned first, unsigned n);
5556 __isl_give isl_union_map *
5557 isl_union_map_project_out_all_params(
5558 __isl_take isl_union_map *umap);
5559 __isl_give isl_set *isl_union_map_params(
5560 __isl_take isl_union_map *umap);
5561 __isl_give isl_union_set *isl_union_map_domain(
5562 __isl_take isl_union_map *umap);
5563 __isl_give isl_union_set *isl_union_map_range(
5564 __isl_take isl_union_map *umap);
5566 The function C<isl_union_map_project_out> can only project out
5569 #include <isl/aff.h>
5570 __isl_give isl_aff *isl_aff_project_domain_on_params(
5571 __isl_take isl_aff *aff);
5572 __isl_give isl_multi_aff *
5573 isl_multi_aff_project_domain_on_params(
5574 __isl_take isl_multi_aff *ma);
5575 __isl_give isl_pw_aff *
5576 isl_pw_aff_project_domain_on_params(
5577 __isl_take isl_pw_aff *pa);
5578 __isl_give isl_multi_pw_aff *
5579 isl_multi_pw_aff_project_domain_on_params(
5580 __isl_take isl_multi_pw_aff *mpa);
5581 __isl_give isl_pw_multi_aff *
5582 isl_pw_multi_aff_project_domain_on_params(
5583 __isl_take isl_pw_multi_aff *pma);
5584 __isl_give isl_set *isl_pw_aff_domain(
5585 __isl_take isl_pw_aff *pwaff);
5586 __isl_give isl_set *isl_pw_multi_aff_domain(
5587 __isl_take isl_pw_multi_aff *pma);
5588 __isl_give isl_set *isl_multi_pw_aff_domain(
5589 __isl_take isl_multi_pw_aff *mpa);
5590 __isl_give isl_union_set *isl_union_pw_aff_domain(
5591 __isl_take isl_union_pw_aff *upa);
5592 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
5593 __isl_take isl_union_pw_multi_aff *upma);
5594 __isl_give isl_union_set *
5595 isl_multi_union_pw_aff_domain(
5596 __isl_take isl_multi_union_pw_aff *mupa);
5597 __isl_give isl_set *isl_pw_aff_params(
5598 __isl_take isl_pw_aff *pwa);
5600 If no explicit domain was set on a zero-dimensional input to
5601 C<isl_multi_union_pw_aff_domain>, then this function will
5602 return a parameter set.
5604 #include <isl/polynomial.h>
5605 __isl_give isl_qpolynomial *
5606 isl_qpolynomial_project_domain_on_params(
5607 __isl_take isl_qpolynomial *qp);
5608 __isl_give isl_pw_qpolynomial *
5609 isl_pw_qpolynomial_project_domain_on_params(
5610 __isl_take isl_pw_qpolynomial *pwqp);
5611 __isl_give isl_pw_qpolynomial_fold *
5612 isl_pw_qpolynomial_fold_project_domain_on_params(
5613 __isl_take isl_pw_qpolynomial_fold *pwf);
5614 __isl_give isl_set *isl_pw_qpolynomial_domain(
5615 __isl_take isl_pw_qpolynomial *pwqp);
5616 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5617 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5618 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5619 __isl_take isl_union_pw_qpolynomial *upwqp);
5621 #include <isl/space.h>
5622 __isl_give isl_space *isl_space_domain_map(
5623 __isl_take isl_space *space);
5624 __isl_give isl_space *isl_space_range_map(
5625 __isl_take isl_space *space);
5627 #include <isl/map.h>
5628 __isl_give isl_map *isl_set_wrapped_domain_map(
5629 __isl_take isl_set *set);
5630 __isl_give isl_basic_map *isl_basic_map_domain_map(
5631 __isl_take isl_basic_map *bmap);
5632 __isl_give isl_basic_map *isl_basic_map_range_map(
5633 __isl_take isl_basic_map *bmap);
5634 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
5635 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
5637 #include <isl/union_map.h>
5638 __isl_give isl_union_map *isl_union_map_domain_map(
5639 __isl_take isl_union_map *umap);
5640 __isl_give isl_union_pw_multi_aff *
5641 isl_union_map_domain_map_union_pw_multi_aff(
5642 __isl_take isl_union_map *umap);
5643 __isl_give isl_union_map *isl_union_map_range_map(
5644 __isl_take isl_union_map *umap);
5645 __isl_give isl_union_map *
5646 isl_union_set_wrapped_domain_map(
5647 __isl_take isl_union_set *uset);
5649 The functions above construct a (basic, regular or union) relation
5650 that maps (a wrapped version of) the input relation to its domain or range.
5651 C<isl_set_wrapped_domain_map> maps the input set to the domain
5652 of its wrapped relation.
5656 __isl_give isl_basic_set *isl_basic_set_eliminate(
5657 __isl_take isl_basic_set *bset,
5658 enum isl_dim_type type,
5659 unsigned first, unsigned n);
5660 __isl_give isl_set *isl_set_eliminate(
5661 __isl_take isl_set *set, enum isl_dim_type type,
5662 unsigned first, unsigned n);
5663 __isl_give isl_basic_map *isl_basic_map_eliminate(
5664 __isl_take isl_basic_map *bmap,
5665 enum isl_dim_type type,
5666 unsigned first, unsigned n);
5667 __isl_give isl_map *isl_map_eliminate(
5668 __isl_take isl_map *map, enum isl_dim_type type,
5669 unsigned first, unsigned n);
5671 Eliminate the coefficients for the given dimensions from the constraints,
5672 without removing the dimensions.
5674 =item * Constructing a set from a parameter domain
5676 A set space of a given dimension and with an optional name
5677 can be created from a parameter space using the following functions.
5679 #include <isl/space.h>
5680 __isl_give isl_space *isl_space_add_unnamed_tuple_ui(
5681 __isl_take isl_space *space, unsigned dim);
5682 __isl_give isl_space *
5683 isl_space_add_named_tuple_id_ui(
5684 __isl_take isl_space *space,
5685 __isl_take isl_id *tuple_id, unsigned dim);
5687 A set with a given tuple can be created from a parameter domain
5688 using the following function.
5690 #include <isl/set.h>
5691 __isl_give isl_set *isl_set_unbind_params(
5692 __isl_take isl_set *set,
5693 __isl_take isl_multi_id *tuple);
5695 Any parameters with identifiers in C<tuple> are reinterpreted
5696 as the corresponding set dimensions.
5698 A zero-dimensional (local) space or (basic) set can be constructed
5699 on a given parameter domain using the following functions.
5701 #include <isl/space.h>
5702 __isl_give isl_space *isl_space_set_from_params(
5703 __isl_take isl_space *space);
5705 #include <isl/local_space.h>
5706 __isl_give isl_local_space *
5707 isl_local_space_set_from_params(
5708 __isl_take isl_local_space *ls);
5710 #include <isl/set.h>
5711 __isl_give isl_basic_set *isl_basic_set_from_params(
5712 __isl_take isl_basic_set *bset);
5713 __isl_give isl_set *isl_set_from_params(
5714 __isl_take isl_set *set);
5716 =item * Constructing a relation from one or two sets
5718 A map space with a range of a given dimension and with an optional name
5719 can be created from a domain space using the functions
5720 C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui>
5723 A relation with a given domain tuple can be created from a set
5724 that will become the range of the relation
5725 using the following function.
5727 #include <isl/set.h>
5728 __isl_give isl_map *
5729 isl_set_unbind_params_insert_domain(
5730 __isl_take isl_set *set,
5731 __isl_take isl_multi_id *domain);
5733 Any parameters with identifiers in C<domain> are reinterpreted
5734 as the corresponding input dimensions.
5736 Similarly, a function defined over a parameter domain can
5737 be converted into one defined over a set domain
5738 using the following functions.
5740 #include <isl/aff.h>
5741 __isl_give isl_aff *
5742 isl_aff_unbind_params_insert_domain(
5743 __isl_take isl_aff *aff,
5744 __isl_take isl_multi_id *domain);
5745 __isl_give isl_multi_aff *
5746 isl_multi_aff_unbind_params_insert_domain(
5747 __isl_take isl_multi_aff *ma,
5748 __isl_take isl_multi_id *domain);
5749 __isl_give isl_multi_pw_aff *
5750 isl_multi_pw_aff_unbind_params_insert_domain(
5751 __isl_take isl_multi_pw_aff *mpa,
5752 __isl_take isl_multi_id *domain);
5755 any parameters with identifiers in C<domain> are reinterpreted
5756 as the corresponding input dimensions.
5758 Create a relation with the given set(s) as domain and/or range.
5759 If only the domain or the range is specified, then
5760 the range or domain of the created relation is a zero-dimensional
5761 flat anonymous space.
5762 If the case of C<isl_space_map_from_set>, the input space
5763 specifies both the domain and the range of the result.
5765 #include <isl/space.h>
5766 __isl_give isl_space *isl_space_from_domain(
5767 __isl_take isl_space *space);
5768 __isl_give isl_space *isl_space_from_range(
5769 __isl_take isl_space *space);
5770 __isl_give isl_space *isl_space_map_from_set(
5771 __isl_take isl_space *space);
5772 __isl_give isl_space *isl_space_map_from_domain_and_range(
5773 __isl_take isl_space *domain,
5774 __isl_take isl_space *range);
5776 #include <isl/local_space.h>
5777 __isl_give isl_local_space *isl_local_space_from_domain(
5778 __isl_take isl_local_space *ls);
5780 #include <isl/map.h>
5781 __isl_give isl_map *isl_set_insert_domain(
5782 __isl_take isl_set *set,
5783 __isl_take isl_space *domain);
5784 __isl_give isl_map *isl_map_from_domain(
5785 __isl_take isl_set *set);
5786 __isl_give isl_map *isl_map_from_range(
5787 __isl_take isl_set *set);
5789 #include <isl/union_map.h>
5790 __isl_give isl_union_map *isl_union_map_from_domain(
5791 __isl_take isl_union_set *uset);
5792 __isl_give isl_union_map *isl_union_map_from_range(
5793 __isl_take isl_union_set *uset);
5794 __isl_give isl_union_map *
5795 isl_union_map_from_domain_and_range(
5796 __isl_take isl_union_set *domain,
5797 __isl_take isl_union_set *range);
5800 __isl_give isl_multi_id *isl_multi_id_from_range(
5801 __isl_take isl_multi_id *mi);
5803 #include <isl/val.h>
5804 __isl_give isl_multi_val *isl_multi_val_from_range(
5805 __isl_take isl_multi_val *mv);
5807 #include <isl/aff.h>
5808 __isl_give isl_multi_aff *
5809 isl_multi_aff_insert_domain(
5810 __isl_take isl_multi_aff *ma,
5811 __isl_take isl_space *domain);
5812 __isl_give isl_pw_aff *isl_pw_aff_insert_domain(
5813 __isl_take isl_pw_aff *pa,
5814 __isl_take isl_space *domain);
5815 __isl_give isl_pw_multi_aff *
5816 isl_pw_multi_aff_insert_domain(
5817 __isl_take isl_pw_multi_aff *pma,
5818 __isl_take isl_space *domain);
5819 __isl_give isl_multi_pw_aff *
5820 isl_multi_pw_aff_insert_domain(
5821 __isl_take isl_multi_pw_aff *mpa,
5822 __isl_take isl_space *domain);
5823 __isl_give isl_aff *isl_aff_from_range(
5824 __isl_take isl_aff *aff);
5825 __isl_give isl_multi_aff *isl_multi_aff_from_range(
5826 __isl_take isl_multi_aff *ma);
5827 __isl_give isl_pw_aff *isl_pw_aff_from_range(
5828 __isl_take isl_pw_aff *pwa);
5829 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
5830 __isl_take isl_multi_pw_aff *mpa);
5831 __isl_give isl_multi_union_pw_aff *
5832 isl_multi_union_pw_aff_from_range(
5833 __isl_take isl_multi_union_pw_aff *mupa);
5834 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5835 __isl_take isl_set *set);
5836 __isl_give isl_union_pw_multi_aff *
5837 isl_union_pw_multi_aff_from_domain(
5838 __isl_take isl_union_set *uset);
5840 #include <isl/polynomial.h>
5841 __isl_give isl_pw_qpolynomial *
5842 isl_pw_qpolynomial_from_range(
5843 __isl_take isl_pw_qpolynomial *pwqp);
5844 __isl_give isl_pw_qpolynomial_fold *
5845 isl_pw_qpolynomial_fold_from_range(
5846 __isl_take isl_pw_qpolynomial_fold *pwf);
5850 #include <isl/set.h>
5851 __isl_give isl_basic_set *isl_basic_set_fix_si(
5852 __isl_take isl_basic_set *bset,
5853 enum isl_dim_type type, unsigned pos, int value);
5854 __isl_give isl_basic_set *isl_basic_set_fix_val(
5855 __isl_take isl_basic_set *bset,
5856 enum isl_dim_type type, unsigned pos,
5857 __isl_take isl_val *v);
5858 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5859 enum isl_dim_type type, unsigned pos, int value);
5860 __isl_give isl_set *isl_set_fix_val(
5861 __isl_take isl_set *set,
5862 enum isl_dim_type type, unsigned pos,
5863 __isl_take isl_val *v);
5865 #include <isl/map.h>
5866 __isl_give isl_basic_map *isl_basic_map_fix_si(
5867 __isl_take isl_basic_map *bmap,
5868 enum isl_dim_type type, unsigned pos, int value);
5869 __isl_give isl_basic_map *isl_basic_map_fix_val(
5870 __isl_take isl_basic_map *bmap,
5871 enum isl_dim_type type, unsigned pos,
5872 __isl_take isl_val *v);
5873 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
5874 enum isl_dim_type type, unsigned pos, int value);
5875 __isl_give isl_map *isl_map_fix_val(
5876 __isl_take isl_map *map,
5877 enum isl_dim_type type, unsigned pos,
5878 __isl_take isl_val *v);
5880 #include <isl/aff.h>
5881 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
5882 __isl_take isl_pw_multi_aff *pma,
5883 enum isl_dim_type type, unsigned pos, int value);
5885 #include <isl/polynomial.h>
5886 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5887 __isl_take isl_pw_qpolynomial *pwqp,
5888 enum isl_dim_type type, unsigned n,
5889 __isl_take isl_val *v);
5890 __isl_give isl_pw_qpolynomial_fold *
5891 isl_pw_qpolynomial_fold_fix_val(
5892 __isl_take isl_pw_qpolynomial_fold *pwf,
5893 enum isl_dim_type type, unsigned n,
5894 __isl_take isl_val *v);
5896 Intersect the set, relation or function domain
5897 with the hyperplane where the given
5898 dimension has the fixed given value.
5900 #include <isl/set.h>
5901 __isl_give isl_basic_set *
5902 isl_basic_set_lower_bound_val(
5903 __isl_take isl_basic_set *bset,
5904 enum isl_dim_type type, unsigned pos,
5905 __isl_take isl_val *value);
5906 __isl_give isl_basic_set *
5907 isl_basic_set_upper_bound_val(
5908 __isl_take isl_basic_set *bset,
5909 enum isl_dim_type type, unsigned pos,
5910 __isl_take isl_val *value);
5911 __isl_give isl_set *isl_set_lower_bound_si(
5912 __isl_take isl_set *set,
5913 enum isl_dim_type type, unsigned pos, int value);
5914 __isl_give isl_set *isl_set_lower_bound_val(
5915 __isl_take isl_set *set,
5916 enum isl_dim_type type, unsigned pos,
5917 __isl_take isl_val *value);
5918 __isl_give isl_set *isl_set_upper_bound_si(
5919 __isl_take isl_set *set,
5920 enum isl_dim_type type, unsigned pos, int value);
5921 __isl_give isl_set *isl_set_upper_bound_val(
5922 __isl_take isl_set *set,
5923 enum isl_dim_type type, unsigned pos,
5924 __isl_take isl_val *value);
5925 __isl_give isl_set *isl_set_lower_bound_multi_val(
5926 __isl_take isl_set *set,
5927 __isl_take isl_multi_val *lower);
5928 __isl_give isl_set *isl_set_upper_bound_multi_val(
5929 __isl_take isl_set *set,
5930 __isl_take isl_multi_val *upper);
5931 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff(
5932 __isl_take isl_set *set,
5933 __isl_take isl_multi_pw_aff *lower);
5934 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff(
5935 __isl_take isl_set *set,
5936 __isl_take isl_multi_pw_aff *upper);
5938 #include <isl/map.h>
5939 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
5940 __isl_take isl_basic_map *bmap,
5941 enum isl_dim_type type, unsigned pos, int value);
5942 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
5943 __isl_take isl_basic_map *bmap,
5944 enum isl_dim_type type, unsigned pos, int value);
5945 __isl_give isl_map *isl_map_lower_bound_si(
5946 __isl_take isl_map *map,
5947 enum isl_dim_type type, unsigned pos, int value);
5948 __isl_give isl_map *isl_map_upper_bound_si(
5949 __isl_take isl_map *map,
5950 enum isl_dim_type type, unsigned pos, int value);
5951 __isl_give isl_map *isl_map_lower_bound_val(
5952 __isl_take isl_map *map,
5953 enum isl_dim_type type, unsigned pos,
5954 __isl_take isl_val *value);
5955 __isl_give isl_map *isl_map_upper_bound_val(
5956 __isl_take isl_map *map,
5957 enum isl_dim_type type, unsigned pos,
5958 __isl_take isl_val *value);
5959 __isl_give isl_map *isl_map_lower_bound_multi_pw_aff(
5960 __isl_take isl_map *map,
5961 __isl_take isl_multi_pw_aff *lower);
5962 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff(
5963 __isl_take isl_map *map,
5964 __isl_take isl_multi_pw_aff *upper);
5966 Intersect the set or relation with the half-space where the given
5967 dimension has a value bounded by the given fixed integer value or
5968 symbolic constant expression.
5969 For functions taking a multi expression,
5970 this applies to all set dimensions.
5971 Those that bound a map, bound the range of that map.
5972 If the multi expression is zero-dimensional but has an explicit domain,
5973 then the (parameter) domain of the set or map is intersected
5974 with this explicit domain.
5976 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
5977 enum isl_dim_type type1, int pos1,
5978 enum isl_dim_type type2, int pos2);
5979 __isl_give isl_basic_map *isl_basic_map_equate(
5980 __isl_take isl_basic_map *bmap,
5981 enum isl_dim_type type1, int pos1,
5982 enum isl_dim_type type2, int pos2);
5983 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
5984 enum isl_dim_type type1, int pos1,
5985 enum isl_dim_type type2, int pos2);
5987 Intersect the set or relation with the hyperplane where the given
5988 dimensions are equal to each other.
5990 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
5991 enum isl_dim_type type1, int pos1,
5992 enum isl_dim_type type2, int pos2);
5994 Intersect the relation with the hyperplane where the given
5995 dimensions have opposite values.
5997 __isl_give isl_map *isl_map_order_le(
5998 __isl_take isl_map *map,
5999 enum isl_dim_type type1, int pos1,
6000 enum isl_dim_type type2, int pos2);
6001 __isl_give isl_basic_map *isl_basic_map_order_ge(
6002 __isl_take isl_basic_map *bmap,
6003 enum isl_dim_type type1, int pos1,
6004 enum isl_dim_type type2, int pos2);
6005 __isl_give isl_map *isl_map_order_ge(
6006 __isl_take isl_map *map,
6007 enum isl_dim_type type1, int pos1,
6008 enum isl_dim_type type2, int pos2);
6009 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
6010 enum isl_dim_type type1, int pos1,
6011 enum isl_dim_type type2, int pos2);
6012 __isl_give isl_basic_map *isl_basic_map_order_gt(
6013 __isl_take isl_basic_map *bmap,
6014 enum isl_dim_type type1, int pos1,
6015 enum isl_dim_type type2, int pos2);
6016 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
6017 enum isl_dim_type type1, int pos1,
6018 enum isl_dim_type type2, int pos2);
6020 Intersect the relation with the half-space where the given
6021 dimensions satisfy the given ordering.
6023 #include <isl/union_set.h>
6024 __isl_give isl_union_map *isl_union_map_remove_map_if(
6025 __isl_take isl_union_map *umap,
6026 isl_bool (*fn)(__isl_keep isl_map *map,
6027 void *user), void *user);
6029 This function calls the callback function once for each
6030 pair of spaces for which there are elements in the input.
6031 If the callback returns C<isl_bool_true>, then all those elements
6032 are removed from the result. The only remaining elements in the output
6033 are then those for which the callback returns C<isl_bool_false>.
6037 #include <isl/aff.h>
6038 __isl_give isl_basic_set *isl_aff_zero_basic_set(
6039 __isl_take isl_aff *aff);
6040 __isl_give isl_basic_set *isl_aff_neg_basic_set(
6041 __isl_take isl_aff *aff);
6042 __isl_give isl_set *isl_pw_aff_pos_set(
6043 __isl_take isl_pw_aff *pa);
6044 __isl_give isl_set *isl_pw_aff_nonneg_set(
6045 __isl_take isl_pw_aff *pwaff);
6046 __isl_give isl_set *isl_pw_aff_zero_set(
6047 __isl_take isl_pw_aff *pwaff);
6048 __isl_give isl_set *isl_pw_aff_non_zero_set(
6049 __isl_take isl_pw_aff *pwaff);
6050 __isl_give isl_union_set *
6051 isl_union_pw_aff_zero_union_set(
6052 __isl_take isl_union_pw_aff *upa);
6053 __isl_give isl_union_set *
6054 isl_multi_union_pw_aff_zero_union_set(
6055 __isl_take isl_multi_union_pw_aff *mupa);
6057 The function C<isl_aff_neg_basic_set> returns a basic set
6058 containing those elements in the domain space
6059 of C<aff> where C<aff> is negative.
6060 The function C<isl_pw_aff_nonneg_set> returns a set
6061 containing those elements in the domain
6062 of C<pwaff> where C<pwaff> is non-negative.
6063 The function C<isl_multi_union_pw_aff_zero_union_set>
6064 returns a union set containing those elements
6065 in the domains of its elements where they are all zero.
6069 __isl_give isl_map *isl_set_identity(
6070 __isl_take isl_set *set);
6071 __isl_give isl_union_map *isl_union_set_identity(
6072 __isl_take isl_union_set *uset);
6073 __isl_give isl_union_pw_multi_aff *
6074 isl_union_set_identity_union_pw_multi_aff(
6075 __isl_take isl_union_set *uset);
6077 Construct an identity relation on the given (union) set.
6079 =item * Function Extraction
6081 A piecewise quasi affine expression that is equal to 1 on a set
6082 and 0 outside the set can be created using the following function.
6084 #include <isl/aff.h>
6085 __isl_give isl_pw_aff *isl_set_indicator_function(
6086 __isl_take isl_set *set);
6088 A piecewise multiple quasi affine expression can be extracted
6089 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
6090 and the C<isl_map> is single-valued.
6091 In case of a conversion from an C<isl_union_map>
6092 to an C<isl_union_pw_multi_aff>, these properties need to hold
6093 in each domain space.
6094 A conversion to a C<isl_multi_union_pw_aff> additionally
6095 requires that the input is non-empty and involves only a single
6098 #include <isl/aff.h>
6099 __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff(
6100 __isl_take isl_set *set);
6101 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
6102 __isl_take isl_set *set);
6103 __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff(
6104 __isl_take isl_map *map);
6105 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
6106 __isl_take isl_map *map);
6108 __isl_give isl_union_pw_multi_aff *
6109 isl_union_pw_multi_aff_from_union_set(
6110 __isl_take isl_union_set *uset);
6111 __isl_give isl_union_pw_multi_aff *
6112 isl_union_map_as_union_pw_multi_aff(
6113 __isl_take isl_union_map *umap);
6114 __isl_give isl_union_pw_multi_aff *
6115 isl_union_pw_multi_aff_from_union_map(
6116 __isl_take isl_union_map *umap);
6118 __isl_give isl_multi_union_pw_aff *
6119 isl_union_map_as_multi_union_pw_aff(
6120 __isl_take isl_union_map *umap);
6121 __isl_give isl_multi_union_pw_aff *
6122 isl_multi_union_pw_aff_from_union_map(
6123 __isl_take isl_union_map *umap);
6125 C<isl_map_as_pw_multi_aff> and C<isl_pw_multi_aff_from_map> perform
6127 Similarly for C<isl_set_as_pw_multi_aff> and
6128 C<isl_pw_multi_aff_from_set>,
6129 for C<isl_union_map_as_union_pw_multi_aff> and
6130 C<isl_union_pw_multi_aff_from_union_map> and
6131 for C<isl_union_map_as_multi_union_pw_aff> and
6132 C<isl_multi_union_pw_aff_from_union_map>.
6136 __isl_give isl_basic_set *isl_basic_map_deltas(
6137 __isl_take isl_basic_map *bmap);
6138 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
6139 __isl_give isl_union_set *isl_union_map_deltas(
6140 __isl_take isl_union_map *umap);
6142 These functions return a (basic) set containing the differences
6143 between image elements and corresponding domain elements in the input.
6145 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6146 __isl_take isl_basic_map *bmap);
6147 __isl_give isl_map *isl_map_deltas_map(
6148 __isl_take isl_map *map);
6149 __isl_give isl_union_map *isl_union_map_deltas_map(
6150 __isl_take isl_union_map *umap);
6152 The functions above construct a (basic, regular or union) relation
6153 that maps (a wrapped version of) the input relation to its delta set.
6157 #include <isl/map.h>
6158 __isl_give isl_map *isl_set_translation(
6159 __isl_take isl_set *deltas);
6161 This function performs essentially the opposite operation
6162 of C<isl_map_deltas>. In particular, it returns pairs
6163 of elements in the same space that have a difference in C<deltas>.
6167 Simplify the representation of a set, relation or functions by trying
6168 to combine pairs of basic sets or relations into a single
6169 basic set or relation.
6171 #include <isl/set.h>
6172 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
6174 #include <isl/map.h>
6175 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
6177 #include <isl/union_set.h>
6178 __isl_give isl_union_set *isl_union_set_coalesce(
6179 __isl_take isl_union_set *uset);
6181 #include <isl/union_map.h>
6182 __isl_give isl_union_map *isl_union_map_coalesce(
6183 __isl_take isl_union_map *umap);
6185 #include <isl/aff.h>
6186 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
6187 __isl_take isl_pw_aff *pa);
6188 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
6189 __isl_take isl_pw_multi_aff *pma);
6190 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
6191 __isl_take isl_multi_pw_aff *mpa);
6192 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
6193 __isl_take isl_union_pw_aff *upa);
6194 __isl_give isl_union_pw_multi_aff *
6195 isl_union_pw_multi_aff_coalesce(
6196 __isl_take isl_union_pw_multi_aff *upma);
6197 __isl_give isl_multi_union_pw_aff *
6198 isl_multi_union_pw_aff_coalesce(
6199 __isl_take isl_multi_union_pw_aff *mupa);
6201 #include <isl/polynomial.h>
6202 __isl_give isl_pw_qpolynomial_fold *
6203 isl_pw_qpolynomial_fold_coalesce(
6204 __isl_take isl_pw_qpolynomial_fold *pwf);
6205 __isl_give isl_union_pw_qpolynomial *
6206 isl_union_pw_qpolynomial_coalesce(
6207 __isl_take isl_union_pw_qpolynomial *upwqp);
6208 __isl_give isl_union_pw_qpolynomial_fold *
6209 isl_union_pw_qpolynomial_fold_coalesce(
6210 __isl_take isl_union_pw_qpolynomial_fold *upwf);
6212 One of the methods for combining pairs of basic sets or relations
6213 can result in coefficients that are much larger than those that appear
6214 in the constraints of the input. By default, the coefficients are
6215 not allowed to grow larger, but this can be changed by unsetting
6216 the following option.
6218 isl_stat isl_options_set_coalesce_bounded_wrapping(
6219 isl_ctx *ctx, int val);
6220 int isl_options_get_coalesce_bounded_wrapping(
6223 One of the other methods tries to combine pairs of basic sets
6224 with different local variables, treating them as existentially
6225 quantified variables even if they have known (but different)
6226 integer division expressions. The result may then also have
6227 existentially quantified variables. Turning on the following
6228 option prevents this from happening.
6230 isl_stat isl_options_set_coalesce_preserve_locals(
6231 isl_ctx *ctx, int val);
6232 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
6234 =item * Detecting equalities
6236 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
6237 __isl_take isl_basic_set *bset);
6238 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
6239 __isl_take isl_basic_map *bmap);
6240 __isl_give isl_set *isl_set_detect_equalities(
6241 __isl_take isl_set *set);
6242 __isl_give isl_map *isl_map_detect_equalities(
6243 __isl_take isl_map *map);
6244 __isl_give isl_union_set *isl_union_set_detect_equalities(
6245 __isl_take isl_union_set *uset);
6246 __isl_give isl_union_map *isl_union_map_detect_equalities(
6247 __isl_take isl_union_map *umap);
6249 Simplify the representation of a set or relation by detecting implicit
6252 =item * Removing redundant constraints
6254 #include <isl/set.h>
6255 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
6256 __isl_take isl_basic_set *bset);
6257 __isl_give isl_set *isl_set_remove_redundancies(
6258 __isl_take isl_set *set);
6260 #include <isl/union_set.h>
6261 __isl_give isl_union_set *
6262 isl_union_set_remove_redundancies(
6263 __isl_take isl_union_set *uset);
6265 #include <isl/map.h>
6266 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
6267 __isl_take isl_basic_map *bmap);
6268 __isl_give isl_map *isl_map_remove_redundancies(
6269 __isl_take isl_map *map);
6271 #include <isl/union_map.h>
6272 __isl_give isl_union_map *
6273 isl_union_map_remove_redundancies(
6274 __isl_take isl_union_map *umap);
6278 __isl_give isl_basic_set *isl_set_convex_hull(
6279 __isl_take isl_set *set);
6280 __isl_give isl_basic_map *isl_map_convex_hull(
6281 __isl_take isl_map *map);
6283 If the input set or relation has any existentially quantified
6284 variables, then the result of these operations is currently undefined.
6288 #include <isl/set.h>
6289 __isl_give isl_basic_set *
6290 isl_set_unshifted_simple_hull(
6291 __isl_take isl_set *set);
6292 __isl_give isl_basic_set *isl_set_simple_hull(
6293 __isl_take isl_set *set);
6294 __isl_give isl_basic_set *
6295 isl_set_plain_unshifted_simple_hull(
6296 __isl_take isl_set *set);
6297 __isl_give isl_basic_set *
6298 isl_set_unshifted_simple_hull_from_set_list(
6299 __isl_take isl_set *set,
6300 __isl_take isl_set_list *list);
6302 #include <isl/map.h>
6303 __isl_give isl_basic_map *
6304 isl_map_unshifted_simple_hull(
6305 __isl_take isl_map *map);
6306 __isl_give isl_basic_map *isl_map_simple_hull(
6307 __isl_take isl_map *map);
6308 __isl_give isl_basic_map *
6309 isl_map_plain_unshifted_simple_hull(
6310 __isl_take isl_map *map);
6311 __isl_give isl_basic_map *
6312 isl_map_unshifted_simple_hull_from_map_list(
6313 __isl_take isl_map *map,
6314 __isl_take isl_map_list *list);
6316 #include <isl/union_map.h>
6317 __isl_give isl_union_map *isl_union_map_simple_hull(
6318 __isl_take isl_union_map *umap);
6320 These functions compute a single basic set or relation
6321 that contains the whole input set or relation.
6322 In particular, the output is described by translates
6323 of the constraints describing the basic sets or relations in the input.
6324 In case of C<isl_set_unshifted_simple_hull>, only the original
6325 constraints are used, without any translation.
6326 In case of C<isl_set_plain_unshifted_simple_hull> and
6327 C<isl_map_plain_unshifted_simple_hull>, the result is described
6328 by original constraints that are obviously satisfied
6329 by the entire input set or relation.
6330 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
6331 C<isl_map_unshifted_simple_hull_from_map_list>, the
6332 constraints are taken from the elements of the second argument.
6336 (See \autoref{s:simple hull}.)
6342 __isl_give isl_basic_set *isl_basic_set_affine_hull(
6343 __isl_take isl_basic_set *bset);
6344 __isl_give isl_basic_set *isl_set_affine_hull(
6345 __isl_take isl_set *set);
6346 __isl_give isl_union_set *isl_union_set_affine_hull(
6347 __isl_take isl_union_set *uset);
6348 __isl_give isl_basic_map *isl_basic_map_affine_hull(
6349 __isl_take isl_basic_map *bmap);
6350 __isl_give isl_basic_map *isl_map_affine_hull(
6351 __isl_take isl_map *map);
6352 __isl_give isl_union_map *isl_union_map_affine_hull(
6353 __isl_take isl_union_map *umap);
6355 In case of union sets and relations, the affine hull is computed
6358 =item * Polyhedral hull
6360 __isl_give isl_basic_set *isl_set_polyhedral_hull(
6361 __isl_take isl_set *set);
6362 __isl_give isl_basic_map *isl_map_polyhedral_hull(
6363 __isl_take isl_map *map);
6364 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
6365 __isl_take isl_union_set *uset);
6366 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
6367 __isl_take isl_union_map *umap);
6369 These functions compute a single basic set or relation
6370 not involving any existentially quantified variables
6371 that contains the whole input set or relation.
6372 In case of union sets and relations, the polyhedral hull is computed
6377 #include <isl/set.h>
6378 __isl_give isl_fixed_box *
6379 isl_set_get_simple_fixed_box_hull(
6380 __isl_keep isl_set *set)
6382 #include <isl/map.h>
6383 __isl_give isl_fixed_box *
6384 isl_map_get_range_simple_fixed_box_hull(
6385 __isl_keep isl_map *map);
6387 These functions try to approximate the set or
6388 the range of the map by a box of fixed size.
6389 The box is described in terms of an offset living in the same space as
6390 the input and a size living in the set or range space. For any element
6391 in the input map, the range value is greater than or equal to
6392 the offset applied to the domain value and the difference with
6393 this offset is strictly smaller than the size.
6394 The same holds for the elements of the input set, where
6395 the offset is a parametric constant value.
6396 If no fixed-size approximation can be found,
6397 an I<invalid> box is returned, i.e., one for which
6398 C<isl_fixed_box_is_valid> below returns false.
6400 The validity, the offset and the size of the box can be obtained using
6401 the following functions.
6403 #include <isl/fixed_box.h>
6404 isl_bool isl_fixed_box_is_valid(
6405 __isl_keep isl_fixed_box *box);
6406 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
6407 __isl_keep isl_fixed_box *box);
6408 __isl_give isl_multi_val *isl_fixed_box_get_size(
6409 __isl_keep isl_fixed_box *box);
6411 The box can be copied and freed using the following functions.
6413 #include <isl/fixed_box.h>
6414 __isl_give isl_fixed_box *isl_fixed_box_copy(
6415 __isl_keep isl_fixed_box *box);
6416 __isl_null isl_fixed_box *isl_fixed_box_free(
6417 __isl_take isl_fixed_box *box);
6419 A representation of the information contained in an object
6420 of type C<isl_fixed_box> can be obtained using
6422 #include <isl/fixed_box.h>
6423 __isl_give isl_printer *isl_printer_print_fixed_box(
6424 __isl_take isl_printer *p,
6425 __isl_keep isl_fixed_box *box);
6426 __isl_give char *isl_fixed_box_to_str(
6427 __isl_keep isl_fixed_box *box);
6429 C<isl_fixed_box_to_str> prints the information in flow format.
6431 =item * Other approximations
6433 #include <isl/set.h>
6434 __isl_give isl_basic_set *
6435 isl_basic_set_drop_constraints_involving_dims(
6436 __isl_take isl_basic_set *bset,
6437 enum isl_dim_type type,
6438 unsigned first, unsigned n);
6439 __isl_give isl_basic_set *
6440 isl_basic_set_drop_constraints_not_involving_dims(
6441 __isl_take isl_basic_set *bset,
6442 enum isl_dim_type type,
6443 unsigned first, unsigned n);
6444 __isl_give isl_set *
6445 isl_set_drop_constraints_involving_dims(
6446 __isl_take isl_set *set,
6447 enum isl_dim_type type,
6448 unsigned first, unsigned n);
6449 __isl_give isl_set *
6450 isl_set_drop_constraints_not_involving_dims(
6451 __isl_take isl_set *set,
6452 enum isl_dim_type type,
6453 unsigned first, unsigned n);
6455 #include <isl/map.h>
6456 __isl_give isl_basic_map *
6457 isl_basic_map_drop_constraints_involving_dims(
6458 __isl_take isl_basic_map *bmap,
6459 enum isl_dim_type type,
6460 unsigned first, unsigned n);
6461 __isl_give isl_basic_map *
6462 isl_basic_map_drop_constraints_not_involving_dims(
6463 __isl_take isl_basic_map *bmap,
6464 enum isl_dim_type type,
6465 unsigned first, unsigned n);
6466 __isl_give isl_map *
6467 isl_map_drop_constraints_involving_dims(
6468 __isl_take isl_map *map,
6469 enum isl_dim_type type,
6470 unsigned first, unsigned n);
6471 __isl_give isl_map *
6472 isl_map_drop_constraints_not_involving_dims(
6473 __isl_take isl_map *map,
6474 enum isl_dim_type type,
6475 unsigned first, unsigned n);
6477 These functions drop any constraints (not) involving the specified dimensions.
6478 Note that the result depends on the representation of the input.
6480 #include <isl/polynomial.h>
6481 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
6482 __isl_take isl_pw_qpolynomial *pwqp, int sign);
6483 __isl_give isl_union_pw_qpolynomial *
6484 isl_union_pw_qpolynomial_to_polynomial(
6485 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
6487 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
6488 the polynomial will be an overapproximation. If C<sign> is negative,
6489 it will be an underapproximation. If C<sign> is zero, the approximation
6490 will lie somewhere in between.
6494 __isl_give isl_basic_set *isl_basic_set_sample(
6495 __isl_take isl_basic_set *bset);
6496 __isl_give isl_basic_set *isl_set_sample(
6497 __isl_take isl_set *set);
6498 __isl_give isl_basic_map *isl_basic_map_sample(
6499 __isl_take isl_basic_map *bmap);
6500 __isl_give isl_basic_map *isl_map_sample(
6501 __isl_take isl_map *map);
6503 If the input (basic) set or relation is non-empty, then return
6504 a singleton subset of the input. Otherwise, return an empty set.
6506 =item * Optimization
6508 #include <isl/ilp.h>
6509 __isl_give isl_val *isl_basic_set_max_val(
6510 __isl_keep isl_basic_set *bset,
6511 __isl_keep isl_aff *obj);
6512 __isl_give isl_val *isl_set_min_val(
6513 __isl_keep isl_set *set,
6514 __isl_keep isl_aff *obj);
6515 __isl_give isl_val *isl_set_max_val(
6516 __isl_keep isl_set *set,
6517 __isl_keep isl_aff *obj);
6518 __isl_give isl_multi_val *
6519 isl_union_set_min_multi_union_pw_aff(
6520 __isl_keep isl_union_set *uset,
6521 __isl_keep isl_multi_union_pw_aff *obj);
6523 Compute the minimum or maximum of the integer affine expression C<obj>
6524 over the points in C<set>.
6525 The result is C<NULL> in case of an error, the optimal value in case
6526 there is one, negative infinity or infinity if the problem is unbounded and
6527 NaN if the problem is empty.
6529 #include <isl/ilp.h>
6530 __isl_give isl_multi_val *
6531 isl_pw_multi_aff_min_multi_val(
6532 __isl_take isl_pw_multi_aff *pma);
6533 __isl_give isl_multi_val *
6534 isl_pw_multi_aff_max_multi_val(
6535 __isl_take isl_pw_multi_aff *pma);
6536 __isl_give isl_multi_val *
6537 isl_multi_pw_aff_min_multi_val(
6538 __isl_take isl_multi_pw_aff *mpa);
6539 __isl_give isl_multi_val *
6540 isl_multi_pw_aff_max_multi_val(
6541 __isl_take isl_multi_pw_aff *mpa);
6542 __isl_give isl_val *isl_union_pw_aff_min_val(
6543 __isl_take isl_union_pw_aff *upa);
6544 __isl_give isl_val *isl_union_pw_aff_max_val(
6545 __isl_take isl_union_pw_aff *upa);
6546 __isl_give isl_multi_val *
6547 isl_multi_union_pw_aff_min_multi_val(
6548 __isl_take isl_multi_union_pw_aff *mupa);
6549 __isl_give isl_multi_val *
6550 isl_multi_union_pw_aff_max_multi_val(
6551 __isl_take isl_multi_union_pw_aff *mupa);
6553 Compute the minimum or maximum of the integer affine expression
6554 over its definition domain.
6555 The result is C<NULL> in case of an error, the optimal value in case
6556 there is one, negative infinity or infinity if the problem is unbounded and
6557 NaN if the problem is empty.
6559 #include <isl/ilp.h>
6560 __isl_give isl_val *isl_basic_set_dim_max_val(
6561 __isl_take isl_basic_set *bset, int pos);
6562 __isl_give isl_val *isl_set_dim_min_val(
6563 __isl_take isl_set *set, int pos);
6564 __isl_give isl_val *isl_set_dim_max_val(
6565 __isl_take isl_set *set, int pos);
6567 Return the minimal or maximal value attained by the given set dimension,
6568 independently of the parameter values and of any other dimensions.
6569 The result is C<NULL> in case of an error, the optimal value in case
6570 there is one, (negative) infinity if the problem is unbounded and
6571 NaN if the input is empty.
6573 =item * Parametric optimization
6575 __isl_give isl_pw_aff *isl_set_dim_min(
6576 __isl_take isl_set *set, int pos);
6577 __isl_give isl_pw_aff *isl_set_dim_max(
6578 __isl_take isl_set *set, int pos);
6579 __isl_give isl_pw_aff *isl_map_dim_min(
6580 __isl_take isl_map *map, int pos);
6581 __isl_give isl_pw_aff *isl_map_dim_max(
6582 __isl_take isl_map *map, int pos);
6583 __isl_give isl_multi_pw_aff *
6584 isl_set_min_multi_pw_aff(
6585 __isl_take isl_set *set);
6586 __isl_give isl_multi_pw_aff *
6587 isl_set_max_multi_pw_aff(
6588 __isl_take isl_set *set);
6589 __isl_give isl_multi_pw_aff *
6590 isl_map_min_multi_pw_aff(
6591 __isl_take isl_map *map);
6592 __isl_give isl_multi_pw_aff *
6593 isl_map_max_multi_pw_aff(
6594 __isl_take isl_map *map);
6596 Compute the minimum or maximum of the (given) set or output dimension(s)
6597 as a function of the parameters (and input dimensions), but independently
6598 of the other set or output dimensions.
6599 For lexicographic optimization, see L<"Lexicographic Optimization">.
6603 The following functions compute either the set of (rational) coefficient
6604 values of valid constraints for the given set or the set of (rational)
6605 values satisfying the constraints with coefficients from the given set.
6606 Internally, these two sets of functions perform essentially the
6607 same operations, except that the set of coefficients is assumed to
6608 be a cone, while the set of values may be any polyhedron.
6609 The current implementation is based on the Farkas lemma and
6610 Fourier-Motzkin elimination, but this may change or be made optional
6611 in future. In particular, future implementations may use different
6612 dualization algorithms or skip the elimination step.
6614 #include <isl/set.h>
6615 __isl_give isl_basic_set *isl_basic_set_coefficients(
6616 __isl_take isl_basic_set *bset);
6617 __isl_give isl_basic_set_list *
6618 isl_basic_set_list_coefficients(
6619 __isl_take isl_basic_set_list *list);
6620 __isl_give isl_basic_set *isl_set_coefficients(
6621 __isl_take isl_set *set);
6622 __isl_give isl_union_set *isl_union_set_coefficients(
6623 __isl_take isl_union_set *bset);
6624 __isl_give isl_basic_set *isl_basic_set_solutions(
6625 __isl_take isl_basic_set *bset);
6626 __isl_give isl_basic_set *isl_set_solutions(
6627 __isl_take isl_set *set);
6628 __isl_give isl_union_set *isl_union_set_solutions(
6629 __isl_take isl_union_set *bset);
6633 __isl_give isl_map *isl_map_fixed_power_val(
6634 __isl_take isl_map *map,
6635 __isl_take isl_val *exp);
6636 __isl_give isl_union_map *
6637 isl_union_map_fixed_power_val(
6638 __isl_take isl_union_map *umap,
6639 __isl_take isl_val *exp);
6641 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
6642 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
6643 of C<map> is computed.
6645 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
6647 __isl_give isl_union_map *isl_union_map_power(
6648 __isl_take isl_union_map *umap, isl_bool *exact);
6650 Compute a parametric representation for all positive powers I<k> of C<map>.
6651 The result maps I<k> to a nested relation corresponding to the
6652 I<k>th power of C<map>.
6653 The result may be an overapproximation. If the result is known to be exact,
6654 then C<*exact> is set to C<1>.
6656 =item * Transitive closure
6658 __isl_give isl_map *isl_map_transitive_closure(
6659 __isl_take isl_map *map, isl_bool *exact);
6660 __isl_give isl_union_map *isl_union_map_transitive_closure(
6661 __isl_take isl_union_map *umap, isl_bool *exact);
6663 Compute the transitive closure of C<map>.
6664 The result may be an overapproximation. If the result is known to be exact,
6665 then C<*exact> is set to C<1>.
6667 =item * Reaching path lengths
6669 __isl_give isl_map *isl_map_reaching_path_lengths(
6670 __isl_take isl_map *map, isl_bool *exact);
6672 Compute a relation that maps each element in the range of C<map>
6673 to the lengths of all paths composed of edges in C<map> that
6674 end up in the given element.
6675 The result may be an overapproximation. If the result is known to be exact,
6676 then C<*exact> is set to C<1>.
6677 To compute the I<maximal> path length, the resulting relation
6678 should be postprocessed by C<isl_map_lexmax>.
6679 In particular, if the input relation is a dependence relation
6680 (mapping sources to sinks), then the maximal path length corresponds
6681 to the free schedule.
6682 Note, however, that C<isl_map_lexmax> expects the maximum to be
6683 finite, so if the path lengths are unbounded (possibly due to
6684 the overapproximation), then you will get an error message.
6688 #include <isl/space.h>
6689 __isl_give isl_space *isl_space_wrap(
6690 __isl_take isl_space *space);
6691 __isl_give isl_space *isl_space_unwrap(
6692 __isl_take isl_space *space);
6694 #include <isl/local_space.h>
6695 __isl_give isl_local_space *isl_local_space_wrap(
6696 __isl_take isl_local_space *ls);
6698 #include <isl/set.h>
6699 __isl_give isl_basic_map *isl_basic_set_unwrap(
6700 __isl_take isl_basic_set *bset);
6701 __isl_give isl_map *isl_set_unwrap(
6702 __isl_take isl_set *set);
6704 #include <isl/map.h>
6705 __isl_give isl_basic_set *isl_basic_map_wrap(
6706 __isl_take isl_basic_map *bmap);
6707 __isl_give isl_set *isl_map_wrap(
6708 __isl_take isl_map *map);
6710 #include <isl/union_set.h>
6711 __isl_give isl_union_map *isl_union_set_unwrap(
6712 __isl_take isl_union_set *uset);
6714 #include <isl/union_map.h>
6715 __isl_give isl_union_set *isl_union_map_wrap(
6716 __isl_take isl_union_map *umap);
6718 The input to C<isl_space_unwrap> should
6719 be the space of a set, while that of
6720 C<isl_space_wrap> should be the space of a relation.
6721 Conversely, the output of C<isl_space_unwrap> is the space
6722 of a relation, while that of C<isl_space_wrap> is the space of a set.
6726 Remove any internal structure of domain (and range) of the given
6727 set or relation. If there is any such internal structure in the input,
6728 then the name of the space is also removed.
6730 #include <isl/space.h>
6731 __isl_give isl_space *isl_space_flatten_domain(
6732 __isl_take isl_space *space);
6733 __isl_give isl_space *isl_space_flatten_range(
6734 __isl_take isl_space *space);
6736 #include <isl/local_space.h>
6737 __isl_give isl_local_space *
6738 isl_local_space_flatten_domain(
6739 __isl_take isl_local_space *ls);
6740 __isl_give isl_local_space *
6741 isl_local_space_flatten_range(
6742 __isl_take isl_local_space *ls);
6744 #include <isl/set.h>
6745 __isl_give isl_basic_set *isl_basic_set_flatten(
6746 __isl_take isl_basic_set *bset);
6747 __isl_give isl_set *isl_set_flatten(
6748 __isl_take isl_set *set);
6750 #include <isl/map.h>
6751 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
6752 __isl_take isl_basic_map *bmap);
6753 __isl_give isl_basic_map *isl_basic_map_flatten_range(
6754 __isl_take isl_basic_map *bmap);
6755 __isl_give isl_map *isl_map_flatten_range(
6756 __isl_take isl_map *map);
6757 __isl_give isl_map *isl_map_flatten_domain(
6758 __isl_take isl_map *map);
6759 __isl_give isl_basic_map *isl_basic_map_flatten(
6760 __isl_take isl_basic_map *bmap);
6761 __isl_give isl_map *isl_map_flatten(
6762 __isl_take isl_map *map);
6765 __isl_give isl_multi_id *isl_multi_id_flatten_range(
6766 __isl_take isl_multi_id *mi);
6768 #include <isl/val.h>
6769 __isl_give isl_multi_val *isl_multi_val_flatten_range(
6770 __isl_take isl_multi_val *mv);
6772 #include <isl/aff.h>
6773 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
6774 __isl_take isl_multi_aff *ma);
6775 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
6776 __isl_take isl_multi_aff *ma);
6777 __isl_give isl_multi_pw_aff *
6778 isl_multi_pw_aff_flatten_range(
6779 __isl_take isl_multi_pw_aff *mpa);
6780 __isl_give isl_multi_union_pw_aff *
6781 isl_multi_union_pw_aff_flatten_range(
6782 __isl_take isl_multi_union_pw_aff *mupa);
6784 #include <isl/map.h>
6785 __isl_give isl_map *isl_set_flatten_map(
6786 __isl_take isl_set *set);
6788 The function above constructs a relation
6789 that maps the input set to a flattened version of the set.
6793 Lift the input set to a space with extra dimensions corresponding
6794 to the existentially quantified variables in the input.
6795 In particular, the result lives in a wrapped map where the domain
6796 is the original space and the range corresponds to the original
6797 existentially quantified variables.
6799 #include <isl/set.h>
6800 __isl_give isl_basic_set *isl_basic_set_lift(
6801 __isl_take isl_basic_set *bset);
6802 __isl_give isl_set *isl_set_lift(
6803 __isl_take isl_set *set);
6804 __isl_give isl_union_set *isl_union_set_lift(
6805 __isl_take isl_union_set *uset);
6807 Given a local space that contains the existentially quantified
6808 variables of a set, a basic relation that, when applied to
6809 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
6810 can be constructed using the following function.
6812 #include <isl/local_space.h>
6813 __isl_give isl_basic_map *isl_local_space_lifting(
6814 __isl_take isl_local_space *ls);
6816 #include <isl/aff.h>
6817 __isl_give isl_multi_aff *isl_multi_aff_lift(
6818 __isl_take isl_multi_aff *maff,
6819 __isl_give isl_local_space **ls);
6821 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
6822 then it is assigned the local space that lies at the basis of
6823 the lifting applied.
6825 =item * Internal Product
6827 #include <isl/space.h>
6828 __isl_give isl_space *isl_space_zip(
6829 __isl_take isl_space *space);
6831 #include <isl/map.h>
6832 __isl_give isl_basic_map *isl_basic_map_zip(
6833 __isl_take isl_basic_map *bmap);
6834 __isl_give isl_map *isl_map_zip(
6835 __isl_take isl_map *map);
6837 #include <isl/union_map.h>
6838 __isl_give isl_union_map *isl_union_map_zip(
6839 __isl_take isl_union_map *umap);
6841 Given a relation with nested relations for domain and range,
6842 interchange the range of the domain with the domain of the range.
6846 #include <isl/space.h>
6847 __isl_give isl_space *isl_space_curry(
6848 __isl_take isl_space *space);
6849 __isl_give isl_space *isl_space_uncurry(
6850 __isl_take isl_space *space);
6852 #include <isl/map.h>
6853 __isl_give isl_basic_map *isl_basic_map_curry(
6854 __isl_take isl_basic_map *bmap);
6855 __isl_give isl_basic_map *isl_basic_map_uncurry(
6856 __isl_take isl_basic_map *bmap);
6857 __isl_give isl_map *isl_map_curry(
6858 __isl_take isl_map *map);
6859 __isl_give isl_map *isl_map_uncurry(
6860 __isl_take isl_map *map);
6862 #include <isl/union_map.h>
6863 __isl_give isl_union_map *isl_union_map_curry(
6864 __isl_take isl_union_map *umap);
6865 __isl_give isl_union_map *isl_union_map_uncurry(
6866 __isl_take isl_union_map *umap);
6868 Given a relation with a nested relation for domain,
6869 the C<curry> functions
6870 move the range of the nested relation out of the domain
6871 and use it as the domain of a nested relation in the range,
6872 with the original range as range of this nested relation.
6873 The C<uncurry> functions perform the inverse operation.
6875 #include <isl/space.h>
6876 __isl_give isl_space *isl_space_range_curry(
6877 __isl_take isl_space *space);
6879 #include <isl/map.h>
6880 __isl_give isl_map *isl_map_range_curry(
6881 __isl_take isl_map *map);
6883 #include <isl/union_map.h>
6884 __isl_give isl_union_map *isl_union_map_range_curry(
6885 __isl_take isl_union_map *umap);
6887 These functions apply the currying to the relation that
6888 is nested inside the range of the input.
6890 =item * Aligning parameters
6892 Change the order of the parameters of the given set, relation
6894 such that the first parameters match those of C<model>.
6895 This may involve the introduction of extra parameters.
6896 All parameters need to be named.
6898 #include <isl/space.h>
6899 __isl_give isl_space *isl_space_align_params(
6900 __isl_take isl_space *space1,
6901 __isl_take isl_space *space2)
6903 #include <isl/set.h>
6904 __isl_give isl_basic_set *isl_basic_set_align_params(
6905 __isl_take isl_basic_set *bset,
6906 __isl_take isl_space *model);
6907 __isl_give isl_set *isl_set_align_params(
6908 __isl_take isl_set *set,
6909 __isl_take isl_space *model);
6911 #include <isl/map.h>
6912 __isl_give isl_basic_map *isl_basic_map_align_params(
6913 __isl_take isl_basic_map *bmap,
6914 __isl_take isl_space *model);
6915 __isl_give isl_map *isl_map_align_params(
6916 __isl_take isl_map *map,
6917 __isl_take isl_space *model);
6920 __isl_give isl_multi_id *isl_multi_id_align_params(
6921 __isl_take isl_multi_id *mi,
6922 __isl_take isl_space *model);
6924 #include <isl/val.h>
6925 __isl_give isl_multi_val *isl_multi_val_align_params(
6926 __isl_take isl_multi_val *mv,
6927 __isl_take isl_space *model);
6929 #include <isl/aff.h>
6930 __isl_give isl_aff *isl_aff_align_params(
6931 __isl_take isl_aff *aff,
6932 __isl_take isl_space *model);
6933 __isl_give isl_multi_aff *isl_multi_aff_align_params(
6934 __isl_take isl_multi_aff *multi,
6935 __isl_take isl_space *model);
6936 __isl_give isl_pw_aff *isl_pw_aff_align_params(
6937 __isl_take isl_pw_aff *pwaff,
6938 __isl_take isl_space *model);
6939 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
6940 __isl_take isl_pw_multi_aff *pma,
6941 __isl_take isl_space *model);
6942 __isl_give isl_union_pw_aff *
6943 isl_union_pw_aff_align_params(
6944 __isl_take isl_union_pw_aff *upa,
6945 __isl_take isl_space *model);
6946 __isl_give isl_union_pw_multi_aff *
6947 isl_union_pw_multi_aff_align_params(
6948 __isl_take isl_union_pw_multi_aff *upma,
6949 __isl_take isl_space *model);
6950 __isl_give isl_multi_union_pw_aff *
6951 isl_multi_union_pw_aff_align_params(
6952 __isl_take isl_multi_union_pw_aff *mupa,
6953 __isl_take isl_space *model);
6955 #include <isl/polynomial.h>
6956 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
6957 __isl_take isl_qpolynomial *qp,
6958 __isl_take isl_space *model);
6960 =item * Drop unused parameters
6962 Drop parameters that are not referenced by the isl object.
6963 All parameters need to be named.
6965 #include <isl/set.h>
6966 __isl_give isl_basic_set *
6967 isl_basic_set_drop_unused_params(
6968 __isl_take isl_basic_set *bset);
6969 __isl_give isl_set *isl_set_drop_unused_params(
6970 __isl_take isl_set *set);
6972 #include <isl/map.h>
6973 __isl_give isl_basic_map *
6974 isl_basic_map_drop_unused_params(
6975 __isl_take isl_basic_map *bmap);
6976 __isl_give isl_map *isl_map_drop_unused_params(
6977 __isl_take isl_map *map);
6979 #include <isl/aff.h>
6980 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
6981 __isl_take isl_pw_aff *pa);
6982 __isl_give isl_pw_multi_aff *
6983 isl_pw_multi_aff_drop_unused_params(
6984 __isl_take isl_pw_multi_aff *pma);
6986 #include <isl/polynomial.h>
6987 __isl_give isl_pw_qpolynomial *
6988 isl_pw_qpolynomial_drop_unused_params(
6989 __isl_take isl_pw_qpolynomial *pwqp);
6990 __isl_give isl_pw_qpolynomial_fold *
6991 isl_pw_qpolynomial_fold_drop_unused_params(
6992 __isl_take isl_pw_qpolynomial_fold *pwf);
6994 =item * Unary Arithmetic Operations
6996 #include <isl/set.h>
6997 __isl_give isl_set *isl_set_neg(
6998 __isl_take isl_set *set);
6999 #include <isl/map.h>
7000 __isl_give isl_map *isl_map_neg(
7001 __isl_take isl_map *map);
7003 C<isl_set_neg> constructs a set containing the opposites of
7004 the elements in its argument.
7005 The domain of the result of C<isl_map_neg> is the same
7006 as the domain of its argument. The corresponding range
7007 elements are the opposites of the corresponding range
7008 elements in the argument.
7010 #include <isl/val.h>
7011 __isl_give isl_multi_val *isl_multi_val_neg(
7012 __isl_take isl_multi_val *mv);
7014 #include <isl/aff.h>
7015 __isl_give isl_aff *isl_aff_neg(
7016 __isl_take isl_aff *aff);
7017 __isl_give isl_multi_aff *isl_multi_aff_neg(
7018 __isl_take isl_multi_aff *ma);
7019 __isl_give isl_pw_aff *isl_pw_aff_neg(
7020 __isl_take isl_pw_aff *pwaff);
7021 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
7022 __isl_take isl_pw_multi_aff *pma);
7023 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
7024 __isl_take isl_multi_pw_aff *mpa);
7025 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
7026 __isl_take isl_union_pw_aff *upa);
7027 __isl_give isl_union_pw_multi_aff *
7028 isl_union_pw_multi_aff_neg(
7029 __isl_take isl_union_pw_multi_aff *upma);
7030 __isl_give isl_multi_union_pw_aff *
7031 isl_multi_union_pw_aff_neg(
7032 __isl_take isl_multi_union_pw_aff *mupa);
7033 __isl_give isl_aff *isl_aff_ceil(
7034 __isl_take isl_aff *aff);
7035 __isl_give isl_pw_aff *isl_pw_aff_ceil(
7036 __isl_take isl_pw_aff *pwaff);
7037 __isl_give isl_aff *isl_aff_floor(
7038 __isl_take isl_aff *aff);
7039 __isl_give isl_multi_aff *isl_multi_aff_floor(
7040 __isl_take isl_multi_aff *ma);
7041 __isl_give isl_pw_aff *isl_pw_aff_floor(
7042 __isl_take isl_pw_aff *pwaff);
7043 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
7044 __isl_take isl_union_pw_aff *upa);
7045 __isl_give isl_multi_union_pw_aff *
7046 isl_multi_union_pw_aff_floor(
7047 __isl_take isl_multi_union_pw_aff *mupa);
7049 #include <isl/aff.h>
7050 __isl_give isl_pw_aff *isl_pw_aff_list_min(
7051 __isl_take isl_pw_aff_list *list);
7052 __isl_give isl_pw_aff *isl_pw_aff_list_max(
7053 __isl_take isl_pw_aff_list *list);
7055 #include <isl/polynomial.h>
7056 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
7057 __isl_take isl_qpolynomial *qp);
7058 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
7059 __isl_take isl_pw_qpolynomial *pwqp);
7060 __isl_give isl_union_pw_qpolynomial *
7061 isl_union_pw_qpolynomial_neg(
7062 __isl_take isl_union_pw_qpolynomial *upwqp);
7063 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
7064 __isl_take isl_qpolynomial *qp,
7066 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
7067 __isl_take isl_pw_qpolynomial *pwqp,
7072 The following functions evaluate a function in a point.
7074 #include <isl/aff.h>
7075 __isl_give isl_val *isl_aff_eval(
7076 __isl_take isl_aff *aff,
7077 __isl_take isl_point *pnt);
7078 __isl_give isl_val *isl_pw_aff_eval(
7079 __isl_take isl_pw_aff *pa,
7080 __isl_take isl_point *pnt);
7082 #include <isl/polynomial.h>
7083 __isl_give isl_val *isl_pw_qpolynomial_eval(
7084 __isl_take isl_pw_qpolynomial *pwqp,
7085 __isl_take isl_point *pnt);
7086 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
7087 __isl_take isl_pw_qpolynomial_fold *pwf,
7088 __isl_take isl_point *pnt);
7089 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
7090 __isl_take isl_union_pw_qpolynomial *upwqp,
7091 __isl_take isl_point *pnt);
7092 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
7093 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7094 __isl_take isl_point *pnt);
7096 These functions return NaN when evaluated at a void point.
7097 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
7098 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
7099 when the function is evaluated outside its explicit domain.
7101 =item * Dimension manipulation
7103 It is usually not advisable to directly change the (input or output)
7104 space of a set or a relation as this removes the name and the internal
7105 structure of the space. However, the functions below can be useful
7106 to add new parameters, assuming
7107 C<isl_set_align_params> and C<isl_map_align_params>
7110 #include <isl/space.h>
7111 __isl_give isl_space *isl_space_add_dims(
7112 __isl_take isl_space *space,
7113 enum isl_dim_type type, unsigned n);
7114 __isl_give isl_space *isl_space_insert_dims(
7115 __isl_take isl_space *space,
7116 enum isl_dim_type type, unsigned pos, unsigned n);
7117 __isl_give isl_space *isl_space_drop_dims(
7118 __isl_take isl_space *space,
7119 enum isl_dim_type type, unsigned first, unsigned n);
7120 __isl_give isl_space *isl_space_move_dims(
7121 __isl_take isl_space *space,
7122 enum isl_dim_type dst_type, unsigned dst_pos,
7123 enum isl_dim_type src_type, unsigned src_pos,
7126 #include <isl/local_space.h>
7127 __isl_give isl_local_space *isl_local_space_add_dims(
7128 __isl_take isl_local_space *ls,
7129 enum isl_dim_type type, unsigned n);
7130 __isl_give isl_local_space *isl_local_space_insert_dims(
7131 __isl_take isl_local_space *ls,
7132 enum isl_dim_type type, unsigned first, unsigned n);
7133 __isl_give isl_local_space *isl_local_space_drop_dims(
7134 __isl_take isl_local_space *ls,
7135 enum isl_dim_type type, unsigned first, unsigned n);
7137 #include <isl/set.h>
7138 __isl_give isl_basic_set *isl_basic_set_add_dims(
7139 __isl_take isl_basic_set *bset,
7140 enum isl_dim_type type, unsigned n);
7141 __isl_give isl_set *isl_set_add_dims(
7142 __isl_take isl_set *set,
7143 enum isl_dim_type type, unsigned n);
7144 __isl_give isl_basic_set *isl_basic_set_insert_dims(
7145 __isl_take isl_basic_set *bset,
7146 enum isl_dim_type type, unsigned pos,
7148 __isl_give isl_set *isl_set_insert_dims(
7149 __isl_take isl_set *set,
7150 enum isl_dim_type type, unsigned pos, unsigned n);
7151 __isl_give isl_basic_set *isl_basic_set_move_dims(
7152 __isl_take isl_basic_set *bset,
7153 enum isl_dim_type dst_type, unsigned dst_pos,
7154 enum isl_dim_type src_type, unsigned src_pos,
7156 __isl_give isl_set *isl_set_move_dims(
7157 __isl_take isl_set *set,
7158 enum isl_dim_type dst_type, unsigned dst_pos,
7159 enum isl_dim_type src_type, unsigned src_pos,
7162 #include <isl/map.h>
7163 __isl_give isl_basic_map *isl_basic_map_add_dims(
7164 __isl_take isl_basic_map *bmap,
7165 enum isl_dim_type type, unsigned n);
7166 __isl_give isl_map *isl_map_add_dims(
7167 __isl_take isl_map *map,
7168 enum isl_dim_type type, unsigned n);
7169 __isl_give isl_basic_map *isl_basic_map_insert_dims(
7170 __isl_take isl_basic_map *bmap,
7171 enum isl_dim_type type, unsigned pos,
7173 __isl_give isl_map *isl_map_insert_dims(
7174 __isl_take isl_map *map,
7175 enum isl_dim_type type, unsigned pos, unsigned n);
7176 __isl_give isl_basic_map *isl_basic_map_move_dims(
7177 __isl_take isl_basic_map *bmap,
7178 enum isl_dim_type dst_type, unsigned dst_pos,
7179 enum isl_dim_type src_type, unsigned src_pos,
7181 __isl_give isl_map *isl_map_move_dims(
7182 __isl_take isl_map *map,
7183 enum isl_dim_type dst_type, unsigned dst_pos,
7184 enum isl_dim_type src_type, unsigned src_pos,
7187 #include <isl/val.h>
7188 __isl_give isl_multi_val *isl_multi_val_insert_dims(
7189 __isl_take isl_multi_val *mv,
7190 enum isl_dim_type type, unsigned first, unsigned n);
7191 __isl_give isl_multi_val *isl_multi_val_add_dims(
7192 __isl_take isl_multi_val *mv,
7193 enum isl_dim_type type, unsigned n);
7194 __isl_give isl_multi_val *isl_multi_val_drop_dims(
7195 __isl_take isl_multi_val *mv,
7196 enum isl_dim_type type, unsigned first, unsigned n);
7198 #include <isl/aff.h>
7199 __isl_give isl_aff *isl_aff_insert_dims(
7200 __isl_take isl_aff *aff,
7201 enum isl_dim_type type, unsigned first, unsigned n);
7202 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
7203 __isl_take isl_multi_aff *ma,
7204 enum isl_dim_type type, unsigned first, unsigned n);
7205 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
7206 __isl_take isl_pw_aff *pwaff,
7207 enum isl_dim_type type, unsigned first, unsigned n);
7208 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
7209 __isl_take isl_multi_pw_aff *mpa,
7210 enum isl_dim_type type, unsigned first, unsigned n);
7211 __isl_give isl_aff *isl_aff_add_dims(
7212 __isl_take isl_aff *aff,
7213 enum isl_dim_type type, unsigned n);
7214 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
7215 __isl_take isl_multi_aff *ma,
7216 enum isl_dim_type type, unsigned n);
7217 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
7218 __isl_take isl_pw_aff *pwaff,
7219 enum isl_dim_type type, unsigned n);
7220 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
7221 __isl_take isl_multi_pw_aff *mpa,
7222 enum isl_dim_type type, unsigned n);
7223 __isl_give isl_aff *isl_aff_drop_dims(
7224 __isl_take isl_aff *aff,
7225 enum isl_dim_type type, unsigned first, unsigned n);
7226 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
7227 __isl_take isl_multi_aff *maff,
7228 enum isl_dim_type type, unsigned first, unsigned n);
7229 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
7230 __isl_take isl_pw_aff *pwaff,
7231 enum isl_dim_type type, unsigned first, unsigned n);
7232 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
7233 __isl_take isl_pw_multi_aff *pma,
7234 enum isl_dim_type type, unsigned first, unsigned n);
7235 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
7236 __isl_take isl_union_pw_aff *upa,
7237 enum isl_dim_type type, unsigned first, unsigned n);
7238 __isl_give isl_union_pw_multi_aff *
7239 isl_union_pw_multi_aff_drop_dims(
7240 __isl_take isl_union_pw_multi_aff *upma,
7241 enum isl_dim_type type,
7242 unsigned first, unsigned n);
7243 __isl_give isl_multi_union_pw_aff *
7244 isl_multi_union_pw_aff_drop_dims(
7245 __isl_take isl_multi_union_pw_aff *mupa,
7246 enum isl_dim_type type, unsigned first,
7248 __isl_give isl_aff *isl_aff_move_dims(
7249 __isl_take isl_aff *aff,
7250 enum isl_dim_type dst_type, unsigned dst_pos,
7251 enum isl_dim_type src_type, unsigned src_pos,
7253 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
7254 __isl_take isl_multi_aff *ma,
7255 enum isl_dim_type dst_type, unsigned dst_pos,
7256 enum isl_dim_type src_type, unsigned src_pos,
7258 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
7259 __isl_take isl_pw_aff *pa,
7260 enum isl_dim_type dst_type, unsigned dst_pos,
7261 enum isl_dim_type src_type, unsigned src_pos,
7263 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
7264 __isl_take isl_multi_pw_aff *pma,
7265 enum isl_dim_type dst_type, unsigned dst_pos,
7266 enum isl_dim_type src_type, unsigned src_pos,
7269 #include <isl/polynomial.h>
7270 __isl_give isl_union_pw_qpolynomial *
7271 isl_union_pw_qpolynomial_drop_dims(
7272 __isl_take isl_union_pw_qpolynomial *upwqp,
7273 enum isl_dim_type type,
7274 unsigned first, unsigned n);
7275 __isl_give isl_union_pw_qpolynomial_fold *
7276 isl_union_pw_qpolynomial_fold_drop_dims(
7277 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7278 enum isl_dim_type type,
7279 unsigned first, unsigned n);
7281 The operations on union expressions can only manipulate parameters.
7285 =head2 Binary Operations
7287 The two arguments of a binary operation not only need to live
7288 in the same C<isl_ctx>, they currently also need to have
7289 the same (number of) parameters.
7291 =head3 Basic Operations
7295 =item * Intersection
7297 #include <isl/local_space.h>
7298 __isl_give isl_local_space *isl_local_space_intersect(
7299 __isl_take isl_local_space *ls1,
7300 __isl_take isl_local_space *ls2);
7302 #include <isl/set.h>
7303 __isl_give isl_basic_set *isl_basic_set_intersect_params(
7304 __isl_take isl_basic_set *bset1,
7305 __isl_take isl_basic_set *bset2);
7306 __isl_give isl_basic_set *isl_basic_set_intersect(
7307 __isl_take isl_basic_set *bset1,
7308 __isl_take isl_basic_set *bset2);
7309 __isl_give isl_basic_set *isl_basic_set_list_intersect(
7310 __isl_take struct isl_basic_set_list *list);
7311 __isl_give isl_set *isl_set_intersect_params(
7312 __isl_take isl_set *set,
7313 __isl_take isl_set *params);
7314 __isl_give isl_set *isl_set_intersect(
7315 __isl_take isl_set *set1,
7316 __isl_take isl_set *set2);
7317 __isl_give isl_set *isl_set_intersect_factor_domain(
7318 __isl_take isl_set *set,
7319 __isl_take isl_set *domain);
7320 __isl_give isl_set *isl_set_intersect_factor_range(
7321 __isl_take isl_set *set,
7322 __isl_take isl_set *range);
7324 #include <isl/map.h>
7325 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
7326 __isl_take isl_basic_map *bmap,
7327 __isl_take isl_basic_set *bset);
7328 __isl_give isl_basic_map *isl_basic_map_intersect_range(
7329 __isl_take isl_basic_map *bmap,
7330 __isl_take isl_basic_set *bset);
7331 __isl_give isl_basic_map *isl_basic_map_intersect(
7332 __isl_take isl_basic_map *bmap1,
7333 __isl_take isl_basic_map *bmap2);
7334 __isl_give isl_basic_map *isl_basic_map_list_intersect(
7335 __isl_take isl_basic_map_list *list);
7336 __isl_give isl_map *isl_map_intersect_params(
7337 __isl_take isl_map *map,
7338 __isl_take isl_set *params);
7339 __isl_give isl_map *isl_map_intersect_domain(
7340 __isl_take isl_map *map,
7341 __isl_take isl_set *set);
7342 __isl_give isl_map *isl_map_intersect_range(
7343 __isl_take isl_map *map,
7344 __isl_take isl_set *set);
7345 __isl_give isl_map *isl_map_intersect(
7346 __isl_take isl_map *map1,
7347 __isl_take isl_map *map2);
7348 __isl_give isl_map *
7349 isl_map_intersect_domain_factor_domain(
7350 __isl_take isl_map *map,
7351 __isl_take isl_map *factor);
7352 __isl_give isl_map *
7353 isl_map_intersect_domain_factor_range(
7354 __isl_take isl_map *map,
7355 __isl_take isl_map *factor);
7356 __isl_give isl_map *
7357 isl_map_intersect_range_factor_domain(
7358 __isl_take isl_map *map,
7359 __isl_take isl_map *factor);
7360 __isl_give isl_map *
7361 isl_map_intersect_range_factor_range(
7362 __isl_take isl_map *map,
7363 __isl_take isl_map *factor);
7365 #include <isl/union_set.h>
7366 __isl_give isl_union_set *isl_union_set_intersect_params(
7367 __isl_take isl_union_set *uset,
7368 __isl_take isl_set *set);
7369 __isl_give isl_union_set *isl_union_set_intersect(
7370 __isl_take isl_union_set *uset1,
7371 __isl_take isl_union_set *uset2);
7373 #include <isl/union_map.h>
7374 __isl_give isl_union_map *isl_union_map_intersect_params(
7375 __isl_take isl_union_map *umap,
7376 __isl_take isl_set *set);
7377 __isl_give isl_union_map *
7378 isl_union_map_intersect_domain_union_set(
7379 __isl_take isl_union_map *umap,
7380 __isl_take isl_union_set *uset);
7381 __isl_give isl_union_map *
7382 isl_union_map_intersect_domain_space(
7383 __isl_take isl_union_map *umap,
7384 __isl_take isl_space *space);
7385 __isl_give isl_union_map *isl_union_map_intersect_domain(
7386 __isl_take isl_union_map *umap,
7387 __isl_take isl_union_set *uset);
7388 __isl_give isl_union_map *
7389 isl_union_map_intersect_range_union_set(
7390 __isl_take isl_union_map *umap,
7391 __isl_take isl_union_set *uset);
7392 __isl_give isl_union_map *
7393 isl_union_map_intersect_range_space(
7394 __isl_take isl_union_map *umap,
7395 __isl_take isl_space *space);
7396 __isl_give isl_union_map *isl_union_map_intersect_range(
7397 __isl_take isl_union_map *umap,
7398 __isl_take isl_union_set *uset);
7399 __isl_give isl_union_map *isl_union_map_intersect(
7400 __isl_take isl_union_map *umap1,
7401 __isl_take isl_union_map *umap2);
7402 __isl_give isl_union_map *
7403 isl_union_map_intersect_domain_factor_domain(
7404 __isl_take isl_union_map *umap,
7405 __isl_take isl_union_map *factor);
7406 __isl_give isl_union_map *
7407 isl_union_map_intersect_domain_factor_range(
7408 __isl_take isl_union_map *umap,
7409 __isl_take isl_union_map *factor);
7410 __isl_give isl_union_map *
7411 isl_union_map_intersect_range_factor_domain(
7412 __isl_take isl_union_map *umap,
7413 __isl_take isl_union_map *factor);
7414 __isl_give isl_union_map *
7415 isl_union_map_intersect_range_factor_range(
7416 __isl_take isl_union_map *umap,
7417 __isl_take isl_union_map *factor);
7419 #include <isl/aff.h>
7420 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
7421 __isl_take isl_pw_aff *pa,
7422 __isl_take isl_set *set);
7423 __isl_give isl_multi_pw_aff *
7424 isl_multi_pw_aff_intersect_domain(
7425 __isl_take isl_multi_pw_aff *mpa,
7426 __isl_take isl_set *domain);
7427 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
7428 __isl_take isl_pw_multi_aff *pma,
7429 __isl_take isl_set *set);
7430 __isl_give isl_union_pw_aff *
7431 isl_union_pw_aff_intersect_domain_space(
7432 __isl_take isl_union_pw_aff *upa,
7433 __isl_take isl_space *space);
7434 __isl_give isl_union_pw_aff *
7435 isl_union_pw_aff_intersect_domain_union_set(
7436 __isl_take isl_union_pw_aff *upa,
7437 __isl_take isl_union_set *uset);
7438 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
7439 __isl_take isl_union_pw_aff *upa,
7440 __isl_take isl_union_set *uset);
7441 __isl_give isl_union_pw_multi_aff *
7442 isl_union_pw_multi_aff_intersect_domain_space(
7443 __isl_take isl_union_pw_multi_aff *upma,
7444 __isl_take isl_space *space);
7445 __isl_give isl_union_pw_multi_aff *
7446 isl_union_pw_multi_aff_intersect_domain_union_set(
7447 __isl_take isl_union_pw_multi_aff *upma,
7448 __isl_take isl_union_set *uset);
7449 __isl_give isl_union_pw_multi_aff *
7450 isl_union_pw_multi_aff_intersect_domain(
7451 __isl_take isl_union_pw_multi_aff *upma,
7452 __isl_take isl_union_set *uset);
7453 __isl_give isl_multi_union_pw_aff *
7454 isl_multi_union_pw_aff_intersect_domain(
7455 __isl_take isl_multi_union_pw_aff *mupa,
7456 __isl_take isl_union_set *uset);
7457 __isl_give isl_pw_aff *
7458 isl_pw_aff_intersect_domain_wrapped_domain(
7459 __isl_take isl_pw_aff *pa,
7460 __isl_take isl_set *set);
7461 __isl_give isl_pw_multi_aff *
7462 isl_pw_multi_aff_intersect_domain_wrapped_domain(
7463 __isl_take isl_pw_multi_aff *pma,
7464 __isl_take isl_set *set);
7465 __isl_give isl_union_pw_aff *
7466 isl_union_pw_aff_intersect_domain_wrapped_domain(
7467 __isl_take isl_union_pw_aff *upa,
7468 __isl_take isl_union_set *uset);
7469 __isl_give isl_union_pw_multi_aff *
7470 isl_union_pw_multi_aff_intersect_domain_wrapped_domain(
7471 __isl_take isl_union_pw_multi_aff *upma,
7472 __isl_take isl_union_set *uset);
7473 __isl_give isl_pw_aff *
7474 isl_pw_aff_intersect_domain_wrapped_range(
7475 __isl_take isl_pw_aff *pa,
7476 __isl_take isl_set *set);
7477 __isl_give isl_pw_multi_aff *
7478 isl_pw_multi_aff_intersect_domain_wrapped_range(
7479 __isl_take isl_pw_multi_aff *pma,
7480 __isl_take isl_set *set);
7481 __isl_give isl_union_pw_multi_aff *
7482 isl_union_pw_multi_aff_intersect_domain_wrapped_range(
7483 __isl_take isl_union_pw_multi_aff *upma,
7484 __isl_take isl_union_set *uset);
7485 __isl_give isl_union_pw_aff *
7486 isl_union_pw_aff_intersect_domain_wrapped_range(
7487 __isl_take isl_union_pw_aff *upa,
7488 __isl_take isl_union_set *uset);
7489 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
7490 __isl_take isl_pw_aff *pa,
7491 __isl_take isl_set *set);
7492 __isl_give isl_multi_pw_aff *
7493 isl_multi_pw_aff_intersect_params(
7494 __isl_take isl_multi_pw_aff *mpa,
7495 __isl_take isl_set *set);
7496 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
7497 __isl_take isl_pw_multi_aff *pma,
7498 __isl_take isl_set *set);
7499 __isl_give isl_union_pw_aff *
7500 isl_union_pw_aff_intersect_params(
7501 __isl_take isl_union_pw_aff *upa,
7502 __isl_take isl_set *set);
7503 __isl_give isl_union_pw_multi_aff *
7504 isl_union_pw_multi_aff_intersect_params(
7505 __isl_take isl_union_pw_multi_aff *upma,
7506 __isl_take isl_set *set);
7507 __isl_give isl_multi_union_pw_aff *
7508 isl_multi_union_pw_aff_intersect_params(
7509 __isl_take isl_multi_union_pw_aff *mupa,
7510 __isl_take isl_set *params);
7511 __isl_give isl_multi_union_pw_aff *
7512 isl_multi_union_pw_aff_intersect_range(
7513 __isl_take isl_multi_union_pw_aff *mupa,
7514 __isl_take isl_set *set);
7516 #include <isl/polynomial.h>
7517 __isl_give isl_pw_qpolynomial *
7518 isl_pw_qpolynomial_intersect_domain(
7519 __isl_take isl_pw_qpolynomial *pwpq,
7520 __isl_take isl_set *set);
7521 __isl_give isl_union_pw_qpolynomial *
7522 isl_union_pw_qpolynomial_intersect_domain_space(
7523 __isl_take isl_union_pw_qpolynomial *upwpq,
7524 __isl_take isl_space *space);
7525 __isl_give isl_union_pw_qpolynomial *
7526 isl_union_pw_qpolynomial_intersect_domain_union_set(
7527 __isl_take isl_union_pw_qpolynomial *upwpq,
7528 __isl_take isl_union_set *uset);
7529 __isl_give isl_union_pw_qpolynomial *
7530 isl_union_pw_qpolynomial_intersect_domain(
7531 __isl_take isl_union_pw_qpolynomial *upwpq,
7532 __isl_take isl_union_set *uset);
7533 __isl_give isl_union_pw_qpolynomial_fold *
7534 isl_union_pw_qpolynomial_fold_intersect_domain_space(
7535 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7536 __isl_take isl_space *space);
7537 __isl_give isl_union_pw_qpolynomial_fold *
7538 isl_union_pw_qpolynomial_fold_intersect_domain_union_set(
7539 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7540 __isl_take isl_union_set *uset);
7541 __isl_give isl_union_pw_qpolynomial_fold *
7542 isl_union_pw_qpolynomial_fold_intersect_domain(
7543 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7544 __isl_take isl_union_set *uset);
7545 __isl_give isl_pw_qpolynomial *
7546 isl_pw_qpolynomial_intersect_domain_wrapped_domain(
7547 __isl_take isl_pw_qpolynomial *pwpq,
7548 __isl_take isl_set *set);
7549 __isl_give isl_pw_qpolynomial_fold *
7550 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7551 __isl_take isl_pw_qpolynomial_fold *pwf,
7552 __isl_take isl_set *set);
7553 __isl_give isl_union_pw_qpolynomial *
7554 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain(
7555 __isl_take isl_union_pw_qpolynomial *upwpq,
7556 __isl_take isl_union_set *uset);
7557 __isl_give isl_union_pw_qpolynomial_fold *
7558 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7559 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7560 __isl_take isl_union_set *uset);
7561 __isl_give isl_pw_qpolynomial *
7562 isl_pw_qpolynomial_intersect_domain_wrapped_range(
7563 __isl_take isl_pw_qpolynomial *pwpq,
7564 __isl_take isl_set *set);
7565 __isl_give isl_pw_qpolynomial_fold *
7566 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7567 __isl_take isl_pw_qpolynomial_fold *pwf,
7568 __isl_take isl_set *set);
7569 __isl_give isl_union_pw_qpolynomial *
7570 isl_union_pw_qpolynomial_intersect_domain_wrapped_range(
7571 __isl_take isl_union_pw_qpolynomial *upwpq,
7572 __isl_take isl_union_set *uset);
7573 __isl_give isl_union_pw_qpolynomial_fold *
7574 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7575 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7576 __isl_take isl_union_set *uset);
7577 __isl_give isl_pw_qpolynomial *
7578 isl_pw_qpolynomial_intersect_params(
7579 __isl_take isl_pw_qpolynomial *pwpq,
7580 __isl_take isl_set *set);
7581 __isl_give isl_pw_qpolynomial_fold *
7582 isl_pw_qpolynomial_fold_intersect_params(
7583 __isl_take isl_pw_qpolynomial_fold *pwf,
7584 __isl_take isl_set *set);
7585 __isl_give isl_union_pw_qpolynomial *
7586 isl_union_pw_qpolynomial_intersect_params(
7587 __isl_take isl_union_pw_qpolynomial *upwpq,
7588 __isl_take isl_set *set);
7589 __isl_give isl_union_pw_qpolynomial_fold *
7590 isl_union_pw_qpolynomial_fold_intersect_params(
7591 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7592 __isl_take isl_set *set);
7594 The second argument to the C<_params> functions needs to be
7595 a parametric (basic) set. For the other functions, a parametric set
7596 for either argument is only allowed if the other argument is
7597 a parametric set as well.
7598 The list passed to C<isl_basic_set_list_intersect> needs to have
7599 at least one element and all elements need to live in the same space.
7600 The function C<isl_multi_union_pw_aff_intersect_range>
7601 restricts the input function to those shared domain elements
7602 that map to the specified range.
7603 C<isl_union_map_intersect_domain> is an alternative name for
7604 C<isl_union_map_intersect_domain_union_set>.
7605 Similarly for the other pairs of functions.
7609 #include <isl/set.h>
7610 __isl_give isl_set *isl_basic_set_union(
7611 __isl_take isl_basic_set *bset1,
7612 __isl_take isl_basic_set *bset2);
7613 __isl_give isl_set *isl_set_union(
7614 __isl_take isl_set *set1,
7615 __isl_take isl_set *set2);
7616 __isl_give isl_set *isl_set_list_union(
7617 __isl_take isl_set_list *list);
7619 #include <isl/map.h>
7620 __isl_give isl_map *isl_basic_map_union(
7621 __isl_take isl_basic_map *bmap1,
7622 __isl_take isl_basic_map *bmap2);
7623 __isl_give isl_map *isl_map_union(
7624 __isl_take isl_map *map1,
7625 __isl_take isl_map *map2);
7627 #include <isl/union_set.h>
7628 __isl_give isl_union_set *isl_union_set_union(
7629 __isl_take isl_union_set *uset1,
7630 __isl_take isl_union_set *uset2);
7631 __isl_give isl_union_set *isl_union_set_list_union(
7632 __isl_take isl_union_set_list *list);
7634 #include <isl/union_map.h>
7635 __isl_give isl_union_map *isl_union_map_union(
7636 __isl_take isl_union_map *umap1,
7637 __isl_take isl_union_map *umap2);
7639 The list passed to C<isl_set_list_union> needs to have
7640 at least one element and all elements need to live in the same space.
7642 =item * Set difference
7644 #include <isl/set.h>
7645 __isl_give isl_set *isl_set_subtract(
7646 __isl_take isl_set *set1,
7647 __isl_take isl_set *set2);
7649 #include <isl/map.h>
7650 __isl_give isl_map *isl_map_subtract(
7651 __isl_take isl_map *map1,
7652 __isl_take isl_map *map2);
7653 __isl_give isl_map *isl_map_subtract_domain(
7654 __isl_take isl_map *map,
7655 __isl_take isl_set *dom);
7656 __isl_give isl_map *isl_map_subtract_range(
7657 __isl_take isl_map *map,
7658 __isl_take isl_set *dom);
7660 #include <isl/union_set.h>
7661 __isl_give isl_union_set *isl_union_set_subtract(
7662 __isl_take isl_union_set *uset1,
7663 __isl_take isl_union_set *uset2);
7665 #include <isl/union_map.h>
7666 __isl_give isl_union_map *isl_union_map_subtract(
7667 __isl_take isl_union_map *umap1,
7668 __isl_take isl_union_map *umap2);
7669 __isl_give isl_union_map *isl_union_map_subtract_domain(
7670 __isl_take isl_union_map *umap,
7671 __isl_take isl_union_set *dom);
7672 __isl_give isl_union_map *isl_union_map_subtract_range(
7673 __isl_take isl_union_map *umap,
7674 __isl_take isl_union_set *dom);
7676 #include <isl/aff.h>
7677 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
7678 __isl_take isl_pw_aff *pa,
7679 __isl_take isl_set *set);
7680 __isl_give isl_pw_multi_aff *
7681 isl_pw_multi_aff_subtract_domain(
7682 __isl_take isl_pw_multi_aff *pma,
7683 __isl_take isl_set *set);
7684 __isl_give isl_union_pw_aff *
7685 isl_union_pw_aff_subtract_domain_union_set(
7686 __isl_take isl_union_pw_aff *upa,
7687 __isl_take isl_union_set *uset);
7688 __isl_give isl_union_pw_aff *
7689 isl_union_pw_aff_subtract_domain_space(
7690 __isl_take isl_union_pw_aff *upa,
7691 __isl_take isl_space *space);
7692 __isl_give isl_union_pw_aff *
7693 isl_union_pw_aff_subtract_domain(
7694 __isl_take isl_union_pw_aff *upa,
7695 __isl_take isl_union_set *uset);
7696 __isl_give isl_union_pw_multi_aff *
7697 isl_union_pw_multi_aff_subtract_domain_union_set(
7698 __isl_take isl_union_pw_multi_aff *upma,
7699 __isl_take isl_set *set);
7700 __isl_give isl_union_pw_multi_aff *
7701 isl_union_pw_multi_aff_subtract_domain_space(
7702 __isl_take isl_union_pw_multi_aff *upma,
7703 __isl_take isl_space *space);
7704 __isl_give isl_union_pw_multi_aff *
7705 isl_union_pw_multi_aff_subtract_domain(
7706 __isl_take isl_union_pw_multi_aff *upma,
7707 __isl_take isl_union_set *uset);
7709 #include <isl/polynomial.h>
7710 __isl_give isl_pw_qpolynomial *
7711 isl_pw_qpolynomial_subtract_domain(
7712 __isl_take isl_pw_qpolynomial *pwpq,
7713 __isl_take isl_set *set);
7714 __isl_give isl_pw_qpolynomial_fold *
7715 isl_pw_qpolynomial_fold_subtract_domain(
7716 __isl_take isl_pw_qpolynomial_fold *pwf,
7717 __isl_take isl_set *set);
7718 __isl_give isl_union_pw_qpolynomial *
7719 isl_union_pw_qpolynomial_subtract_domain_union_set(
7720 __isl_take isl_union_pw_qpolynomial *upwpq,
7721 __isl_take isl_union_set *uset);
7722 __isl_give isl_union_pw_qpolynomial *
7723 isl_union_pw_qpolynomial_subtract_domain_space(
7724 __isl_take isl_union_pw_qpolynomial *upwpq,
7725 __isl_take isl_space *space);
7726 __isl_give isl_union_pw_qpolynomial *
7727 isl_union_pw_qpolynomial_subtract_domain(
7728 __isl_take isl_union_pw_qpolynomial *upwpq,
7729 __isl_take isl_union_set *uset);
7730 __isl_give isl_union_pw_qpolynomial_fold *
7731 isl_union_pw_qpolynomial_fold_subtract_domain_union_set(
7732 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7733 __isl_take isl_union_set *uset);
7734 __isl_give isl_union_pw_qpolynomial_fold *
7735 isl_union_pw_qpolynomial_fold_subtract_domain_space(
7736 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7737 __isl_take isl_space *space);
7738 __isl_give isl_union_pw_qpolynomial_fold *
7739 isl_union_pw_qpolynomial_fold_subtract_domain(
7740 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7741 __isl_take isl_union_set *uset);
7743 C<isl_union_pw_aff_subtract_domain> is an alternative name for
7744 C<isl_union_pw_aff_subtract_domain_union_set>.
7745 Similarly for the other pairs of functions.
7749 #include <isl/space.h>
7750 __isl_give isl_space *isl_space_join(
7751 __isl_take isl_space *left,
7752 __isl_take isl_space *right);
7754 #include <isl/set.h>
7755 __isl_give isl_basic_set *isl_basic_set_apply(
7756 __isl_take isl_basic_set *bset,
7757 __isl_take isl_basic_map *bmap);
7758 __isl_give isl_set *isl_set_apply(
7759 __isl_take isl_set *set,
7760 __isl_take isl_map *map);
7762 #include <isl/union_set.h>
7763 __isl_give isl_union_set *isl_union_set_apply(
7764 __isl_take isl_union_set *uset,
7765 __isl_take isl_union_map *umap);
7767 #include <isl/map.h>
7768 __isl_give isl_basic_map *isl_basic_map_apply_domain(
7769 __isl_take isl_basic_map *bmap1,
7770 __isl_take isl_basic_map *bmap2);
7771 __isl_give isl_basic_map *isl_basic_map_apply_range(
7772 __isl_take isl_basic_map *bmap1,
7773 __isl_take isl_basic_map *bmap2);
7774 __isl_give isl_map *isl_map_apply_domain(
7775 __isl_take isl_map *map1,
7776 __isl_take isl_map *map2);
7777 __isl_give isl_map *isl_map_apply_range(
7778 __isl_take isl_map *map1,
7779 __isl_take isl_map *map2);
7781 #include <isl/union_map.h>
7782 __isl_give isl_union_map *isl_union_map_apply_domain(
7783 __isl_take isl_union_map *umap1,
7784 __isl_take isl_union_map *umap2);
7785 __isl_give isl_union_map *isl_union_map_apply_range(
7786 __isl_take isl_union_map *umap1,
7787 __isl_take isl_union_map *umap2);
7789 #include <isl/aff.h>
7790 __isl_give isl_union_pw_multi_aff *
7791 isl_union_pw_multi_aff_apply_union_pw_multi_aff(
7792 __isl_take isl_union_pw_multi_aff *upma1,
7793 __isl_take isl_union_pw_multi_aff *upma2);
7794 __isl_give isl_union_pw_aff *
7795 isl_multi_union_pw_aff_apply_aff(
7796 __isl_take isl_multi_union_pw_aff *mupa,
7797 __isl_take isl_aff *aff);
7798 __isl_give isl_union_pw_aff *
7799 isl_multi_union_pw_aff_apply_pw_aff(
7800 __isl_take isl_multi_union_pw_aff *mupa,
7801 __isl_take isl_pw_aff *pa);
7802 __isl_give isl_multi_union_pw_aff *
7803 isl_multi_union_pw_aff_apply_multi_aff(
7804 __isl_take isl_multi_union_pw_aff *mupa,
7805 __isl_take isl_multi_aff *ma);
7806 __isl_give isl_multi_union_pw_aff *
7807 isl_multi_union_pw_aff_apply_pw_multi_aff(
7808 __isl_take isl_multi_union_pw_aff *mupa,
7809 __isl_take isl_pw_multi_aff *pma);
7811 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
7812 over the shared domain of the elements of the input. The dimension is
7813 required to be greater than zero.
7814 The C<isl_multi_union_pw_aff> argument of
7815 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
7816 but only if the range of the C<isl_multi_aff> argument
7817 is also zero-dimensional.
7818 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
7820 #include <isl/polynomial.h>
7821 __isl_give isl_pw_qpolynomial_fold *
7822 isl_set_apply_pw_qpolynomial_fold(
7823 __isl_take isl_set *set,
7824 __isl_take isl_pw_qpolynomial_fold *pwf,
7826 __isl_give isl_pw_qpolynomial_fold *
7827 isl_map_apply_pw_qpolynomial_fold(
7828 __isl_take isl_map *map,
7829 __isl_take isl_pw_qpolynomial_fold *pwf,
7831 __isl_give isl_union_pw_qpolynomial_fold *
7832 isl_union_set_apply_union_pw_qpolynomial_fold(
7833 __isl_take isl_union_set *uset,
7834 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7836 __isl_give isl_union_pw_qpolynomial_fold *
7837 isl_union_map_apply_union_pw_qpolynomial_fold(
7838 __isl_take isl_union_map *umap,
7839 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7842 The functions taking a map
7843 compose the given map with the given piecewise quasipolynomial reduction.
7844 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
7845 over all elements in the intersection of the range of the map
7846 and the domain of the piecewise quasipolynomial reduction
7847 as a function of an element in the domain of the map.
7848 The functions taking a set compute a bound over all elements in the
7849 intersection of the set and the domain of the
7850 piecewise quasipolynomial reduction.
7854 #include <isl/set.h>
7855 __isl_give isl_basic_set *
7856 isl_basic_set_preimage_multi_aff(
7857 __isl_take isl_basic_set *bset,
7858 __isl_take isl_multi_aff *ma);
7859 __isl_give isl_set *isl_set_preimage_multi_aff(
7860 __isl_take isl_set *set,
7861 __isl_take isl_multi_aff *ma);
7862 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
7863 __isl_take isl_set *set,
7864 __isl_take isl_pw_multi_aff *pma);
7865 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
7866 __isl_take isl_set *set,
7867 __isl_take isl_multi_pw_aff *mpa);
7869 #include <isl/union_set.h>
7870 __isl_give isl_union_set *
7871 isl_union_set_preimage_multi_aff(
7872 __isl_take isl_union_set *uset,
7873 __isl_take isl_multi_aff *ma);
7874 __isl_give isl_union_set *
7875 isl_union_set_preimage_pw_multi_aff(
7876 __isl_take isl_union_set *uset,
7877 __isl_take isl_pw_multi_aff *pma);
7878 __isl_give isl_union_set *
7879 isl_union_set_preimage_union_pw_multi_aff(
7880 __isl_take isl_union_set *uset,
7881 __isl_take isl_union_pw_multi_aff *upma);
7883 #include <isl/map.h>
7884 __isl_give isl_basic_map *
7885 isl_basic_map_preimage_domain_multi_aff(
7886 __isl_take isl_basic_map *bmap,
7887 __isl_take isl_multi_aff *ma);
7888 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
7889 __isl_take isl_map *map,
7890 __isl_take isl_multi_aff *ma);
7891 __isl_give isl_map *isl_map_preimage_range_multi_aff(
7892 __isl_take isl_map *map,
7893 __isl_take isl_multi_aff *ma);
7894 __isl_give isl_map *
7895 isl_map_preimage_domain_pw_multi_aff(
7896 __isl_take isl_map *map,
7897 __isl_take isl_pw_multi_aff *pma);
7898 __isl_give isl_map *
7899 isl_map_preimage_range_pw_multi_aff(
7900 __isl_take isl_map *map,
7901 __isl_take isl_pw_multi_aff *pma);
7902 __isl_give isl_map *
7903 isl_map_preimage_domain_multi_pw_aff(
7904 __isl_take isl_map *map,
7905 __isl_take isl_multi_pw_aff *mpa);
7906 __isl_give isl_basic_map *
7907 isl_basic_map_preimage_range_multi_aff(
7908 __isl_take isl_basic_map *bmap,
7909 __isl_take isl_multi_aff *ma);
7911 #include <isl/union_map.h>
7912 __isl_give isl_union_map *
7913 isl_union_map_preimage_domain_multi_aff(
7914 __isl_take isl_union_map *umap,
7915 __isl_take isl_multi_aff *ma);
7916 __isl_give isl_union_map *
7917 isl_union_map_preimage_range_multi_aff(
7918 __isl_take isl_union_map *umap,
7919 __isl_take isl_multi_aff *ma);
7920 __isl_give isl_union_map *
7921 isl_union_map_preimage_domain_pw_multi_aff(
7922 __isl_take isl_union_map *umap,
7923 __isl_take isl_pw_multi_aff *pma);
7924 __isl_give isl_union_map *
7925 isl_union_map_preimage_range_pw_multi_aff(
7926 __isl_take isl_union_map *umap,
7927 __isl_take isl_pw_multi_aff *pma);
7928 __isl_give isl_union_map *
7929 isl_union_map_preimage_domain_union_pw_multi_aff(
7930 __isl_take isl_union_map *umap,
7931 __isl_take isl_union_pw_multi_aff *upma);
7932 __isl_give isl_union_map *
7933 isl_union_map_preimage_range_union_pw_multi_aff(
7934 __isl_take isl_union_map *umap,
7935 __isl_take isl_union_pw_multi_aff *upma);
7937 #include <isl/aff.h>
7938 __isl_give isl_pw_multi_aff *
7939 isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff(
7940 __isl_take isl_pw_multi_aff *pma1,
7941 __isl_take isl_pw_multi_aff *pma2);
7942 __isl_give isl_union_pw_multi_aff *
7943 isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff(
7944 __isl_take isl_union_pw_multi_aff *upma1,
7945 __isl_take isl_union_pw_multi_aff *upma2);
7947 These functions compute the preimage of the given set or map domain/range under
7948 the given function. In other words, the expression is plugged
7949 into the set description or into the domain/range of the map or function.
7953 #include <isl/aff.h>
7954 __isl_give isl_aff *isl_aff_pullback_aff(
7955 __isl_take isl_aff *aff1,
7956 __isl_take isl_aff *aff2);
7957 __isl_give isl_aff *isl_aff_pullback_multi_aff(
7958 __isl_take isl_aff *aff,
7959 __isl_take isl_multi_aff *ma);
7960 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
7961 __isl_take isl_pw_aff *pa,
7962 __isl_take isl_multi_aff *ma);
7963 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
7964 __isl_take isl_pw_aff *pa,
7965 __isl_take isl_pw_multi_aff *pma);
7966 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
7967 __isl_take isl_pw_aff *pa,
7968 __isl_take isl_multi_pw_aff *mpa);
7969 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
7970 __isl_take isl_multi_aff *ma1,
7971 __isl_take isl_multi_aff *ma2);
7972 __isl_give isl_pw_multi_aff *
7973 isl_pw_multi_aff_pullback_multi_aff(
7974 __isl_take isl_pw_multi_aff *pma,
7975 __isl_take isl_multi_aff *ma);
7976 __isl_give isl_multi_pw_aff *
7977 isl_multi_pw_aff_pullback_multi_aff(
7978 __isl_take isl_multi_pw_aff *mpa,
7979 __isl_take isl_multi_aff *ma);
7980 __isl_give isl_pw_multi_aff *
7981 isl_pw_multi_aff_pullback_pw_multi_aff(
7982 __isl_take isl_pw_multi_aff *pma1,
7983 __isl_take isl_pw_multi_aff *pma2);
7984 __isl_give isl_multi_pw_aff *
7985 isl_multi_pw_aff_pullback_pw_multi_aff(
7986 __isl_take isl_multi_pw_aff *mpa,
7987 __isl_take isl_pw_multi_aff *pma);
7988 __isl_give isl_multi_pw_aff *
7989 isl_multi_pw_aff_pullback_multi_pw_aff(
7990 __isl_take isl_multi_pw_aff *mpa1,
7991 __isl_take isl_multi_pw_aff *mpa2);
7992 __isl_give isl_union_pw_aff *
7993 isl_union_pw_aff_pullback_union_pw_multi_aff(
7994 __isl_take isl_union_pw_aff *upa,
7995 __isl_take isl_union_pw_multi_aff *upma);
7996 __isl_give isl_union_pw_multi_aff *
7997 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
7998 __isl_take isl_union_pw_multi_aff *upma1,
7999 __isl_take isl_union_pw_multi_aff *upma2);
8000 __isl_give isl_multi_union_pw_aff *
8001 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
8002 __isl_take isl_multi_union_pw_aff *mupa,
8003 __isl_take isl_union_pw_multi_aff *upma);
8005 These functions precompose the first expression by the second function.
8006 In other words, the second function is plugged
8007 into the first expression.
8011 #include <isl/aff.h>
8012 __isl_give isl_basic_set *isl_aff_eq_basic_set(
8013 __isl_take isl_aff *aff1,
8014 __isl_take isl_aff *aff2);
8015 __isl_give isl_set *isl_aff_eq_set(
8016 __isl_take isl_aff *aff1,
8017 __isl_take isl_aff *aff2);
8018 __isl_give isl_set *isl_aff_ne_set(
8019 __isl_take isl_aff *aff1,
8020 __isl_take isl_aff *aff2);
8021 __isl_give isl_basic_set *isl_aff_le_basic_set(
8022 __isl_take isl_aff *aff1,
8023 __isl_take isl_aff *aff2);
8024 __isl_give isl_set *isl_aff_le_set(
8025 __isl_take isl_aff *aff1,
8026 __isl_take isl_aff *aff2);
8027 __isl_give isl_basic_set *isl_aff_lt_basic_set(
8028 __isl_take isl_aff *aff1,
8029 __isl_take isl_aff *aff2);
8030 __isl_give isl_set *isl_aff_lt_set(
8031 __isl_take isl_aff *aff1,
8032 __isl_take isl_aff *aff2);
8033 __isl_give isl_basic_set *isl_aff_ge_basic_set(
8034 __isl_take isl_aff *aff1,
8035 __isl_take isl_aff *aff2);
8036 __isl_give isl_set *isl_aff_ge_set(
8037 __isl_take isl_aff *aff1,
8038 __isl_take isl_aff *aff2);
8039 __isl_give isl_basic_set *isl_aff_gt_basic_set(
8040 __isl_take isl_aff *aff1,
8041 __isl_take isl_aff *aff2);
8042 __isl_give isl_set *isl_aff_gt_set(
8043 __isl_take isl_aff *aff1,
8044 __isl_take isl_aff *aff2);
8045 __isl_give isl_set *isl_pw_aff_eq_set(
8046 __isl_take isl_pw_aff *pwaff1,
8047 __isl_take isl_pw_aff *pwaff2);
8048 __isl_give isl_set *isl_pw_aff_ne_set(
8049 __isl_take isl_pw_aff *pwaff1,
8050 __isl_take isl_pw_aff *pwaff2);
8051 __isl_give isl_set *isl_pw_aff_le_set(
8052 __isl_take isl_pw_aff *pwaff1,
8053 __isl_take isl_pw_aff *pwaff2);
8054 __isl_give isl_set *isl_pw_aff_lt_set(
8055 __isl_take isl_pw_aff *pwaff1,
8056 __isl_take isl_pw_aff *pwaff2);
8057 __isl_give isl_set *isl_pw_aff_ge_set(
8058 __isl_take isl_pw_aff *pwaff1,
8059 __isl_take isl_pw_aff *pwaff2);
8060 __isl_give isl_set *isl_pw_aff_gt_set(
8061 __isl_take isl_pw_aff *pwaff1,
8062 __isl_take isl_pw_aff *pwaff2);
8064 __isl_give isl_set *isl_multi_aff_lex_le_set(
8065 __isl_take isl_multi_aff *ma1,
8066 __isl_take isl_multi_aff *ma2);
8067 __isl_give isl_set *isl_multi_aff_lex_lt_set(
8068 __isl_take isl_multi_aff *ma1,
8069 __isl_take isl_multi_aff *ma2);
8070 __isl_give isl_set *isl_multi_aff_lex_ge_set(
8071 __isl_take isl_multi_aff *ma1,
8072 __isl_take isl_multi_aff *ma2);
8073 __isl_give isl_set *isl_multi_aff_lex_gt_set(
8074 __isl_take isl_multi_aff *ma1,
8075 __isl_take isl_multi_aff *ma2);
8077 __isl_give isl_set *isl_pw_aff_list_eq_set(
8078 __isl_take isl_pw_aff_list *list1,
8079 __isl_take isl_pw_aff_list *list2);
8080 __isl_give isl_set *isl_pw_aff_list_ne_set(
8081 __isl_take isl_pw_aff_list *list1,
8082 __isl_take isl_pw_aff_list *list2);
8083 __isl_give isl_set *isl_pw_aff_list_le_set(
8084 __isl_take isl_pw_aff_list *list1,
8085 __isl_take isl_pw_aff_list *list2);
8086 __isl_give isl_set *isl_pw_aff_list_lt_set(
8087 __isl_take isl_pw_aff_list *list1,
8088 __isl_take isl_pw_aff_list *list2);
8089 __isl_give isl_set *isl_pw_aff_list_ge_set(
8090 __isl_take isl_pw_aff_list *list1,
8091 __isl_take isl_pw_aff_list *list2);
8092 __isl_give isl_set *isl_pw_aff_list_gt_set(
8093 __isl_take isl_pw_aff_list *list1,
8094 __isl_take isl_pw_aff_list *list2);
8096 The function C<isl_aff_ge_basic_set> returns a basic set
8097 containing those elements in the shared space
8098 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
8099 The function C<isl_pw_aff_ge_set> returns a set
8100 containing those elements in the shared domain
8101 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
8102 greater than or equal to C<pwaff2>.
8103 The function C<isl_multi_aff_lex_le_set> returns a set
8104 containing those elements in the shared domain space
8105 where C<ma1> is lexicographically smaller than or
8107 The functions operating on C<isl_pw_aff_list> apply the corresponding
8108 C<isl_pw_aff> function to each pair of elements in the two lists.
8110 #include <isl/aff.h>
8111 __isl_give isl_map *isl_pw_aff_eq_map(
8112 __isl_take isl_pw_aff *pa1,
8113 __isl_take isl_pw_aff *pa2);
8114 __isl_give isl_map *isl_pw_aff_le_map(
8115 __isl_take isl_pw_aff *pa1,
8116 __isl_take isl_pw_aff *pa2);
8117 __isl_give isl_map *isl_pw_aff_lt_map(
8118 __isl_take isl_pw_aff *pa1,
8119 __isl_take isl_pw_aff *pa2);
8120 __isl_give isl_map *isl_pw_aff_ge_map(
8121 __isl_take isl_pw_aff *pa1,
8122 __isl_take isl_pw_aff *pa2);
8123 __isl_give isl_map *isl_pw_aff_gt_map(
8124 __isl_take isl_pw_aff *pa1,
8125 __isl_take isl_pw_aff *pa2);
8127 __isl_give isl_map *isl_multi_pw_aff_eq_map(
8128 __isl_take isl_multi_pw_aff *mpa1,
8129 __isl_take isl_multi_pw_aff *mpa2);
8130 __isl_give isl_map *isl_multi_pw_aff_lex_le_map(
8131 __isl_take isl_multi_pw_aff *mpa1,
8132 __isl_take isl_multi_pw_aff *mpa2);
8133 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
8134 __isl_take isl_multi_pw_aff *mpa1,
8135 __isl_take isl_multi_pw_aff *mpa2);
8136 __isl_give isl_map *isl_multi_pw_aff_lex_ge_map(
8137 __isl_take isl_multi_pw_aff *mpa1,
8138 __isl_take isl_multi_pw_aff *mpa2);
8139 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
8140 __isl_take isl_multi_pw_aff *mpa1,
8141 __isl_take isl_multi_pw_aff *mpa2);
8143 These functions return a map between domain elements of the arguments
8144 where the function values satisfy the given relation.
8146 #include <isl/map.h>
8147 __isl_give isl_map *isl_map_eq_at_multi_pw_aff(
8148 __isl_take isl_map *map,
8149 __isl_take isl_multi_pw_aff *mpa);
8150 __isl_give isl_map *isl_map_lex_lt_at_multi_pw_aff(
8151 __isl_take isl_map *map,
8152 __isl_take isl_multi_pw_aff *mpa);
8153 __isl_give isl_map *isl_map_lex_le_at_multi_pw_aff(
8154 __isl_take isl_map *map,
8155 __isl_take isl_multi_pw_aff *mpa);
8156 __isl_give isl_map *isl_map_lex_gt_at_multi_pw_aff(
8157 __isl_take isl_map *map,
8158 __isl_take isl_multi_pw_aff *mpa);
8159 __isl_give isl_map *isl_map_lex_ge_at_multi_pw_aff(
8160 __isl_take isl_map *map,
8161 __isl_take isl_multi_pw_aff *mpa);
8163 #include <isl/union_map.h>
8164 __isl_give isl_union_map *
8165 isl_union_map_eq_at_multi_union_pw_aff(
8166 __isl_take isl_union_map *umap,
8167 __isl_take isl_multi_union_pw_aff *mupa);
8168 __isl_give isl_union_map *
8169 isl_union_map_lex_lt_at_multi_union_pw_aff(
8170 __isl_take isl_union_map *umap,
8171 __isl_take isl_multi_union_pw_aff *mupa);
8172 __isl_give isl_union_map *
8173 isl_union_map_lex_le_at_multi_union_pw_aff(
8174 __isl_take isl_union_map *umap,
8175 __isl_take isl_multi_union_pw_aff *mupa);
8176 __isl_give isl_union_map *
8177 isl_union_map_lex_gt_at_multi_union_pw_aff(
8178 __isl_take isl_union_map *umap,
8179 __isl_take isl_multi_union_pw_aff *mupa);
8180 __isl_give isl_union_map *
8181 isl_union_map_lex_ge_at_multi_union_pw_aff(
8182 __isl_take isl_union_map *umap,
8183 __isl_take isl_multi_union_pw_aff *mupa);
8185 These functions select the subset of elements in the union map
8186 that have an equal or lexicographically smaller or greater function value.
8188 =item * Cartesian Product
8190 #include <isl/space.h>
8191 __isl_give isl_space *isl_space_product(
8192 __isl_take isl_space *space1,
8193 __isl_take isl_space *space2);
8194 __isl_give isl_space *isl_space_domain_product(
8195 __isl_take isl_space *space1,
8196 __isl_take isl_space *space2);
8197 __isl_give isl_space *isl_space_range_product(
8198 __isl_take isl_space *space1,
8199 __isl_take isl_space *space2);
8202 C<isl_space_product>, C<isl_space_domain_product>
8203 and C<isl_space_range_product> take pairs or relation spaces and
8204 produce a single relations space, where either the domain, the range
8205 or both domain and range are wrapped spaces of relations between
8206 the domains and/or ranges of the input spaces.
8207 If the product is only constructed over the domain or the range
8208 then the ranges or the domains of the inputs should be the same.
8209 The function C<isl_space_product> also accepts a pair of set spaces,
8210 in which case it returns a wrapped space of a relation between the
8213 #include <isl/set.h>
8214 __isl_give isl_set *isl_set_product(
8215 __isl_take isl_set *set1,
8216 __isl_take isl_set *set2);
8218 #include <isl/map.h>
8219 __isl_give isl_basic_map *isl_basic_map_domain_product(
8220 __isl_take isl_basic_map *bmap1,
8221 __isl_take isl_basic_map *bmap2);
8222 __isl_give isl_basic_map *isl_basic_map_range_product(
8223 __isl_take isl_basic_map *bmap1,
8224 __isl_take isl_basic_map *bmap2);
8225 __isl_give isl_basic_map *isl_basic_map_product(
8226 __isl_take isl_basic_map *bmap1,
8227 __isl_take isl_basic_map *bmap2);
8228 __isl_give isl_map *isl_map_domain_product(
8229 __isl_take isl_map *map1,
8230 __isl_take isl_map *map2);
8231 __isl_give isl_map *isl_map_range_product(
8232 __isl_take isl_map *map1,
8233 __isl_take isl_map *map2);
8234 __isl_give isl_map *isl_map_product(
8235 __isl_take isl_map *map1,
8236 __isl_take isl_map *map2);
8238 #include <isl/union_set.h>
8239 __isl_give isl_union_set *isl_union_set_product(
8240 __isl_take isl_union_set *uset1,
8241 __isl_take isl_union_set *uset2);
8243 #include <isl/union_map.h>
8244 __isl_give isl_union_map *isl_union_map_domain_product(
8245 __isl_take isl_union_map *umap1,
8246 __isl_take isl_union_map *umap2);
8247 __isl_give isl_union_map *isl_union_map_range_product(
8248 __isl_take isl_union_map *umap1,
8249 __isl_take isl_union_map *umap2);
8250 __isl_give isl_union_map *isl_union_map_product(
8251 __isl_take isl_union_map *umap1,
8252 __isl_take isl_union_map *umap2);
8255 __isl_give isl_multi_id *isl_multi_id_range_product(
8256 __isl_take isl_multi_id *mi1,
8257 __isl_take isl_multi_id *mi2);
8259 #include <isl/val.h>
8260 __isl_give isl_multi_val *isl_multi_val_range_product(
8261 __isl_take isl_multi_val *mv1,
8262 __isl_take isl_multi_val *mv2);
8263 __isl_give isl_multi_val *isl_multi_val_product(
8264 __isl_take isl_multi_val *mv1,
8265 __isl_take isl_multi_val *mv2);
8267 #include <isl/aff.h>
8268 __isl_give isl_multi_aff *isl_multi_aff_range_product(
8269 __isl_take isl_multi_aff *ma1,
8270 __isl_take isl_multi_aff *ma2);
8271 __isl_give isl_multi_aff *isl_multi_aff_product(
8272 __isl_take isl_multi_aff *ma1,
8273 __isl_take isl_multi_aff *ma2);
8274 __isl_give isl_multi_pw_aff *
8275 isl_multi_pw_aff_range_product(
8276 __isl_take isl_multi_pw_aff *mpa1,
8277 __isl_take isl_multi_pw_aff *mpa2);
8278 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
8279 __isl_take isl_multi_pw_aff *mpa1,
8280 __isl_take isl_multi_pw_aff *mpa2);
8281 __isl_give isl_pw_multi_aff *
8282 isl_pw_multi_aff_range_product(
8283 __isl_take isl_pw_multi_aff *pma1,
8284 __isl_take isl_pw_multi_aff *pma2);
8285 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
8286 __isl_take isl_pw_multi_aff *pma1,
8287 __isl_take isl_pw_multi_aff *pma2);
8288 __isl_give isl_union_pw_multi_aff *
8289 isl_union_pw_multi_aff_range_product(
8290 __isl_take isl_union_pw_multi_aff *upma1,
8291 __isl_take isl_union_pw_multi_aff *upma2);
8292 __isl_give isl_multi_union_pw_aff *
8293 isl_multi_union_pw_aff_range_product(
8294 __isl_take isl_multi_union_pw_aff *mupa1,
8295 __isl_take isl_multi_union_pw_aff *mupa2);
8297 The above functions compute the cross product of the given
8298 sets, relations or functions. The domains and ranges of the results
8299 are wrapped maps between domains and ranges of the inputs.
8300 To obtain a ``flat'' product, use the following functions
8303 #include <isl/set.h>
8304 __isl_give isl_basic_set *isl_basic_set_flat_product(
8305 __isl_take isl_basic_set *bset1,
8306 __isl_take isl_basic_set *bset2);
8307 __isl_give isl_set *isl_set_flat_product(
8308 __isl_take isl_set *set1,
8309 __isl_take isl_set *set2);
8311 #include <isl/map.h>
8312 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8313 __isl_take isl_basic_map *bmap1,
8314 __isl_take isl_basic_map *bmap2);
8315 __isl_give isl_map *isl_map_flat_domain_product(
8316 __isl_take isl_map *map1,
8317 __isl_take isl_map *map2);
8318 __isl_give isl_map *isl_map_flat_range_product(
8319 __isl_take isl_map *map1,
8320 __isl_take isl_map *map2);
8321 __isl_give isl_basic_map *isl_basic_map_flat_product(
8322 __isl_take isl_basic_map *bmap1,
8323 __isl_take isl_basic_map *bmap2);
8324 __isl_give isl_map *isl_map_flat_product(
8325 __isl_take isl_map *map1,
8326 __isl_take isl_map *map2);
8328 #include <isl/union_map.h>
8329 __isl_give isl_union_map *
8330 isl_union_map_flat_domain_product(
8331 __isl_take isl_union_map *umap1,
8332 __isl_take isl_union_map *umap2);
8333 __isl_give isl_union_map *
8334 isl_union_map_flat_range_product(
8335 __isl_take isl_union_map *umap1,
8336 __isl_take isl_union_map *umap2);
8339 __isl_give isl_multi_id *
8340 isl_multi_id_flat_range_product(
8341 __isl_take isl_multi_id *mi1,
8342 __isl_take isl_multi_id *mi2);
8344 #include <isl/val.h>
8345 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
8346 __isl_take isl_multi_val *mv1,
8347 __isl_take isl_multi_val *mv2);
8349 #include <isl/aff.h>
8350 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
8351 __isl_take isl_multi_aff *ma1,
8352 __isl_take isl_multi_aff *ma2);
8353 __isl_give isl_pw_multi_aff *
8354 isl_pw_multi_aff_flat_range_product(
8355 __isl_take isl_pw_multi_aff *pma1,
8356 __isl_take isl_pw_multi_aff *pma2);
8357 __isl_give isl_multi_pw_aff *
8358 isl_multi_pw_aff_flat_range_product(
8359 __isl_take isl_multi_pw_aff *mpa1,
8360 __isl_take isl_multi_pw_aff *mpa2);
8361 __isl_give isl_union_pw_multi_aff *
8362 isl_union_pw_multi_aff_flat_range_product(
8363 __isl_take isl_union_pw_multi_aff *upma1,
8364 __isl_take isl_union_pw_multi_aff *upma2);
8365 __isl_give isl_multi_union_pw_aff *
8366 isl_multi_union_pw_aff_flat_range_product(
8367 __isl_take isl_multi_union_pw_aff *mupa1,
8368 __isl_take isl_multi_union_pw_aff *mupa2);
8370 #include <isl/space.h>
8371 __isl_give isl_space *isl_space_factor_domain(
8372 __isl_take isl_space *space);
8373 __isl_give isl_space *isl_space_factor_range(
8374 __isl_take isl_space *space);
8375 __isl_give isl_space *isl_space_domain_factor_domain(
8376 __isl_take isl_space *space);
8377 __isl_give isl_space *isl_space_domain_factor_range(
8378 __isl_take isl_space *space);
8379 __isl_give isl_space *isl_space_range_factor_domain(
8380 __isl_take isl_space *space);
8381 __isl_give isl_space *isl_space_range_factor_range(
8382 __isl_take isl_space *space);
8384 The functions C<isl_space_range_factor_domain> and
8385 C<isl_space_range_factor_range> extract the two arguments from
8386 the result of a call to C<isl_space_range_product>.
8388 The arguments of a call to a product can be extracted
8389 from the result using the following functions.
8391 #include <isl/map.h>
8392 __isl_give isl_map *isl_map_factor_domain(
8393 __isl_take isl_map *map);
8394 __isl_give isl_map *isl_map_factor_range(
8395 __isl_take isl_map *map);
8396 __isl_give isl_map *isl_map_domain_factor_domain(
8397 __isl_take isl_map *map);
8398 __isl_give isl_map *isl_map_domain_factor_range(
8399 __isl_take isl_map *map);
8400 __isl_give isl_map *isl_map_range_factor_domain(
8401 __isl_take isl_map *map);
8402 __isl_give isl_map *isl_map_range_factor_range(
8403 __isl_take isl_map *map);
8405 #include <isl/union_map.h>
8406 __isl_give isl_union_map *isl_union_map_factor_domain(
8407 __isl_take isl_union_map *umap);
8408 __isl_give isl_union_map *isl_union_map_factor_range(
8409 __isl_take isl_union_map *umap);
8410 __isl_give isl_union_map *
8411 isl_union_map_domain_factor_domain(
8412 __isl_take isl_union_map *umap);
8413 __isl_give isl_union_map *
8414 isl_union_map_domain_factor_range(
8415 __isl_take isl_union_map *umap);
8416 __isl_give isl_union_map *
8417 isl_union_map_range_factor_domain(
8418 __isl_take isl_union_map *umap);
8419 __isl_give isl_union_map *
8420 isl_union_map_range_factor_range(
8421 __isl_take isl_union_map *umap);
8424 __isl_give isl_multi_id *isl_multi_id_factor_range(
8425 __isl_take isl_multi_id *mi);
8426 __isl_give isl_multi_id *
8427 isl_multi_id_range_factor_domain(
8428 __isl_take isl_multi_id *mi);
8429 __isl_give isl_multi_id *
8430 isl_multi_id_range_factor_range(
8431 __isl_take isl_multi_id *mi);
8433 #include <isl/val.h>
8434 __isl_give isl_multi_val *isl_multi_val_factor_range(
8435 __isl_take isl_multi_val *mv);
8436 __isl_give isl_multi_val *
8437 isl_multi_val_range_factor_domain(
8438 __isl_take isl_multi_val *mv);
8439 __isl_give isl_multi_val *
8440 isl_multi_val_range_factor_range(
8441 __isl_take isl_multi_val *mv);
8443 #include <isl/aff.h>
8444 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
8445 __isl_take isl_multi_aff *ma);
8446 __isl_give isl_multi_aff *
8447 isl_multi_aff_range_factor_domain(
8448 __isl_take isl_multi_aff *ma);
8449 __isl_give isl_multi_aff *
8450 isl_multi_aff_range_factor_range(
8451 __isl_take isl_multi_aff *ma);
8452 __isl_give isl_multi_pw_aff *
8453 isl_multi_pw_aff_factor_range(
8454 __isl_take isl_multi_pw_aff *mpa);
8455 __isl_give isl_multi_pw_aff *
8456 isl_multi_pw_aff_range_factor_domain(
8457 __isl_take isl_multi_pw_aff *mpa);
8458 __isl_give isl_multi_pw_aff *
8459 isl_multi_pw_aff_range_factor_range(
8460 __isl_take isl_multi_pw_aff *mpa);
8461 __isl_give isl_pw_multi_aff *
8462 isl_pw_multi_aff_range_factor_domain(
8463 __isl_take isl_pw_multi_aff *pma);
8464 __isl_give isl_pw_multi_aff *
8465 isl_pw_multi_aff_range_factor_range(
8466 __isl_take isl_pw_multi_aff *pma);
8467 __isl_give isl_union_pw_multi_aff *
8468 isl_union_pw_multi_aff_range_factor_domain(
8469 __isl_take isl_union_pw_multi_aff *upma);
8470 __isl_give isl_union_pw_multi_aff *
8471 isl_union_pw_multi_aff_range_factor_range(
8472 __isl_take isl_union_pw_multi_aff *upma);
8473 __isl_give isl_multi_union_pw_aff *
8474 isl_multi_union_pw_aff_factor_range(
8475 __isl_take isl_multi_union_pw_aff *mupa);
8476 __isl_give isl_multi_union_pw_aff *
8477 isl_multi_union_pw_aff_range_factor_domain(
8478 __isl_take isl_multi_union_pw_aff *mupa);
8479 __isl_give isl_multi_union_pw_aff *
8480 isl_multi_union_pw_aff_range_factor_range(
8481 __isl_take isl_multi_union_pw_aff *mupa);
8483 The splice functions are a generalization of the flat product functions,
8484 where the second argument may be inserted at any position inside
8485 the first argument rather than being placed at the end.
8486 The functions C<isl_multi_val_factor_range>,
8487 C<isl_multi_aff_factor_range>,
8488 C<isl_multi_pw_aff_factor_range> and
8489 C<isl_multi_union_pw_aff_factor_range>
8490 take functions that live in a set space.
8493 __isl_give isl_multi_id *isl_multi_id_range_splice(
8494 __isl_take isl_multi_id *mi1, unsigned pos,
8495 __isl_take isl_multi_id *mi2);
8497 #include <isl/val.h>
8498 __isl_give isl_multi_val *isl_multi_val_range_splice(
8499 __isl_take isl_multi_val *mv1, unsigned pos,
8500 __isl_take isl_multi_val *mv2);
8502 #include <isl/aff.h>
8503 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
8504 __isl_take isl_multi_aff *ma1, unsigned pos,
8505 __isl_take isl_multi_aff *ma2);
8506 __isl_give isl_multi_aff *isl_multi_aff_splice(
8507 __isl_take isl_multi_aff *ma1,
8508 unsigned in_pos, unsigned out_pos,
8509 __isl_take isl_multi_aff *ma2);
8510 __isl_give isl_multi_pw_aff *
8511 isl_multi_pw_aff_range_splice(
8512 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
8513 __isl_take isl_multi_pw_aff *mpa2);
8514 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
8515 __isl_take isl_multi_pw_aff *mpa1,
8516 unsigned in_pos, unsigned out_pos,
8517 __isl_take isl_multi_pw_aff *mpa2);
8518 __isl_give isl_multi_union_pw_aff *
8519 isl_multi_union_pw_aff_range_splice(
8520 __isl_take isl_multi_union_pw_aff *mupa1,
8522 __isl_take isl_multi_union_pw_aff *mupa2);
8524 =item * Simplification
8526 When applied to a set or relation,
8527 the gist operation returns a set or relation that has the
8528 same intersection with the context as the input set or relation.
8529 Any implicit equality in the intersection is made explicit in the result,
8530 while all inequalities that are redundant with respect to the intersection
8532 In case of union sets and relations, the gist operation is performed
8535 When applied to a function,
8536 the gist operation applies the set gist operation to each of
8537 the cells in the domain of the input piecewise expression.
8538 The context is also exploited
8539 to simplify the expression associated to each cell.
8541 #include <isl/set.h>
8542 __isl_give isl_basic_set *isl_basic_set_gist(
8543 __isl_take isl_basic_set *bset,
8544 __isl_take isl_basic_set *context);
8545 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
8546 __isl_take isl_set *context);
8547 __isl_give isl_set *isl_set_gist_params(
8548 __isl_take isl_set *set,
8549 __isl_take isl_set *context);
8551 #include <isl/map.h>
8552 __isl_give isl_basic_map *isl_basic_map_gist(
8553 __isl_take isl_basic_map *bmap,
8554 __isl_take isl_basic_map *context);
8555 __isl_give isl_basic_map *isl_basic_map_gist_domain(
8556 __isl_take isl_basic_map *bmap,
8557 __isl_take isl_basic_set *context);
8558 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
8559 __isl_take isl_map *context);
8560 __isl_give isl_map *isl_map_gist_params(
8561 __isl_take isl_map *map,
8562 __isl_take isl_set *context);
8563 __isl_give isl_map *isl_map_gist_domain(
8564 __isl_take isl_map *map,
8565 __isl_take isl_set *context);
8566 __isl_give isl_map *isl_map_gist_range(
8567 __isl_take isl_map *map,
8568 __isl_take isl_set *context);
8570 #include <isl/union_set.h>
8571 __isl_give isl_union_set *isl_union_set_gist(
8572 __isl_take isl_union_set *uset,
8573 __isl_take isl_union_set *context);
8574 __isl_give isl_union_set *isl_union_set_gist_params(
8575 __isl_take isl_union_set *uset,
8576 __isl_take isl_set *set);
8578 #include <isl/union_map.h>
8579 __isl_give isl_union_map *isl_union_map_gist(
8580 __isl_take isl_union_map *umap,
8581 __isl_take isl_union_map *context);
8582 __isl_give isl_union_map *isl_union_map_gist_params(
8583 __isl_take isl_union_map *umap,
8584 __isl_take isl_set *set);
8585 __isl_give isl_union_map *isl_union_map_gist_domain(
8586 __isl_take isl_union_map *umap,
8587 __isl_take isl_union_set *uset);
8588 __isl_give isl_union_map *isl_union_map_gist_range(
8589 __isl_take isl_union_map *umap,
8590 __isl_take isl_union_set *uset);
8592 #include <isl/aff.h>
8593 __isl_give isl_aff *isl_aff_gist_params(
8594 __isl_take isl_aff *aff,
8595 __isl_take isl_set *context);
8596 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
8597 __isl_take isl_set *context);
8598 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
8599 __isl_take isl_multi_aff *maff,
8600 __isl_take isl_set *context);
8601 __isl_give isl_multi_aff *isl_multi_aff_gist(
8602 __isl_take isl_multi_aff *maff,
8603 __isl_take isl_set *context);
8604 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
8605 __isl_take isl_pw_aff *pwaff,
8606 __isl_take isl_set *context);
8607 __isl_give isl_pw_aff *isl_pw_aff_gist(
8608 __isl_take isl_pw_aff *pwaff,
8609 __isl_take isl_set *context);
8610 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
8611 __isl_take isl_pw_multi_aff *pma,
8612 __isl_take isl_set *set);
8613 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
8614 __isl_take isl_pw_multi_aff *pma,
8615 __isl_take isl_set *set);
8616 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
8617 __isl_take isl_multi_pw_aff *mpa,
8618 __isl_take isl_set *set);
8619 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
8620 __isl_take isl_multi_pw_aff *mpa,
8621 __isl_take isl_set *set);
8622 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
8623 __isl_take isl_union_pw_aff *upa,
8624 __isl_take isl_union_set *context);
8625 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
8626 __isl_take isl_union_pw_aff *upa,
8627 __isl_take isl_set *context);
8628 __isl_give isl_union_pw_multi_aff *
8629 isl_union_pw_multi_aff_gist_params(
8630 __isl_take isl_union_pw_multi_aff *upma,
8631 __isl_take isl_set *context);
8632 __isl_give isl_union_pw_multi_aff *
8633 isl_union_pw_multi_aff_gist(
8634 __isl_take isl_union_pw_multi_aff *upma,
8635 __isl_take isl_union_set *context);
8636 __isl_give isl_multi_union_pw_aff *
8637 isl_multi_union_pw_aff_gist_params(
8638 __isl_take isl_multi_union_pw_aff *mupa,
8639 __isl_take isl_set *context);
8640 __isl_give isl_multi_union_pw_aff *
8641 isl_multi_union_pw_aff_gist(
8642 __isl_take isl_multi_union_pw_aff *mupa,
8643 __isl_take isl_union_set *context);
8645 #include <isl/polynomial.h>
8646 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
8647 __isl_take isl_qpolynomial *qp,
8648 __isl_take isl_set *context);
8649 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
8650 __isl_take isl_qpolynomial *qp,
8651 __isl_take isl_set *context);
8652 __isl_give isl_qpolynomial_fold *
8653 isl_qpolynomial_fold_gist_params(
8654 __isl_take isl_qpolynomial_fold *fold,
8655 __isl_take isl_set *context);
8656 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
8657 __isl_take isl_qpolynomial_fold *fold,
8658 __isl_take isl_set *context);
8659 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
8660 __isl_take isl_pw_qpolynomial *pwqp,
8661 __isl_take isl_set *context);
8662 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
8663 __isl_take isl_pw_qpolynomial *pwqp,
8664 __isl_take isl_set *context);
8665 __isl_give isl_pw_qpolynomial_fold *
8666 isl_pw_qpolynomial_fold_gist(
8667 __isl_take isl_pw_qpolynomial_fold *pwf,
8668 __isl_take isl_set *context);
8669 __isl_give isl_pw_qpolynomial_fold *
8670 isl_pw_qpolynomial_fold_gist_params(
8671 __isl_take isl_pw_qpolynomial_fold *pwf,
8672 __isl_take isl_set *context);
8673 __isl_give isl_union_pw_qpolynomial *
8674 isl_union_pw_qpolynomial_gist_params(
8675 __isl_take isl_union_pw_qpolynomial *upwqp,
8676 __isl_take isl_set *context);
8677 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
8678 __isl_take isl_union_pw_qpolynomial *upwqp,
8679 __isl_take isl_union_set *context);
8680 __isl_give isl_union_pw_qpolynomial_fold *
8681 isl_union_pw_qpolynomial_fold_gist(
8682 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8683 __isl_take isl_union_set *context);
8684 __isl_give isl_union_pw_qpolynomial_fold *
8685 isl_union_pw_qpolynomial_fold_gist_params(
8686 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8687 __isl_take isl_set *context);
8689 =item * Binary Arithmetic Operations
8691 #include <isl/set.h>
8692 __isl_give isl_set *isl_set_sum(
8693 __isl_take isl_set *set1,
8694 __isl_take isl_set *set2);
8695 #include <isl/map.h>
8696 __isl_give isl_map *isl_map_sum(
8697 __isl_take isl_map *map1,
8698 __isl_take isl_map *map2);
8700 C<isl_set_sum> computes the Minkowski sum of its two arguments,
8701 i.e., the set containing the sums of pairs of elements from
8702 C<set1> and C<set2>.
8703 The domain of the result of C<isl_map_sum> is the intersection
8704 of the domains of its two arguments. The corresponding range
8705 elements are the sums of the corresponding range elements
8706 in the two arguments.
8708 #include <isl/val.h>
8709 __isl_give isl_multi_val *isl_multi_val_add(
8710 __isl_take isl_multi_val *mv1,
8711 __isl_take isl_multi_val *mv2);
8712 __isl_give isl_multi_val *isl_multi_val_sub(
8713 __isl_take isl_multi_val *mv1,
8714 __isl_take isl_multi_val *mv2);
8715 __isl_give isl_multi_val *isl_multi_val_min(
8716 __isl_take isl_multi_val *mv1,
8717 __isl_take isl_multi_val *mv2);
8718 __isl_give isl_multi_val *isl_multi_val_max(
8719 __isl_take isl_multi_val *mv1,
8720 __isl_take isl_multi_val *mv2);
8722 #include <isl/aff.h>
8723 __isl_give isl_aff *isl_aff_add(
8724 __isl_take isl_aff *aff1,
8725 __isl_take isl_aff *aff2);
8726 __isl_give isl_multi_aff *isl_multi_aff_add(
8727 __isl_take isl_multi_aff *maff1,
8728 __isl_take isl_multi_aff *maff2);
8729 __isl_give isl_pw_aff *isl_pw_aff_add(
8730 __isl_take isl_pw_aff *pwaff1,
8731 __isl_take isl_pw_aff *pwaff2);
8732 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
8733 __isl_take isl_multi_pw_aff *mpa1,
8734 __isl_take isl_multi_pw_aff *mpa2);
8735 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
8736 __isl_take isl_pw_multi_aff *pma1,
8737 __isl_take isl_pw_multi_aff *pma2);
8738 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
8739 __isl_take isl_union_pw_aff *upa1,
8740 __isl_take isl_union_pw_aff *upa2);
8741 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
8742 __isl_take isl_union_pw_multi_aff *upma1,
8743 __isl_take isl_union_pw_multi_aff *upma2);
8744 __isl_give isl_multi_union_pw_aff *
8745 isl_multi_union_pw_aff_add(
8746 __isl_take isl_multi_union_pw_aff *mupa1,
8747 __isl_take isl_multi_union_pw_aff *mupa2);
8748 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val(
8749 __isl_take isl_pw_aff *pa,
8750 __isl_take isl_val *v);
8751 __isl_give isl_multi_aff *
8752 isl_multi_aff_add_constant_val(
8753 __isl_take isl_multi_aff *pa,
8754 __isl_take isl_val *v);
8755 __isl_give isl_pw_multi_aff *
8756 isl_pw_multi_aff_add_constant_val(
8757 __isl_take isl_pw_multi_aff *pma,
8758 __isl_take isl_val *v);
8759 __isl_give isl_pw_multi_aff *
8760 isl_pw_multi_aff_add_constant_multi_val(
8761 __isl_take isl_pw_multi_aff *pma,
8762 __isl_take isl_multi_val *mv);
8763 __isl_give isl_multi_pw_aff *
8764 isl_multi_pw_aff_add_constant_val(
8765 __isl_take isl_multi_pw_aff *mpa,
8766 __isl_take isl_val *v);
8767 __isl_give isl_multi_aff *
8768 isl_multi_aff_add_constant_multi_val(
8769 __isl_take isl_multi_aff *pa,
8770 __isl_take isl_multi_val *mv);
8771 __isl_give isl_multi_pw_aff *
8772 isl_multi_pw_aff_add_constant_multi_val(
8773 __isl_take isl_multi_pw_aff *mpa,
8774 __isl_take isl_multi_val *mv);
8775 __isl_give isl_pw_aff *isl_pw_aff_min(
8776 __isl_take isl_pw_aff *pwaff1,
8777 __isl_take isl_pw_aff *pwaff2);
8778 __isl_give isl_pw_aff *isl_pw_aff_max(
8779 __isl_take isl_pw_aff *pwaff1,
8780 __isl_take isl_pw_aff *pwaff2);
8781 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min(
8782 __isl_take isl_multi_pw_aff *mpa1,
8783 __isl_take isl_multi_pw_aff *mpa2);
8784 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max(
8785 __isl_take isl_multi_pw_aff *mpa1,
8786 __isl_take isl_multi_pw_aff *mpa2);
8787 __isl_give isl_aff *isl_aff_sub(
8788 __isl_take isl_aff *aff1,
8789 __isl_take isl_aff *aff2);
8790 __isl_give isl_multi_aff *isl_multi_aff_sub(
8791 __isl_take isl_multi_aff *ma1,
8792 __isl_take isl_multi_aff *ma2);
8793 __isl_give isl_pw_aff *isl_pw_aff_sub(
8794 __isl_take isl_pw_aff *pwaff1,
8795 __isl_take isl_pw_aff *pwaff2);
8796 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
8797 __isl_take isl_multi_pw_aff *mpa1,
8798 __isl_take isl_multi_pw_aff *mpa2);
8799 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
8800 __isl_take isl_pw_multi_aff *pma1,
8801 __isl_take isl_pw_multi_aff *pma2);
8802 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
8803 __isl_take isl_union_pw_aff *upa1,
8804 __isl_take isl_union_pw_aff *upa2);
8805 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
8806 __isl_take isl_union_pw_multi_aff *upma1,
8807 __isl_take isl_union_pw_multi_aff *upma2);
8808 __isl_give isl_multi_union_pw_aff *
8809 isl_multi_union_pw_aff_sub(
8810 __isl_take isl_multi_union_pw_aff *mupa1,
8811 __isl_take isl_multi_union_pw_aff *mupa2);
8813 C<isl_aff_sub> subtracts the second argument from the first.
8815 #include <isl/polynomial.h>
8816 __isl_give isl_qpolynomial *isl_qpolynomial_add(
8817 __isl_take isl_qpolynomial *qp1,
8818 __isl_take isl_qpolynomial *qp2);
8819 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
8820 __isl_take isl_pw_qpolynomial *pwqp1,
8821 __isl_take isl_pw_qpolynomial *pwqp2);
8822 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
8823 __isl_take isl_pw_qpolynomial *pwqp1,
8824 __isl_take isl_pw_qpolynomial *pwqp2);
8825 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
8826 __isl_take isl_pw_qpolynomial_fold *pwf1,
8827 __isl_take isl_pw_qpolynomial_fold *pwf2);
8828 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
8829 __isl_take isl_union_pw_qpolynomial *upwqp1,
8830 __isl_take isl_union_pw_qpolynomial *upwqp2);
8831 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
8832 __isl_take isl_qpolynomial *qp1,
8833 __isl_take isl_qpolynomial *qp2);
8834 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
8835 __isl_take isl_pw_qpolynomial *pwqp1,
8836 __isl_take isl_pw_qpolynomial *pwqp2);
8837 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
8838 __isl_take isl_union_pw_qpolynomial *upwqp1,
8839 __isl_take isl_union_pw_qpolynomial *upwqp2);
8840 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
8841 __isl_take isl_pw_qpolynomial_fold *pwf1,
8842 __isl_take isl_pw_qpolynomial_fold *pwf2);
8843 __isl_give isl_union_pw_qpolynomial_fold *
8844 isl_union_pw_qpolynomial_fold_fold(
8845 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
8846 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
8848 #include <isl/aff.h>
8849 __isl_give isl_pw_aff *isl_pw_aff_union_add(
8850 __isl_take isl_pw_aff *pwaff1,
8851 __isl_take isl_pw_aff *pwaff2);
8852 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add(
8853 __isl_take isl_multi_pw_aff *mpa1,
8854 __isl_take isl_multi_pw_aff *mpa2);
8855 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
8856 __isl_take isl_pw_multi_aff *pma1,
8857 __isl_take isl_pw_multi_aff *pma2);
8858 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
8859 __isl_take isl_union_pw_aff *upa1,
8860 __isl_take isl_union_pw_aff *upa2);
8861 __isl_give isl_union_pw_multi_aff *
8862 isl_union_pw_multi_aff_union_add(
8863 __isl_take isl_union_pw_multi_aff *upma1,
8864 __isl_take isl_union_pw_multi_aff *upma2);
8865 __isl_give isl_multi_union_pw_aff *
8866 isl_multi_union_pw_aff_union_add(
8867 __isl_take isl_multi_union_pw_aff *mupa1,
8868 __isl_take isl_multi_union_pw_aff *mupa2);
8869 __isl_give isl_pw_aff *isl_pw_aff_union_min(
8870 __isl_take isl_pw_aff *pwaff1,
8871 __isl_take isl_pw_aff *pwaff2);
8872 __isl_give isl_pw_aff *isl_pw_aff_union_max(
8873 __isl_take isl_pw_aff *pwaff1,
8874 __isl_take isl_pw_aff *pwaff2);
8876 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
8877 expression with a domain that is the union of those of C<pwaff1> and
8878 C<pwaff2> and such that on each cell, the quasi-affine expression is
8879 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
8880 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
8881 associated expression is the defined one.
8882 This in contrast to the C<isl_pw_aff_max> function, which is
8883 only defined on the shared definition domain of the arguments.
8885 #include <isl/val.h>
8886 __isl_give isl_multi_val *isl_multi_val_add_val(
8887 __isl_take isl_multi_val *mv,
8888 __isl_take isl_val *v);
8889 __isl_give isl_multi_val *isl_multi_val_mod_val(
8890 __isl_take isl_multi_val *mv,
8891 __isl_take isl_val *v);
8892 __isl_give isl_multi_val *isl_multi_val_scale_val(
8893 __isl_take isl_multi_val *mv,
8894 __isl_take isl_val *v);
8895 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
8896 __isl_take isl_multi_val *mv,
8897 __isl_take isl_val *v);
8899 #include <isl/aff.h>
8900 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
8901 __isl_take isl_val *mod);
8902 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
8903 __isl_take isl_pw_aff *pa,
8904 __isl_take isl_val *mod);
8905 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
8906 __isl_take isl_union_pw_aff *upa,
8907 __isl_take isl_val *f);
8908 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
8909 __isl_take isl_val *v);
8910 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
8911 __isl_take isl_multi_aff *ma,
8912 __isl_take isl_val *v);
8913 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
8914 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
8915 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
8916 __isl_take isl_multi_pw_aff *mpa,
8917 __isl_take isl_val *v);
8918 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
8919 __isl_take isl_pw_multi_aff *pma,
8920 __isl_take isl_val *v);
8921 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
8922 __isl_take isl_union_pw_aff *upa,
8923 __isl_take isl_val *f);
8924 __isl_give isl_union_pw_multi_aff *
8925 isl_union_pw_multi_aff_scale_val(
8926 __isl_take isl_union_pw_multi_aff *upma,
8927 __isl_take isl_val *val);
8928 __isl_give isl_multi_union_pw_aff *
8929 isl_multi_union_pw_aff_scale_val(
8930 __isl_take isl_multi_union_pw_aff *mupa,
8931 __isl_take isl_val *v);
8932 __isl_give isl_aff *isl_aff_scale_down_ui(
8933 __isl_take isl_aff *aff, unsigned f);
8934 __isl_give isl_aff *isl_aff_scale_down_val(
8935 __isl_take isl_aff *aff, __isl_take isl_val *v);
8936 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
8937 __isl_take isl_multi_aff *ma,
8938 __isl_take isl_val *v);
8939 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
8940 __isl_take isl_pw_aff *pa,
8941 __isl_take isl_val *f);
8942 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
8943 __isl_take isl_multi_pw_aff *mpa,
8944 __isl_take isl_val *v);
8945 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
8946 __isl_take isl_pw_multi_aff *pma,
8947 __isl_take isl_val *v);
8948 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
8949 __isl_take isl_union_pw_aff *upa,
8950 __isl_take isl_val *v);
8951 __isl_give isl_union_pw_multi_aff *
8952 isl_union_pw_multi_aff_scale_down_val(
8953 __isl_take isl_union_pw_multi_aff *upma,
8954 __isl_take isl_val *val);
8955 __isl_give isl_multi_union_pw_aff *
8956 isl_multi_union_pw_aff_scale_down_val(
8957 __isl_take isl_multi_union_pw_aff *mupa,
8958 __isl_take isl_val *v);
8960 #include <isl/polynomial.h>
8961 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
8962 __isl_take isl_qpolynomial *qp,
8963 __isl_take isl_val *v);
8964 __isl_give isl_qpolynomial_fold *
8965 isl_qpolynomial_fold_scale_val(
8966 __isl_take isl_qpolynomial_fold *fold,
8967 __isl_take isl_val *v);
8968 __isl_give isl_pw_qpolynomial *
8969 isl_pw_qpolynomial_scale_val(
8970 __isl_take isl_pw_qpolynomial *pwqp,
8971 __isl_take isl_val *v);
8972 __isl_give isl_pw_qpolynomial_fold *
8973 isl_pw_qpolynomial_fold_scale_val(
8974 __isl_take isl_pw_qpolynomial_fold *pwf,
8975 __isl_take isl_val *v);
8976 __isl_give isl_union_pw_qpolynomial *
8977 isl_union_pw_qpolynomial_scale_val(
8978 __isl_take isl_union_pw_qpolynomial *upwqp,
8979 __isl_take isl_val *v);
8980 __isl_give isl_union_pw_qpolynomial_fold *
8981 isl_union_pw_qpolynomial_fold_scale_val(
8982 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8983 __isl_take isl_val *v);
8984 __isl_give isl_qpolynomial *
8985 isl_qpolynomial_scale_down_val(
8986 __isl_take isl_qpolynomial *qp,
8987 __isl_take isl_val *v);
8988 __isl_give isl_qpolynomial_fold *
8989 isl_qpolynomial_fold_scale_down_val(
8990 __isl_take isl_qpolynomial_fold *fold,
8991 __isl_take isl_val *v);
8992 __isl_give isl_pw_qpolynomial *
8993 isl_pw_qpolynomial_scale_down_val(
8994 __isl_take isl_pw_qpolynomial *pwqp,
8995 __isl_take isl_val *v);
8996 __isl_give isl_pw_qpolynomial_fold *
8997 isl_pw_qpolynomial_fold_scale_down_val(
8998 __isl_take isl_pw_qpolynomial_fold *pwf,
8999 __isl_take isl_val *v);
9000 __isl_give isl_union_pw_qpolynomial *
9001 isl_union_pw_qpolynomial_scale_down_val(
9002 __isl_take isl_union_pw_qpolynomial *upwqp,
9003 __isl_take isl_val *v);
9004 __isl_give isl_union_pw_qpolynomial_fold *
9005 isl_union_pw_qpolynomial_fold_scale_down_val(
9006 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9007 __isl_take isl_val *v);
9009 #include <isl/val.h>
9010 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
9011 __isl_take isl_multi_val *mv1,
9012 __isl_take isl_multi_val *mv2);
9013 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
9014 __isl_take isl_multi_val *mv1,
9015 __isl_take isl_multi_val *mv2);
9016 __isl_give isl_multi_val *
9017 isl_multi_val_scale_down_multi_val(
9018 __isl_take isl_multi_val *mv1,
9019 __isl_take isl_multi_val *mv2);
9021 #include <isl/aff.h>
9022 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
9023 __isl_take isl_multi_aff *ma,
9024 __isl_take isl_multi_val *mv);
9025 __isl_give isl_multi_union_pw_aff *
9026 isl_multi_union_pw_aff_mod_multi_val(
9027 __isl_take isl_multi_union_pw_aff *upma,
9028 __isl_take isl_multi_val *mv);
9029 __isl_give isl_multi_pw_aff *
9030 isl_multi_pw_aff_mod_multi_val(
9031 __isl_take isl_multi_pw_aff *mpa,
9032 __isl_take isl_multi_val *mv);
9033 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
9034 __isl_take isl_multi_aff *ma,
9035 __isl_take isl_multi_val *mv);
9036 __isl_give isl_pw_multi_aff *
9037 isl_pw_multi_aff_scale_multi_val(
9038 __isl_take isl_pw_multi_aff *pma,
9039 __isl_take isl_multi_val *mv);
9040 __isl_give isl_multi_pw_aff *
9041 isl_multi_pw_aff_scale_multi_val(
9042 __isl_take isl_multi_pw_aff *mpa,
9043 __isl_take isl_multi_val *mv);
9044 __isl_give isl_multi_union_pw_aff *
9045 isl_multi_union_pw_aff_scale_multi_val(
9046 __isl_take isl_multi_union_pw_aff *mupa,
9047 __isl_take isl_multi_val *mv);
9048 __isl_give isl_union_pw_multi_aff *
9049 isl_union_pw_multi_aff_scale_multi_val(
9050 __isl_take isl_union_pw_multi_aff *upma,
9051 __isl_take isl_multi_val *mv);
9052 __isl_give isl_multi_aff *
9053 isl_multi_aff_scale_down_multi_val(
9054 __isl_take isl_multi_aff *ma,
9055 __isl_take isl_multi_val *mv);
9056 __isl_give isl_multi_pw_aff *
9057 isl_multi_pw_aff_scale_down_multi_val(
9058 __isl_take isl_multi_pw_aff *mpa,
9059 __isl_take isl_multi_val *mv);
9060 __isl_give isl_multi_union_pw_aff *
9061 isl_multi_union_pw_aff_scale_down_multi_val(
9062 __isl_take isl_multi_union_pw_aff *mupa,
9063 __isl_take isl_multi_val *mv);
9065 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
9066 by the corresponding elements of C<mv>.
9068 #include <isl/aff.h>
9069 __isl_give isl_aff *isl_aff_mul(
9070 __isl_take isl_aff *aff1,
9071 __isl_take isl_aff *aff2);
9072 __isl_give isl_aff *isl_aff_div(
9073 __isl_take isl_aff *aff1,
9074 __isl_take isl_aff *aff2);
9075 __isl_give isl_pw_aff *isl_pw_aff_mul(
9076 __isl_take isl_pw_aff *pwaff1,
9077 __isl_take isl_pw_aff *pwaff2);
9078 __isl_give isl_pw_aff *isl_pw_aff_div(
9079 __isl_take isl_pw_aff *pa1,
9080 __isl_take isl_pw_aff *pa2);
9081 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
9082 __isl_take isl_pw_aff *pa1,
9083 __isl_take isl_pw_aff *pa2);
9084 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
9085 __isl_take isl_pw_aff *pa1,
9086 __isl_take isl_pw_aff *pa2);
9088 When multiplying two affine expressions, at least one of the two needs
9089 to be a constant. Similarly, when dividing an affine expression by another,
9090 the second expression needs to be a constant.
9091 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
9092 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
9095 #include <isl/polynomial.h>
9096 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
9097 __isl_take isl_qpolynomial *qp1,
9098 __isl_take isl_qpolynomial *qp2);
9099 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
9100 __isl_take isl_pw_qpolynomial *pwqp1,
9101 __isl_take isl_pw_qpolynomial *pwqp2);
9102 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
9103 __isl_take isl_union_pw_qpolynomial *upwqp1,
9104 __isl_take isl_union_pw_qpolynomial *upwqp2);
9108 =head3 Lexicographic Optimization
9110 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
9111 the following functions
9112 compute a set that contains the lexicographic minimum or maximum
9113 of the elements in C<set> (or C<bset>) for those values of the parameters
9114 that satisfy C<dom>.
9115 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9116 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
9118 In other words, the union of the parameter values
9119 for which the result is non-empty and of C<*empty>
9122 #include <isl/set.h>
9123 __isl_give isl_set *isl_basic_set_partial_lexmin(
9124 __isl_take isl_basic_set *bset,
9125 __isl_take isl_basic_set *dom,
9126 __isl_give isl_set **empty);
9127 __isl_give isl_set *isl_basic_set_partial_lexmax(
9128 __isl_take isl_basic_set *bset,
9129 __isl_take isl_basic_set *dom,
9130 __isl_give isl_set **empty);
9131 __isl_give isl_set *isl_set_partial_lexmin(
9132 __isl_take isl_set *set, __isl_take isl_set *dom,
9133 __isl_give isl_set **empty);
9134 __isl_give isl_set *isl_set_partial_lexmax(
9135 __isl_take isl_set *set, __isl_take isl_set *dom,
9136 __isl_give isl_set **empty);
9138 Given a (basic) set C<set> (or C<bset>), the following functions simply
9139 return a set containing the lexicographic minimum or maximum
9140 of the elements in C<set> (or C<bset>).
9141 In case of union sets, the optimum is computed per space.
9143 #include <isl/set.h>
9144 __isl_give isl_set *isl_basic_set_lexmin(
9145 __isl_take isl_basic_set *bset);
9146 __isl_give isl_set *isl_basic_set_lexmax(
9147 __isl_take isl_basic_set *bset);
9148 __isl_give isl_set *isl_set_lexmin(
9149 __isl_take isl_set *set);
9150 __isl_give isl_set *isl_set_lexmax(
9151 __isl_take isl_set *set);
9152 __isl_give isl_union_set *isl_union_set_lexmin(
9153 __isl_take isl_union_set *uset);
9154 __isl_give isl_union_set *isl_union_set_lexmax(
9155 __isl_take isl_union_set *uset);
9157 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
9158 the following functions
9159 compute a relation that maps each element of C<dom>
9160 to the single lexicographic minimum or maximum
9161 of the elements that are associated to that same
9162 element in C<map> (or C<bmap>).
9163 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9164 that contains the elements in C<dom> that do not map
9165 to any elements in C<map> (or C<bmap>).
9166 In other words, the union of the domain of the result and of C<*empty>
9169 #include <isl/map.h>
9170 __isl_give isl_map *isl_basic_map_partial_lexmax(
9171 __isl_take isl_basic_map *bmap,
9172 __isl_take isl_basic_set *dom,
9173 __isl_give isl_set **empty);
9174 __isl_give isl_map *isl_basic_map_partial_lexmin(
9175 __isl_take isl_basic_map *bmap,
9176 __isl_take isl_basic_set *dom,
9177 __isl_give isl_set **empty);
9178 __isl_give isl_map *isl_map_partial_lexmax(
9179 __isl_take isl_map *map, __isl_take isl_set *dom,
9180 __isl_give isl_set **empty);
9181 __isl_give isl_map *isl_map_partial_lexmin(
9182 __isl_take isl_map *map, __isl_take isl_set *dom,
9183 __isl_give isl_set **empty);
9185 Given a (basic) map C<map> (or C<bmap>), the following functions simply
9186 return a map mapping each element in the domain of
9187 C<map> (or C<bmap>) to the lexicographic minimum or maximum
9188 of all elements associated to that element.
9189 In case of union relations, the optimum is computed per space.
9191 #include <isl/map.h>
9192 __isl_give isl_map *isl_basic_map_lexmin(
9193 __isl_take isl_basic_map *bmap);
9194 __isl_give isl_map *isl_basic_map_lexmax(
9195 __isl_take isl_basic_map *bmap);
9196 __isl_give isl_map *isl_map_lexmin(
9197 __isl_take isl_map *map);
9198 __isl_give isl_map *isl_map_lexmax(
9199 __isl_take isl_map *map);
9200 __isl_give isl_union_map *isl_union_map_lexmin(
9201 __isl_take isl_union_map *umap);
9202 __isl_give isl_union_map *isl_union_map_lexmax(
9203 __isl_take isl_union_map *umap);
9205 The following functions return their result in the form of
9206 a piecewise multi-affine expression,
9207 but are otherwise equivalent to the corresponding functions
9208 returning a basic set or relation.
9210 #include <isl/set.h>
9211 __isl_give isl_pw_multi_aff *
9212 isl_basic_set_partial_lexmin_pw_multi_aff(
9213 __isl_take isl_basic_set *bset,
9214 __isl_take isl_basic_set *dom,
9215 __isl_give isl_set **empty);
9216 __isl_give isl_pw_multi_aff *
9217 isl_basic_set_partial_lexmax_pw_multi_aff(
9218 __isl_take isl_basic_set *bset,
9219 __isl_take isl_basic_set *dom,
9220 __isl_give isl_set **empty);
9221 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
9222 __isl_take isl_set *set);
9223 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
9224 __isl_take isl_set *set);
9226 #include <isl/map.h>
9227 __isl_give isl_pw_multi_aff *
9228 isl_basic_map_lexmin_pw_multi_aff(
9229 __isl_take isl_basic_map *bmap);
9230 __isl_give isl_pw_multi_aff *
9231 isl_basic_map_partial_lexmin_pw_multi_aff(
9232 __isl_take isl_basic_map *bmap,
9233 __isl_take isl_basic_set *dom,
9234 __isl_give isl_set **empty);
9235 __isl_give isl_pw_multi_aff *
9236 isl_basic_map_partial_lexmax_pw_multi_aff(
9237 __isl_take isl_basic_map *bmap,
9238 __isl_take isl_basic_set *dom,
9239 __isl_give isl_set **empty);
9240 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
9241 __isl_take isl_map *map);
9242 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
9243 __isl_take isl_map *map);
9245 The following functions return the lexicographic minimum or maximum
9246 on the shared domain of the inputs and the single defined function
9247 on those parts of the domain where only a single function is defined.
9249 #include <isl/aff.h>
9250 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
9251 __isl_take isl_pw_multi_aff *pma1,
9252 __isl_take isl_pw_multi_aff *pma2);
9253 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
9254 __isl_take isl_pw_multi_aff *pma1,
9255 __isl_take isl_pw_multi_aff *pma2);
9257 If the input to a lexicographic optimization problem has
9258 multiple constraints with the same coefficients for the optimized
9259 variables, then, by default, this symmetry is exploited by
9260 replacing those constraints by a single constraint with
9261 an abstract bound, which is in turn bounded by the corresponding terms
9262 in the original constraints.
9263 Without this optimization, the solver would typically consider
9264 all possible orderings of those original bounds, resulting in a needless
9265 decomposition of the domain.
9266 However, the optimization can also result in slowdowns since
9267 an extra parameter is introduced that may get used in additional
9269 The following option determines whether symmetry detection is applied
9270 during lexicographic optimization.
9272 #include <isl/options.h>
9273 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
9275 int isl_options_get_pip_symmetry(isl_ctx *ctx);
9279 See also \autoref{s:offline}.
9283 =head2 Ternary Operations
9285 #include <isl/aff.h>
9286 __isl_give isl_pw_aff *isl_pw_aff_cond(
9287 __isl_take isl_pw_aff *cond,
9288 __isl_take isl_pw_aff *pwaff_true,
9289 __isl_take isl_pw_aff *pwaff_false);
9291 The function C<isl_pw_aff_cond> performs a conditional operator
9292 and returns an expression that is equal to C<pwaff_true>
9293 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
9294 where C<cond> is zero.
9298 Lists are defined over several element types, including
9299 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
9300 C<isl_union_pw_aff>,
9301 C<isl_union_pw_multi_aff>,
9302 C<isl_qpolynomial>, C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
9304 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
9305 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
9306 Here we take lists of C<isl_set>s as an example.
9307 Lists can be created, copied, modified and freed using the following functions.
9309 #include <isl/set.h>
9310 __isl_give isl_set_list *isl_set_to_list(
9311 __isl_take isl_set *el);
9312 __isl_give isl_set_list *isl_set_list_from_set(
9313 __isl_take isl_set *el);
9314 __isl_give isl_set_list *isl_set_list_alloc(
9315 isl_ctx *ctx, int n);
9316 __isl_give isl_set_list *isl_set_list_copy(
9317 __isl_keep isl_set_list *list);
9318 __isl_give isl_set_list *isl_set_list_insert(
9319 __isl_take isl_set_list *list, unsigned pos,
9320 __isl_take isl_set *el);
9321 __isl_give isl_set_list *isl_set_list_add(
9322 __isl_take isl_set_list *list,
9323 __isl_take isl_set *el);
9324 __isl_give isl_set_list *isl_set_list_drop(
9325 __isl_take isl_set_list *list,
9326 unsigned first, unsigned n);
9327 __isl_give isl_set_list *isl_set_list_clear(
9328 __isl_take isl_set_list *list);
9329 __isl_give isl_set_list *isl_set_list_swap(
9330 __isl_take isl_set_list *list,
9331 unsigned pos1, unsigned pos2);
9332 __isl_give isl_set_list *isl_set_list_reverse(
9333 __isl_take isl_set_list *list);
9334 __isl_give isl_set_list *isl_set_list_set_set(
9335 __isl_take isl_set_list *list, int index,
9336 __isl_take isl_set *set);
9337 __isl_give isl_set_list *isl_set_list_concat(
9338 __isl_take isl_set_list *list1,
9339 __isl_take isl_set_list *list2);
9340 __isl_give isl_set_list *isl_set_list_map(
9341 __isl_take isl_set_list *list,
9342 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
9345 __isl_give isl_set_list *isl_set_list_sort(
9346 __isl_take isl_set_list *list,
9347 int (*cmp)(__isl_keep isl_set *a,
9348 __isl_keep isl_set *b, void *user),
9350 __isl_null isl_set_list *isl_set_list_free(
9351 __isl_take isl_set_list *list);
9353 C<isl_set_list_alloc> creates an empty list with an initial capacity
9354 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
9355 add elements to a list, increasing its capacity as needed.
9356 C<isl_set_to_list> creates a list with a single element.
9357 C<isl_set_list_from_set> performs the same operation.
9358 C<isl_set_list_clear> removes all elements from a list.
9359 C<isl_set_list_swap> swaps the elements at the specified locations.
9360 C<isl_set_list_reverse> reverses the elements in the list.
9362 Lists can be inspected using the following functions.
9364 #include <isl/set.h>
9365 isl_size isl_set_list_size(__isl_keep isl_set_list *list);
9366 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list);
9367 __isl_give isl_set *isl_set_list_get_at(
9368 __isl_keep isl_set_list *list, int index);
9369 __isl_give isl_set *isl_set_list_get_set(
9370 __isl_keep isl_set_list *list, int index);
9371 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
9372 isl_stat (*fn)(__isl_take isl_set *el, void *user),
9374 isl_bool isl_set_list_every(__isl_keep isl_set_list *list,
9375 isl_bool (*test)(__isl_take isl_set *el,
9378 isl_stat isl_set_list_foreach_scc(
9379 __isl_keep isl_set_list *list,
9380 isl_bool (*follows)(__isl_keep isl_set *a,
9381 __isl_keep isl_set *b, void *user),
9383 isl_stat (*fn)(__isl_take isl_set_list *scc,
9387 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
9389 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
9390 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
9391 strongly connected components of the graph with as vertices the elements
9392 of C<list> and a directed edge from vertex C<b> to vertex C<a>
9393 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
9394 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
9396 Lists can be printed using
9398 #include <isl/set.h>
9399 __isl_give isl_printer *isl_printer_print_set_list(
9400 __isl_take isl_printer *p,
9401 __isl_keep isl_set_list *list);
9403 Alternatively, a string representation can be obtained
9404 directly using the following function, which always prints
9407 #include <isl/set.h>
9408 __isl_give char *isl_set_list_to_str(
9409 __isl_keep isl_set_list *list);
9411 An C<isl_val_list>, C<isl_id_list>,
9412 C<isl_aff_list>, C<isl_pw_aff_list>, C<isl_pw_multi_aff_list>,
9413 C<isl_union_pw_aff_list>,
9414 C<isl_set_list>, C<isl_map_list> or C<isl_union_set_list> object
9415 can also be read from input using the following functions.
9417 #include <isl/val.h>
9418 __isl_give isl_val_list *isl_val_list_read_from_str(
9419 isl_ctx *ctx, const char *str);
9422 __isl_give isl_id_list *isl_id_list_read_from_str(
9423 isl_ctx *ctx, const char *str);
9425 #include <isl/aff.h>
9426 __isl_give isl_aff_list *
9427 isl_aff_list_read_from_str(isl_ctx *ctx,
9429 __isl_give isl_pw_aff_list *
9430 isl_pw_aff_list_read_from_str(isl_ctx *ctx,
9432 __isl_give isl_pw_multi_aff_list *
9433 isl_pw_multi_aff_list_read_from_str(isl_ctx *ctx,
9435 __isl_give isl_union_pw_aff_list *
9436 isl_union_pw_aff_list_read_from_str(isl_ctx *ctx,
9439 #include <isl/set.h>
9440 __isl_give isl_set_list *isl_set_list_read_from_str(
9441 isl_ctx *ctx, const char *str);
9443 #include <isl/map.h>
9444 __isl_give isl_map_list *isl_map_list_read_from_str(
9445 isl_ctx *ctx, const char *str);
9447 #include <isl/union_set.h>
9448 __isl_give isl_union_set_list *
9449 isl_union_set_list_read_from_str(isl_ctx *ctx,
9452 =head2 Associative arrays
9454 Associative arrays map isl objects of a specific type to isl objects
9455 of some (other) specific type. They are defined for several pairs
9456 of types, including (C<isl_map>, C<isl_basic_set>),
9457 (C<isl_id>, C<isl_ast_expr>),
9458 (C<isl_id>, C<isl_id>) and
9459 (C<isl_id>, C<isl_pw_aff>).
9460 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
9463 Associative arrays can be created, copied and freed using
9464 the following functions.
9466 #include <isl/id_to_ast_expr.h>
9467 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
9468 isl_ctx *ctx, int min_size);
9469 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
9470 __isl_keep isl_id_to_ast_expr *id2expr);
9471 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
9472 __isl_take isl_id_to_ast_expr *id2expr);
9474 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
9475 to specify the expected size of the associative array.
9476 The associative array will be grown automatically as needed.
9478 Associative arrays can be inspected using the following functions.
9480 #include <isl/id_to_ast_expr.h>
9481 __isl_give isl_maybe_isl_ast_expr
9482 isl_id_to_ast_expr_try_get(
9483 __isl_keep isl_id_to_ast_expr *id2expr,
9484 __isl_keep isl_id *key);
9485 isl_bool isl_id_to_ast_expr_has(
9486 __isl_keep isl_id_to_ast_expr *id2expr,
9487 __isl_keep isl_id *key);
9488 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
9489 __isl_keep isl_id_to_ast_expr *id2expr,
9490 __isl_take isl_id *key);
9491 isl_stat isl_id_to_ast_expr_foreach(
9492 __isl_keep isl_id_to_ast_expr *id2expr,
9493 isl_stat (*fn)(__isl_take isl_id *key,
9494 __isl_take isl_ast_expr *val, void *user),
9497 The function C<isl_id_to_ast_expr_try_get> returns a structure
9498 containing two elements, C<valid> and C<value>.
9499 If there is a value associated to the key, then C<valid>
9500 is set to C<isl_bool_true> and C<value> contains a copy of
9501 the associated value. Otherwise C<value> is C<NULL> and
9502 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
9503 on whether some error has occurred or there simply is no associated value.
9504 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
9505 in the structure and
9506 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
9508 Associative arrays can be modified using the following functions.
9510 #include <isl/id_to_ast_expr.h>
9511 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
9512 __isl_take isl_id_to_ast_expr *id2expr,
9513 __isl_take isl_id *key,
9514 __isl_take isl_ast_expr *val);
9515 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
9516 __isl_take isl_id_to_ast_expr *id2expr,
9517 __isl_take isl_id *key);
9519 Associative arrays can be printed using the following function.
9521 #include <isl/id_to_ast_expr.h>
9522 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
9523 __isl_take isl_printer *p,
9524 __isl_keep isl_id_to_ast_expr *id2expr);
9528 Vectors can be created, copied and freed using the following functions.
9530 #include <isl/vec.h>
9531 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
9533 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
9535 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
9536 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
9538 Note that the elements of a vector created by C<isl_vec_alloc>
9539 may have arbitrary values.
9540 A vector created by C<isl_vec_zero> has elements with value zero.
9541 The elements can be changed and inspected using the following functions.
9543 isl_size isl_vec_size(__isl_keep isl_vec *vec);
9544 __isl_give isl_val *isl_vec_get_element_val(
9545 __isl_keep isl_vec *vec, int pos);
9546 __isl_give isl_vec *isl_vec_set_element_si(
9547 __isl_take isl_vec *vec, int pos, int v);
9548 __isl_give isl_vec *isl_vec_set_element_val(
9549 __isl_take isl_vec *vec, int pos,
9550 __isl_take isl_val *v);
9551 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
9553 __isl_give isl_vec *isl_vec_set_val(
9554 __isl_take isl_vec *vec, __isl_take isl_val *v);
9555 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
9556 __isl_keep isl_vec *vec2, int pos);
9558 C<isl_vec_get_element> will return a negative value if anything went wrong.
9559 In that case, the value of C<*v> is undefined.
9561 The following function can be used to concatenate two vectors.
9563 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
9564 __isl_take isl_vec *vec2);
9568 Matrices can be created, copied and freed using the following functions.
9570 #include <isl/mat.h>
9571 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
9572 unsigned n_row, unsigned n_col);
9573 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
9574 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
9576 Note that the elements of a newly created matrix may have arbitrary values.
9577 The elements can be changed and inspected using the following functions.
9579 isl_size isl_mat_rows(__isl_keep isl_mat *mat);
9580 isl_size isl_mat_cols(__isl_keep isl_mat *mat);
9581 __isl_give isl_val *isl_mat_get_element_val(
9582 __isl_keep isl_mat *mat, int row, int col);
9583 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
9584 int row, int col, int v);
9585 __isl_give isl_mat *isl_mat_set_element_val(
9586 __isl_take isl_mat *mat, int row, int col,
9587 __isl_take isl_val *v);
9589 The following function computes the rank of a matrix.
9590 The return value may be -1 if some error occurred.
9592 #include <isl/mat.h>
9593 isl_size isl_mat_rank(__isl_keep isl_mat *mat);
9595 The following function can be used to compute the (right) inverse
9596 of a matrix, i.e., a matrix such that the product of the original
9597 and the inverse (in that order) is a multiple of the identity matrix.
9598 The input matrix is assumed to be of full row-rank.
9600 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
9602 The following function can be used to compute the (right) kernel
9603 (or null space) of a matrix, i.e., a matrix such that the product of
9604 the original and the kernel (in that order) is the zero matrix.
9606 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
9608 The following function computes a basis for the space spanned
9609 by the rows of a matrix.
9611 __isl_give isl_mat *isl_mat_row_basis(
9612 __isl_take isl_mat *mat);
9614 The following function computes rows that extend a basis of C<mat1>
9615 to a basis that also covers C<mat2>.
9617 __isl_give isl_mat *isl_mat_row_basis_extension(
9618 __isl_take isl_mat *mat1,
9619 __isl_take isl_mat *mat2);
9621 The following function checks whether there is no linear dependence
9622 among the combined rows of "mat1" and "mat2" that is not already present
9623 in "mat1" or "mat2" individually.
9624 If "mat1" and "mat2" have linearly independent rows by themselves,
9625 then this means that there is no linear dependence among all rows together.
9627 isl_bool isl_mat_has_linearly_independent_rows(
9628 __isl_keep isl_mat *mat1,
9629 __isl_keep isl_mat *mat2);
9631 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
9633 The following functions determine
9634 an upper or lower bound on a quasipolynomial over its domain.
9636 __isl_give isl_pw_qpolynomial_fold *
9637 isl_pw_qpolynomial_bound(
9638 __isl_take isl_pw_qpolynomial *pwqp,
9639 enum isl_fold type, isl_bool *tight);
9641 __isl_give isl_union_pw_qpolynomial_fold *
9642 isl_union_pw_qpolynomial_bound(
9643 __isl_take isl_union_pw_qpolynomial *upwqp,
9644 enum isl_fold type, isl_bool *tight);
9646 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
9647 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
9648 is the returned bound is known be tight, i.e., for each value
9649 of the parameters there is at least
9650 one element in the domain that reaches the bound.
9651 If the domain of C<pwqp> is not wrapping, then the bound is computed
9652 over all elements in that domain and the result has a purely parametric
9653 domain. If the domain of C<pwqp> is wrapping, then the bound is
9654 computed over the range of the wrapped relation. The domain of the
9655 wrapped relation becomes the domain of the result.
9657 =head2 Parametric Vertex Enumeration
9659 The parametric vertex enumeration described in this section
9660 is mainly intended to be used internally and by the C<barvinok>
9663 #include <isl/vertices.h>
9664 __isl_give isl_vertices *isl_basic_set_compute_vertices(
9665 __isl_keep isl_basic_set *bset);
9667 The function C<isl_basic_set_compute_vertices> performs the
9668 actual computation of the parametric vertices and the chamber
9669 decomposition and stores the result in an C<isl_vertices> object.
9670 This information can be queried by either iterating over all
9671 the vertices or iterating over all the chambers or cells
9672 and then iterating over all vertices that are active on the chamber.
9674 isl_stat isl_vertices_foreach_vertex(
9675 __isl_keep isl_vertices *vertices,
9676 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9677 void *user), void *user);
9679 isl_stat isl_vertices_foreach_cell(
9680 __isl_keep isl_vertices *vertices,
9681 isl_stat (*fn)(__isl_take isl_cell *cell,
9682 void *user), void *user);
9683 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
9684 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9685 void *user), void *user);
9687 Other operations that can be performed on an C<isl_vertices> object are
9690 isl_size isl_vertices_get_n_vertices(
9691 __isl_keep isl_vertices *vertices);
9692 __isl_null isl_vertices *isl_vertices_free(
9693 __isl_take isl_vertices *vertices);
9695 Vertices can be inspected and destroyed using the following functions.
9697 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex);
9698 __isl_give isl_basic_set *isl_vertex_get_domain(
9699 __isl_keep isl_vertex *vertex);
9700 __isl_give isl_multi_aff *isl_vertex_get_expr(
9701 __isl_keep isl_vertex *vertex);
9702 __isl_null isl_vertex *isl_vertex_free(
9703 __isl_take isl_vertex *vertex);
9705 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
9706 describing the vertex in terms of the parameters,
9707 while C<isl_vertex_get_domain> returns the activity domain
9710 Chambers can be inspected and destroyed using the following functions.
9712 __isl_give isl_basic_set *isl_cell_get_domain(
9713 __isl_keep isl_cell *cell);
9714 __isl_null isl_cell *isl_cell_free(
9715 __isl_take isl_cell *cell);
9717 =head1 Polyhedral Compilation Library
9719 This section collects functionality in C<isl> that has been specifically
9720 designed for use during polyhedral compilation.
9722 =head2 Schedule Trees
9724 A schedule tree is a structured representation of a schedule,
9725 assigning a relative order to a set of domain elements.
9726 The relative order expressed by the schedule tree is
9727 defined recursively. In particular, the order between
9728 two domain elements is determined by the node that is closest
9729 to the root that refers to both elements and that orders them apart.
9730 Each node in the tree is of one of several types.
9731 The root node is always of type C<isl_schedule_node_domain>
9732 (or C<isl_schedule_node_extension>)
9733 and it describes the (extra) domain elements to which the schedule applies.
9734 The other types of nodes are as follows.
9738 =item C<isl_schedule_node_band>
9740 A band of schedule dimensions. Each schedule dimension is represented
9741 by a union piecewise quasi-affine expression. If this expression
9742 assigns a different value to two domain elements, while all previous
9743 schedule dimensions in the same band assign them the same value,
9744 then the two domain elements are ordered according to these two
9746 Each expression is required to be total in the domain elements
9747 that reach the band node.
9749 =item C<isl_schedule_node_expansion>
9751 An expansion node maps each of the domain elements that reach the node
9752 to one or more domain elements. The image of this mapping forms
9753 the set of domain elements that reach the child of the expansion node.
9754 The function that maps each of the expanded domain elements
9755 to the original domain element from which it was expanded
9756 is called the contraction.
9758 =item C<isl_schedule_node_filter>
9760 A filter node does not impose any ordering, but rather intersects
9761 the set of domain elements that the current subtree refers to
9762 with a given union set. The subtree of the filter node only
9763 refers to domain elements in the intersection.
9764 A filter node is typically only used as a child of a sequence or
9767 =item C<isl_schedule_node_leaf>
9769 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
9771 =item C<isl_schedule_node_mark>
9773 A mark node can be used to attach any kind of information to a subtree
9774 of the schedule tree.
9776 =item C<isl_schedule_node_sequence>
9778 A sequence node has one or more children, each of which is a filter node.
9779 The filters on these filter nodes form a partition of
9780 the domain elements that the current subtree refers to.
9781 If two domain elements appear in distinct filters then the sequence
9782 node orders them according to the child positions of the corresponding
9785 =item C<isl_schedule_node_set>
9787 A set node is similar to a sequence node, except that
9788 it expresses that domain elements appearing in distinct filters
9789 may have any order. The order of the children of a set node
9790 is therefore also immaterial.
9794 The following node types are only supported by the AST generator.
9798 =item C<isl_schedule_node_context>
9800 The context describes constraints on the parameters and
9801 the schedule dimensions of outer
9802 bands that the AST generator may assume to hold. It is also the only
9803 kind of node that may introduce additional parameters.
9804 The space of the context is that of the flat product of the outer
9805 band nodes. In particular, if there are no outer band nodes, then
9806 this space is the unnamed zero-dimensional space.
9807 Since a context node references the outer band nodes, any tree
9808 containing a context node is considered to be anchored.
9810 =item C<isl_schedule_node_extension>
9812 An extension node instructs the AST generator to add additional
9813 domain elements that need to be scheduled.
9814 The additional domain elements are described by the range of
9815 the extension map in terms of the outer schedule dimensions,
9816 i.e., the flat product of the outer band nodes.
9817 Note that domain elements are added whenever the AST generator
9818 reaches the extension node, meaning that there are still some
9819 active domain elements for which an AST needs to be generated.
9820 The conditions under which some domain elements are still active
9821 may however not be completely described by the outer AST nodes
9822 generated at that point.
9823 Since an extension node references the outer band nodes, any tree
9824 containing an extension node is considered to be anchored.
9826 An extension node may also appear as the root of a schedule tree,
9827 when it is intended to be inserted into another tree
9828 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
9829 In this case, the domain of the extension node should
9830 correspond to the flat product of the outer band nodes
9831 in this other schedule tree at the point where the extension tree
9834 =item C<isl_schedule_node_guard>
9836 The guard describes constraints on the parameters and
9837 the schedule dimensions of outer
9838 bands that need to be enforced by the outer nodes
9839 in the generated AST.
9840 That is, the part of the AST that is generated from descendants
9841 of the guard node can assume that these constraints are satisfied.
9842 The space of the guard is that of the flat product of the outer
9843 band nodes. In particular, if there are no outer band nodes, then
9844 this space is the unnamed zero-dimensional space.
9845 Since a guard node references the outer band nodes, any tree
9846 containing a guard node is considered to be anchored.
9850 Except for the C<isl_schedule_node_context> nodes,
9851 none of the nodes may introduce any parameters that were not
9852 already present in the root domain node.
9854 A schedule tree is encapsulated in an C<isl_schedule> object.
9855 The simplest such objects, those with a tree consisting of single domain node,
9856 can be created using the following functions with either an empty
9857 domain or a given domain.
9859 #include <isl/schedule.h>
9860 __isl_give isl_schedule *isl_schedule_empty(
9861 __isl_take isl_space *space);
9862 __isl_give isl_schedule *isl_schedule_from_domain(
9863 __isl_take isl_union_set *domain);
9865 The function C<isl_schedule_constraints_compute_schedule> described
9866 in L</"Scheduling"> can also be used to construct schedules.
9868 C<isl_schedule> objects may be copied and freed using the following functions.
9870 #include <isl/schedule.h>
9871 __isl_give isl_schedule *isl_schedule_copy(
9872 __isl_keep isl_schedule *sched);
9873 __isl_null isl_schedule *isl_schedule_free(
9874 __isl_take isl_schedule *sched);
9876 The following functions checks whether two C<isl_schedule> objects
9877 are obviously the same.
9879 #include <isl/schedule.h>
9880 isl_bool isl_schedule_plain_is_equal(
9881 __isl_keep isl_schedule *schedule1,
9882 __isl_keep isl_schedule *schedule2);
9884 The domain of the schedule, i.e., the domain described by the root node,
9885 can be obtained using the following function.
9887 #include <isl/schedule.h>
9888 __isl_give isl_union_set *isl_schedule_get_domain(
9889 __isl_keep isl_schedule *schedule);
9891 An extra top-level band node (right underneath the domain node) can
9892 be introduced into the schedule using the following function.
9893 The schedule tree is assumed not to have any anchored nodes.
9895 #include <isl/schedule.h>
9896 __isl_give isl_schedule *
9897 isl_schedule_insert_partial_schedule(
9898 __isl_take isl_schedule *schedule,
9899 __isl_take isl_multi_union_pw_aff *partial);
9901 A top-level context node (right underneath the domain node) can
9902 be introduced into the schedule using the following function.
9904 #include <isl/schedule.h>
9905 __isl_give isl_schedule *isl_schedule_insert_context(
9906 __isl_take isl_schedule *schedule,
9907 __isl_take isl_set *context)
9909 A top-level guard node (right underneath the domain node) can
9910 be introduced into the schedule using the following function.
9912 #include <isl/schedule.h>
9913 __isl_give isl_schedule *isl_schedule_insert_guard(
9914 __isl_take isl_schedule *schedule,
9915 __isl_take isl_set *guard)
9917 A schedule that combines two schedules either in the given
9918 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
9919 or an C<isl_schedule_node_set> node,
9920 can be created using the following functions.
9922 #include <isl/schedule.h>
9923 __isl_give isl_schedule *isl_schedule_sequence(
9924 __isl_take isl_schedule *schedule1,
9925 __isl_take isl_schedule *schedule2);
9926 __isl_give isl_schedule *isl_schedule_set(
9927 __isl_take isl_schedule *schedule1,
9928 __isl_take isl_schedule *schedule2);
9930 The domains of the two input schedules need to be disjoint.
9932 The following function can be used to restrict the domain
9933 of a schedule with a domain node as root to be a subset of the given union set.
9934 This operation may remove nodes in the tree that have become
9937 #include <isl/schedule.h>
9938 __isl_give isl_schedule *isl_schedule_intersect_domain(
9939 __isl_take isl_schedule *schedule,
9940 __isl_take isl_union_set *domain);
9942 The following function can be used to simplify the domain
9943 of a schedule with a domain node as root with respect to the given
9946 #include <isl/schedule.h>
9947 __isl_give isl_schedule *isl_schedule_gist_domain_params(
9948 __isl_take isl_schedule *schedule,
9949 __isl_take isl_set *context);
9951 The following function resets the user pointers on all parameter
9952 and tuple identifiers referenced by the nodes of the given schedule.
9954 #include <isl/schedule.h>
9955 __isl_give isl_schedule *isl_schedule_reset_user(
9956 __isl_take isl_schedule *schedule);
9958 The following function aligns the parameters of all nodes
9959 in the given schedule to the given space.
9961 #include <isl/schedule.h>
9962 __isl_give isl_schedule *isl_schedule_align_params(
9963 __isl_take isl_schedule *schedule,
9964 __isl_take isl_space *space);
9966 The following function allows the user to plug in a given function
9967 in the iteration domains. The input schedule is not allowed to contain
9968 any expansion nodes.
9970 #include <isl/schedule.h>
9971 __isl_give isl_schedule *
9972 isl_schedule_pullback_union_pw_multi_aff(
9973 __isl_take isl_schedule *schedule,
9974 __isl_take isl_union_pw_multi_aff *upma);
9976 The following function can be used to plug in the schedule C<expansion>
9977 in the leaves of C<schedule>, where C<contraction> describes how
9978 the domain elements of C<expansion> map to the domain elements
9979 at the original leaves of C<schedule>.
9980 The resulting schedule will contain expansion nodes, unless
9981 C<contraction> is an identity function.
9983 #include <isl/schedule.h>
9984 __isl_give isl_schedule *isl_schedule_expand(
9985 __isl_take isl_schedule *schedule,
9986 __isl_take isl_union_pw_multi_aff *contraction,
9987 __isl_take isl_schedule *expansion);
9989 An C<isl_union_map> representation of the schedule can be obtained
9990 from an C<isl_schedule> using the following function.
9992 #include <isl/schedule.h>
9993 __isl_give isl_union_map *isl_schedule_get_map(
9994 __isl_keep isl_schedule *sched);
9996 The resulting relation encodes the same relative ordering as
9997 the schedule by mapping the domain elements to a common schedule space.
9998 If the schedule_separate_components option is set, then the order
9999 of the children of a set node is explicitly encoded in the result.
10000 If the tree contains any expansion nodes, then the relation
10001 is formulated in terms of the expanded domain elements.
10003 Schedules can be read from input using the following functions.
10005 #include <isl/schedule.h>
10006 __isl_give isl_schedule *isl_schedule_read_from_file(
10007 isl_ctx *ctx, FILE *input);
10008 __isl_give isl_schedule *isl_schedule_read_from_str(
10009 isl_ctx *ctx, const char *str);
10011 A representation of the schedule can be printed using
10013 #include <isl/schedule.h>
10014 __isl_give isl_printer *isl_printer_print_schedule(
10015 __isl_take isl_printer *p,
10016 __isl_keep isl_schedule *schedule);
10017 __isl_give char *isl_schedule_to_str(
10018 __isl_keep isl_schedule *schedule);
10020 C<isl_schedule_to_str> prints the schedule in flow format.
10022 The schedule tree can be traversed through the use of
10023 C<isl_schedule_node> objects that point to a particular
10024 position in the schedule tree. Whenever a C<isl_schedule_node>
10025 is used to modify a node in the schedule tree, the original schedule
10026 tree is left untouched and the modifications are performed to a copy
10027 of the tree. The returned C<isl_schedule_node> then points to
10028 this modified copy of the tree.
10030 The root of the schedule tree can be obtained using the following function.
10032 #include <isl/schedule.h>
10033 __isl_give isl_schedule_node *isl_schedule_get_root(
10034 __isl_keep isl_schedule *schedule);
10036 A pointer to a newly created schedule tree with a single domain
10037 node can be created using the following functions.
10039 #include <isl/schedule_node.h>
10040 __isl_give isl_schedule_node *
10041 isl_schedule_node_from_domain(
10042 __isl_take isl_union_set *domain);
10043 __isl_give isl_schedule_node *
10044 isl_schedule_node_from_extension(
10045 __isl_take isl_union_map *extension);
10047 C<isl_schedule_node_from_extension> creates a tree with an extension
10050 Schedule nodes can be copied and freed using the following functions.
10052 #include <isl/schedule_node.h>
10053 __isl_give isl_schedule_node *isl_schedule_node_copy(
10054 __isl_keep isl_schedule_node *node);
10055 __isl_null isl_schedule_node *isl_schedule_node_free(
10056 __isl_take isl_schedule_node *node);
10058 The following functions can be used to check if two schedule
10059 nodes point to the same position in the same schedule.
10061 #include <isl/schedule_node.h>
10062 isl_bool isl_schedule_node_is_equal(
10063 __isl_keep isl_schedule_node *node1,
10064 __isl_keep isl_schedule_node *node2);
10066 The following properties can be obtained from a schedule node.
10068 #include <isl/schedule_node.h>
10069 enum isl_schedule_node_type isl_schedule_node_get_type(
10070 __isl_keep isl_schedule_node *node);
10071 enum isl_schedule_node_type
10072 isl_schedule_node_get_parent_type(
10073 __isl_keep isl_schedule_node *node);
10074 __isl_give isl_schedule *isl_schedule_node_get_schedule(
10075 __isl_keep isl_schedule_node *node);
10077 The function C<isl_schedule_node_get_type> returns the type of
10078 the node, while C<isl_schedule_node_get_parent_type> returns
10079 type of the parent of the node, which is required to exist.
10080 The function C<isl_schedule_node_get_schedule> returns a copy
10081 to the schedule to which the node belongs.
10083 The following functions can be used to move the schedule node
10084 to a different position in the tree or to check if such a position
10087 #include <isl/schedule_node.h>
10088 isl_bool isl_schedule_node_has_parent(
10089 __isl_keep isl_schedule_node *node);
10090 __isl_give isl_schedule_node *isl_schedule_node_parent(
10091 __isl_take isl_schedule_node *node);
10092 __isl_give isl_schedule_node *isl_schedule_node_root(
10093 __isl_take isl_schedule_node *node);
10094 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
10095 __isl_take isl_schedule_node *node,
10097 isl_size isl_schedule_node_n_children(
10098 __isl_keep isl_schedule_node *node);
10099 __isl_give isl_schedule_node *isl_schedule_node_child(
10100 __isl_take isl_schedule_node *node, int pos);
10101 isl_bool isl_schedule_node_has_children(
10102 __isl_keep isl_schedule_node *node);
10103 __isl_give isl_schedule_node *isl_schedule_node_first_child(
10104 __isl_take isl_schedule_node *node);
10105 isl_bool isl_schedule_node_has_previous_sibling(
10106 __isl_keep isl_schedule_node *node);
10107 __isl_give isl_schedule_node *
10108 isl_schedule_node_previous_sibling(
10109 __isl_take isl_schedule_node *node);
10110 isl_bool isl_schedule_node_has_next_sibling(
10111 __isl_keep isl_schedule_node *node);
10112 __isl_give isl_schedule_node *
10113 isl_schedule_node_next_sibling(
10114 __isl_take isl_schedule_node *node);
10116 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
10117 is the node itself, the ancestor of generation 1 is its parent and so on.
10119 It is also possible to query the number of ancestors of a node,
10120 the position of the current node
10121 within the children of its parent, the position of the subtree
10122 containing a node within the children of an ancestor
10123 or to obtain a copy of a given
10124 child without destroying the current node.
10125 Given two nodes that point to the same schedule, their closest
10126 shared ancestor can be obtained using
10127 C<isl_schedule_node_get_shared_ancestor>.
10129 #include <isl/schedule_node.h>
10130 isl_size isl_schedule_node_get_tree_depth(
10131 __isl_keep isl_schedule_node *node);
10132 isl_size isl_schedule_node_get_child_position(
10133 __isl_keep isl_schedule_node *node);
10134 isl_size isl_schedule_node_get_ancestor_child_position(
10135 __isl_keep isl_schedule_node *node,
10136 __isl_keep isl_schedule_node *ancestor);
10137 __isl_give isl_schedule_node *isl_schedule_node_get_child(
10138 __isl_keep isl_schedule_node *node, int pos);
10139 __isl_give isl_schedule_node *
10140 isl_schedule_node_get_shared_ancestor(
10141 __isl_keep isl_schedule_node *node1,
10142 __isl_keep isl_schedule_node *node2);
10144 All nodes in a schedule tree or
10145 all descendants of a specific node (including the node) can be visited
10146 in depth-first pre-order using the following functions.
10148 #include <isl/schedule.h>
10149 isl_stat isl_schedule_foreach_schedule_node_top_down(
10150 __isl_keep isl_schedule *sched,
10151 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10152 void *user), void *user);
10154 #include <isl/schedule_node.h>
10155 isl_stat isl_schedule_node_foreach_descendant_top_down(
10156 __isl_keep isl_schedule_node *node,
10157 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10158 void *user), void *user);
10160 The callback function is slightly different from the usual
10161 callbacks in that it not only indicates success (non-negative result)
10162 or failure (negative result), but also indicates whether the children
10163 of the given node should be visited. In particular, if the callback
10164 returns a positive value, then the children are visited, but if
10165 the callback returns zero, then the children are not visited.
10167 The following functions checks whether
10168 all descendants of a specific node (including the node itself)
10169 satisfy a user-specified test.
10171 #include <isl/schedule_node.h>
10172 isl_bool isl_schedule_node_every_descendant(
10173 __isl_keep isl_schedule_node *node,
10174 isl_bool (*test)(__isl_keep isl_schedule_node *node,
10175 void *user), void *user)
10177 The ancestors of a node in a schedule tree can be visited from
10178 the root down to and including the parent of the node using
10179 the following function.
10181 #include <isl/schedule_node.h>
10182 isl_stat isl_schedule_node_foreach_ancestor_top_down(
10183 __isl_keep isl_schedule_node *node,
10184 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
10185 void *user), void *user);
10187 The following functions allows for a depth-first post-order
10188 traversal of the nodes in a schedule tree or
10189 of the descendants of a specific node (including the node
10190 itself), where the user callback is allowed to modify the
10193 #include <isl/schedule.h>
10194 __isl_give isl_schedule *
10195 isl_schedule_map_schedule_node_bottom_up(
10196 __isl_take isl_schedule *schedule,
10197 __isl_give isl_schedule_node *(*fn)(
10198 __isl_take isl_schedule_node *node,
10199 void *user), void *user);
10201 #include <isl/schedule_node.h>
10202 __isl_give isl_schedule_node *
10203 isl_schedule_node_map_descendant_bottom_up(
10204 __isl_take isl_schedule_node *node,
10205 __isl_give isl_schedule_node *(*fn)(
10206 __isl_take isl_schedule_node *node,
10207 void *user), void *user);
10209 The traversal continues from the node returned by the callback function.
10210 It is the responsibility of the user to ensure that this does not
10211 lead to an infinite loop. It is safest to always return a pointer
10212 to the same position (same ancestors and child positions) as the input node.
10214 The following function removes a node (along with its descendants)
10215 from a schedule tree and returns a pointer to the leaf at the
10216 same position in the updated tree.
10217 It is not allowed to remove the root of a schedule tree or
10218 a child of a set or sequence node.
10220 #include <isl/schedule_node.h>
10221 __isl_give isl_schedule_node *isl_schedule_node_cut(
10222 __isl_take isl_schedule_node *node);
10224 The following function removes a single node
10225 from a schedule tree and returns a pointer to the child
10226 of the node, now located at the position of the original node
10227 or to a leaf node at that position if there was no child.
10228 It is not allowed to remove the root of a schedule tree,
10229 a set or sequence node, a child of a set or sequence node or
10230 a band node with an anchored subtree.
10232 #include <isl/schedule_node.h>
10233 __isl_give isl_schedule_node *isl_schedule_node_delete(
10234 __isl_take isl_schedule_node *node);
10236 Most nodes in a schedule tree only contain local information.
10237 In some cases, however, a node may also refer to the schedule dimensions
10238 of its outer band nodes.
10239 This means that the position of the node within the tree should
10240 not be changed, or at least that no changes are performed to the
10241 outer band nodes. The following function can be used to test
10242 whether the subtree rooted at a given node contains any such nodes.
10244 #include <isl/schedule_node.h>
10245 isl_bool isl_schedule_node_is_subtree_anchored(
10246 __isl_keep isl_schedule_node *node);
10248 The following function resets the user pointers on all parameter
10249 and tuple identifiers referenced by the given schedule node.
10251 #include <isl/schedule_node.h>
10252 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
10253 __isl_take isl_schedule_node *node);
10255 The following function aligns the parameters of the given schedule
10256 node to the given space.
10258 #include <isl/schedule_node.h>
10259 __isl_give isl_schedule_node *
10260 isl_schedule_node_align_params(
10261 __isl_take isl_schedule_node *node,
10262 __isl_take isl_space *space);
10264 Several node types have their own functions for querying
10265 (and in some cases setting) some node type specific properties.
10267 #include <isl/schedule_node.h>
10268 __isl_give isl_space *isl_schedule_node_band_get_space(
10269 __isl_keep isl_schedule_node *node);
10270 __isl_give isl_multi_union_pw_aff *
10271 isl_schedule_node_band_get_partial_schedule(
10272 __isl_keep isl_schedule_node *node);
10273 __isl_give isl_union_map *
10274 isl_schedule_node_band_get_partial_schedule_union_map(
10275 __isl_keep isl_schedule_node *node);
10276 isl_size isl_schedule_node_band_n_member(
10277 __isl_keep isl_schedule_node *node);
10278 isl_bool isl_schedule_node_band_member_get_coincident(
10279 __isl_keep isl_schedule_node *node, int pos);
10280 __isl_give isl_schedule_node *
10281 isl_schedule_node_band_member_set_coincident(
10282 __isl_take isl_schedule_node *node, int pos,
10284 isl_bool isl_schedule_node_band_get_permutable(
10285 __isl_keep isl_schedule_node *node);
10286 __isl_give isl_schedule_node *
10287 isl_schedule_node_band_set_permutable(
10288 __isl_take isl_schedule_node *node, int permutable);
10289 enum isl_ast_loop_type
10290 isl_schedule_node_band_member_get_ast_loop_type(
10291 __isl_keep isl_schedule_node *node, int pos);
10292 __isl_give isl_schedule_node *
10293 isl_schedule_node_band_member_set_ast_loop_type(
10294 __isl_take isl_schedule_node *node, int pos,
10295 enum isl_ast_loop_type type);
10296 enum isl_ast_loop_type
10297 isl_schedule_node_band_member_get_isolate_ast_loop_type(
10298 __isl_keep isl_schedule_node *node, int pos);
10299 __isl_give isl_schedule_node *
10300 isl_schedule_node_band_member_set_isolate_ast_loop_type(
10301 __isl_take isl_schedule_node *node, int pos,
10302 enum isl_ast_loop_type type);
10303 __isl_give isl_union_set *
10304 isl_schedule_node_band_get_ast_build_options(
10305 __isl_keep isl_schedule_node *node);
10306 __isl_give isl_schedule_node *
10307 isl_schedule_node_band_set_ast_build_options(
10308 __isl_take isl_schedule_node *node,
10309 __isl_take isl_union_set *options);
10310 __isl_give isl_set *
10311 isl_schedule_node_band_get_ast_isolate_option(
10312 __isl_keep isl_schedule_node *node);
10314 The function C<isl_schedule_node_band_get_space> returns the space
10315 of the partial schedule of the band.
10316 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
10317 returns a representation of the partial schedule of the band node
10318 in the form of an C<isl_union_map>.
10319 The coincident and permutable properties are set by
10320 C<isl_schedule_constraints_compute_schedule> on the schedule tree
10322 A scheduling dimension is considered to be ``coincident''
10323 if it satisfies the coincidence constraints within its band.
10324 That is, if the dependence distances of the coincidence
10325 constraints are all zero in that direction (for fixed
10326 iterations of outer bands).
10327 A band is marked permutable if it was produced using the Pluto-like scheduler.
10328 Note that the scheduler may have to resort to a Feautrier style scheduling
10329 step even if the default scheduler is used.
10330 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
10331 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
10332 For the meaning of these loop AST generation types and the difference
10333 between the regular loop AST generation type and the isolate
10334 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
10335 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
10336 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
10337 may return C<isl_ast_loop_error> if an error occurs.
10338 The AST build options govern how an AST is generated for
10339 the individual schedule dimensions during AST generation.
10340 See L</"AST Generation Options (Schedule Tree)">.
10341 The isolate option for the given node can be extracted from these
10342 AST build options using the function
10343 C<isl_schedule_node_band_get_ast_isolate_option>.
10345 #include <isl/schedule_node.h>
10346 __isl_give isl_set *
10347 isl_schedule_node_context_get_context(
10348 __isl_keep isl_schedule_node *node);
10350 #include <isl/schedule_node.h>
10351 __isl_give isl_union_set *
10352 isl_schedule_node_domain_get_domain(
10353 __isl_keep isl_schedule_node *node);
10355 #include <isl/schedule_node.h>
10356 __isl_give isl_union_map *
10357 isl_schedule_node_expansion_get_expansion(
10358 __isl_keep isl_schedule_node *node);
10359 __isl_give isl_union_pw_multi_aff *
10360 isl_schedule_node_expansion_get_contraction(
10361 __isl_keep isl_schedule_node *node);
10363 #include <isl/schedule_node.h>
10364 __isl_give isl_union_map *
10365 isl_schedule_node_extension_get_extension(
10366 __isl_keep isl_schedule_node *node);
10368 #include <isl/schedule_node.h>
10369 __isl_give isl_union_set *
10370 isl_schedule_node_filter_get_filter(
10371 __isl_keep isl_schedule_node *node);
10373 #include <isl/schedule_node.h>
10374 __isl_give isl_set *isl_schedule_node_guard_get_guard(
10375 __isl_keep isl_schedule_node *node);
10377 #include <isl/schedule_node.h>
10378 __isl_give isl_id *isl_schedule_node_mark_get_id(
10379 __isl_keep isl_schedule_node *node);
10381 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
10382 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
10383 partial schedules related to the node.
10385 #include <isl/schedule_node.h>
10386 __isl_give isl_multi_union_pw_aff *
10387 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
10388 __isl_keep isl_schedule_node *node);
10389 __isl_give isl_union_pw_multi_aff *
10390 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
10391 __isl_keep isl_schedule_node *node);
10392 __isl_give isl_union_map *
10393 isl_schedule_node_get_prefix_schedule_union_map(
10394 __isl_keep isl_schedule_node *node);
10395 __isl_give isl_union_map *
10396 isl_schedule_node_get_prefix_schedule_relation(
10397 __isl_keep isl_schedule_node *node);
10398 __isl_give isl_union_map *
10399 isl_schedule_node_get_subtree_schedule_union_map(
10400 __isl_keep isl_schedule_node *node);
10402 In particular, the functions
10403 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
10404 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
10405 and C<isl_schedule_node_get_prefix_schedule_union_map>
10406 return a relative ordering on the domain elements that reach the given
10407 node determined by its ancestors.
10408 The function C<isl_schedule_node_get_prefix_schedule_relation>
10409 additionally includes the domain constraints in the result.
10410 The function C<isl_schedule_node_get_subtree_schedule_union_map>
10411 returns a representation of the partial schedule defined by the
10412 subtree rooted at the given node.
10413 If the tree contains any expansion nodes, then the subtree schedule
10414 is formulated in terms of the expanded domain elements.
10415 The tree passed to functions returning a prefix schedule
10416 may only contain extension nodes if these would not affect
10417 the result of these functions. That is, if one of the ancestors
10418 is an extension node, then all of the domain elements that were
10419 added by the extension node need to have been filtered out
10420 by filter nodes between the extension node and the input node.
10421 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
10422 may not contain in extension nodes in the selected subtree.
10424 The expansion/contraction defined by an entire subtree, combining
10425 the expansions/contractions
10426 on the expansion nodes in the subtree, can be obtained using
10427 the following functions.
10429 #include <isl/schedule_node.h>
10430 __isl_give isl_union_map *
10431 isl_schedule_node_get_subtree_expansion(
10432 __isl_keep isl_schedule_node *node);
10433 __isl_give isl_union_pw_multi_aff *
10434 isl_schedule_node_get_subtree_contraction(
10435 __isl_keep isl_schedule_node *node);
10437 The total number of outer band members of given node, i.e.,
10438 the shared output dimension of the maps in the result
10439 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
10440 using the following function.
10442 #include <isl/schedule_node.h>
10443 isl_size isl_schedule_node_get_schedule_depth(
10444 __isl_keep isl_schedule_node *node);
10446 The following functions return the elements that reach the given node
10447 or the union of universes in the spaces that contain these elements.
10449 #include <isl/schedule_node.h>
10450 __isl_give isl_union_set *
10451 isl_schedule_node_get_domain(
10452 __isl_keep isl_schedule_node *node);
10453 __isl_give isl_union_set *
10454 isl_schedule_node_get_universe_domain(
10455 __isl_keep isl_schedule_node *node);
10457 The input tree of C<isl_schedule_node_get_domain>
10458 may only contain extension nodes if these would not affect
10459 the result of this function. That is, if one of the ancestors
10460 is an extension node, then all of the domain elements that were
10461 added by the extension node need to have been filtered out
10462 by filter nodes between the extension node and the input node.
10464 The following functions can be used to introduce additional nodes
10465 in the schedule tree. The new node is introduced at the point
10466 in the tree where the C<isl_schedule_node> points to and
10467 the results points to the new node.
10469 #include <isl/schedule_node.h>
10470 __isl_give isl_schedule_node *
10471 isl_schedule_node_insert_partial_schedule(
10472 __isl_take isl_schedule_node *node,
10473 __isl_take isl_multi_union_pw_aff *schedule);
10475 This function inserts a new band node with (the greatest integer
10476 part of) the given partial schedule.
10477 The subtree rooted at the given node is assumed not to have
10478 any anchored nodes.
10480 #include <isl/schedule_node.h>
10481 __isl_give isl_schedule_node *
10482 isl_schedule_node_insert_context(
10483 __isl_take isl_schedule_node *node,
10484 __isl_take isl_set *context);
10486 This function inserts a new context node with the given context constraints.
10488 #include <isl/schedule_node.h>
10489 __isl_give isl_schedule_node *
10490 isl_schedule_node_insert_filter(
10491 __isl_take isl_schedule_node *node,
10492 __isl_take isl_union_set *filter);
10494 This function inserts a new filter node with the given filter.
10495 If the original node already pointed to a filter node, then the
10496 two filter nodes are merged into one.
10498 #include <isl/schedule_node.h>
10499 __isl_give isl_schedule_node *
10500 isl_schedule_node_insert_guard(
10501 __isl_take isl_schedule_node *node,
10502 __isl_take isl_set *guard);
10504 This function inserts a new guard node with the given guard constraints.
10506 #include <isl/schedule_node.h>
10507 __isl_give isl_schedule_node *
10508 isl_schedule_node_insert_mark(
10509 __isl_take isl_schedule_node *node,
10510 __isl_take isl_id *mark);
10512 This function inserts a new mark node with the give mark identifier.
10514 #include <isl/schedule_node.h>
10515 __isl_give isl_schedule_node *
10516 isl_schedule_node_insert_sequence(
10517 __isl_take isl_schedule_node *node,
10518 __isl_take isl_union_set_list *filters);
10519 __isl_give isl_schedule_node *
10520 isl_schedule_node_insert_set(
10521 __isl_take isl_schedule_node *node,
10522 __isl_take isl_union_set_list *filters);
10524 These functions insert a new sequence or set node with the given
10525 filters as children.
10527 #include <isl/schedule_node.h>
10528 __isl_give isl_schedule_node *isl_schedule_node_group(
10529 __isl_take isl_schedule_node *node,
10530 __isl_take isl_id *group_id);
10532 This function introduces an expansion node in between the current
10533 node and its parent that expands instances of a space with tuple
10534 identifier C<group_id> to the original domain elements that reach
10535 the node. The group instances are identified by the prefix schedule
10536 of those domain elements. The ancestors of the node are adjusted
10537 to refer to the group instances instead of the original domain
10538 elements. The return value points to the same node in the updated
10539 schedule tree as the input node, i.e., to the child of the newly
10540 introduced expansion node. Grouping instances of different statements
10541 ensures that they will be treated as a single statement by the
10542 AST generator up to the point of the expansion node.
10544 The following function can be used to flatten a nested
10547 #include <isl/schedule_node.h>
10548 __isl_give isl_schedule_node *
10549 isl_schedule_node_sequence_splice_child(
10550 __isl_take isl_schedule_node *node, int pos);
10552 That is, given a sequence node C<node> that has another sequence node
10553 in its child at position C<pos> (in particular, the child of that filter
10554 node is a sequence node), attach the children of that other sequence
10555 node as children of C<node>, replacing the original child at position
10558 The partial schedule of a band node can be scaled (down) or reduced using
10559 the following functions.
10561 #include <isl/schedule_node.h>
10562 __isl_give isl_schedule_node *
10563 isl_schedule_node_band_scale(
10564 __isl_take isl_schedule_node *node,
10565 __isl_take isl_multi_val *mv);
10566 __isl_give isl_schedule_node *
10567 isl_schedule_node_band_scale_down(
10568 __isl_take isl_schedule_node *node,
10569 __isl_take isl_multi_val *mv);
10570 __isl_give isl_schedule_node *
10571 isl_schedule_node_band_mod(
10572 __isl_take isl_schedule_node *node,
10573 __isl_take isl_multi_val *mv);
10575 The spaces of the two arguments need to match.
10576 After scaling, the partial schedule is replaced by its greatest
10577 integer part to ensure that the schedule remains integral.
10579 The partial schedule of a band node can be shifted by an
10580 C<isl_multi_union_pw_aff> with a domain that is a superset
10581 of the domain of the partial schedule using
10582 the following function.
10584 #include <isl/schedule_node.h>
10585 __isl_give isl_schedule_node *
10586 isl_schedule_node_band_shift(
10587 __isl_take isl_schedule_node *node,
10588 __isl_take isl_multi_union_pw_aff *shift);
10590 A band node can be tiled using the following function.
10592 #include <isl/schedule_node.h>
10593 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
10594 __isl_take isl_schedule_node *node,
10595 __isl_take isl_multi_val *sizes);
10597 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
10599 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
10600 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
10602 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
10604 The C<isl_schedule_node_band_tile> function tiles
10605 the band using the given tile sizes inside its schedule.
10606 A new child band node is created to represent the point loops and it is
10607 inserted between the modified band and its children.
10608 The subtree rooted at the given node is assumed not to have
10609 any anchored nodes.
10610 The C<tile_scale_tile_loops> option specifies whether the tile
10611 loops iterators should be scaled by the tile sizes.
10612 If the C<tile_shift_point_loops> option is set, then the point loops
10613 are shifted to start at zero.
10615 A band node can be split into two nested band nodes
10616 using the following function.
10618 #include <isl/schedule_node.h>
10619 __isl_give isl_schedule_node *isl_schedule_node_band_split(
10620 __isl_take isl_schedule_node *node, int pos);
10622 The resulting outer band node contains the first C<pos> dimensions of
10623 the schedule of C<node> while the inner band contains the remaining dimensions.
10624 The schedules of the two band nodes live in anonymous spaces.
10625 The loop AST generation type options and the isolate option
10626 are split over the two band nodes.
10628 A band node can be moved down to the leaves of the subtree rooted
10629 at the band node using the following function.
10631 #include <isl/schedule_node.h>
10632 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
10633 __isl_take isl_schedule_node *node);
10635 The subtree rooted at the given node is assumed not to have
10636 any anchored nodes.
10637 The result points to the node in the resulting tree that is in the same
10638 position as the node pointed to by C<node> in the original tree.
10640 #include <isl/schedule_node.h>
10641 __isl_give isl_schedule_node *
10642 isl_schedule_node_order_before(
10643 __isl_take isl_schedule_node *node,
10644 __isl_take isl_union_set *filter);
10645 __isl_give isl_schedule_node *
10646 isl_schedule_node_order_after(
10647 __isl_take isl_schedule_node *node,
10648 __isl_take isl_union_set *filter);
10650 These functions split the domain elements that reach C<node>
10651 into those that satisfy C<filter> and those that do not and
10652 arranges for the elements that do satisfy the filter to be
10653 executed before (in case of C<isl_schedule_node_order_before>)
10654 or after (in case of C<isl_schedule_node_order_after>)
10655 those that do not. The order is imposed by
10656 a sequence node, possibly reusing the grandparent of C<node>
10657 on two copies of the subtree attached to the original C<node>.
10658 Both copies are simplified with respect to their filter.
10660 Return a pointer to the copy of the subtree that does not
10661 satisfy C<filter>. If there is no such copy (because all
10662 reaching domain elements satisfy the filter), then return
10663 the original pointer.
10665 #include <isl/schedule_node.h>
10666 __isl_give isl_schedule_node *
10667 isl_schedule_node_graft_before(
10668 __isl_take isl_schedule_node *node,
10669 __isl_take isl_schedule_node *graft);
10670 __isl_give isl_schedule_node *
10671 isl_schedule_node_graft_after(
10672 __isl_take isl_schedule_node *node,
10673 __isl_take isl_schedule_node *graft);
10675 This function inserts the C<graft> tree into the tree containing C<node>
10676 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
10677 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
10678 The root node of C<graft>
10679 should be an extension node where the domain of the extension
10680 is the flat product of all outer band nodes of C<node>.
10681 The root node may also be a domain node.
10682 The elements of the domain or the range of the extension may not
10683 intersect with the domain elements that reach "node".
10684 The schedule tree of C<graft> may not be anchored.
10686 The schedule tree of C<node> is modified to include an extension node
10687 corresponding to the root node of C<graft> as a child of the original
10688 parent of C<node>. The original node that C<node> points to and the
10689 child of the root node of C<graft> are attached to this extension node
10690 through a sequence, with appropriate filters and with the child
10691 of C<graft> appearing before or after the original C<node>.
10693 If C<node> already appears inside a sequence that is the child of
10694 an extension node and if the spaces of the new domain elements
10695 do not overlap with those of the original domain elements,
10696 then that extension node is extended with the new extension
10697 rather than introducing a new segment of extension and sequence nodes.
10699 Return a pointer to the same node in the modified tree that
10700 C<node> pointed to in the original tree.
10702 A representation of the schedule node can be printed using
10704 #include <isl/schedule_node.h>
10705 __isl_give isl_printer *isl_printer_print_schedule_node(
10706 __isl_take isl_printer *p,
10707 __isl_keep isl_schedule_node *node);
10708 __isl_give char *isl_schedule_node_to_str(
10709 __isl_keep isl_schedule_node *node);
10711 C<isl_schedule_node_to_str> prints the schedule node in block format.
10713 =head2 Dependence Analysis
10715 C<isl> contains specialized functionality for performing
10716 array dataflow analysis. That is, given a I<sink> access relation,
10717 a collection of possible I<source> accesses and
10718 a collection of I<kill> accesses,
10719 C<isl> can compute relations that describe
10720 for each iteration of the sink access, which iterations
10721 of which of the source access relations may have
10722 accessed the same data element before the given iteration
10723 of the sink access without any intermediate kill of that data element.
10724 The resulting dependence relations map source iterations
10725 to either the corresponding sink iterations or
10726 pairs of corresponding sink iterations and accessed data elements.
10727 To compute standard flow dependences, the sink should be
10728 a read, while the sources should be writes.
10729 If no kills are specified,
10730 then memory based dependence analysis is performed.
10731 If, on the other hand, all sources are also kills,
10732 then value based dependence analysis is performed.
10733 If any of the source accesses are marked as being I<must>
10734 accesses, then they are also treated as kills.
10735 Furthermore, the specification of must-sources results
10736 in the computation of must-dependences.
10737 Only dependences originating in a must access not coscheduled
10738 with any other access to the same element and without
10739 any may accesses between the must access and the sink access
10740 are considered to be must dependences.
10742 =head3 High-level Interface
10744 A high-level interface to dependence analysis is provided
10745 by the following function.
10747 #include <isl/flow.h>
10748 __isl_give isl_union_flow *
10749 isl_union_access_info_compute_flow(
10750 __isl_take isl_union_access_info *access);
10752 The input C<isl_union_access_info> object describes the sink
10753 access relations, the source access relations and a schedule,
10754 while the output C<isl_union_flow> object describes
10755 the resulting dependence relations and the subsets of the
10756 sink relations for which no source was found.
10758 An C<isl_union_access_info> is created, modified, copied and freed using
10759 the following functions.
10761 #include <isl/flow.h>
10762 __isl_give isl_union_access_info *
10763 isl_union_access_info_from_sink(
10764 __isl_take isl_union_map *sink);
10765 __isl_give isl_union_access_info *
10766 isl_union_access_info_set_kill(
10767 __isl_take isl_union_access_info *access,
10768 __isl_take isl_union_map *kill);
10769 __isl_give isl_union_access_info *
10770 isl_union_access_info_set_may_source(
10771 __isl_take isl_union_access_info *access,
10772 __isl_take isl_union_map *may_source);
10773 __isl_give isl_union_access_info *
10774 isl_union_access_info_set_must_source(
10775 __isl_take isl_union_access_info *access,
10776 __isl_take isl_union_map *must_source);
10777 __isl_give isl_union_access_info *
10778 isl_union_access_info_set_schedule(
10779 __isl_take isl_union_access_info *access,
10780 __isl_take isl_schedule *schedule);
10781 __isl_give isl_union_access_info *
10782 isl_union_access_info_set_schedule_map(
10783 __isl_take isl_union_access_info *access,
10784 __isl_take isl_union_map *schedule_map);
10785 __isl_give isl_union_access_info *
10786 isl_union_access_info_copy(
10787 __isl_keep isl_union_access_info *access);
10788 __isl_null isl_union_access_info *
10789 isl_union_access_info_free(
10790 __isl_take isl_union_access_info *access);
10792 The may sources set by C<isl_union_access_info_set_may_source>
10793 do not need to include the must sources set by
10794 C<isl_union_access_info_set_must_source> as a subset.
10795 The kills set by C<isl_union_access_info_set_kill> may overlap
10796 with the may-sources and/or must-sources.
10797 The user is free not to call one (or more) of these functions,
10798 in which case the corresponding set is kept to its empty default.
10799 Similarly, the default schedule initialized by
10800 C<isl_union_access_info_from_sink> is empty.
10801 The current schedule is determined by the last call to either
10802 C<isl_union_access_info_set_schedule> or
10803 C<isl_union_access_info_set_schedule_map>.
10804 The domain of the schedule corresponds to the domains of
10805 the access relations. In particular, the domains of the access
10806 relations are effectively intersected with the domain of the schedule
10807 and only the resulting accesses are considered by the dependence analysis.
10809 An C<isl_union_access_info> object can be read from input
10810 using the following function.
10812 #include <isl/flow.h>
10813 __isl_give isl_union_access_info *
10814 isl_union_access_info_read_from_file(isl_ctx *ctx,
10817 A representation of the information contained in an object
10818 of type C<isl_union_access_info> can be obtained using
10820 #include <isl/flow.h>
10821 __isl_give isl_printer *
10822 isl_printer_print_union_access_info(
10823 __isl_take isl_printer *p,
10824 __isl_keep isl_union_access_info *access);
10825 __isl_give char *isl_union_access_info_to_str(
10826 __isl_keep isl_union_access_info *access);
10828 C<isl_union_access_info_to_str> prints the information in flow format.
10830 The output of C<isl_union_access_info_compute_flow> can be examined,
10831 copied, and freed using the following functions.
10833 #include <isl/flow.h>
10834 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
10835 __isl_keep isl_union_flow *flow);
10836 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
10837 __isl_keep isl_union_flow *flow);
10838 __isl_give isl_union_map *
10839 isl_union_flow_get_full_must_dependence(
10840 __isl_keep isl_union_flow *flow);
10841 __isl_give isl_union_map *
10842 isl_union_flow_get_full_may_dependence(
10843 __isl_keep isl_union_flow *flow);
10844 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
10845 __isl_keep isl_union_flow *flow);
10846 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
10847 __isl_keep isl_union_flow *flow);
10848 __isl_give isl_union_flow *isl_union_flow_copy(
10849 __isl_keep isl_union_flow *flow);
10850 __isl_null isl_union_flow *isl_union_flow_free(
10851 __isl_take isl_union_flow *flow);
10853 The relation returned by C<isl_union_flow_get_must_dependence>
10854 relates domain elements of must sources to domain elements of the sink.
10855 The relation returned by C<isl_union_flow_get_may_dependence>
10856 relates domain elements of must or may sources to domain elements of the sink
10857 and includes the previous relation as a subset.
10858 The relation returned by C<isl_union_flow_get_full_must_dependence>
10859 relates domain elements of must sources to pairs of domain elements of the sink
10860 and accessed data elements.
10861 The relation returned by C<isl_union_flow_get_full_may_dependence>
10862 relates domain elements of must or may sources to pairs of
10863 domain elements of the sink and accessed data elements.
10864 This relation includes the previous relation as a subset.
10865 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
10866 of the sink relation for which no dependences have been found.
10867 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
10868 of the sink relation for which no definite dependences have been found.
10869 That is, it contains those sink access that do not contribute to any
10870 of the elements in the relation returned
10871 by C<isl_union_flow_get_must_dependence>.
10873 A representation of the information contained in an object
10874 of type C<isl_union_flow> can be obtained using
10876 #include <isl/flow.h>
10877 __isl_give isl_printer *isl_printer_print_union_flow(
10878 __isl_take isl_printer *p,
10879 __isl_keep isl_union_flow *flow);
10880 __isl_give char *isl_union_flow_to_str(
10881 __isl_keep isl_union_flow *flow);
10883 C<isl_union_flow_to_str> prints the information in flow format.
10885 =head3 Low-level Interface
10887 A lower-level interface is provided by the following functions.
10889 #include <isl/flow.h>
10891 typedef int (*isl_access_level_before)(void *first, void *second);
10893 __isl_give isl_access_info *isl_access_info_alloc(
10894 __isl_take isl_map *sink,
10895 void *sink_user, isl_access_level_before fn,
10897 __isl_give isl_access_info *isl_access_info_add_source(
10898 __isl_take isl_access_info *acc,
10899 __isl_take isl_map *source, int must,
10900 void *source_user);
10901 __isl_null isl_access_info *isl_access_info_free(
10902 __isl_take isl_access_info *acc);
10904 __isl_give isl_flow *isl_access_info_compute_flow(
10905 __isl_take isl_access_info *acc);
10907 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
10908 isl_stat (*fn)(__isl_take isl_map *dep, int must,
10909 void *dep_user, void *user),
10911 __isl_give isl_map *isl_flow_get_no_source(
10912 __isl_keep isl_flow *deps, int must);
10913 __isl_null isl_flow *isl_flow_free(
10914 __isl_take isl_flow *deps);
10916 The function C<isl_access_info_compute_flow> performs the actual
10917 dependence analysis. The other functions are used to construct
10918 the input for this function or to read off the output.
10920 The input is collected in an C<isl_access_info>, which can
10921 be created through a call to C<isl_access_info_alloc>.
10922 The arguments to this functions are the sink access relation
10923 C<sink>, a token C<sink_user> used to identify the sink
10924 access to the user, a callback function for specifying the
10925 relative order of source and sink accesses, and the number
10926 of source access relations that will be added.
10928 The callback function has type C<int (*)(void *first, void *second)>.
10929 The function is called with two user supplied tokens identifying
10930 either a source or the sink and it should return the shared nesting
10931 level and the relative order of the two accesses.
10932 In particular, let I<n> be the number of loops shared by
10933 the two accesses. If C<first> precedes C<second> textually,
10934 then the function should return I<2 * n + 1>; otherwise,
10935 it should return I<2 * n>.
10936 The low-level interface assumes that no sources are coscheduled.
10937 If the information returned by the callback does not allow
10938 the relative order to be determined, then one of the sources
10939 is arbitrarily taken to be executed after the other(s).
10941 The sources can be added to the C<isl_access_info> object by performing
10942 (at most) C<max_source> calls to C<isl_access_info_add_source>.
10943 C<must> indicates whether the source is a I<must> access
10944 or a I<may> access. Note that a multi-valued access relation
10945 should only be marked I<must> if every iteration in the domain
10946 of the relation accesses I<all> elements in its image.
10947 The C<source_user> token is again used to identify
10948 the source access. The range of the source access relation
10949 C<source> should have the same dimension as the range
10950 of the sink access relation.
10951 The C<isl_access_info_free> function should usually not be
10952 called explicitly, because it is already called implicitly by
10953 C<isl_access_info_compute_flow>.
10955 The result of the dependence analysis is collected in an
10956 C<isl_flow>. There may be elements of
10957 the sink access for which no preceding source access could be
10958 found or for which all preceding sources are I<may> accesses.
10959 The relations containing these elements can be obtained through
10960 calls to C<isl_flow_get_no_source>, the first with C<must> set
10961 and the second with C<must> unset.
10962 In the case of standard flow dependence analysis,
10963 with the sink a read and the sources I<must> writes,
10964 the first relation corresponds to the reads from uninitialized
10965 array elements and the second relation is empty.
10966 The actual flow dependences can be extracted using
10967 C<isl_flow_foreach>. This function will call the user-specified
10968 callback function C<fn> for each B<non-empty> dependence between
10969 a source and the sink. The callback function is called
10970 with four arguments, the actual flow dependence relation
10971 mapping source iterations to sink iterations, a boolean that
10972 indicates whether it is a I<must> or I<may> dependence, a token
10973 identifying the source and an additional C<void *> with value
10974 equal to the third argument of the C<isl_flow_foreach> call.
10975 A dependence is marked I<must> if it originates from a I<must>
10976 source and if it is not followed by any I<may> sources.
10978 After finishing with an C<isl_flow>, the user should call
10979 C<isl_flow_free> to free all associated memory.
10981 =head3 Interaction with the Low-level Interface
10983 During the dependence analysis, we frequently need to perform
10984 the following operation. Given a relation between sink iterations
10985 and potential source iterations from a particular source domain,
10986 what is the last potential source iteration corresponding to each
10987 sink iteration. It can sometimes be convenient to adjust
10988 the set of potential source iterations before or after each such operation.
10989 The prototypical example is fuzzy array dataflow analysis,
10990 where we need to analyze if, based on data-dependent constraints,
10991 the sink iteration can ever be executed without one or more of
10992 the corresponding potential source iterations being executed.
10993 If so, we can introduce extra parameters and select an unknown
10994 but fixed source iteration from the potential source iterations.
10995 To be able to perform such manipulations, C<isl> provides the following
10998 #include <isl/flow.h>
11000 typedef __isl_give isl_restriction *(*isl_access_restrict)(
11001 __isl_keep isl_map *source_map,
11002 __isl_keep isl_set *sink, void *source_user,
11004 __isl_give isl_access_info *isl_access_info_set_restrict(
11005 __isl_take isl_access_info *acc,
11006 isl_access_restrict fn, void *user);
11008 The function C<isl_access_info_set_restrict> should be called
11009 before calling C<isl_access_info_compute_flow> and registers a callback function
11010 that will be called any time C<isl> is about to compute the last
11011 potential source. The first argument is the (reverse) proto-dependence,
11012 mapping sink iterations to potential source iterations.
11013 The second argument represents the sink iterations for which
11014 we want to compute the last source iteration.
11015 The third argument is the token corresponding to the source
11016 and the final argument is the token passed to C<isl_access_info_set_restrict>.
11017 The callback is expected to return a restriction on either the input or
11018 the output of the operation computing the last potential source.
11019 If the input needs to be restricted then restrictions are needed
11020 for both the source and the sink iterations. The sink iterations
11021 and the potential source iterations will be intersected with these sets.
11022 If the output needs to be restricted then only a restriction on the source
11023 iterations is required.
11024 If any error occurs, the callback should return C<NULL>.
11025 An C<isl_restriction> object can be created, freed and inspected
11026 using the following functions.
11028 #include <isl/flow.h>
11030 __isl_give isl_restriction *isl_restriction_input(
11031 __isl_take isl_set *source_restr,
11032 __isl_take isl_set *sink_restr);
11033 __isl_give isl_restriction *isl_restriction_output(
11034 __isl_take isl_set *source_restr);
11035 __isl_give isl_restriction *isl_restriction_none(
11036 __isl_take isl_map *source_map);
11037 __isl_give isl_restriction *isl_restriction_empty(
11038 __isl_take isl_map *source_map);
11039 __isl_null isl_restriction *isl_restriction_free(
11040 __isl_take isl_restriction *restr);
11042 C<isl_restriction_none> and C<isl_restriction_empty> are special
11043 cases of C<isl_restriction_input>. C<isl_restriction_none>
11044 is essentially equivalent to
11046 isl_restriction_input(isl_set_universe(
11047 isl_space_range(isl_map_get_space(source_map))),
11049 isl_space_domain(isl_map_get_space(source_map))));
11051 whereas C<isl_restriction_empty> is essentially equivalent to
11053 isl_restriction_input(isl_set_empty(
11054 isl_space_range(isl_map_get_space(source_map))),
11056 isl_space_domain(isl_map_get_space(source_map))));
11060 #include <isl/schedule.h>
11061 __isl_give isl_schedule *
11062 isl_schedule_constraints_compute_schedule(
11063 __isl_take isl_schedule_constraints *sc);
11065 The function C<isl_schedule_constraints_compute_schedule> can be
11066 used to compute a schedule that satisfies the given schedule constraints.
11067 These schedule constraints include the iteration domain for which
11068 a schedule should be computed and dependences between pairs of
11069 iterations. In particular, these dependences include
11070 I<validity> dependences and I<proximity> dependences.
11071 By default, the algorithm used to construct the schedule is similar
11072 to that of C<Pluto>.
11073 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
11075 The generated schedule respects all validity dependences.
11076 That is, all dependence distances over these dependences in the
11077 scheduled space are lexicographically positive.
11079 The default algorithm tries to ensure that the dependence distances
11080 over coincidence constraints are zero and to minimize the
11081 dependence distances over proximity dependences.
11082 Moreover, it tries to obtain sequences (bands) of schedule dimensions
11083 for groups of domains where the dependence distances over validity
11084 dependences have only non-negative values.
11085 Note that when minimizing the maximal dependence distance
11086 over proximity dependences, a single affine expression in the parameters
11087 is constructed that bounds all dependence distances. If no such expression
11088 exists, then the algorithm will fail and resort to an alternative
11089 scheduling algorithm. In particular, this means that adding proximity
11090 dependences may eliminate valid solutions. A typical example where this
11091 phenomenon may occur is when some subset of the proximity dependences
11092 has no restriction on some parameter, forcing the coefficient of that
11093 parameter to be zero, while some other subset forces the dependence
11094 distance to depend on that parameter, requiring the same coefficient
11096 When using Feautrier's algorithm, the coincidence and proximity constraints
11097 are only taken into account during the extension to a
11098 full-dimensional schedule.
11100 An C<isl_schedule_constraints> object can be constructed
11101 and manipulated using the following functions.
11103 #include <isl/schedule.h>
11104 __isl_give isl_schedule_constraints *
11105 isl_schedule_constraints_copy(
11106 __isl_keep isl_schedule_constraints *sc);
11107 __isl_give isl_schedule_constraints *
11108 isl_schedule_constraints_on_domain(
11109 __isl_take isl_union_set *domain);
11110 __isl_give isl_schedule_constraints *
11111 isl_schedule_constraints_set_context(
11112 __isl_take isl_schedule_constraints *sc,
11113 __isl_take isl_set *context);
11114 __isl_give isl_schedule_constraints *
11115 isl_schedule_constraints_set_validity(
11116 __isl_take isl_schedule_constraints *sc,
11117 __isl_take isl_union_map *validity);
11118 __isl_give isl_schedule_constraints *
11119 isl_schedule_constraints_set_coincidence(
11120 __isl_take isl_schedule_constraints *sc,
11121 __isl_take isl_union_map *coincidence);
11122 __isl_give isl_schedule_constraints *
11123 isl_schedule_constraints_set_proximity(
11124 __isl_take isl_schedule_constraints *sc,
11125 __isl_take isl_union_map *proximity);
11126 __isl_give isl_schedule_constraints *
11127 isl_schedule_constraints_set_conditional_validity(
11128 __isl_take isl_schedule_constraints *sc,
11129 __isl_take isl_union_map *condition,
11130 __isl_take isl_union_map *validity);
11131 __isl_give isl_schedule_constraints *
11132 isl_schedule_constraints_apply(
11133 __isl_take isl_schedule_constraints *sc,
11134 __isl_take isl_union_map *umap);
11135 __isl_null isl_schedule_constraints *
11136 isl_schedule_constraints_free(
11137 __isl_take isl_schedule_constraints *sc);
11139 The initial C<isl_schedule_constraints> object created by
11140 C<isl_schedule_constraints_on_domain> does not impose any constraints.
11141 That is, it has an empty set of dependences.
11142 The function C<isl_schedule_constraints_set_context> allows the user
11143 to specify additional constraints on the parameters that may
11144 be assumed to hold during the construction of the schedule.
11145 The function C<isl_schedule_constraints_set_validity> replaces the
11146 validity dependences, mapping domain elements I<i> to domain
11147 elements that should be scheduled after I<i>.
11148 The function C<isl_schedule_constraints_set_coincidence> replaces the
11149 coincidence dependences, mapping domain elements I<i> to domain
11150 elements that should be scheduled together with I<I>, if possible.
11151 The function C<isl_schedule_constraints_set_proximity> replaces the
11152 proximity dependences, mapping domain elements I<i> to domain
11153 elements that should be scheduled either before I<I>
11154 or as early as possible after I<i>.
11156 The function C<isl_schedule_constraints_set_conditional_validity>
11157 replaces the conditional validity constraints.
11158 A conditional validity constraint is only imposed when any of the corresponding
11159 conditions is satisfied, i.e., when any of them is non-zero.
11160 That is, the scheduler ensures that within each band if the dependence
11161 distances over the condition constraints are not all zero
11162 then all corresponding conditional validity constraints are respected.
11163 A conditional validity constraint corresponds to a condition
11164 if the two are adjacent, i.e., if the domain of one relation intersect
11165 the range of the other relation.
11166 The typical use case of conditional validity constraints is
11167 to allow order constraints between live ranges to be violated
11168 as long as the live ranges themselves are local to the band.
11169 To allow more fine-grained control over which conditions correspond
11170 to which conditional validity constraints, the domains and ranges
11171 of these relations may include I<tags>. That is, the domains and
11172 ranges of those relation may themselves be wrapped relations
11173 where the iteration domain appears in the domain of those wrapped relations
11174 and the range of the wrapped relations can be arbitrarily chosen
11175 by the user. Conditions and conditional validity constraints are only
11176 considered adjacent to each other if the entire wrapped relation matches.
11177 In particular, a relation with a tag will never be considered adjacent
11178 to a relation without a tag.
11180 The function C<isl_schedule_constraints_apply> takes
11181 schedule constraints that are defined on some set of domain elements
11182 and transforms them to schedule constraints on the elements
11183 to which these domain elements are mapped by the given transformation.
11185 An C<isl_schedule_constraints> object can be inspected
11186 using the following functions.
11188 #include <isl/schedule.h>
11189 __isl_give isl_union_set *
11190 isl_schedule_constraints_get_domain(
11191 __isl_keep isl_schedule_constraints *sc);
11192 __isl_give isl_set *isl_schedule_constraints_get_context(
11193 __isl_keep isl_schedule_constraints *sc);
11194 __isl_give isl_union_map *
11195 isl_schedule_constraints_get_validity(
11196 __isl_keep isl_schedule_constraints *sc);
11197 __isl_give isl_union_map *
11198 isl_schedule_constraints_get_coincidence(
11199 __isl_keep isl_schedule_constraints *sc);
11200 __isl_give isl_union_map *
11201 isl_schedule_constraints_get_proximity(
11202 __isl_keep isl_schedule_constraints *sc);
11203 __isl_give isl_union_map *
11204 isl_schedule_constraints_get_conditional_validity(
11205 __isl_keep isl_schedule_constraints *sc);
11206 __isl_give isl_union_map *
11207 isl_schedule_constraints_get_conditional_validity_condition(
11208 __isl_keep isl_schedule_constraints *sc);
11210 An C<isl_schedule_constraints> object can be read from input
11211 using the following functions.
11213 #include <isl/schedule.h>
11214 __isl_give isl_schedule_constraints *
11215 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
11217 __isl_give isl_schedule_constraints *
11218 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
11221 The contents of an C<isl_schedule_constraints> object can be printed
11222 using the following functions.
11224 #include <isl/schedule.h>
11225 __isl_give isl_printer *
11226 isl_printer_print_schedule_constraints(
11227 __isl_take isl_printer *p,
11228 __isl_keep isl_schedule_constraints *sc);
11229 __isl_give char *isl_schedule_constraints_to_str(
11230 __isl_keep isl_schedule_constraints *sc);
11232 The following function computes a schedule directly from
11233 an iteration domain and validity and proximity dependences
11234 and is implemented in terms of the functions described above.
11235 The use of C<isl_union_set_compute_schedule> is discouraged.
11237 #include <isl/schedule.h>
11238 __isl_give isl_schedule *isl_union_set_compute_schedule(
11239 __isl_take isl_union_set *domain,
11240 __isl_take isl_union_map *validity,
11241 __isl_take isl_union_map *proximity);
11243 The generated schedule represents a schedule tree.
11244 For more information on schedule trees, see
11245 L</"Schedule Trees">.
11249 #include <isl/schedule.h>
11250 isl_stat isl_options_set_schedule_max_coefficient(
11251 isl_ctx *ctx, int val);
11252 int isl_options_get_schedule_max_coefficient(
11254 isl_stat isl_options_set_schedule_max_constant_term(
11255 isl_ctx *ctx, int val);
11256 int isl_options_get_schedule_max_constant_term(
11258 isl_stat isl_options_set_schedule_serialize_sccs(
11259 isl_ctx *ctx, int val);
11260 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
11261 isl_stat isl_options_set_schedule_whole_component(
11262 isl_ctx *ctx, int val);
11263 int isl_options_get_schedule_whole_component(
11265 isl_stat isl_options_set_schedule_maximize_band_depth(
11266 isl_ctx *ctx, int val);
11267 int isl_options_get_schedule_maximize_band_depth(
11269 isl_stat isl_options_set_schedule_maximize_coincidence(
11270 isl_ctx *ctx, int val);
11271 int isl_options_get_schedule_maximize_coincidence(
11273 isl_stat isl_options_set_schedule_outer_coincidence(
11274 isl_ctx *ctx, int val);
11275 int isl_options_get_schedule_outer_coincidence(
11277 isl_stat isl_options_set_schedule_split_scaled(
11278 isl_ctx *ctx, int val);
11279 int isl_options_get_schedule_split_scaled(
11281 isl_stat isl_options_set_schedule_treat_coalescing(
11282 isl_ctx *ctx, int val);
11283 int isl_options_get_schedule_treat_coalescing(
11285 isl_stat isl_options_set_schedule_algorithm(
11286 isl_ctx *ctx, int val);
11287 int isl_options_get_schedule_algorithm(
11289 isl_stat isl_options_set_schedule_carry_self_first(
11290 isl_ctx *ctx, int val);
11291 int isl_options_get_schedule_carry_self_first(
11293 isl_stat isl_options_set_schedule_separate_components(
11294 isl_ctx *ctx, int val);
11295 int isl_options_get_schedule_separate_components(
11300 =item * schedule_max_coefficient
11302 This option enforces that the coefficients for variable and parameter
11303 dimensions in the calculated schedule are not larger than the specified value.
11304 This option can significantly increase the speed of the scheduling calculation
11305 and may also prevent fusing of unrelated dimensions. A value of -1 means that
11306 this option does not introduce bounds on the variable or parameter
11308 This option has no effect on the Feautrier style scheduler.
11310 =item * schedule_max_constant_term
11312 This option enforces that the constant coefficients in the calculated schedule
11313 are not larger than the maximal constant term. This option can significantly
11314 increase the speed of the scheduling calculation and may also prevent fusing of
11315 unrelated dimensions. A value of -1 means that this option does not introduce
11316 bounds on the constant coefficients.
11318 =item * schedule_serialize_sccs
11320 If this option is set, then all strongly connected components
11321 in the dependence graph are serialized as soon as they are detected.
11322 This means in particular that instances of statements will only
11323 appear in the same band node if these statements belong
11324 to the same strongly connected component at the point where
11325 the band node is constructed.
11327 =item * schedule_whole_component
11329 If this option is set, then entire (weakly) connected
11330 components in the dependence graph are scheduled together
11332 Otherwise, each strongly connected component within
11333 such a weakly connected component is first scheduled separately
11334 and then combined with other strongly connected components.
11335 This option has no effect if C<schedule_serialize_sccs> is set.
11337 =item * schedule_maximize_band_depth
11339 If this option is set, then the scheduler tries to maximize
11340 the width of the bands. Wider bands give more possibilities for tiling.
11341 In particular, if the C<schedule_whole_component> option is set,
11342 then bands are split if this might result in wider bands.
11343 Otherwise, the effect of this option is to only allow
11344 strongly connected components to be combined if this does
11345 not reduce the width of the bands.
11346 Note that if the C<schedule_serialize_sccs> options is set, then
11347 the C<schedule_maximize_band_depth> option therefore has no effect.
11349 =item * schedule_maximize_coincidence
11351 This option is only effective if the C<schedule_whole_component>
11352 option is turned off.
11353 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
11354 strongly connected components are only combined with each other
11355 if this does not reduce the number of coincident band members.
11357 =item * schedule_outer_coincidence
11359 If this option is set, then we try to construct schedules
11360 where the outermost scheduling dimension in each band
11361 satisfies the coincidence constraints.
11363 =item * schedule_algorithm
11365 Selects the scheduling algorithm to be used.
11366 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
11367 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
11369 =item * schedule_split_scaled
11371 If this option is set, then we try to construct schedules in which the
11372 constant term is split off from the linear part if the linear parts of
11373 the scheduling rows for all nodes in the graph have a common non-trivial
11375 The constant term is then dropped and the linear
11377 This option is only effective when the Feautrier style scheduler is
11378 being used, either as the main scheduler or as a fallback for the
11379 Pluto-like scheduler.
11381 =item * schedule_treat_coalescing
11383 If this option is set, then the scheduler will try and avoid
11384 producing schedules that perform loop coalescing.
11385 In particular, for the Pluto-like scheduler, this option places
11386 bounds on the schedule coefficients based on the sizes of the instance sets.
11387 For the Feautrier style scheduler, this option detects potentially
11388 coalescing schedules and then tries to adjust the schedule to avoid
11391 =item * schedule_carry_self_first
11393 If this option is set, then the Feautrier style scheduler
11394 (when used as a fallback for the Pluto-like scheduler) will
11395 first try to only carry self-dependences.
11397 =item * schedule_separate_components
11399 If this option is set then the function C<isl_schedule_get_map>
11400 will treat set nodes in the same way as sequence nodes.
11404 =head2 AST Generation
11406 This section describes the C<isl> functionality for generating
11407 ASTs that visit all the elements
11408 in a domain in an order specified by a schedule tree or
11410 In case the schedule given as a C<isl_union_map>, an AST is generated
11411 that visits all the elements in the domain of the C<isl_union_map>
11412 according to the lexicographic order of the corresponding image
11413 element(s). If the range of the C<isl_union_map> consists of
11414 elements in more than one space, then each of these spaces is handled
11415 separately in an arbitrary order.
11416 It should be noted that the schedule tree or the image elements
11417 in a schedule map only specify the I<order>
11418 in which the corresponding domain elements should be visited.
11419 No direct relation between the partial schedule values
11420 or the image elements on the one hand and the loop iterators
11421 in the generated AST on the other hand should be assumed.
11423 Each AST is generated within a build. The initial build
11424 simply specifies the constraints on the parameters (if any)
11425 and can be created, inspected, copied and freed using the following functions.
11427 #include <isl/ast_build.h>
11428 __isl_give isl_ast_build *isl_ast_build_alloc(
11430 __isl_give isl_ast_build *isl_ast_build_from_context(
11431 __isl_take isl_set *set);
11432 __isl_give isl_ast_build *isl_ast_build_copy(
11433 __isl_keep isl_ast_build *build);
11434 __isl_null isl_ast_build *isl_ast_build_free(
11435 __isl_take isl_ast_build *build);
11437 The C<set> argument is usually a parameter set with zero or more parameters.
11438 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
11439 this set is required to be a parameter set.
11440 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
11441 specify any parameter constraints.
11442 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
11443 and L</"Fine-grained Control over AST Generation">.
11444 Finally, the AST itself can be constructed using one of the following
11447 #include <isl/ast_build.h>
11448 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
11449 __isl_keep isl_ast_build *build,
11450 __isl_take isl_schedule *schedule);
11451 __isl_give isl_ast_node *
11452 isl_ast_build_node_from_schedule_map(
11453 __isl_keep isl_ast_build *build,
11454 __isl_take isl_union_map *schedule);
11456 =head3 Inspecting the AST
11458 The basic properties of an AST node can be obtained as follows.
11460 #include <isl/ast.h>
11461 enum isl_ast_node_type isl_ast_node_get_type(
11462 __isl_keep isl_ast_node *node);
11464 The type of an AST node is one of
11465 C<isl_ast_node_for>,
11466 C<isl_ast_node_if>,
11467 C<isl_ast_node_block>,
11468 C<isl_ast_node_mark> or
11469 C<isl_ast_node_user>.
11470 An C<isl_ast_node_for> represents a for node.
11471 An C<isl_ast_node_if> represents an if node.
11472 An C<isl_ast_node_block> represents a compound node.
11473 An C<isl_ast_node_mark> introduces a mark in the AST.
11474 An C<isl_ast_node_user> represents an expression statement.
11475 An expression statement typically corresponds to a domain element, i.e.,
11476 one of the elements that is visited by the AST.
11478 Each type of node has its own additional properties.
11480 #include <isl/ast.h>
11481 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
11482 __isl_keep isl_ast_node *node);
11483 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
11484 __isl_keep isl_ast_node *node);
11485 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
11486 __isl_keep isl_ast_node *node);
11487 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
11488 __isl_keep isl_ast_node *node);
11489 __isl_give isl_ast_node *isl_ast_node_for_get_body(
11490 __isl_keep isl_ast_node *node);
11491 isl_bool isl_ast_node_for_is_degenerate(
11492 __isl_keep isl_ast_node *node);
11494 An C<isl_ast_for> is considered degenerate if it is known to execute
11497 #include <isl/ast.h>
11498 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
11499 __isl_keep isl_ast_node *node);
11500 __isl_give isl_ast_node *isl_ast_node_if_get_then_node(
11501 __isl_keep isl_ast_node *node);
11502 __isl_give isl_ast_node *isl_ast_node_if_get_then(
11503 __isl_keep isl_ast_node *node);
11504 isl_bool isl_ast_node_if_has_else_node(
11505 __isl_keep isl_ast_node *node);
11506 isl_bool isl_ast_node_if_has_else(
11507 __isl_keep isl_ast_node *node);
11508 __isl_give isl_ast_node *isl_ast_node_if_get_else_node(
11509 __isl_keep isl_ast_node *node);
11510 __isl_give isl_ast_node *isl_ast_node_if_get_else(
11511 __isl_keep isl_ast_node *node);
11513 C<isl_ast_node_if_get_then>,
11514 C<isl_ast_node_if_has_else> and
11515 C<isl_ast_node_if_get_else>
11516 are alternative names for
11517 C<isl_ast_node_if_get_then_node>,
11518 C<isl_ast_node_if_has_else_node> and
11519 C<isl_ast_node_if_get_else_node>, respectively.
11521 __isl_give isl_ast_node_list *
11522 isl_ast_node_block_get_children(
11523 __isl_keep isl_ast_node *node);
11525 __isl_give isl_id *isl_ast_node_mark_get_id(
11526 __isl_keep isl_ast_node *node);
11527 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
11528 __isl_keep isl_ast_node *node);
11530 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
11531 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
11533 #include <isl/ast.h>
11534 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
11535 __isl_keep isl_ast_node *node);
11537 All descendants of a specific node in the AST (including the node itself)
11539 in depth-first pre-order using the following function.
11541 #include <isl/ast.h>
11542 isl_stat isl_ast_node_foreach_descendant_top_down(
11543 __isl_keep isl_ast_node *node,
11544 isl_bool (*fn)(__isl_keep isl_ast_node *node,
11545 void *user), void *user);
11547 The callback function should return C<isl_bool_true> if the children
11548 of the given node should be visited and C<isl_bool_false> if they should not.
11549 It should return C<isl_bool_error> in case of failure, in which case
11550 the entire traversal is aborted.
11552 Each of the returned C<isl_ast_expr>s can in turn be inspected using
11553 the following functions.
11555 #include <isl/ast.h>
11556 enum isl_ast_expr_type isl_ast_expr_get_type(
11557 __isl_keep isl_ast_expr *expr);
11559 The type of an AST expression is one of
11560 C<isl_ast_expr_op>,
11561 C<isl_ast_expr_id> or
11562 C<isl_ast_expr_int>.
11563 An C<isl_ast_expr_op> represents the result of an operation.
11564 An C<isl_ast_expr_id> represents an identifier.
11565 An C<isl_ast_expr_int> represents an integer value.
11567 Each type of expression has its own additional properties.
11569 #include <isl/ast.h>
11570 enum isl_ast_expr_op_type isl_ast_expr_op_get_type(
11571 __isl_keep isl_ast_expr *expr);
11572 enum isl_ast_expr_op_type isl_ast_expr_get_op_type(
11573 __isl_keep isl_ast_expr *expr);
11574 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr);
11575 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
11576 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg(
11577 __isl_keep isl_ast_expr *expr, int pos);
11578 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
11579 __isl_keep isl_ast_expr *expr, int pos);
11580 isl_stat isl_ast_expr_foreach_ast_expr_op_type(
11581 __isl_keep isl_ast_expr *expr,
11582 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11583 void *user), void *user);
11584 isl_stat isl_ast_expr_foreach_ast_op_type(
11585 __isl_keep isl_ast_expr *expr,
11586 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11587 void *user), void *user);
11588 isl_stat isl_ast_node_foreach_ast_expr_op_type(
11589 __isl_keep isl_ast_node *node,
11590 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11591 void *user), void *user);
11592 isl_stat isl_ast_node_foreach_ast_op_type(
11593 __isl_keep isl_ast_node *node,
11594 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11595 void *user), void *user);
11597 C<isl_ast_expr_op_get_type> returns the type of the operation
11598 performed. C<isl_ast_expr_op_get_n_arg> returns the number of
11599 arguments. C<isl_ast_expr_get_op_arg> returns the specified
11601 C<isl_ast_expr_get_op_type> is an alternative name for
11602 C<isl_ast_expr_op_get_type>.
11604 C<isl_ast_expr_get_op_n_arg> is an alternative name for
11605 C<isl_ast_expr_op_get_n_arg> and
11606 C<isl_ast_expr_get_op_arg> is an alternative name for
11607 C<isl_ast_expr_op_get_arg>.
11609 C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct
11610 C<isl_ast_expr_op_type> that appears in C<expr>.
11611 C<isl_ast_expr_foreach_ast_op_type> is an alternative name for
11612 C<isl_ast_expr_foreach_ast_expr_op_type>.
11613 C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct
11614 C<isl_ast_expr_op_type> that appears in C<node>.
11615 C<isl_ast_node_foreach_ast_op_type> is an alternative name for
11616 C<isl_ast_node_foreach_ast_expr_op_type>.
11617 The operation type is one of the following.
11621 =item C<isl_ast_expr_op_and>
11623 Logical I<and> of two arguments.
11624 Both arguments can be evaluated.
11626 =item C<isl_ast_expr_op_and_then>
11628 Logical I<and> of two arguments.
11629 The second argument can only be evaluated if the first evaluates to true.
11631 =item C<isl_ast_expr_op_or>
11633 Logical I<or> of two arguments.
11634 Both arguments can be evaluated.
11636 =item C<isl_ast_expr_op_or_else>
11638 Logical I<or> of two arguments.
11639 The second argument can only be evaluated if the first evaluates to false.
11641 =item C<isl_ast_expr_op_max>
11643 Maximum of two or more arguments.
11645 =item C<isl_ast_expr_op_min>
11647 Minimum of two or more arguments.
11649 =item C<isl_ast_expr_op_minus>
11653 =item C<isl_ast_expr_op_add>
11655 Sum of two arguments.
11657 =item C<isl_ast_expr_op_sub>
11659 Difference of two arguments.
11661 =item C<isl_ast_expr_op_mul>
11663 Product of two arguments.
11665 =item C<isl_ast_expr_op_div>
11667 Exact division. That is, the result is known to be an integer.
11669 =item C<isl_ast_expr_op_fdiv_q>
11671 Result of integer division, rounded towards negative
11673 The divisor is known to be positive.
11675 =item C<isl_ast_expr_op_pdiv_q>
11677 Result of integer division, where dividend is known to be non-negative.
11678 The divisor is known to be positive.
11680 =item C<isl_ast_expr_op_pdiv_r>
11682 Remainder of integer division, where dividend is known to be non-negative.
11683 The divisor is known to be positive.
11685 =item C<isl_ast_expr_op_zdiv_r>
11687 Equal to zero iff the remainder on integer division is zero.
11688 The divisor is known to be positive.
11690 =item C<isl_ast_expr_op_cond>
11692 Conditional operator defined on three arguments.
11693 If the first argument evaluates to true, then the result
11694 is equal to the second argument. Otherwise, the result
11695 is equal to the third argument.
11696 The second and third argument may only be evaluated if
11697 the first argument evaluates to true and false, respectively.
11698 Corresponds to C<a ? b : c> in C.
11700 =item C<isl_ast_expr_op_select>
11702 Conditional operator defined on three arguments.
11703 If the first argument evaluates to true, then the result
11704 is equal to the second argument. Otherwise, the result
11705 is equal to the third argument.
11706 The second and third argument may be evaluated independently
11707 of the value of the first argument.
11708 Corresponds to C<a * b + (1 - a) * c> in C.
11710 =item C<isl_ast_expr_op_eq>
11714 =item C<isl_ast_expr_op_le>
11716 Less than or equal relation.
11718 =item C<isl_ast_expr_op_lt>
11720 Less than relation.
11722 =item C<isl_ast_expr_op_ge>
11724 Greater than or equal relation.
11726 =item C<isl_ast_expr_op_gt>
11728 Greater than relation.
11730 =item C<isl_ast_expr_op_call>
11733 The number of arguments of the C<isl_ast_expr> is one more than
11734 the number of arguments in the function call, the first argument
11735 representing the function being called.
11737 =item C<isl_ast_expr_op_access>
11740 The number of arguments of the C<isl_ast_expr> is one more than
11741 the number of index expressions in the array access, the first argument
11742 representing the array being accessed.
11744 =item C<isl_ast_expr_op_member>
11747 This operation has two arguments, a structure and the name of
11748 the member of the structure being accessed.
11752 #include <isl/ast.h>
11753 __isl_give isl_id *isl_ast_expr_id_get_id(
11754 __isl_keep isl_ast_expr *expr);
11755 __isl_give isl_id *isl_ast_expr_get_id(
11756 __isl_keep isl_ast_expr *expr);
11758 Return the identifier represented by the AST expression.
11759 C<isl_ast_expr_get_id> is an alternative name for
11760 C<isl_ast_expr_id_get_id>.
11762 #include <isl/ast.h>
11763 __isl_give isl_val *isl_ast_expr_int_get_val(
11764 __isl_keep isl_ast_expr *expr);
11765 __isl_give isl_val *isl_ast_expr_get_val(
11766 __isl_keep isl_ast_expr *expr);
11768 Return the integer represented by the AST expression.
11769 C<isl_ast_expr_get_val> is an alternative name for
11770 C<isl_ast_expr_int_get_val>.
11772 =head3 Properties of ASTs
11774 #include <isl/ast.h>
11775 isl_bool isl_ast_expr_is_equal(
11776 __isl_keep isl_ast_expr *expr1,
11777 __isl_keep isl_ast_expr *expr2);
11779 Check if two C<isl_ast_expr>s are equal to each other.
11781 =head3 Manipulating and printing the AST
11783 AST nodes can be copied and freed using the following functions.
11785 #include <isl/ast.h>
11786 __isl_give isl_ast_node *isl_ast_node_copy(
11787 __isl_keep isl_ast_node *node);
11788 __isl_null isl_ast_node *isl_ast_node_free(
11789 __isl_take isl_ast_node *node);
11791 AST expressions can be copied and freed using the following functions.
11793 #include <isl/ast.h>
11794 __isl_give isl_ast_expr *isl_ast_expr_copy(
11795 __isl_keep isl_ast_expr *expr);
11796 __isl_null isl_ast_expr *isl_ast_expr_free(
11797 __isl_take isl_ast_expr *expr);
11799 New AST expressions can be created either directly or within
11800 the context of an C<isl_ast_build>.
11802 #include <isl/ast.h>
11803 __isl_give isl_ast_expr *isl_ast_expr_from_val(
11804 __isl_take isl_val *v);
11805 __isl_give isl_ast_expr *isl_ast_expr_from_id(
11806 __isl_take isl_id *id);
11807 __isl_give isl_ast_expr *isl_ast_expr_neg(
11808 __isl_take isl_ast_expr *expr);
11809 __isl_give isl_ast_expr *isl_ast_expr_address_of(
11810 __isl_take isl_ast_expr *expr);
11811 __isl_give isl_ast_expr *isl_ast_expr_add(
11812 __isl_take isl_ast_expr *expr1,
11813 __isl_take isl_ast_expr *expr2);
11814 __isl_give isl_ast_expr *isl_ast_expr_sub(
11815 __isl_take isl_ast_expr *expr1,
11816 __isl_take isl_ast_expr *expr2);
11817 __isl_give isl_ast_expr *isl_ast_expr_mul(
11818 __isl_take isl_ast_expr *expr1,
11819 __isl_take isl_ast_expr *expr2);
11820 __isl_give isl_ast_expr *isl_ast_expr_div(
11821 __isl_take isl_ast_expr *expr1,
11822 __isl_take isl_ast_expr *expr2);
11823 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
11824 __isl_take isl_ast_expr *expr1,
11825 __isl_take isl_ast_expr *expr2);
11826 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
11827 __isl_take isl_ast_expr *expr1,
11828 __isl_take isl_ast_expr *expr2);
11829 __isl_give isl_ast_expr *isl_ast_expr_and(
11830 __isl_take isl_ast_expr *expr1,
11831 __isl_take isl_ast_expr *expr2)
11832 __isl_give isl_ast_expr *isl_ast_expr_and_then(
11833 __isl_take isl_ast_expr *expr1,
11834 __isl_take isl_ast_expr *expr2)
11835 __isl_give isl_ast_expr *isl_ast_expr_or(
11836 __isl_take isl_ast_expr *expr1,
11837 __isl_take isl_ast_expr *expr2)
11838 __isl_give isl_ast_expr *isl_ast_expr_or_else(
11839 __isl_take isl_ast_expr *expr1,
11840 __isl_take isl_ast_expr *expr2)
11841 __isl_give isl_ast_expr *isl_ast_expr_eq(
11842 __isl_take isl_ast_expr *expr1,
11843 __isl_take isl_ast_expr *expr2);
11844 __isl_give isl_ast_expr *isl_ast_expr_le(
11845 __isl_take isl_ast_expr *expr1,
11846 __isl_take isl_ast_expr *expr2);
11847 __isl_give isl_ast_expr *isl_ast_expr_lt(
11848 __isl_take isl_ast_expr *expr1,
11849 __isl_take isl_ast_expr *expr2);
11850 __isl_give isl_ast_expr *isl_ast_expr_ge(
11851 __isl_take isl_ast_expr *expr1,
11852 __isl_take isl_ast_expr *expr2);
11853 __isl_give isl_ast_expr *isl_ast_expr_gt(
11854 __isl_take isl_ast_expr *expr1,
11855 __isl_take isl_ast_expr *expr2);
11856 __isl_give isl_ast_expr *isl_ast_expr_access(
11857 __isl_take isl_ast_expr *array,
11858 __isl_take isl_ast_expr_list *indices);
11859 __isl_give isl_ast_expr *isl_ast_expr_call(
11860 __isl_take isl_ast_expr *function,
11861 __isl_take isl_ast_expr_list *arguments);
11863 The function C<isl_ast_expr_address_of> can be applied to an
11864 C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant
11865 to represent the address of the C<isl_ast_expr_access>.
11866 The second argument of the functions C<isl_ast_expr_pdiv_q> and
11867 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
11869 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
11870 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
11872 #include <isl/ast_build.h>
11873 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
11874 __isl_keep isl_ast_build *build,
11875 __isl_take isl_set *set);
11876 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
11877 __isl_keep isl_ast_build *build,
11878 __isl_take isl_pw_aff *pa);
11879 __isl_give isl_ast_expr *
11880 isl_ast_build_access_from_pw_multi_aff(
11881 __isl_keep isl_ast_build *build,
11882 __isl_take isl_pw_multi_aff *pma);
11883 __isl_give isl_ast_expr *
11884 isl_ast_build_access_from_multi_pw_aff(
11885 __isl_keep isl_ast_build *build,
11886 __isl_take isl_multi_pw_aff *mpa);
11887 __isl_give isl_ast_expr *
11888 isl_ast_build_call_from_pw_multi_aff(
11889 __isl_keep isl_ast_build *build,
11890 __isl_take isl_pw_multi_aff *pma);
11891 __isl_give isl_ast_expr *
11892 isl_ast_build_call_from_multi_pw_aff(
11893 __isl_keep isl_ast_build *build,
11894 __isl_take isl_multi_pw_aff *mpa);
11897 the domains of C<pa>, C<mpa> and C<pma> should correspond
11898 to the schedule space of C<build>.
11899 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
11900 the function being called.
11901 If the accessed space is a nested relation, then it is taken
11902 to represent an access of the member specified by the range
11903 of this nested relation of the structure specified by the domain
11904 of the nested relation.
11906 The following functions can be used to modify an C<isl_ast_expr>.
11908 #include <isl/ast.h>
11909 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
11910 __isl_take isl_ast_expr *expr, int pos,
11911 __isl_take isl_ast_expr *arg);
11913 Replace the argument of C<expr> at position C<pos> by C<arg>.
11915 #include <isl/ast.h>
11916 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
11917 __isl_take isl_ast_expr *expr,
11918 __isl_take isl_id_to_ast_expr *id2expr);
11920 The function C<isl_ast_expr_substitute_ids> replaces the
11921 subexpressions of C<expr> of type C<isl_ast_expr_id>
11922 by the corresponding expression in C<id2expr>, if there is any.
11925 User specified data can be attached to an C<isl_ast_node> and obtained
11926 from the same C<isl_ast_node> using the following functions.
11928 #include <isl/ast.h>
11929 __isl_give isl_ast_node *isl_ast_node_set_annotation(
11930 __isl_take isl_ast_node *node,
11931 __isl_take isl_id *annotation);
11932 __isl_give isl_id *isl_ast_node_get_annotation(
11933 __isl_keep isl_ast_node *node);
11935 Basic printing can be performed using the following functions.
11937 #include <isl/ast.h>
11938 __isl_give isl_printer *isl_printer_print_ast_expr(
11939 __isl_take isl_printer *p,
11940 __isl_keep isl_ast_expr *expr);
11941 __isl_give isl_printer *isl_printer_print_ast_node(
11942 __isl_take isl_printer *p,
11943 __isl_keep isl_ast_node *node);
11944 __isl_give char *isl_ast_expr_to_str(
11945 __isl_keep isl_ast_expr *expr);
11946 __isl_give char *isl_ast_node_to_str(
11947 __isl_keep isl_ast_node *node);
11948 __isl_give char *isl_ast_expr_to_C_str(
11949 __isl_keep isl_ast_expr *expr);
11950 __isl_give char *isl_ast_node_to_C_str(
11951 __isl_keep isl_ast_node *node);
11953 The functions C<isl_ast_expr_to_C_str> and
11954 C<isl_ast_node_to_C_str> are convenience functions
11955 that return a string representation of the input in C format.
11957 More advanced printing can be performed using the following functions.
11959 #include <isl/ast.h>
11960 __isl_give isl_printer *
11961 isl_ast_expr_op_type_set_print_name(
11962 __isl_take isl_printer *p,
11963 enum isl_ast_expr_op_type type,
11964 __isl_keep const char *name);
11965 __isl_give isl_printer *isl_ast_op_type_set_print_name(
11966 __isl_take isl_printer *p,
11967 enum isl_ast_expr_op_type type,
11968 __isl_keep const char *name);
11969 isl_stat isl_options_set_ast_print_macro_once(
11970 isl_ctx *ctx, int val);
11971 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
11972 __isl_give isl_printer *isl_ast_expr_op_type_print_macro(
11973 enum isl_ast_expr_op_type type,
11974 __isl_take isl_printer *p);
11975 __isl_give isl_printer *isl_ast_op_type_print_macro(
11976 enum isl_ast_expr_op_type type,
11977 __isl_take isl_printer *p);
11978 __isl_give isl_printer *isl_ast_expr_print_macros(
11979 __isl_keep isl_ast_expr *expr,
11980 __isl_take isl_printer *p);
11981 __isl_give isl_printer *isl_ast_node_print_macros(
11982 __isl_keep isl_ast_node *node,
11983 __isl_take isl_printer *p);
11984 __isl_give isl_printer *isl_ast_node_print(
11985 __isl_keep isl_ast_node *node,
11986 __isl_take isl_printer *p,
11987 __isl_take isl_ast_print_options *options);
11988 __isl_give isl_printer *isl_ast_node_for_print(
11989 __isl_keep isl_ast_node *node,
11990 __isl_take isl_printer *p,
11991 __isl_take isl_ast_print_options *options);
11992 __isl_give isl_printer *isl_ast_node_if_print(
11993 __isl_keep isl_ast_node *node,
11994 __isl_take isl_printer *p,
11995 __isl_take isl_ast_print_options *options);
11997 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
11998 C<isl> may print out an AST that makes use of macros such
11999 as C<floord>, C<min> and C<max>.
12000 The names of these macros may be modified by a call
12001 to C<isl_ast_expr_op_type_set_print_name>. The user-specified
12002 names are associated to the printer object.
12003 C<isl_ast_op_type_set_print_name> is an alternative name for
12004 C<isl_ast_expr_op_type_set_print_name>.
12005 C<isl_ast_expr_op_type_print_macro> prints out the macro
12006 corresponding to a specific C<isl_ast_expr_op_type>.
12007 If the print-macro-once option is set, then a given macro definition
12008 is only printed once to any given printer object.
12009 C<isl_ast_op_type_print_macro> is an alternative name for
12010 C<isl_ast_expr_op_type_print_macro>.
12011 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
12012 for subexpressions where these macros would be used and prints
12013 out the required macro definitions.
12014 Essentially, C<isl_ast_expr_print_macros> calls
12015 C<isl_ast_expr_foreach_ast_expr_op_type> with
12016 C<isl_ast_expr_op_type_print_macro>
12017 as function argument.
12018 C<isl_ast_node_print_macros> does the same
12019 for expressions in its C<isl_ast_node> argument.
12020 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
12021 C<isl_ast_node_if_print> print an C<isl_ast_node>
12022 in C<ISL_FORMAT_C>, but allow for some extra control
12023 through an C<isl_ast_print_options> object.
12024 This object can be created using the following functions.
12026 #include <isl/ast.h>
12027 __isl_give isl_ast_print_options *
12028 isl_ast_print_options_alloc(isl_ctx *ctx);
12029 __isl_give isl_ast_print_options *
12030 isl_ast_print_options_copy(
12031 __isl_keep isl_ast_print_options *options);
12032 __isl_null isl_ast_print_options *
12033 isl_ast_print_options_free(
12034 __isl_take isl_ast_print_options *options);
12036 __isl_give isl_ast_print_options *
12037 isl_ast_print_options_set_print_user(
12038 __isl_take isl_ast_print_options *options,
12039 __isl_give isl_printer *(*print_user)(
12040 __isl_take isl_printer *p,
12041 __isl_take isl_ast_print_options *options,
12042 __isl_keep isl_ast_node *node, void *user),
12044 __isl_give isl_ast_print_options *
12045 isl_ast_print_options_set_print_for(
12046 __isl_take isl_ast_print_options *options,
12047 __isl_give isl_printer *(*print_for)(
12048 __isl_take isl_printer *p,
12049 __isl_take isl_ast_print_options *options,
12050 __isl_keep isl_ast_node *node, void *user),
12053 The callback set by C<isl_ast_print_options_set_print_user>
12054 is called whenever a node of type C<isl_ast_node_user> needs to
12056 The callback set by C<isl_ast_print_options_set_print_for>
12057 is called whenever a node of type C<isl_ast_node_for> needs to
12059 Note that C<isl_ast_node_for_print> will I<not> call the
12060 callback set by C<isl_ast_print_options_set_print_for> on the node
12061 on which C<isl_ast_node_for_print> is called, but only on nested
12062 nodes of type C<isl_ast_node_for>. It is therefore safe to
12063 call C<isl_ast_node_for_print> from within the callback set by
12064 C<isl_ast_print_options_set_print_for>.
12066 The following option determines the type to be used for iterators
12067 while printing the AST.
12069 isl_stat isl_options_set_ast_iterator_type(
12070 isl_ctx *ctx, const char *val);
12071 const char *isl_options_get_ast_iterator_type(
12074 The AST printer only prints body nodes of C<if> and C<for> nodes
12076 blocks cannot be safely omitted.
12077 For example, a C<for> node with one body node will not be
12078 surrounded with braces in C<ISL_FORMAT_C>.
12079 A block will always be printed by setting the following option.
12081 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
12083 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
12085 Explicit block nodes that appear inside the AST are always printed as blocks.
12086 If the block node appears as the outermost node,
12087 then it is only printed if the following option is set.
12089 isl_stat isl_options_set_ast_print_outermost_block(
12090 isl_ctx *ctx, int val);
12091 int isl_options_get_ast_print_outermost_block(
12096 #include <isl/ast_build.h>
12097 isl_stat isl_options_set_ast_build_atomic_upper_bound(
12098 isl_ctx *ctx, int val);
12099 int isl_options_get_ast_build_atomic_upper_bound(
12101 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
12103 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
12104 isl_stat isl_options_set_ast_build_detect_min_max(
12105 isl_ctx *ctx, int val);
12106 int isl_options_get_ast_build_detect_min_max(
12108 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
12109 isl_ctx *ctx, int val);
12110 int isl_options_get_ast_build_exploit_nested_bounds(
12112 isl_stat isl_options_set_ast_build_group_coscheduled(
12113 isl_ctx *ctx, int val);
12114 int isl_options_get_ast_build_group_coscheduled(
12116 isl_stat isl_options_set_ast_build_separation_bounds(
12117 isl_ctx *ctx, int val);
12118 int isl_options_get_ast_build_separation_bounds(
12120 isl_stat isl_options_set_ast_build_scale_strides(
12121 isl_ctx *ctx, int val);
12122 int isl_options_get_ast_build_scale_strides(
12124 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
12126 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
12127 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
12129 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
12133 =item * ast_build_atomic_upper_bound
12135 Generate loop upper bounds that consist of the current loop iterator,
12136 an operator and an expression not involving the iterator.
12137 If this option is not set, then the current loop iterator may appear
12138 several times in the upper bound.
12139 For example, when this option is turned off, AST generation
12142 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
12146 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
12149 When the option is turned on, the following AST is generated
12151 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
12154 =item * ast_build_prefer_pdiv
12156 If this option is turned off, then the AST generation will
12157 produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q>
12158 operators, but no C<isl_ast_expr_op_pdiv_q> or
12159 C<isl_ast_expr_op_pdiv_r> operators.
12160 If this option is turned on, then C<isl> will try to convert
12161 some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing)
12162 C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators.
12164 =item * ast_build_detect_min_max
12166 If this option is turned on, then C<isl> will try and detect
12167 min or max-expressions when building AST expressions from
12168 piecewise affine expressions.
12170 =item * ast_build_exploit_nested_bounds
12172 Simplify conditions based on bounds of nested for loops.
12173 In particular, remove conditions that are implied by the fact
12174 that one or more nested loops have at least one iteration,
12175 meaning that the upper bound is at least as large as the lower bound.
12176 For example, when this option is turned off, AST generation
12179 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
12185 for (int c0 = 0; c0 <= N; c0 += 1)
12186 for (int c1 = 0; c1 <= M; c1 += 1)
12189 When the option is turned on, the following AST is generated
12191 for (int c0 = 0; c0 <= N; c0 += 1)
12192 for (int c1 = 0; c1 <= M; c1 += 1)
12195 =item * ast_build_group_coscheduled
12197 If two domain elements are assigned the same schedule point, then
12198 they may be executed in any order and they may even appear in different
12199 loops. If this options is set, then the AST generator will make
12200 sure that coscheduled domain elements do not appear in separate parts
12201 of the AST. This is useful in case of nested AST generation
12202 if the outer AST generation is given only part of a schedule
12203 and the inner AST generation should handle the domains that are
12204 coscheduled by this initial part of the schedule together.
12205 For example if an AST is generated for a schedule
12207 { A[i] -> [0]; B[i] -> [0] }
12209 then the C<isl_ast_build_set_create_leaf> callback described
12210 below may get called twice, once for each domain.
12211 Setting this option ensures that the callback is only called once
12212 on both domains together.
12214 =item * ast_build_separation_bounds
12216 This option specifies which bounds to use during separation.
12217 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
12218 then all (possibly implicit) bounds on the current dimension will
12219 be used during separation.
12220 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
12221 then only those bounds that are explicitly available will
12222 be used during separation.
12224 =item * ast_build_scale_strides
12226 This option specifies whether the AST generator is allowed
12227 to scale down iterators of strided loops.
12229 =item * ast_build_allow_else
12231 This option specifies whether the AST generator is allowed
12232 to construct if statements with else branches.
12234 =item * ast_build_allow_or
12236 This option specifies whether the AST generator is allowed
12237 to construct if conditions with disjunctions.
12241 =head3 AST Generation Options (Schedule Tree)
12243 In case of AST construction from a schedule tree, the options
12244 that control how an AST is created from the individual schedule
12245 dimensions are stored in the band nodes of the tree
12246 (see L</"Schedule Trees">).
12248 In particular, a schedule dimension can be handled in four
12249 different ways, atomic, separate, unroll or the default.
12250 This loop AST generation type can be set using
12251 C<isl_schedule_node_band_member_set_ast_loop_type>.
12253 the first three can be selected by including a one-dimensional
12254 element with as value the position of the schedule dimension
12255 within the band and as name one of C<atomic>, C<separate>
12256 or C<unroll> in the options
12257 set by C<isl_schedule_node_band_set_ast_build_options>.
12258 Only one of these three may be specified for
12259 any given schedule dimension within a band node.
12260 If none of these is specified, then the default
12261 is used. The meaning of the options is as follows.
12267 When this option is specified, the AST generator will make
12268 sure that a given domain space only appears in a single
12269 loop at the specified level.
12271 For example, for the schedule tree
12273 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12275 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12276 options: "{ atomic[x] }"
12278 the following AST will be generated
12280 for (int c0 = 0; c0 <= 10; c0 += 1) {
12287 On the other hand, for the schedule tree
12289 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12291 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12292 options: "{ separate[x] }"
12294 the following AST will be generated
12298 for (int c0 = 1; c0 <= 9; c0 += 1) {
12305 If neither C<atomic> nor C<separate> is specified, then the AST generator
12306 may produce either of these two results or some intermediate form.
12310 When this option is specified, the AST generator will
12311 split the domain of the specified schedule dimension
12312 into pieces with a fixed set of statements for which
12313 instances need to be executed by the iterations in
12314 the schedule domain part. This option tends to avoid
12315 the generation of guards inside the corresponding loops.
12316 See also the C<atomic> option.
12320 When this option is specified, the AST generator will
12321 I<completely> unroll the corresponding schedule dimension.
12322 It is the responsibility of the user to ensure that such
12323 unrolling is possible.
12324 To obtain a partial unrolling, the user should apply an additional
12325 strip-mining to the schedule and fully unroll the inner schedule
12330 The C<isolate> option is a bit more involved. It allows the user
12331 to isolate a range of schedule dimension values from smaller and
12332 greater values. Additionally, the user may specify a different
12333 atomic/separate/unroll choice for the isolated part and the remaining
12334 parts. The typical use case of the C<isolate> option is to isolate
12335 full tiles from partial tiles.
12336 The part that needs to be isolated may depend on outer schedule dimensions.
12337 The option therefore needs to be able to reference those outer schedule
12338 dimensions. In particular, the space of the C<isolate> option is that
12339 of a wrapped map with as domain the flat product of all outer band nodes
12340 and as range the space of the current band node.
12341 The atomic/separate/unroll choice for the isolated part is determined
12342 by an option that lives in an unnamed wrapped space with as domain
12343 a zero-dimensional C<isolate> space and as range the regular
12344 C<atomic>, C<separate> or C<unroll> space.
12345 This option may also be set directly using
12346 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
12347 The atomic/separate/unroll choice for the remaining part is determined
12348 by the regular C<atomic>, C<separate> or C<unroll> option.
12349 Since the C<isolate> option references outer schedule dimensions,
12350 its use in a band node causes any tree containing the node
12351 to be considered anchored.
12353 As an example, consider the isolation of full tiles from partial tiles
12354 in a tiling of a triangular domain. The original schedule is as follows.
12356 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12358 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12359 { A[i,j] -> [floor(j/10)] }, \
12360 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12364 for (int c0 = 0; c0 <= 10; c0 += 1)
12365 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12366 for (int c2 = 10 * c0;
12367 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12368 for (int c3 = 10 * c1;
12369 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12372 Isolating the full tiles, we have the following input
12374 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12376 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12377 { A[i,j] -> [floor(j/10)] }, \
12378 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12379 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12380 10a+9+10b+9 <= 100 }"
12385 for (int c0 = 0; c0 <= 8; c0 += 1) {
12386 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12387 for (int c2 = 10 * c0;
12388 c2 <= 10 * c0 + 9; c2 += 1)
12389 for (int c3 = 10 * c1;
12390 c3 <= 10 * c1 + 9; c3 += 1)
12392 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12393 for (int c2 = 10 * c0;
12394 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12395 for (int c3 = 10 * c1;
12396 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12399 for (int c0 = 9; c0 <= 10; c0 += 1)
12400 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12401 for (int c2 = 10 * c0;
12402 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12403 for (int c3 = 10 * c1;
12404 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12408 We may then additionally unroll the innermost loop of the isolated part
12410 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12412 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12413 { A[i,j] -> [floor(j/10)] }, \
12414 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12415 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12416 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
12421 for (int c0 = 0; c0 <= 8; c0 += 1) {
12422 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12423 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
12425 A(c2, 10 * c1 + 1);
12426 A(c2, 10 * c1 + 2);
12427 A(c2, 10 * c1 + 3);
12428 A(c2, 10 * c1 + 4);
12429 A(c2, 10 * c1 + 5);
12430 A(c2, 10 * c1 + 6);
12431 A(c2, 10 * c1 + 7);
12432 A(c2, 10 * c1 + 8);
12433 A(c2, 10 * c1 + 9);
12435 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12436 for (int c2 = 10 * c0;
12437 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12438 for (int c3 = 10 * c1;
12439 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12442 for (int c0 = 9; c0 <= 10; c0 += 1)
12443 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12444 for (int c2 = 10 * c0;
12445 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12446 for (int c3 = 10 * c1;
12447 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12452 =head3 AST Generation Options (Schedule Map)
12454 In case of AST construction using
12455 C<isl_ast_build_node_from_schedule_map>, the options
12456 that control how an AST is created from the individual schedule
12457 dimensions are stored in the C<isl_ast_build>.
12458 They can be set using the following function.
12460 #include <isl/ast_build.h>
12461 __isl_give isl_ast_build *
12462 isl_ast_build_set_options(
12463 __isl_take isl_ast_build *build,
12464 __isl_take isl_union_map *options);
12466 The options are encoded in an C<isl_union_map>.
12467 The domain of this union relation refers to the schedule domain,
12468 i.e., the range of the schedule passed
12469 to C<isl_ast_build_node_from_schedule_map>.
12470 In the case of nested AST generation (see L</"Nested AST Generation">),
12471 the domain of C<options> should refer to the extra piece of the schedule.
12472 That is, it should be equal to the range of the wrapped relation in the
12473 range of the schedule.
12474 The range of the options can consist of elements in one or more spaces,
12475 the names of which determine the effect of the option.
12476 The values of the range typically also refer to the schedule dimension
12477 to which the option applies, with value C<0> representing
12478 the outermost schedule dimension. In case of nested AST generation
12479 (see L</"Nested AST Generation">), these values refer to the position
12480 of the schedule dimension within the innermost AST generation.
12481 The constraints on the domain elements of
12482 the option should only refer to this dimension and earlier dimensions.
12483 We consider the following spaces.
12487 =item C<separation_class>
12489 B<This option has been deprecated. Use the isolate option on
12490 schedule trees instead.>
12492 This space is a wrapped relation between two one dimensional spaces.
12493 The input space represents the schedule dimension to which the option
12494 applies and the output space represents the separation class.
12495 While constructing a loop corresponding to the specified schedule
12496 dimension(s), the AST generator will try to generate separate loops
12497 for domain elements that are assigned different classes.
12498 If only some of the elements are assigned a class, then those elements
12499 that are not assigned any class will be treated as belonging to a class
12500 that is separate from the explicitly assigned classes.
12501 The typical use case for this option is to separate full tiles from
12503 The other options, described below, are applied after the separation
12506 As an example, consider the separation into full and partial tiles
12507 of a tiling of a triangular domain.
12508 Take, for example, the domain
12510 { A[i,j] : 0 <= i,j and i + j <= 100 }
12512 and a tiling into tiles of 10 by 10. The input to the AST generator
12513 is then the schedule
12515 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
12518 Without any options, the following AST is generated
12520 for (int c0 = 0; c0 <= 10; c0 += 1)
12521 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12522 for (int c2 = 10 * c0;
12523 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12525 for (int c3 = 10 * c1;
12526 c3 <= min(10 * c1 + 9, -c2 + 100);
12530 Separation into full and partial tiles can be obtained by assigning
12531 a class, say C<0>, to the full tiles. The full tiles are represented by those
12532 values of the first and second schedule dimensions for which there are
12533 values of the third and fourth dimensions to cover an entire tile.
12534 That is, we need to specify the following option
12536 { [a,b,c,d] -> separation_class[[0]->[0]] :
12537 exists b': 0 <= 10a,10b' and
12538 10a+9+10b'+9 <= 100;
12539 [a,b,c,d] -> separation_class[[1]->[0]] :
12540 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
12542 which simplifies to
12544 { [a, b, c, d] -> separation_class[[1] -> [0]] :
12545 a >= 0 and b >= 0 and b <= 8 - a;
12546 [a, b, c, d] -> separation_class[[0] -> [0]] :
12547 a >= 0 and a <= 8 }
12549 With this option, the generated AST is as follows
12552 for (int c0 = 0; c0 <= 8; c0 += 1) {
12553 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12554 for (int c2 = 10 * c0;
12555 c2 <= 10 * c0 + 9; c2 += 1)
12556 for (int c3 = 10 * c1;
12557 c3 <= 10 * c1 + 9; c3 += 1)
12559 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12560 for (int c2 = 10 * c0;
12561 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12563 for (int c3 = 10 * c1;
12564 c3 <= min(-c2 + 100, 10 * c1 + 9);
12568 for (int c0 = 9; c0 <= 10; c0 += 1)
12569 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12570 for (int c2 = 10 * c0;
12571 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12573 for (int c3 = 10 * c1;
12574 c3 <= min(10 * c1 + 9, -c2 + 100);
12581 This is a single-dimensional space representing the schedule dimension(s)
12582 to which ``separation'' should be applied. Separation tries to split
12583 a loop into several pieces if this can avoid the generation of guards
12585 See also the C<atomic> option.
12589 This is a single-dimensional space representing the schedule dimension(s)
12590 for which the domains should be considered ``atomic''. That is, the
12591 AST generator will make sure that any given domain space will only appear
12592 in a single loop at the specified level.
12594 Consider the following schedule
12596 { a[i] -> [i] : 0 <= i < 10;
12597 b[i] -> [i+1] : 0 <= i < 10 }
12599 If the following option is specified
12601 { [i] -> separate[x] }
12603 then the following AST will be generated
12607 for (int c0 = 1; c0 <= 9; c0 += 1) {
12614 If, on the other hand, the following option is specified
12616 { [i] -> atomic[x] }
12618 then the following AST will be generated
12620 for (int c0 = 0; c0 <= 10; c0 += 1) {
12627 If neither C<atomic> nor C<separate> is specified, then the AST generator
12628 may produce either of these two results or some intermediate form.
12632 This is a single-dimensional space representing the schedule dimension(s)
12633 that should be I<completely> unrolled.
12634 To obtain a partial unrolling, the user should apply an additional
12635 strip-mining to the schedule and fully unroll the inner loop.
12639 =head3 Fine-grained Control over AST Generation
12641 Besides specifying the constraints on the parameters,
12642 an C<isl_ast_build> object can be used to control
12643 various aspects of the AST generation process.
12644 In case of AST construction using
12645 C<isl_ast_build_node_from_schedule_map>,
12646 the most prominent way of control is through ``options'',
12647 as explained above.
12649 Additional control is available through the following functions.
12651 #include <isl/ast_build.h>
12652 __isl_give isl_ast_build *
12653 isl_ast_build_set_iterators(
12654 __isl_take isl_ast_build *build,
12655 __isl_take isl_id_list *iterators);
12657 The function C<isl_ast_build_set_iterators> allows the user to
12658 specify a list of iterator C<isl_id>s to be used as iterators.
12659 If the input schedule is injective, then
12660 the number of elements in this list should be as large as the dimension
12661 of the schedule space, but no direct correspondence should be assumed
12662 between dimensions and elements.
12663 If the input schedule is not injective, then an additional number
12664 of C<isl_id>s equal to the largest dimension of the input domains
12666 If the number of provided C<isl_id>s is insufficient, then additional
12667 names are automatically generated.
12669 #include <isl/ast_build.h>
12670 __isl_give isl_ast_build *
12671 isl_ast_build_set_create_leaf(
12672 __isl_take isl_ast_build *build,
12673 __isl_give isl_ast_node *(*fn)(
12674 __isl_take isl_ast_build *build,
12675 void *user), void *user);
12678 C<isl_ast_build_set_create_leaf> function allows for the
12679 specification of a callback that should be called whenever the AST
12680 generator arrives at an element of the schedule domain.
12681 The callback should return an AST node that should be inserted
12682 at the corresponding position of the AST. The default action (when
12683 the callback is not set) is to continue generating parts of the AST to scan
12684 all the domain elements associated to the schedule domain element
12685 and to insert user nodes, ``calling'' the domain element, for each of them.
12686 The C<build> argument contains the current state of the C<isl_ast_build>.
12687 To ease nested AST generation (see L</"Nested AST Generation">),
12688 all control information that is
12689 specific to the current AST generation such as the options and
12690 the callbacks has been removed from this C<isl_ast_build>.
12691 The callback would typically return the result of a nested
12692 AST generation or a
12693 user defined node created using the following function.
12695 #include <isl/ast.h>
12696 __isl_give isl_ast_node *isl_ast_node_alloc_user(
12697 __isl_take isl_ast_expr *expr);
12699 #include <isl/ast_build.h>
12700 __isl_give isl_ast_build *
12701 isl_ast_build_set_at_each_domain(
12702 __isl_take isl_ast_build *build,
12703 __isl_give isl_ast_node *(*fn)(
12704 __isl_take isl_ast_node *node,
12705 __isl_keep isl_ast_build *build,
12706 void *user), void *user);
12707 __isl_give isl_ast_build *
12708 isl_ast_build_set_before_each_for(
12709 __isl_take isl_ast_build *build,
12710 __isl_give isl_id *(*fn)(
12711 __isl_keep isl_ast_build *build,
12712 void *user), void *user);
12713 __isl_give isl_ast_build *
12714 isl_ast_build_set_after_each_for(
12715 __isl_take isl_ast_build *build,
12716 __isl_give isl_ast_node *(*fn)(
12717 __isl_take isl_ast_node *node,
12718 __isl_keep isl_ast_build *build,
12719 void *user), void *user);
12720 __isl_give isl_ast_build *
12721 isl_ast_build_set_before_each_mark(
12722 __isl_take isl_ast_build *build,
12723 isl_stat (*fn)(__isl_keep isl_id *mark,
12724 __isl_keep isl_ast_build *build,
12725 void *user), void *user);
12726 __isl_give isl_ast_build *
12727 isl_ast_build_set_after_each_mark(
12728 __isl_take isl_ast_build *build,
12729 __isl_give isl_ast_node *(*fn)(
12730 __isl_take isl_ast_node *node,
12731 __isl_keep isl_ast_build *build,
12732 void *user), void *user);
12734 The callback set by C<isl_ast_build_set_at_each_domain> will
12735 be called for each domain AST node.
12736 The callbacks set by C<isl_ast_build_set_before_each_for>
12737 and C<isl_ast_build_set_after_each_for> will be called
12738 for each for AST node. The first will be called in depth-first
12739 pre-order, while the second will be called in depth-first post-order.
12740 Since C<isl_ast_build_set_before_each_for> is called before the for
12741 node is actually constructed, it is only passed an C<isl_ast_build>.
12742 The returned C<isl_id> will be added as an annotation (using
12743 C<isl_ast_node_set_annotation>) to the constructed for node.
12744 In particular, if the user has also specified an C<after_each_for>
12745 callback, then the annotation can be retrieved from the node passed to
12746 that callback using C<isl_ast_node_get_annotation>.
12747 The callbacks set by C<isl_ast_build_set_before_each_mark>
12748 and C<isl_ast_build_set_after_each_mark> will be called for each
12749 mark AST node that is created, i.e., for each mark schedule node
12750 in the input schedule tree. The first will be called in depth-first
12751 pre-order, while the second will be called in depth-first post-order.
12752 Since the callback set by C<isl_ast_build_set_before_each_mark>
12753 is called before the mark AST node is actually constructed, it is passed
12754 the identifier of the mark node.
12755 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
12756 The given C<isl_ast_build> can be used to create new
12757 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
12758 or C<isl_ast_build_call_from_pw_multi_aff>.
12760 =head3 Nested AST Generation
12762 C<isl> allows the user to create an AST within the context
12763 of another AST. These nested ASTs are created using the
12764 same C<isl_ast_build_node_from_schedule_map> function that is used to create
12765 the outer AST. The C<build> argument should be an C<isl_ast_build>
12766 passed to a callback set by
12767 C<isl_ast_build_set_create_leaf>.
12768 The space of the range of the C<schedule> argument should refer
12769 to this build. In particular, the space should be a wrapped
12770 relation and the domain of this wrapped relation should be the
12771 same as that of the range of the schedule returned by
12772 C<isl_ast_build_get_schedule> below.
12773 In practice, the new schedule is typically
12774 created by calling C<isl_union_map_range_product> on the old schedule
12775 and some extra piece of the schedule.
12776 The space of the schedule domain is also available from
12777 the C<isl_ast_build>.
12779 #include <isl/ast_build.h>
12780 __isl_give isl_union_map *isl_ast_build_get_schedule(
12781 __isl_keep isl_ast_build *build);
12782 __isl_give isl_space *isl_ast_build_get_schedule_space(
12783 __isl_keep isl_ast_build *build);
12784 __isl_give isl_ast_build *isl_ast_build_restrict(
12785 __isl_take isl_ast_build *build,
12786 __isl_take isl_set *set);
12788 The C<isl_ast_build_get_schedule> function returns a (partial)
12789 schedule for the domains elements for which part of the AST still needs to
12790 be generated in the current build.
12791 In particular, the domain elements are mapped to those iterations of the loops
12792 enclosing the current point of the AST generation inside which
12793 the domain elements are executed.
12794 No direct correspondence between
12795 the input schedule and this schedule should be assumed.
12796 The space obtained from C<isl_ast_build_get_schedule_space> can be used
12797 to create a set for C<isl_ast_build_restrict> to intersect
12798 with the current build. In particular, the set passed to
12799 C<isl_ast_build_restrict> can have additional parameters.
12800 The ids of the set dimensions in the space returned by
12801 C<isl_ast_build_get_schedule_space> correspond to the
12802 iterators of the already generated loops.
12803 The user should not rely on the ids of the output dimensions
12804 of the relations in the union relation returned by
12805 C<isl_ast_build_get_schedule> having any particular value.
12807 =head1 Applications
12809 Although C<isl> is mainly meant to be used as a library,
12810 it also contains some basic applications that use some
12811 of the functionality of C<isl>.
12812 For applications that take one or more polytopes or polyhedra
12813 as input, this input may be specified in either the L<isl format>
12814 or the L<PolyLib format>.
12816 =head2 C<isl_polyhedron_sample>
12818 C<isl_polyhedron_sample> takes a polyhedron as input and prints
12819 an integer element of the polyhedron, if there is any.
12820 The first column in the output is the denominator and is always
12821 equal to 1. If the polyhedron contains no integer points,
12822 then a vector of length zero is printed.
12826 C<isl_pip> takes the same input as the C<example> program
12827 from the C<piplib> distribution, i.e., a set of constraints
12828 on the parameters, a line containing only -1 and finally a set
12829 of constraints on a parametric polyhedron.
12830 The coefficients of the parameters appear in the last columns
12831 (but before the final constant column).
12832 The output is the lexicographic minimum of the parametric polyhedron.
12833 As C<isl> currently does not have its own output format, the output
12834 is just a dump of the internal state.
12836 =head2 C<isl_polyhedron_minimize>
12838 C<isl_polyhedron_minimize> computes the minimum of some linear
12839 or affine objective function over the integer points in a polyhedron.
12840 If an affine objective function
12841 is given, then the constant should appear in the last column.
12843 =head2 C<isl_polytope_scan>
12845 Given a polytope, C<isl_polytope_scan> prints
12846 all integer points in the polytope.
12850 Given an C<isl_union_access_info> object as input,
12851 C<isl_flow> prints out the corresponding dependences,
12852 as computed by C<isl_union_access_info_compute_flow>.
12854 =head2 C<isl_codegen>
12856 Given either a schedule tree or a sequence consisting of
12857 a schedule map, a context set and an options relation,
12858 C<isl_codegen> prints out an AST that scans the domain elements
12859 of the schedule in the order of their image(s) taking into account
12860 the constraints in the context set.
12862 =head2 C<isl_schedule>
12864 Given an C<isl_schedule_constraints> object as input,
12865 C<isl_schedule> prints out a schedule that satisfies the given