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> undefined for NaN.
801 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
802 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
804 The following unary operations are available on C<isl_val>s.
807 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
808 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
809 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
810 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
811 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
812 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
814 The following binary operations are available on C<isl_val>s.
817 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
818 __isl_take isl_val *v2);
819 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
820 __isl_take isl_val *v2);
821 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
822 __isl_take isl_val *v2);
823 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
825 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
826 __isl_take isl_val *v2);
827 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
829 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
830 __isl_take isl_val *v2);
831 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
833 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
834 __isl_take isl_val *v2);
835 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
838 On integer values, we additionally have the following operations.
841 __isl_give isl_val *isl_val_pow2(__isl_take isl_val *v);
842 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
843 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
844 __isl_take isl_val *v2);
845 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
846 __isl_take isl_val *v2);
847 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
848 __isl_take isl_val *v2, __isl_give isl_val **x,
849 __isl_give isl_val **y);
851 C<isl_val_2exp> is an alternative name for C<isl_val_pow2>.
852 The function C<isl_val_gcdext> returns the greatest common divisor g
853 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
854 that C<*x> * C<v1> + C<*y> * C<v2> = g.
856 =head3 GMP specific functions
858 These functions are only available if C<isl> has been compiled with C<GMP>
861 Specific integer and rational values can be created from C<GMP> values using
862 the following functions.
864 #include <isl/val_gmp.h>
865 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
867 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
868 const mpz_t n, const mpz_t d);
870 The numerator and denominator of a rational value can be extracted as
871 C<GMP> values using the following functions.
873 #include <isl/val_gmp.h>
874 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
875 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
877 =head2 Sets and Relations
879 C<isl> uses six types of objects for representing sets and relations,
880 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
881 C<isl_union_set> and C<isl_union_map>.
882 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
883 can be described as a conjunction of affine constraints, while
884 C<isl_set> and C<isl_map> represent unions of
885 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
886 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
887 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
888 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
889 where spaces are considered different if they have a different number
890 of dimensions and/or different names (see L<"Spaces">).
891 The difference between sets and relations (maps) is that sets have
892 one set of variables, while relations have two sets of variables,
893 input variables and output variables.
895 =head2 Error Handling
897 C<isl> supports different ways to react in case a runtime error is triggered.
898 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
899 with two maps that have incompatible spaces. There are three possible ways
900 to react on error: to warn, to continue or to abort.
902 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
903 the last error in the corresponding C<isl_ctx> and the function in which the
904 error was triggered returns a value indicating that some error has
905 occurred. In case of functions returning a pointer, this value is
906 C<NULL>. In case of functions returning an C<isl_size>, C<isl_bool> or an
907 C<isl_stat>, this value is C<isl_size_error>,
908 C<isl_bool_error> or C<isl_stat_error>.
909 An error does not corrupt internal state,
910 such that isl can continue to be used. C<isl> also provides functions to
911 read the last error, including the specific error message,
912 the isl source file where the error occurred and the line number,
913 and to reset all information about the last error. The
914 last error is only stored for information purposes. Its presence does not
915 change the behavior of C<isl>. Hence, resetting an error is not required to
916 continue to use isl, but only to observe new errors.
919 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
920 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
921 const char *isl_ctx_last_error_file(isl_ctx *ctx);
922 int isl_ctx_last_error_line(isl_ctx *ctx);
923 void isl_ctx_reset_error(isl_ctx *ctx);
925 If no error has occurred since the last call to C<isl_ctx_reset_error>,
926 then the functions C<isl_ctx_last_error_msg> and
927 C<isl_ctx_last_error_file> return C<NULL>.
929 Another option is to continue on error. This is similar to warn on error mode,
930 except that C<isl> does not print any warning. This allows a program to
931 implement its own error reporting.
933 The last option is to directly abort the execution of the program from within
934 the isl library. This makes it obviously impossible to recover from an error,
935 but it allows to directly spot the error location. By aborting on error,
936 debuggers break at the location the error occurred and can provide a stack
937 trace. Other tools that automatically provide stack traces on abort or that do
938 not want to continue execution after an error was triggered may also prefer to
941 The on error behavior of isl can be specified by calling
942 C<isl_options_set_on_error> or by setting the command line option
943 C<--isl-on-error>. Valid arguments for the function call are
944 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
945 choices for the command line option are C<warn>, C<continue> and C<abort>.
946 It is also possible to query the current error mode.
948 #include <isl/options.h>
949 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
950 int isl_options_get_on_error(isl_ctx *ctx);
954 Identifiers are used to identify both individual dimensions
955 and tuples of dimensions. They consist of an optional name and an optional
956 user pointer. The name and the user pointer cannot both be C<NULL>, however.
957 Identifiers with the same name but different pointer values
958 are considered to be distinct.
959 Similarly, identifiers with different names but the same pointer value
960 are also considered to be distinct.
961 Equal identifiers are represented using the same object.
962 Pairs of identifiers can therefore be tested for equality using the
964 Identifiers can be constructed, copied, freed, inspected and printed
965 using the following functions.
968 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
969 __isl_keep const char *name, void *user);
970 __isl_give isl_id *isl_id_set_free_user(
971 __isl_take isl_id *id,
972 void (*free_user)(void *user));
973 __isl_give isl_id *isl_id_copy(isl_id *id);
974 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
976 void *isl_id_get_user(__isl_keep isl_id *id);
977 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
979 __isl_give isl_printer *isl_printer_print_id(
980 __isl_take isl_printer *p, __isl_keep isl_id *id);
982 The callback set by C<isl_id_set_free_user> is called on the user
983 pointer when the last reference to the C<isl_id> is freed.
984 Note that C<isl_id_get_name> returns a pointer to some internal
985 data structure, so the result can only be used while the
986 corresponding C<isl_id> is alive.
990 Whenever a new set, relation or similar object is created from scratch,
991 the space in which it lives needs to be specified using an C<isl_space>.
992 Each space involves zero or more parameters and zero, one or two
993 tuples of set or input/output dimensions. The parameters and dimensions
994 are identified by an C<isl_dim_type> and a position.
995 The type C<isl_dim_param> refers to parameters,
996 the type C<isl_dim_set> refers to set dimensions (for spaces
997 with a single tuple of dimensions) and the types C<isl_dim_in>
998 and C<isl_dim_out> refer to input and output dimensions
999 (for spaces with two tuples of dimensions).
1000 Local spaces (see L</"Local Spaces">) also contain dimensions
1001 of type C<isl_dim_div>.
1002 Note that parameters are only identified by their position within
1003 a given object. Across different objects, parameters are (usually)
1004 identified by their names or identifiers. Only unnamed parameters
1005 are identified by their positions across objects. The use of unnamed
1006 parameters is discouraged.
1008 #include <isl/space.h>
1009 __isl_give isl_space *isl_space_unit(isl_ctx *ctx);
1010 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
1011 unsigned nparam, unsigned n_in, unsigned n_out);
1012 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
1014 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
1015 unsigned nparam, unsigned dim);
1016 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
1017 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
1019 The space used for creating a parameter domain
1020 needs to be created using C<isl_space_unit> or C<isl_space_params_alloc>.
1021 For other sets, the space
1022 needs to be created using C<isl_space_set_alloc>, while
1023 for a relation, the space
1024 needs to be created using C<isl_space_alloc>.
1025 The use of C<isl_space_params_alloc>,
1026 C<isl_space_set_alloc> and C<isl_space_alloc> is discouraged as they allow
1027 for the introduction of unnamed parameters.
1029 To check whether a given space is that of a set or a map
1030 or whether it is a parameter space, use these functions:
1032 #include <isl/space.h>
1033 isl_bool isl_space_is_params(__isl_keep isl_space *space);
1034 isl_bool isl_space_is_set(__isl_keep isl_space *space);
1035 isl_bool isl_space_is_map(__isl_keep isl_space *space);
1037 Spaces can be compared using the following functions:
1039 #include <isl/space.h>
1040 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
1041 __isl_keep isl_space *space2);
1042 isl_bool isl_space_has_equal_params(
1043 __isl_keep isl_space *space1,
1044 __isl_keep isl_space *space2);
1045 isl_bool isl_space_has_equal_tuples(
1046 __isl_keep isl_space *space1,
1047 __isl_keep isl_space *space2);
1048 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
1049 __isl_keep isl_space *space2);
1050 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
1051 __isl_keep isl_space *space2);
1052 isl_bool isl_space_tuple_is_equal(
1053 __isl_keep isl_space *space1,
1054 enum isl_dim_type type1,
1055 __isl_keep isl_space *space2,
1056 enum isl_dim_type type2);
1058 C<isl_space_is_domain> checks whether the first argument is equal
1059 to the domain of the second argument. This requires in particular that
1060 the first argument is a set space and that the second argument
1061 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1062 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1063 spaces are the same. That is, it checks if they have the same
1064 identifier (if any), the same dimension and the same internal structure
1067 C<isl_space_has_equal_params> checks whether two spaces
1068 have the same parameters in the same order.
1069 C<isl_space_has_equal_tuples> check whether two spaces have
1070 the same tuples. In contrast to C<isl_space_is_equal> below,
1071 it does not check the
1072 parameters. This is useful because many C<isl> functions align the
1073 parameters before they perform their operations, such that equivalence
1075 C<isl_space_is_equal> checks whether two spaces are identical,
1076 meaning that they have the same parameters and the same tuples.
1077 That is, it checks whether both C<isl_space_has_equal_params> and
1078 C<isl_space_has_equal_tuples> hold.
1080 It is often useful to create objects that live in the
1081 same space as some other object. This can be accomplished
1082 by creating the new objects
1083 (see L</"Creating New Sets and Relations"> or
1084 L</"Functions">) based on the space
1085 of the original object.
1087 #include <isl/set.h>
1088 __isl_give isl_space *isl_basic_set_get_space(
1089 __isl_keep isl_basic_set *bset);
1090 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1092 #include <isl/union_set.h>
1093 __isl_give isl_space *isl_union_set_get_space(
1094 __isl_keep isl_union_set *uset);
1096 #include <isl/map.h>
1097 __isl_give isl_space *isl_basic_map_get_space(
1098 __isl_keep isl_basic_map *bmap);
1099 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1101 #include <isl/union_map.h>
1102 __isl_give isl_space *isl_union_map_get_space(
1103 __isl_keep isl_union_map *umap);
1105 #include <isl/constraint.h>
1106 __isl_give isl_space *isl_constraint_get_space(
1107 __isl_keep isl_constraint *constraint);
1109 #include <isl/polynomial.h>
1110 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1111 __isl_keep isl_qpolynomial *qp);
1112 __isl_give isl_space *isl_qpolynomial_get_space(
1113 __isl_keep isl_qpolynomial *qp);
1114 __isl_give isl_space *
1115 isl_qpolynomial_fold_get_domain_space(
1116 __isl_keep isl_qpolynomial_fold *fold);
1117 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1118 __isl_keep isl_qpolynomial_fold *fold);
1119 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1120 __isl_keep isl_pw_qpolynomial *pwqp);
1121 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1122 __isl_keep isl_pw_qpolynomial *pwqp);
1123 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1124 __isl_keep isl_pw_qpolynomial_fold *pwf);
1125 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1126 __isl_keep isl_pw_qpolynomial_fold *pwf);
1127 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1128 __isl_keep isl_union_pw_qpolynomial *upwqp);
1129 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1130 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1133 __isl_give isl_space *isl_multi_id_get_space(
1134 __isl_keep isl_multi_id *mi);
1136 #include <isl/val.h>
1137 __isl_give isl_space *isl_multi_val_get_space(
1138 __isl_keep isl_multi_val *mv);
1140 #include <isl/aff.h>
1141 __isl_give isl_space *isl_aff_get_domain_space(
1142 __isl_keep isl_aff *aff);
1143 __isl_give isl_space *isl_aff_get_space(
1144 __isl_keep isl_aff *aff);
1145 __isl_give isl_space *isl_pw_aff_get_domain_space(
1146 __isl_keep isl_pw_aff *pwaff);
1147 __isl_give isl_space *isl_pw_aff_get_space(
1148 __isl_keep isl_pw_aff *pwaff);
1149 __isl_give isl_space *isl_multi_aff_get_domain_space(
1150 __isl_keep isl_multi_aff *maff);
1151 __isl_give isl_space *isl_multi_aff_get_space(
1152 __isl_keep isl_multi_aff *maff);
1153 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1154 __isl_keep isl_pw_multi_aff *pma);
1155 __isl_give isl_space *isl_pw_multi_aff_get_space(
1156 __isl_keep isl_pw_multi_aff *pma);
1157 __isl_give isl_space *isl_union_pw_aff_get_space(
1158 __isl_keep isl_union_pw_aff *upa);
1159 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1160 __isl_keep isl_union_pw_multi_aff *upma);
1161 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1162 __isl_keep isl_multi_pw_aff *mpa);
1163 __isl_give isl_space *isl_multi_pw_aff_get_space(
1164 __isl_keep isl_multi_pw_aff *mpa);
1165 __isl_give isl_space *
1166 isl_multi_union_pw_aff_get_domain_space(
1167 __isl_keep isl_multi_union_pw_aff *mupa);
1168 __isl_give isl_space *
1169 isl_multi_union_pw_aff_get_space(
1170 __isl_keep isl_multi_union_pw_aff *mupa);
1172 #include <isl/point.h>
1173 __isl_give isl_space *isl_point_get_space(
1174 __isl_keep isl_point *pnt);
1176 #include <isl/fixed_box.h>
1177 __isl_give isl_space *isl_fixed_box_get_space(
1178 __isl_keep isl_fixed_box *box);
1180 The number of dimensions of a given type of space
1181 may be read off from a space or an object that lives
1182 in a space using the following functions.
1183 In case of C<isl_space_dim>, type may be
1184 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1185 C<isl_dim_out> (only for relations), C<isl_dim_set>
1186 (only for sets) or C<isl_dim_all>.
1188 #include <isl/space.h>
1189 isl_size isl_space_dim(__isl_keep isl_space *space,
1190 enum isl_dim_type type);
1192 #include <isl/local_space.h>
1193 isl_size isl_local_space_dim(__isl_keep isl_local_space *ls,
1194 enum isl_dim_type type);
1196 #include <isl/set.h>
1197 isl_size isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1198 enum isl_dim_type type);
1199 isl_size isl_set_dim(__isl_keep isl_set *set,
1200 enum isl_dim_type type);
1202 #include <isl/union_set.h>
1203 isl_size isl_union_set_dim(__isl_keep isl_union_set *uset,
1204 enum isl_dim_type type);
1206 #include <isl/map.h>
1207 isl_size isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1208 enum isl_dim_type type);
1209 isl_size isl_map_dim(__isl_keep isl_map *map,
1210 enum isl_dim_type type);
1212 #include <isl/union_map.h>
1213 isl_size isl_union_map_dim(__isl_keep isl_union_map *umap,
1214 enum isl_dim_type type);
1216 #include <isl/val.h>
1217 isl_size isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1218 enum isl_dim_type type);
1220 #include <isl/aff.h>
1221 isl_size isl_aff_dim(__isl_keep isl_aff *aff,
1222 enum isl_dim_type type);
1223 isl_size isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1224 enum isl_dim_type type);
1225 isl_size isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1226 enum isl_dim_type type);
1227 isl_size isl_pw_multi_aff_dim(
1228 __isl_keep isl_pw_multi_aff *pma,
1229 enum isl_dim_type type);
1230 isl_size isl_multi_pw_aff_dim(
1231 __isl_keep isl_multi_pw_aff *mpa,
1232 enum isl_dim_type type);
1233 isl_size isl_union_pw_aff_dim(
1234 __isl_keep isl_union_pw_aff *upa,
1235 enum isl_dim_type type);
1236 isl_size isl_union_pw_multi_aff_dim(
1237 __isl_keep isl_union_pw_multi_aff *upma,
1238 enum isl_dim_type type);
1239 isl_size isl_multi_union_pw_aff_dim(
1240 __isl_keep isl_multi_union_pw_aff *mupa,
1241 enum isl_dim_type type);
1243 #include <isl/polynomial.h>
1244 isl_size isl_union_pw_qpolynomial_dim(
1245 __isl_keep isl_union_pw_qpolynomial *upwqp,
1246 enum isl_dim_type type);
1247 isl_size isl_union_pw_qpolynomial_fold_dim(
1248 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1249 enum isl_dim_type type);
1251 Note that an C<isl_union_set>, an C<isl_union_map>,
1252 an C<isl_union_pw_multi_aff>,
1253 an C<isl_union_pw_qpolynomial> and
1254 an C<isl_union_pw_qpolynomial_fold>
1255 only have parameters.
1257 Additional parameters can be added to a space using the following function.
1259 #include <isl/space.h>
1260 __isl_give isl_space *isl_space_add_param_id(
1261 __isl_take isl_space *space,
1262 __isl_take isl_id *id);
1264 If a parameter with the given identifier already appears in the space,
1265 then it is not added again.
1267 Conversely, all parameters can be removed from a space
1268 using the following function.
1270 #include <isl/space.h>
1271 __isl_give isl_space *isl_space_drop_all_params(
1272 __isl_take isl_space *space);
1274 The identifiers or names of the individual dimensions of spaces
1275 may be set or read off using the following functions on spaces
1276 or objects that live in spaces.
1277 These functions are mostly useful to obtain the identifiers, positions
1278 or names of the parameters. Identifiers of individual dimensions are
1279 essentially only useful for printing. They are ignored by all other
1280 operations and may not be preserved across those operations.
1281 To keep track of a space along with names/identifiers of
1282 the set dimensions, use an C<isl_multi_id> as described in
1285 #include <isl/space.h>
1286 __isl_give isl_space *isl_space_set_dim_id(
1287 __isl_take isl_space *space,
1288 enum isl_dim_type type, unsigned pos,
1289 __isl_take isl_id *id);
1290 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1291 enum isl_dim_type type, unsigned pos);
1292 __isl_give isl_id *isl_space_get_dim_id(
1293 __isl_keep isl_space *space,
1294 enum isl_dim_type type, unsigned pos);
1295 __isl_give isl_space *isl_space_set_dim_name(
1296 __isl_take isl_space *space,
1297 enum isl_dim_type type, unsigned pos,
1298 __isl_keep const char *name);
1299 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1300 enum isl_dim_type type, unsigned pos);
1301 __isl_keep const char *isl_space_get_dim_name(
1302 __isl_keep isl_space *space,
1303 enum isl_dim_type type, unsigned pos);
1305 #include <isl/local_space.h>
1306 __isl_give isl_local_space *isl_local_space_set_dim_id(
1307 __isl_take isl_local_space *ls,
1308 enum isl_dim_type type, unsigned pos,
1309 __isl_take isl_id *id);
1310 isl_bool isl_local_space_has_dim_id(
1311 __isl_keep isl_local_space *ls,
1312 enum isl_dim_type type, unsigned pos);
1313 __isl_give isl_id *isl_local_space_get_dim_id(
1314 __isl_keep isl_local_space *ls,
1315 enum isl_dim_type type, unsigned pos);
1316 __isl_give isl_local_space *isl_local_space_set_dim_name(
1317 __isl_take isl_local_space *ls,
1318 enum isl_dim_type type, unsigned pos, const char *s);
1319 isl_bool isl_local_space_has_dim_name(
1320 __isl_keep isl_local_space *ls,
1321 enum isl_dim_type type, unsigned pos)
1322 const char *isl_local_space_get_dim_name(
1323 __isl_keep isl_local_space *ls,
1324 enum isl_dim_type type, unsigned pos);
1326 #include <isl/constraint.h>
1327 const char *isl_constraint_get_dim_name(
1328 __isl_keep isl_constraint *constraint,
1329 enum isl_dim_type type, unsigned pos);
1331 #include <isl/set.h>
1332 __isl_give isl_id *isl_basic_set_get_dim_id(
1333 __isl_keep isl_basic_set *bset,
1334 enum isl_dim_type type, unsigned pos);
1335 __isl_give isl_set *isl_set_set_dim_id(
1336 __isl_take isl_set *set, enum isl_dim_type type,
1337 unsigned pos, __isl_take isl_id *id);
1338 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1339 enum isl_dim_type type, unsigned pos);
1340 __isl_give isl_id *isl_set_get_dim_id(
1341 __isl_keep isl_set *set, enum isl_dim_type type,
1343 const char *isl_basic_set_get_dim_name(
1344 __isl_keep isl_basic_set *bset,
1345 enum isl_dim_type type, unsigned pos);
1346 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1347 enum isl_dim_type type, unsigned pos);
1348 const char *isl_set_get_dim_name(
1349 __isl_keep isl_set *set,
1350 enum isl_dim_type type, unsigned pos);
1352 #include <isl/map.h>
1353 __isl_give isl_map *isl_map_set_dim_id(
1354 __isl_take isl_map *map, enum isl_dim_type type,
1355 unsigned pos, __isl_take isl_id *id);
1356 isl_bool isl_basic_map_has_dim_id(
1357 __isl_keep isl_basic_map *bmap,
1358 enum isl_dim_type type, unsigned pos);
1359 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1360 enum isl_dim_type type, unsigned pos);
1361 __isl_give isl_id *isl_map_get_dim_id(
1362 __isl_keep isl_map *map, enum isl_dim_type type,
1364 __isl_give isl_id *isl_union_map_get_dim_id(
1365 __isl_keep isl_union_map *umap,
1366 enum isl_dim_type type, unsigned pos);
1367 const char *isl_basic_map_get_dim_name(
1368 __isl_keep isl_basic_map *bmap,
1369 enum isl_dim_type type, unsigned pos);
1370 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1371 enum isl_dim_type type, unsigned pos);
1372 const char *isl_map_get_dim_name(
1373 __isl_keep isl_map *map,
1374 enum isl_dim_type type, unsigned pos);
1376 #include <isl/val.h>
1377 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1378 __isl_take isl_multi_val *mv,
1379 enum isl_dim_type type, unsigned pos,
1380 __isl_take isl_id *id);
1381 __isl_give isl_id *isl_multi_val_get_dim_id(
1382 __isl_keep isl_multi_val *mv,
1383 enum isl_dim_type type, unsigned pos);
1384 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1385 __isl_take isl_multi_val *mv,
1386 enum isl_dim_type type, unsigned pos, const char *s);
1388 #include <isl/aff.h>
1389 __isl_give isl_aff *isl_aff_set_dim_id(
1390 __isl_take isl_aff *aff, enum isl_dim_type type,
1391 unsigned pos, __isl_take isl_id *id);
1392 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1393 __isl_take isl_multi_aff *maff,
1394 enum isl_dim_type type, unsigned pos,
1395 __isl_take isl_id *id);
1396 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1397 __isl_take isl_pw_aff *pma,
1398 enum isl_dim_type type, unsigned pos,
1399 __isl_take isl_id *id);
1400 __isl_give isl_multi_pw_aff *
1401 isl_multi_pw_aff_set_dim_id(
1402 __isl_take isl_multi_pw_aff *mpa,
1403 enum isl_dim_type type, unsigned pos,
1404 __isl_take isl_id *id);
1405 __isl_give isl_multi_union_pw_aff *
1406 isl_multi_union_pw_aff_set_dim_id(
1407 __isl_take isl_multi_union_pw_aff *mupa,
1408 enum isl_dim_type type, unsigned pos,
1409 __isl_take isl_id *id);
1410 __isl_give isl_id *isl_multi_aff_get_dim_id(
1411 __isl_keep isl_multi_aff *ma,
1412 enum isl_dim_type type, unsigned pos);
1413 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1414 enum isl_dim_type type, unsigned pos);
1415 __isl_give isl_id *isl_pw_aff_get_dim_id(
1416 __isl_keep isl_pw_aff *pa,
1417 enum isl_dim_type type, unsigned pos);
1418 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1419 __isl_keep isl_pw_multi_aff *pma,
1420 enum isl_dim_type type, unsigned pos);
1421 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1422 __isl_keep isl_multi_pw_aff *mpa,
1423 enum isl_dim_type type, unsigned pos);
1424 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1425 __isl_keep isl_multi_union_pw_aff *mupa,
1426 enum isl_dim_type type, unsigned pos);
1427 __isl_give isl_aff *isl_aff_set_dim_name(
1428 __isl_take isl_aff *aff, enum isl_dim_type type,
1429 unsigned pos, const char *s);
1430 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1431 __isl_take isl_multi_aff *maff,
1432 enum isl_dim_type type, unsigned pos, const char *s);
1433 __isl_give isl_multi_pw_aff *
1434 isl_multi_pw_aff_set_dim_name(
1435 __isl_take isl_multi_pw_aff *mpa,
1436 enum isl_dim_type type, unsigned pos, const char *s);
1437 __isl_give isl_union_pw_aff *
1438 isl_union_pw_aff_set_dim_name(
1439 __isl_take isl_union_pw_aff *upa,
1440 enum isl_dim_type type, unsigned pos,
1442 __isl_give isl_union_pw_multi_aff *
1443 isl_union_pw_multi_aff_set_dim_name(
1444 __isl_take isl_union_pw_multi_aff *upma,
1445 enum isl_dim_type type, unsigned pos,
1447 __isl_give isl_multi_union_pw_aff *
1448 isl_multi_union_pw_aff_set_dim_name(
1449 __isl_take isl_multi_union_pw_aff *mupa,
1450 enum isl_dim_type type, unsigned pos,
1452 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1453 enum isl_dim_type type, unsigned pos);
1454 const char *isl_pw_aff_get_dim_name(
1455 __isl_keep isl_pw_aff *pa,
1456 enum isl_dim_type type, unsigned pos);
1457 const char *isl_pw_multi_aff_get_dim_name(
1458 __isl_keep isl_pw_multi_aff *pma,
1459 enum isl_dim_type type, unsigned pos);
1461 #include <isl/polynomial.h>
1462 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1463 __isl_take isl_qpolynomial *qp,
1464 enum isl_dim_type type, unsigned pos,
1466 __isl_give isl_pw_qpolynomial *
1467 isl_pw_qpolynomial_set_dim_name(
1468 __isl_take isl_pw_qpolynomial *pwqp,
1469 enum isl_dim_type type, unsigned pos,
1471 __isl_give isl_pw_qpolynomial_fold *
1472 isl_pw_qpolynomial_fold_set_dim_name(
1473 __isl_take isl_pw_qpolynomial_fold *pwf,
1474 enum isl_dim_type type, unsigned pos,
1476 __isl_give isl_union_pw_qpolynomial *
1477 isl_union_pw_qpolynomial_set_dim_name(
1478 __isl_take isl_union_pw_qpolynomial *upwqp,
1479 enum isl_dim_type type, unsigned pos,
1481 __isl_give isl_union_pw_qpolynomial_fold *
1482 isl_union_pw_qpolynomial_fold_set_dim_name(
1483 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1484 enum isl_dim_type type, unsigned pos,
1487 Note that C<isl_space_get_name> returns a pointer to some internal
1488 data structure, so the result can only be used while the
1489 corresponding C<isl_space> is alive.
1490 Also note that every function that operates on two sets or relations
1491 requires that both arguments have the same parameters. This also
1492 means that if one of the arguments has named parameters, then the
1493 other needs to have named parameters too and the names need to match.
1494 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1495 arguments may have different parameters (as long as they are named),
1496 in which case the result will have as parameters the union of the parameters of
1499 Given the identifier or name of a dimension (typically a parameter),
1500 its position can be obtained from the following functions.
1502 #include <isl/space.h>
1503 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1504 enum isl_dim_type type, __isl_keep isl_id *id);
1505 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1506 enum isl_dim_type type, const char *name);
1508 #include <isl/local_space.h>
1509 int isl_local_space_find_dim_by_name(
1510 __isl_keep isl_local_space *ls,
1511 enum isl_dim_type type, const char *name);
1513 #include <isl/val.h>
1514 int isl_multi_val_find_dim_by_id(
1515 __isl_keep isl_multi_val *mv,
1516 enum isl_dim_type type, __isl_keep isl_id *id);
1517 int isl_multi_val_find_dim_by_name(
1518 __isl_keep isl_multi_val *mv,
1519 enum isl_dim_type type, const char *name);
1521 #include <isl/set.h>
1522 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1523 enum isl_dim_type type, __isl_keep isl_id *id);
1524 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1525 enum isl_dim_type type, const char *name);
1527 #include <isl/map.h>
1528 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1529 enum isl_dim_type type, __isl_keep isl_id *id);
1530 int isl_basic_map_find_dim_by_name(
1531 __isl_keep isl_basic_map *bmap,
1532 enum isl_dim_type type, const char *name);
1533 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1534 enum isl_dim_type type, const char *name);
1535 int isl_union_map_find_dim_by_name(
1536 __isl_keep isl_union_map *umap,
1537 enum isl_dim_type type, const char *name);
1539 #include <isl/aff.h>
1540 int isl_multi_aff_find_dim_by_id(
1541 __isl_keep isl_multi_aff *ma,
1542 enum isl_dim_type type, __isl_keep isl_id *id);
1543 int isl_multi_pw_aff_find_dim_by_id(
1544 __isl_keep isl_multi_pw_aff *mpa,
1545 enum isl_dim_type type, __isl_keep isl_id *id);
1546 int isl_multi_union_pw_aff_find_dim_by_id(
1547 __isl_keep isl_multi_union_pw_aff *mupa,
1548 enum isl_dim_type type, __isl_keep isl_id *id);
1549 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1550 enum isl_dim_type type, const char *name);
1551 int isl_multi_aff_find_dim_by_name(
1552 __isl_keep isl_multi_aff *ma,
1553 enum isl_dim_type type, const char *name);
1554 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1555 enum isl_dim_type type, const char *name);
1556 int isl_multi_pw_aff_find_dim_by_name(
1557 __isl_keep isl_multi_pw_aff *mpa,
1558 enum isl_dim_type type, const char *name);
1559 int isl_pw_multi_aff_find_dim_by_name(
1560 __isl_keep isl_pw_multi_aff *pma,
1561 enum isl_dim_type type, const char *name);
1562 int isl_union_pw_aff_find_dim_by_name(
1563 __isl_keep isl_union_pw_aff *upa,
1564 enum isl_dim_type type, const char *name);
1565 int isl_union_pw_multi_aff_find_dim_by_name(
1566 __isl_keep isl_union_pw_multi_aff *upma,
1567 enum isl_dim_type type, const char *name);
1568 int isl_multi_union_pw_aff_find_dim_by_name(
1569 __isl_keep isl_multi_union_pw_aff *mupa,
1570 enum isl_dim_type type, const char *name);
1572 #include <isl/polynomial.h>
1573 int isl_pw_qpolynomial_find_dim_by_name(
1574 __isl_keep isl_pw_qpolynomial *pwqp,
1575 enum isl_dim_type type, const char *name);
1576 int isl_pw_qpolynomial_fold_find_dim_by_name(
1577 __isl_keep isl_pw_qpolynomial_fold *pwf,
1578 enum isl_dim_type type, const char *name);
1579 int isl_union_pw_qpolynomial_find_dim_by_name(
1580 __isl_keep isl_union_pw_qpolynomial *upwqp,
1581 enum isl_dim_type type, const char *name);
1582 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1583 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1584 enum isl_dim_type type, const char *name);
1586 The identifiers or names of entire spaces may be set or read off
1587 using the following functions.
1589 #include <isl/space.h>
1590 __isl_give isl_space *isl_space_set_tuple_id(
1591 __isl_take isl_space *space,
1592 enum isl_dim_type type, __isl_take isl_id *id);
1593 __isl_give isl_space *isl_space_reset_tuple_id(
1594 __isl_take isl_space *space, enum isl_dim_type type);
1595 isl_bool isl_space_has_tuple_id(
1596 __isl_keep isl_space *space,
1597 enum isl_dim_type type);
1598 __isl_give isl_id *isl_space_get_tuple_id(
1599 __isl_keep isl_space *space, enum isl_dim_type type);
1600 __isl_give isl_space *isl_space_set_tuple_name(
1601 __isl_take isl_space *space,
1602 enum isl_dim_type type, const char *s);
1603 isl_bool isl_space_has_tuple_name(
1604 __isl_keep isl_space *space,
1605 enum isl_dim_type type);
1606 __isl_keep const char *isl_space_get_tuple_name(
1607 __isl_keep isl_space *space,
1608 enum isl_dim_type type);
1610 #include <isl/local_space.h>
1611 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1612 __isl_take isl_local_space *ls,
1613 enum isl_dim_type type, __isl_take isl_id *id);
1615 #include <isl/set.h>
1616 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1617 __isl_take isl_basic_set *bset,
1618 __isl_take isl_id *id);
1619 __isl_give isl_set *isl_set_set_tuple_id(
1620 __isl_take isl_set *set, __isl_take isl_id *id);
1621 __isl_give isl_set *isl_set_reset_tuple_id(
1622 __isl_take isl_set *set);
1623 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1624 __isl_give isl_id *isl_set_get_tuple_id(
1625 __isl_keep isl_set *set);
1626 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1627 __isl_take isl_basic_set *set, const char *s);
1628 __isl_give isl_set *isl_set_set_tuple_name(
1629 __isl_take isl_set *set, const char *s);
1630 const char *isl_basic_set_get_tuple_name(
1631 __isl_keep isl_basic_set *bset);
1632 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1633 const char *isl_set_get_tuple_name(
1634 __isl_keep isl_set *set);
1636 #include <isl/map.h>
1637 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1638 __isl_take isl_basic_map *bmap,
1639 enum isl_dim_type type, __isl_take isl_id *id);
1640 __isl_give isl_map *isl_map_set_tuple_id(
1641 __isl_take isl_map *map, enum isl_dim_type type,
1642 __isl_take isl_id *id);
1643 __isl_give isl_map *isl_map_reset_tuple_id(
1644 __isl_take isl_map *map, enum isl_dim_type type);
1645 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1646 enum isl_dim_type type);
1647 __isl_give isl_id *isl_map_get_tuple_id(
1648 __isl_keep isl_map *map, enum isl_dim_type type);
1649 __isl_give isl_map *isl_map_set_tuple_name(
1650 __isl_take isl_map *map,
1651 enum isl_dim_type type, const char *s);
1652 const char *isl_basic_map_get_tuple_name(
1653 __isl_keep isl_basic_map *bmap,
1654 enum isl_dim_type type);
1655 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1656 __isl_take isl_basic_map *bmap,
1657 enum isl_dim_type type, const char *s);
1658 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1659 enum isl_dim_type type);
1660 const char *isl_map_get_tuple_name(
1661 __isl_keep isl_map *map,
1662 enum isl_dim_type type);
1664 #include <isl/val.h>
1665 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1666 __isl_take isl_multi_val *mv,
1667 enum isl_dim_type type, __isl_take isl_id *id);
1668 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1669 __isl_take isl_multi_val *mv,
1670 enum isl_dim_type type);
1671 isl_bool isl_multi_val_has_tuple_id(
1672 __isl_keep isl_multi_val *mv,
1673 enum isl_dim_type type);
1674 __isl_give isl_id *isl_multi_val_get_tuple_id(
1675 __isl_keep isl_multi_val *mv,
1676 enum isl_dim_type type);
1677 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1678 __isl_take isl_multi_val *mv,
1679 enum isl_dim_type type, const char *s);
1680 const char *isl_multi_val_get_tuple_name(
1681 __isl_keep isl_multi_val *mv,
1682 enum isl_dim_type type);
1684 #include <isl/aff.h>
1685 __isl_give isl_aff *isl_aff_set_tuple_id(
1686 __isl_take isl_aff *aff,
1687 enum isl_dim_type type, __isl_take isl_id *id);
1688 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1689 __isl_take isl_multi_aff *maff,
1690 enum isl_dim_type type, __isl_take isl_id *id);
1691 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1692 __isl_take isl_pw_aff *pwaff,
1693 enum isl_dim_type type, __isl_take isl_id *id);
1694 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1695 __isl_take isl_pw_multi_aff *pma,
1696 enum isl_dim_type type, __isl_take isl_id *id);
1697 __isl_give isl_multi_union_pw_aff *
1698 isl_multi_union_pw_aff_set_tuple_id(
1699 __isl_take isl_multi_union_pw_aff *mupa,
1700 enum isl_dim_type type, __isl_take isl_id *id);
1701 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1702 __isl_take isl_multi_aff *ma,
1703 enum isl_dim_type type);
1704 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1705 __isl_take isl_pw_aff *pa,
1706 enum isl_dim_type type);
1707 __isl_give isl_multi_pw_aff *
1708 isl_multi_pw_aff_reset_tuple_id(
1709 __isl_take isl_multi_pw_aff *mpa,
1710 enum isl_dim_type type);
1711 __isl_give isl_pw_multi_aff *
1712 isl_pw_multi_aff_reset_tuple_id(
1713 __isl_take isl_pw_multi_aff *pma,
1714 enum isl_dim_type type);
1715 __isl_give isl_multi_union_pw_aff *
1716 isl_multi_union_pw_aff_reset_tuple_id(
1717 __isl_take isl_multi_union_pw_aff *mupa,
1718 enum isl_dim_type type);
1719 isl_bool isl_multi_aff_has_tuple_id(
1720 __isl_keep isl_multi_aff *ma,
1721 enum isl_dim_type type);
1722 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1723 __isl_keep isl_multi_aff *ma,
1724 enum isl_dim_type type);
1725 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1726 enum isl_dim_type type);
1727 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1728 __isl_keep isl_pw_aff *pa,
1729 enum isl_dim_type type);
1730 isl_bool isl_pw_multi_aff_has_tuple_id(
1731 __isl_keep isl_pw_multi_aff *pma,
1732 enum isl_dim_type type);
1733 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1734 __isl_keep isl_pw_multi_aff *pma,
1735 enum isl_dim_type type);
1736 isl_bool isl_multi_pw_aff_has_tuple_id(
1737 __isl_keep isl_multi_pw_aff *mpa,
1738 enum isl_dim_type type);
1739 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1740 __isl_keep isl_multi_pw_aff *mpa,
1741 enum isl_dim_type type);
1742 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1743 __isl_keep isl_multi_union_pw_aff *mupa,
1744 enum isl_dim_type type);
1745 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1746 __isl_keep isl_multi_union_pw_aff *mupa,
1747 enum isl_dim_type type);
1748 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1749 __isl_take isl_multi_aff *maff,
1750 enum isl_dim_type type, const char *s);
1751 __isl_give isl_multi_pw_aff *
1752 isl_multi_pw_aff_set_tuple_name(
1753 __isl_take isl_multi_pw_aff *mpa,
1754 enum isl_dim_type type, const char *s);
1755 __isl_give isl_multi_union_pw_aff *
1756 isl_multi_union_pw_aff_set_tuple_name(
1757 __isl_take isl_multi_union_pw_aff *mupa,
1758 enum isl_dim_type type, const char *s);
1759 const char *isl_multi_aff_get_tuple_name(
1760 __isl_keep isl_multi_aff *multi,
1761 enum isl_dim_type type);
1762 isl_bool isl_pw_multi_aff_has_tuple_name(
1763 __isl_keep isl_pw_multi_aff *pma,
1764 enum isl_dim_type type);
1765 const char *isl_pw_multi_aff_get_tuple_name(
1766 __isl_keep isl_pw_multi_aff *pma,
1767 enum isl_dim_type type);
1768 const char *isl_multi_union_pw_aff_get_tuple_name(
1769 __isl_keep isl_multi_union_pw_aff *mupa,
1770 enum isl_dim_type type);
1772 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1773 or C<isl_dim_set>. As with C<isl_space_get_name>,
1774 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1776 Binary operations require the corresponding spaces of their arguments
1777 to have the same name.
1779 To keep the names of all parameters and tuples, but reset the user pointers
1780 of all the corresponding identifiers, use the following function.
1782 #include <isl/space.h>
1783 __isl_give isl_space *isl_space_reset_user(
1784 __isl_take isl_space *space);
1786 #include <isl/set.h>
1787 __isl_give isl_set *isl_set_reset_user(
1788 __isl_take isl_set *set);
1790 #include <isl/map.h>
1791 __isl_give isl_map *isl_map_reset_user(
1792 __isl_take isl_map *map);
1794 #include <isl/union_set.h>
1795 __isl_give isl_union_set *isl_union_set_reset_user(
1796 __isl_take isl_union_set *uset);
1798 #include <isl/union_map.h>
1799 __isl_give isl_union_map *isl_union_map_reset_user(
1800 __isl_take isl_union_map *umap);
1803 __isl_give isl_multi_id *isl_multi_id_reset_user(
1804 __isl_take isl_multi_id *mi);
1806 #include <isl/val.h>
1807 __isl_give isl_multi_val *isl_multi_val_reset_user(
1808 __isl_take isl_multi_val *mv);
1810 #include <isl/aff.h>
1811 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1812 __isl_take isl_multi_aff *ma);
1813 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1814 __isl_take isl_pw_aff *pa);
1815 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1816 __isl_take isl_multi_pw_aff *mpa);
1817 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1818 __isl_take isl_pw_multi_aff *pma);
1819 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1820 __isl_take isl_union_pw_aff *upa);
1821 __isl_give isl_multi_union_pw_aff *
1822 isl_multi_union_pw_aff_reset_user(
1823 __isl_take isl_multi_union_pw_aff *mupa);
1824 __isl_give isl_union_pw_multi_aff *
1825 isl_union_pw_multi_aff_reset_user(
1826 __isl_take isl_union_pw_multi_aff *upma);
1828 #include <isl/polynomial.h>
1829 __isl_give isl_pw_qpolynomial *
1830 isl_pw_qpolynomial_reset_user(
1831 __isl_take isl_pw_qpolynomial *pwqp);
1832 __isl_give isl_union_pw_qpolynomial *
1833 isl_union_pw_qpolynomial_reset_user(
1834 __isl_take isl_union_pw_qpolynomial *upwqp);
1835 __isl_give isl_pw_qpolynomial_fold *
1836 isl_pw_qpolynomial_fold_reset_user(
1837 __isl_take isl_pw_qpolynomial_fold *pwf);
1838 __isl_give isl_union_pw_qpolynomial_fold *
1839 isl_union_pw_qpolynomial_fold_reset_user(
1840 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1842 Spaces can be nested. In particular, the domain of a set or
1843 the domain or range of a relation can be a nested relation.
1844 This process is also called I<wrapping>.
1845 The functions for detecting, constructing and deconstructing
1846 such nested spaces can be found in the wrapping properties
1847 of L</"Unary Properties">, the wrapping operations
1848 of L</"Unary Operations"> and the Cartesian product operations
1849 of L</"Basic Operations">.
1851 Spaces can be created from other spaces
1852 using the functions described in L</"Unary Operations">
1853 and L</"Binary Operations">.
1857 A local space is essentially a space with
1858 zero or more existentially quantified variables.
1859 The local space of various objects can be obtained
1860 using the following functions.
1862 #include <isl/constraint.h>
1863 __isl_give isl_local_space *isl_constraint_get_local_space(
1864 __isl_keep isl_constraint *constraint);
1866 #include <isl/set.h>
1867 __isl_give isl_local_space *isl_basic_set_get_local_space(
1868 __isl_keep isl_basic_set *bset);
1870 #include <isl/map.h>
1871 __isl_give isl_local_space *isl_basic_map_get_local_space(
1872 __isl_keep isl_basic_map *bmap);
1874 #include <isl/aff.h>
1875 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1876 __isl_keep isl_aff *aff);
1877 __isl_give isl_local_space *isl_aff_get_local_space(
1878 __isl_keep isl_aff *aff);
1880 A new local space can be created from a space using
1882 #include <isl/local_space.h>
1883 __isl_give isl_local_space *isl_local_space_from_space(
1884 __isl_take isl_space *space);
1886 They can be inspected, modified, copied and freed using the following functions.
1888 #include <isl/local_space.h>
1889 isl_bool isl_local_space_is_params(
1890 __isl_keep isl_local_space *ls);
1891 isl_bool isl_local_space_is_set(
1892 __isl_keep isl_local_space *ls);
1893 __isl_give isl_space *isl_local_space_get_space(
1894 __isl_keep isl_local_space *ls);
1895 __isl_give isl_aff *isl_local_space_get_div(
1896 __isl_keep isl_local_space *ls, int pos);
1897 __isl_give isl_local_space *isl_local_space_copy(
1898 __isl_keep isl_local_space *ls);
1899 __isl_null isl_local_space *isl_local_space_free(
1900 __isl_take isl_local_space *ls);
1902 Note that C<isl_local_space_get_div> can only be used on local spaces
1905 Two local spaces can be compared using
1907 isl_bool isl_local_space_is_equal(
1908 __isl_keep isl_local_space *ls1,
1909 __isl_keep isl_local_space *ls2);
1911 Local spaces can be created from other local spaces
1912 using the functions described in L</"Unary Operations">
1913 and L</"Binary Operations">.
1915 =head2 Creating New Sets and Relations
1917 C<isl> has functions for creating some standard sets and relations.
1921 =item * Empty sets and relations
1923 __isl_give isl_basic_set *isl_basic_set_empty(
1924 __isl_take isl_space *space);
1925 __isl_give isl_basic_map *isl_basic_map_empty(
1926 __isl_take isl_space *space);
1927 __isl_give isl_set *isl_set_empty(
1928 __isl_take isl_space *space);
1929 __isl_give isl_map *isl_map_empty(
1930 __isl_take isl_space *space);
1931 __isl_give isl_union_set *isl_union_set_empty_ctx(
1933 __isl_give isl_union_set *isl_union_set_empty_space(
1934 __isl_take isl_space *space);
1935 __isl_give isl_union_set *isl_union_set_empty(
1936 __isl_take isl_space *space);
1937 __isl_give isl_union_map *isl_union_map_empty_ctx(
1939 __isl_give isl_union_map *isl_union_map_empty_space(
1940 __isl_take isl_space *space);
1941 __isl_give isl_union_map *isl_union_map_empty(
1942 __isl_take isl_space *space);
1944 For C<isl_union_set>s and C<isl_union_map>s, the space
1945 is only used to specify the parameters.
1946 C<isl_union_set_empty> is an alternative name for
1947 C<isl_union_set_empty_space>.
1948 Similarly for the other pair of functions.
1950 =item * Universe sets and relations
1952 __isl_give isl_basic_set *isl_basic_set_universe(
1953 __isl_take isl_space *space);
1954 __isl_give isl_basic_map *isl_basic_map_universe(
1955 __isl_take isl_space *space);
1956 __isl_give isl_set *isl_set_universe(
1957 __isl_take isl_space *space);
1958 __isl_give isl_map *isl_map_universe(
1959 __isl_take isl_space *space);
1960 __isl_give isl_union_set *isl_union_set_universe(
1961 __isl_take isl_union_set *uset);
1962 __isl_give isl_union_map *isl_union_map_universe(
1963 __isl_take isl_union_map *umap);
1965 The sets and relations constructed by the functions above
1966 contain all integer values, while those constructed by the
1967 functions below only contain non-negative values.
1969 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1970 __isl_take isl_space *space);
1971 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1972 __isl_take isl_space *space);
1973 __isl_give isl_set *isl_set_nat_universe(
1974 __isl_take isl_space *space);
1975 __isl_give isl_map *isl_map_nat_universe(
1976 __isl_take isl_space *space);
1978 =item * Identity relations
1980 __isl_give isl_basic_map *isl_basic_map_identity(
1981 __isl_take isl_space *space);
1982 __isl_give isl_map *isl_map_identity(
1983 __isl_take isl_space *space);
1985 The number of input and output dimensions in C<space> needs
1988 =item * Lexicographic order
1990 __isl_give isl_map *isl_map_lex_lt(
1991 __isl_take isl_space *set_space);
1992 __isl_give isl_map *isl_map_lex_le(
1993 __isl_take isl_space *set_space);
1994 __isl_give isl_map *isl_map_lex_gt(
1995 __isl_take isl_space *set_space);
1996 __isl_give isl_map *isl_map_lex_ge(
1997 __isl_take isl_space *set_space);
1998 __isl_give isl_map *isl_map_lex_lt_first(
1999 __isl_take isl_space *space, unsigned n);
2000 __isl_give isl_map *isl_map_lex_le_first(
2001 __isl_take isl_space *space, unsigned n);
2002 __isl_give isl_map *isl_map_lex_gt_first(
2003 __isl_take isl_space *space, unsigned n);
2004 __isl_give isl_map *isl_map_lex_ge_first(
2005 __isl_take isl_space *space, unsigned n);
2007 The first four functions take a space for a B<set>
2008 and return relations that express that the elements in the domain
2009 are lexicographically less
2010 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
2011 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
2012 than the elements in the range.
2013 The last four functions take a space for a map
2014 and return relations that express that the first C<n> dimensions
2015 in the domain are lexicographically less
2016 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
2017 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
2018 than the first C<n> dimensions in the range.
2022 A basic set or relation can be converted to a set or relation
2023 using the following functions.
2025 __isl_give isl_set *isl_set_from_basic_set(
2026 __isl_take isl_basic_set *bset);
2027 __isl_give isl_map *isl_map_from_basic_map(
2028 __isl_take isl_basic_map *bmap);
2030 Sets and relations can be converted to union sets and relations
2031 using the following functions.
2033 __isl_give isl_union_set *isl_union_set_from_basic_set(
2034 __isl_take isl_basic_set *bset);
2035 __isl_give isl_union_map *isl_union_map_from_basic_map(
2036 __isl_take isl_basic_map *bmap);
2037 __isl_give isl_union_set *isl_union_set_from_set(
2038 __isl_take isl_set *set);
2039 __isl_give isl_union_map *isl_union_map_from_map(
2040 __isl_take isl_map *map);
2042 The inverse conversions below can only be used if the input
2043 union set or relation is known to contain elements in exactly one
2046 #include <isl/union_set.h>
2047 isl_bool isl_union_set_isa_set(
2048 __isl_keep isl_union_set *uset);
2049 __isl_give isl_set *isl_set_from_union_set(
2050 __isl_take isl_union_set *uset);
2052 #include <isl/union_map.h>
2053 isl_bool isl_union_map_isa_map(
2054 __isl_keep isl_union_map *umap);
2055 __isl_give isl_map *isl_map_from_union_map(
2056 __isl_take isl_union_map *umap);
2058 Sets and relations can be copied and freed again using the following
2061 __isl_give isl_basic_set *isl_basic_set_copy(
2062 __isl_keep isl_basic_set *bset);
2063 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
2064 __isl_give isl_union_set *isl_union_set_copy(
2065 __isl_keep isl_union_set *uset);
2066 __isl_give isl_basic_map *isl_basic_map_copy(
2067 __isl_keep isl_basic_map *bmap);
2068 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
2069 __isl_give isl_union_map *isl_union_map_copy(
2070 __isl_keep isl_union_map *umap);
2071 __isl_null isl_basic_set *isl_basic_set_free(
2072 __isl_take isl_basic_set *bset);
2073 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
2074 __isl_null isl_union_set *isl_union_set_free(
2075 __isl_take isl_union_set *uset);
2076 __isl_null isl_basic_map *isl_basic_map_free(
2077 __isl_take isl_basic_map *bmap);
2078 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
2079 __isl_null isl_union_map *isl_union_map_free(
2080 __isl_take isl_union_map *umap);
2082 Other sets and relations can be constructed by starting
2083 from a universe set or relation, adding equality and/or
2084 inequality constraints and then projecting out the
2085 existentially quantified variables, if any.
2086 Constraints can be constructed, manipulated and
2087 added to (or removed from) (basic) sets and relations
2088 using the following functions.
2090 #include <isl/constraint.h>
2091 __isl_give isl_constraint *isl_constraint_alloc_equality(
2092 __isl_take isl_local_space *ls);
2093 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2094 __isl_take isl_local_space *ls);
2095 __isl_give isl_constraint *isl_constraint_set_constant_si(
2096 __isl_take isl_constraint *constraint, int v);
2097 __isl_give isl_constraint *isl_constraint_set_constant_val(
2098 __isl_take isl_constraint *constraint,
2099 __isl_take isl_val *v);
2100 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2101 __isl_take isl_constraint *constraint,
2102 enum isl_dim_type type, int pos, int v);
2103 __isl_give isl_constraint *
2104 isl_constraint_set_coefficient_val(
2105 __isl_take isl_constraint *constraint,
2106 enum isl_dim_type type, int pos,
2107 __isl_take isl_val *v);
2108 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2109 __isl_take isl_basic_map *bmap,
2110 __isl_take isl_constraint *constraint);
2111 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2112 __isl_take isl_basic_set *bset,
2113 __isl_take isl_constraint *constraint);
2114 __isl_give isl_map *isl_map_add_constraint(
2115 __isl_take isl_map *map,
2116 __isl_take isl_constraint *constraint);
2117 __isl_give isl_set *isl_set_add_constraint(
2118 __isl_take isl_set *set,
2119 __isl_take isl_constraint *constraint);
2121 For example, to create a set containing the even integers
2122 between 10 and 42, you could use the following code.
2125 isl_local_space *ls;
2127 isl_basic_set *bset;
2129 space = isl_space_set_alloc(ctx, 0, 2);
2130 bset = isl_basic_set_universe(isl_space_copy(space));
2131 ls = isl_local_space_from_space(space);
2133 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2134 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2135 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2136 bset = isl_basic_set_add_constraint(bset, c);
2138 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2139 c = isl_constraint_set_constant_si(c, -10);
2140 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2141 bset = isl_basic_set_add_constraint(bset, c);
2143 c = isl_constraint_alloc_inequality(ls);
2144 c = isl_constraint_set_constant_si(c, 42);
2145 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2146 bset = isl_basic_set_add_constraint(bset, c);
2148 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2150 However, this is considered to be a fairly low-level approach.
2151 It is more appropriate to construct a (basic) set by means
2152 of affine expressions (defined below in L</"Functions">).
2153 For example, the same set could be constructed as follows.
2159 isl_basic_set *bset;
2161 space = isl_space_unit(ctx);
2162 space = isl_space_add_unnamed_tuple_ui(space, 1);
2163 ma = isl_multi_aff_identity_on_domain_space(
2164 isl_space_copy(space));
2165 var = isl_multi_aff_get_at(ma, 0);
2166 v = isl_val_int_from_si(ctx, 10);
2167 cst = isl_aff_val_on_domain_space(isl_space_copy(space), v);
2168 bset = isl_aff_ge_basic_set(isl_aff_copy(var), cst);
2170 v = isl_val_int_from_si(ctx, 42);
2171 cst = isl_aff_val_on_domain_space(space, v);
2172 bset = isl_basic_set_intersect(bset,
2173 isl_aff_le_basic_set(var, cst));
2175 two = isl_val_int_from_si(ctx, 2);
2176 ma = isl_multi_aff_scale_val(ma, isl_val_copy(two));
2177 bset = isl_basic_set_preimage_multi_aff(bset,
2178 isl_multi_aff_copy(ma));
2179 ma = isl_multi_aff_scale_down_val(ma, isl_val_copy(two));
2180 ma = isl_multi_aff_scale_down_val(ma, two);
2181 bset = isl_basic_set_preimage_multi_aff(bset, ma);
2183 Alternatively, the set can be parsed from a string representation.
2185 isl_basic_set *bset;
2186 bset = isl_basic_set_read_from_str(ctx,
2187 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2189 A basic set or relation can also be constructed from two matrices
2190 describing the equalities and the inequalities.
2192 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2193 __isl_take isl_space *space,
2194 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2195 enum isl_dim_type c1,
2196 enum isl_dim_type c2, enum isl_dim_type c3,
2197 enum isl_dim_type c4);
2198 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2199 __isl_take isl_space *space,
2200 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2201 enum isl_dim_type c1,
2202 enum isl_dim_type c2, enum isl_dim_type c3,
2203 enum isl_dim_type c4, enum isl_dim_type c5);
2205 The C<isl_dim_type> arguments indicate the order in which
2206 different kinds of variables appear in the input matrices
2207 and should be a permutation of C<isl_dim_cst> (the constant term),
2208 C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div> for sets and
2209 of C<isl_dim_cst>, C<isl_dim_param>,
2210 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2212 A (basic or union) set or relation can also be constructed from a
2213 (union) (piecewise) (multiple) affine expression
2214 or a list of affine expressions
2215 (See L</"Functions">), provided these affine expressions do not
2218 #include <isl/set.h>
2219 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2220 __isl_take isl_multi_aff *ma);
2221 __isl_give isl_set *isl_set_from_multi_aff(
2222 __isl_take isl_multi_aff *ma);
2224 #include <isl/map.h>
2225 __isl_give isl_basic_map *isl_basic_map_from_aff(
2226 __isl_take isl_aff *aff);
2227 __isl_give isl_map *isl_map_from_aff(
2228 __isl_take isl_aff *aff);
2229 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2230 __isl_take isl_space *domain_space,
2231 __isl_take isl_aff_list *list);
2232 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2233 __isl_take isl_multi_aff *maff)
2234 __isl_give isl_map *isl_map_from_multi_aff(
2235 __isl_take isl_multi_aff *maff)
2237 #include <isl/aff.h>
2238 __isl_give isl_set *isl_set_from_pw_aff(
2239 __isl_take isl_pw_aff *pwaff);
2240 __isl_give isl_map *isl_map_from_pw_aff(
2241 __isl_take isl_pw_aff *pwaff);
2242 __isl_give isl_set *isl_set_from_pw_multi_aff(
2243 __isl_take isl_pw_multi_aff *pma);
2244 __isl_give isl_map *isl_map_from_pw_multi_aff(
2245 __isl_take isl_pw_multi_aff *pma);
2246 __isl_give isl_set *isl_set_from_multi_pw_aff(
2247 __isl_take isl_multi_pw_aff *mpa);
2248 __isl_give isl_map *isl_map_from_multi_pw_aff(
2249 __isl_take isl_multi_pw_aff *mpa);
2250 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2251 __isl_take isl_union_pw_aff *upa);
2252 __isl_give isl_union_map *
2253 isl_union_map_from_union_pw_multi_aff(
2254 __isl_take isl_union_pw_multi_aff *upma);
2255 __isl_give isl_union_map *
2256 isl_union_map_from_multi_union_pw_aff(
2257 __isl_take isl_multi_union_pw_aff *mupa);
2259 The C<domain_space> argument describes the domain of the resulting
2260 basic relation. It is required because the C<list> may consist
2261 of zero affine expressions.
2262 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2263 is not allowed to be zero-dimensional. The domain of the result
2264 is the shared domain of the union piecewise affine elements.
2266 =head2 Inspecting Sets and Relations
2268 Usually, the user should not have to care about the actual constraints
2269 of the sets and maps, but should instead apply the abstract operations
2270 explained in the following sections.
2271 Occasionally, however, it may be required to inspect the individual
2272 coefficients of the constraints. This section explains how to do so.
2273 In these cases, it may also be useful to have C<isl> compute
2274 an explicit representation of the existentially quantified variables.
2276 __isl_give isl_set *isl_set_compute_divs(
2277 __isl_take isl_set *set);
2278 __isl_give isl_map *isl_map_compute_divs(
2279 __isl_take isl_map *map);
2280 __isl_give isl_union_set *isl_union_set_compute_divs(
2281 __isl_take isl_union_set *uset);
2282 __isl_give isl_union_map *isl_union_map_compute_divs(
2283 __isl_take isl_union_map *umap);
2285 This explicit representation defines the existentially quantified
2286 variables as integer divisions of the other variables, possibly
2287 including earlier existentially quantified variables.
2288 An explicitly represented existentially quantified variable therefore
2289 has a unique value when the values of the other variables are known.
2291 Alternatively, the existentially quantified variables can be removed
2292 using the following functions, which compute an overapproximation.
2294 #include <isl/set.h>
2295 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2296 __isl_take isl_basic_set *bset);
2297 __isl_give isl_set *isl_set_remove_divs(
2298 __isl_take isl_set *set);
2300 #include <isl/map.h>
2301 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2302 __isl_take isl_basic_map *bmap);
2303 __isl_give isl_map *isl_map_remove_divs(
2304 __isl_take isl_map *map);
2306 #include <isl/union_set.h>
2307 __isl_give isl_union_set *isl_union_set_remove_divs(
2308 __isl_take isl_union_set *bset);
2310 #include <isl/union_map.h>
2311 __isl_give isl_union_map *isl_union_map_remove_divs(
2312 __isl_take isl_union_map *bmap);
2314 It is also possible to only remove those divs that are defined
2315 in terms of a given range of dimensions or only those for which
2316 no explicit representation is known.
2318 __isl_give isl_basic_set *
2319 isl_basic_set_remove_divs_involving_dims(
2320 __isl_take isl_basic_set *bset,
2321 enum isl_dim_type type,
2322 unsigned first, unsigned n);
2323 __isl_give isl_basic_map *
2324 isl_basic_map_remove_divs_involving_dims(
2325 __isl_take isl_basic_map *bmap,
2326 enum isl_dim_type type,
2327 unsigned first, unsigned n);
2328 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2329 __isl_take isl_set *set, enum isl_dim_type type,
2330 unsigned first, unsigned n);
2331 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2332 __isl_take isl_map *map, enum isl_dim_type type,
2333 unsigned first, unsigned n);
2335 __isl_give isl_basic_set *
2336 isl_basic_set_remove_unknown_divs(
2337 __isl_take isl_basic_set *bset);
2338 __isl_give isl_set *isl_set_remove_unknown_divs(
2339 __isl_take isl_set *set);
2340 __isl_give isl_map *isl_map_remove_unknown_divs(
2341 __isl_take isl_map *map);
2343 To iterate over all the sets or maps in a union set or map, use
2345 #include <isl/union_set.h>
2346 isl_stat isl_union_set_foreach_set(
2347 __isl_keep isl_union_set *uset,
2348 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2350 isl_bool isl_union_set_every_set(
2351 __isl_keep isl_union_set *uset,
2352 isl_bool (*test)(__isl_keep isl_set *set,
2356 #include <isl/union_map.h>
2357 isl_stat isl_union_map_foreach_map(
2358 __isl_keep isl_union_map *umap,
2359 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2361 isl_bool isl_union_map_every_map(
2362 __isl_keep isl_union_map *umap,
2363 isl_bool (*test)(__isl_keep isl_map *map,
2367 These functions call the callback function once for each
2368 (pair of) space(s) for which there are elements in the input.
2369 The argument to the callback contains all elements in the input
2370 with that (pair of) space(s).
2371 The C<isl_union_set_every_set> and
2372 C<isl_union_map_every_map> variants check whether each
2373 call to the callback returns true and stops checking as soon as one
2374 of these calls returns false.
2376 The number of sets or maps in a union set or map can be obtained
2379 isl_size isl_union_set_n_set(__isl_keep isl_union_set *uset);
2380 isl_size isl_union_map_n_map(__isl_keep isl_union_map *umap);
2382 To extract the set or map in a given space from a union, use
2384 __isl_give isl_set *isl_union_set_extract_set(
2385 __isl_keep isl_union_set *uset,
2386 __isl_take isl_space *space);
2387 __isl_give isl_map *isl_union_map_extract_map(
2388 __isl_keep isl_union_map *umap,
2389 __isl_take isl_space *space);
2391 To iterate over all the basic sets or maps in a set or map, use
2393 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2394 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2397 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2398 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2402 The callback function C<fn> should return C<isl_stat_ok> if successful and
2403 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2404 occurs, the above functions will return C<isl_stat_error>.
2406 It should be noted that C<isl> does not guarantee that
2407 the basic sets or maps passed to C<fn> are disjoint.
2408 If this is required, then the user should call one of
2409 the following functions first.
2411 __isl_give isl_set *isl_set_make_disjoint(
2412 __isl_take isl_set *set);
2413 __isl_give isl_map *isl_map_make_disjoint(
2414 __isl_take isl_map *map);
2416 The number of basic sets in a set can be obtained
2417 or the number of basic maps in a map can be obtained
2420 #include <isl/set.h>
2421 isl_size isl_set_n_basic_set(__isl_keep isl_set *set);
2423 #include <isl/map.h>
2424 isl_size isl_map_n_basic_map(__isl_keep isl_map *map);
2426 It is also possible to obtain a list of (basic) sets from a set
2427 or union set, a list of basic maps from a map and a list of maps from a union
2430 #include <isl/set.h>
2431 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2432 __isl_keep isl_set *set);
2434 #include <isl/union_set.h>
2435 __isl_give isl_basic_set_list *
2436 isl_union_set_get_basic_set_list(
2437 __isl_keep isl_union_set *uset);
2438 __isl_give isl_set_list *isl_union_set_get_set_list(
2439 __isl_keep isl_union_set *uset);
2441 #include <isl/map.h>
2442 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2443 __isl_keep isl_map *map);
2445 #include <isl/union_map.h>
2446 __isl_give isl_map_list *isl_union_map_get_map_list(
2447 __isl_keep isl_union_map *umap);
2449 The returned list can be manipulated using the functions in L<"Lists">.
2451 To iterate over the constraints of a basic set or map, use
2453 #include <isl/constraint.h>
2455 isl_size isl_basic_set_n_constraint(
2456 __isl_keep isl_basic_set *bset);
2457 isl_stat isl_basic_set_foreach_constraint(
2458 __isl_keep isl_basic_set *bset,
2459 isl_stat (*fn)(__isl_take isl_constraint *c,
2462 isl_size isl_basic_map_n_constraint(
2463 __isl_keep isl_basic_map *bmap);
2464 isl_stat isl_basic_map_foreach_constraint(
2465 __isl_keep isl_basic_map *bmap,
2466 isl_stat (*fn)(__isl_take isl_constraint *c,
2469 __isl_null isl_constraint *isl_constraint_free(
2470 __isl_take isl_constraint *c);
2472 Again, the callback function C<fn> should return C<isl_stat_ok>
2474 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2475 occurs, the above functions will return C<isl_stat_error>.
2476 The constraint C<c> represents either an equality or an inequality.
2477 Use the following function to find out whether a constraint
2478 represents an equality. If not, it represents an inequality.
2480 isl_bool isl_constraint_is_equality(
2481 __isl_keep isl_constraint *constraint);
2483 It is also possible to obtain a list of constraints from a basic
2486 #include <isl/constraint.h>
2487 __isl_give isl_constraint_list *
2488 isl_basic_map_get_constraint_list(
2489 __isl_keep isl_basic_map *bmap);
2490 __isl_give isl_constraint_list *
2491 isl_basic_set_get_constraint_list(
2492 __isl_keep isl_basic_set *bset);
2494 These functions require that all existentially quantified variables
2495 have an explicit representation.
2496 The returned list can be manipulated using the functions in L<"Lists">.
2498 The coefficients of the constraints can be inspected using
2499 the following functions.
2501 isl_bool isl_constraint_is_lower_bound(
2502 __isl_keep isl_constraint *constraint,
2503 enum isl_dim_type type, unsigned pos);
2504 isl_bool isl_constraint_is_upper_bound(
2505 __isl_keep isl_constraint *constraint,
2506 enum isl_dim_type type, unsigned pos);
2507 __isl_give isl_val *isl_constraint_get_constant_val(
2508 __isl_keep isl_constraint *constraint);
2509 __isl_give isl_val *isl_constraint_get_coefficient_val(
2510 __isl_keep isl_constraint *constraint,
2511 enum isl_dim_type type, int pos);
2513 The explicit representations of the existentially quantified
2514 variables can be inspected using the following function.
2515 Note that the user is only allowed to use this function
2516 if the inspected set or map is the result of a call
2517 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2518 The existentially quantified variable is equal to the floor
2519 of the returned affine expression. The affine expression
2520 itself can be inspected using the functions in
2523 __isl_give isl_aff *isl_constraint_get_div(
2524 __isl_keep isl_constraint *constraint, int pos);
2526 To obtain the constraints of a basic set or map in matrix
2527 form, use the following functions.
2529 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2530 __isl_keep isl_basic_set *bset,
2531 enum isl_dim_type c1, enum isl_dim_type c2,
2532 enum isl_dim_type c3, enum isl_dim_type c4);
2533 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2534 __isl_keep isl_basic_set *bset,
2535 enum isl_dim_type c1, enum isl_dim_type c2,
2536 enum isl_dim_type c3, enum isl_dim_type c4);
2537 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2538 __isl_keep isl_basic_map *bmap,
2539 enum isl_dim_type c1,
2540 enum isl_dim_type c2, enum isl_dim_type c3,
2541 enum isl_dim_type c4, enum isl_dim_type c5);
2542 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2543 __isl_keep isl_basic_map *bmap,
2544 enum isl_dim_type c1,
2545 enum isl_dim_type c2, enum isl_dim_type c3,
2546 enum isl_dim_type c4, enum isl_dim_type c5);
2548 The C<isl_dim_type> arguments dictate the order in which
2549 different kinds of variables appear in the resulting matrix.
2550 For set inputs, they should be a permutation of
2551 C<isl_dim_cst> (the constant term), C<isl_dim_param>, C<isl_dim_set> and
2553 For map inputs, they should be a permutation of
2554 C<isl_dim_cst>, C<isl_dim_param>,
2555 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2559 Points are elements of a set. They can be used to construct
2560 simple sets (boxes) or they can be used to represent the
2561 individual elements of a set.
2562 The zero point (the origin) can be created using
2564 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2566 The coordinates of a point can be inspected, set and changed
2569 #include <isl/point.h>
2570 __isl_give isl_multi_val *isl_point_get_multi_val(
2571 __isl_keep isl_point *pnt);
2572 __isl_give isl_val *isl_point_get_coordinate_val(
2573 __isl_keep isl_point *pnt,
2574 enum isl_dim_type type, int pos);
2575 __isl_give isl_point *isl_point_set_coordinate_val(
2576 __isl_take isl_point *pnt,
2577 enum isl_dim_type type, int pos,
2578 __isl_take isl_val *v);
2580 __isl_give isl_point *isl_point_add_ui(
2581 __isl_take isl_point *pnt,
2582 enum isl_dim_type type, int pos, unsigned val);
2583 __isl_give isl_point *isl_point_sub_ui(
2584 __isl_take isl_point *pnt,
2585 enum isl_dim_type type, int pos, unsigned val);
2587 Points can be copied or freed using
2589 __isl_give isl_point *isl_point_copy(
2590 __isl_keep isl_point *pnt);
2591 __isl_null isl_point *isl_point_free(
2592 __isl_take isl_point *pnt);
2594 A singleton set can be created from a point using
2596 __isl_give isl_basic_set *isl_basic_set_from_point(
2597 __isl_take isl_point *pnt);
2598 __isl_give isl_set *isl_set_from_point(
2599 __isl_take isl_point *pnt);
2600 __isl_give isl_union_set *isl_union_set_from_point(
2601 __isl_take isl_point *pnt);
2603 and a box can be created from two opposite extremal points using
2605 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2606 __isl_take isl_point *pnt1,
2607 __isl_take isl_point *pnt2);
2608 __isl_give isl_set *isl_set_box_from_points(
2609 __isl_take isl_point *pnt1,
2610 __isl_take isl_point *pnt2);
2612 All elements of a B<bounded> (union) set can be enumerated using
2613 the following functions.
2615 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2616 isl_stat (*fn)(__isl_take isl_point *pnt,
2619 isl_stat isl_union_set_foreach_point(
2620 __isl_keep isl_union_set *uset,
2621 isl_stat (*fn)(__isl_take isl_point *pnt,
2625 The function C<fn> is called for each integer point in
2626 C<set> with as second argument the last argument of
2627 the C<isl_set_foreach_point> call. The function C<fn>
2628 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2629 In the latter case, C<isl_set_foreach_point> will stop
2630 enumerating and return C<isl_stat_error> as well.
2631 If the enumeration is performed successfully and to completion,
2632 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2634 To obtain a single point of a (basic or union) set, use
2636 __isl_give isl_point *isl_basic_set_sample_point(
2637 __isl_take isl_basic_set *bset);
2638 __isl_give isl_point *isl_set_sample_point(
2639 __isl_take isl_set *set);
2640 __isl_give isl_point *isl_union_set_sample_point(
2641 __isl_take isl_union_set *uset);
2643 If C<set> does not contain any (integer) points, then the
2644 resulting point will be ``void'', a property that can be
2647 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2651 Besides sets and relation, C<isl> also supports various types of functions.
2652 Each of these types is derived from the value type (see L</"Values">)
2653 or from one of two primitive function types
2654 through the application of zero or more type constructors.
2655 As a special case, a multiple expression can also be derived
2656 from an identifier (see L</"Identifiers">) although the result
2657 is not really a function.
2658 We first describe the primitive type and then we describe
2659 the types derived from these primitive types.
2661 =head3 Primitive Functions
2663 C<isl> support two primitive function types, quasi-affine
2664 expressions and quasipolynomials.
2665 A quasi-affine expression is defined either over a parameter
2666 space or over a set and is composed of integer constants,
2667 parameters and set variables, addition, subtraction and
2668 integer division by an integer constant.
2669 For example, the quasi-affine expression
2671 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2673 maps C<x> to C<2*floor((4 n + x)/9>.
2674 A quasipolynomial is a polynomial expression in quasi-affine
2675 expression. That is, it additionally allows for multiplication.
2676 Note, though, that it is not allowed to construct an integer
2677 division of an expression involving multiplications.
2678 Here is an example of a quasipolynomial that is not
2679 quasi-affine expression
2681 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2683 Note that the external representations of quasi-affine expressions
2684 and quasipolynomials are different. Quasi-affine expressions
2685 use a notation with square brackets just like binary relations,
2686 while quasipolynomials do not. This might change at some point.
2688 If a primitive function is defined over a parameter space,
2689 then the space of the function itself is that of a set.
2690 If it is defined over a set, then the space of the function
2691 is that of a relation. In both cases, the set space (or
2692 the output space) is single-dimensional, anonymous and unstructured.
2693 To create functions with multiple dimensions or with other kinds
2694 of set or output spaces, use multiple expressions
2695 (see L</"Multiple Expressions">).
2699 =item * Quasi-affine Expressions
2701 Besides the expressions described above, a quasi-affine
2702 expression can also be set to NaN. Such expressions
2703 typically represent a failure to represent a result
2704 as a quasi-affine expression.
2706 The zero quasi affine expression or the quasi affine expression
2707 that is equal to a given value, parameter or
2708 a specified dimension on a given domain can be created using
2710 #include <isl/aff.h>
2711 __isl_give isl_aff *isl_aff_zero_on_domain_space(
2712 __isl_take isl_space *space);
2713 __isl_give isl_aff *isl_aff_zero_on_domain(
2714 __isl_take isl_local_space *ls);
2715 __isl_give isl_aff *isl_aff_val_on_domain_space(
2716 __isl_take isl_space *space,
2717 __isl_take isl_val *val);
2718 __isl_give isl_aff *isl_aff_val_on_domain(
2719 __isl_take isl_local_space *ls,
2720 __isl_take isl_val *val);
2721 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2722 __isl_take isl_space *space,
2723 __isl_take isl_id *id);
2724 __isl_give isl_aff *isl_aff_var_on_domain(
2725 __isl_take isl_local_space *ls,
2726 enum isl_dim_type type, unsigned pos);
2727 __isl_give isl_aff *isl_aff_nan_on_domain(
2728 __isl_take isl_local_space *ls);
2730 The space passed to C<isl_aff_param_on_domain_space_id>
2731 is required to have a parameter with the given identifier.
2733 Quasi affine expressions can be copied and freed using
2735 #include <isl/aff.h>
2736 __isl_give isl_aff *isl_aff_copy(
2737 __isl_keep isl_aff *aff);
2738 __isl_null isl_aff *isl_aff_free(
2739 __isl_take isl_aff *aff);
2741 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2742 using the following function. The constraint is required to have
2743 a non-zero coefficient for the specified dimension.
2745 #include <isl/constraint.h>
2746 __isl_give isl_aff *isl_constraint_get_bound(
2747 __isl_keep isl_constraint *constraint,
2748 enum isl_dim_type type, int pos);
2750 The entire affine expression of the constraint can also be extracted
2751 using the following function.
2753 #include <isl/constraint.h>
2754 __isl_give isl_aff *isl_constraint_get_aff(
2755 __isl_keep isl_constraint *constraint);
2757 Conversely, an equality constraint equating
2758 the affine expression to zero or an inequality constraint enforcing
2759 the affine expression to be non-negative, can be constructed using
2761 __isl_give isl_constraint *isl_equality_from_aff(
2762 __isl_take isl_aff *aff);
2763 __isl_give isl_constraint *isl_inequality_from_aff(
2764 __isl_take isl_aff *aff);
2766 The coefficients and the integer divisions of an affine expression
2767 can be inspected using the following functions.
2769 #include <isl/aff.h>
2770 __isl_give isl_val *isl_aff_get_constant_val(
2771 __isl_keep isl_aff *aff);
2772 __isl_give isl_val *isl_aff_get_coefficient_val(
2773 __isl_keep isl_aff *aff,
2774 enum isl_dim_type type, int pos);
2775 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2776 enum isl_dim_type type, int pos);
2777 __isl_give isl_val *isl_aff_get_denominator_val(
2778 __isl_keep isl_aff *aff);
2779 __isl_give isl_aff *isl_aff_get_div(
2780 __isl_keep isl_aff *aff, int pos);
2782 They can be modified using the following functions.
2784 #include <isl/aff.h>
2785 __isl_give isl_aff *isl_aff_set_constant_si(
2786 __isl_take isl_aff *aff, int v);
2787 __isl_give isl_aff *isl_aff_set_constant_val(
2788 __isl_take isl_aff *aff, __isl_take isl_val *v);
2789 __isl_give isl_aff *isl_aff_set_coefficient_si(
2790 __isl_take isl_aff *aff,
2791 enum isl_dim_type type, int pos, int v);
2792 __isl_give isl_aff *isl_aff_set_coefficient_val(
2793 __isl_take isl_aff *aff,
2794 enum isl_dim_type type, int pos,
2795 __isl_take isl_val *v);
2797 __isl_give isl_aff *isl_aff_add_constant_si(
2798 __isl_take isl_aff *aff, int v);
2799 __isl_give isl_aff *isl_aff_add_constant_val(
2800 __isl_take isl_aff *aff, __isl_take isl_val *v);
2801 __isl_give isl_aff *isl_aff_add_constant_num_si(
2802 __isl_take isl_aff *aff, int v);
2803 __isl_give isl_aff *isl_aff_add_coefficient_si(
2804 __isl_take isl_aff *aff,
2805 enum isl_dim_type type, int pos, int v);
2806 __isl_give isl_aff *isl_aff_add_coefficient_val(
2807 __isl_take isl_aff *aff,
2808 enum isl_dim_type type, int pos,
2809 __isl_take isl_val *v);
2811 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2812 set the I<numerator> of the constant or coefficient, while
2813 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2814 the constant or coefficient as a whole.
2815 The C<add_constant> and C<add_coefficient> functions add an integer
2816 or rational value to
2817 the possibly rational constant or coefficient.
2818 The C<add_constant_num> functions add an integer value to
2821 =item * Quasipolynomials
2823 Some simple quasipolynomials can be created using the following functions.
2825 #include <isl/polynomial.h>
2826 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2827 __isl_take isl_space *domain);
2828 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2829 __isl_take isl_space *domain);
2830 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2831 __isl_take isl_space *domain);
2832 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2833 __isl_take isl_space *domain);
2834 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2835 __isl_take isl_space *domain);
2836 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2837 __isl_take isl_space *domain,
2838 __isl_take isl_val *val);
2839 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2840 __isl_take isl_space *domain,
2841 enum isl_dim_type type, unsigned pos);
2842 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2843 __isl_take isl_aff *aff);
2845 Recall that the space in which a quasipolynomial lives is a map space
2846 with a one-dimensional range. The C<domain> argument in some of
2847 the functions above corresponds to the domain of this map space.
2849 Quasipolynomials can be copied and freed again using the following
2852 #include <isl/polynomial.h>
2853 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2854 __isl_keep isl_qpolynomial *qp);
2855 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2856 __isl_take isl_qpolynomial *qp);
2858 The constant term of a quasipolynomial can be extracted using
2860 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2861 __isl_keep isl_qpolynomial *qp);
2863 To iterate over all terms in a quasipolynomial,
2866 isl_stat isl_qpolynomial_foreach_term(
2867 __isl_keep isl_qpolynomial *qp,
2868 isl_stat (*fn)(__isl_take isl_term *term,
2869 void *user), void *user);
2871 The terms themselves can be inspected and freed using
2874 isl_size isl_term_dim(__isl_keep isl_term *term,
2875 enum isl_dim_type type);
2876 __isl_give isl_val *isl_term_get_coefficient_val(
2877 __isl_keep isl_term *term);
2878 isl_size isl_term_get_exp(__isl_keep isl_term *term,
2879 enum isl_dim_type type, unsigned pos);
2880 __isl_give isl_aff *isl_term_get_div(
2881 __isl_keep isl_term *term, unsigned pos);
2882 __isl_null isl_term *isl_term_free(
2883 __isl_take isl_term *term);
2885 Each term is a product of parameters, set variables and
2886 integer divisions. The function C<isl_term_get_exp>
2887 returns the exponent of a given dimensions in the given term.
2893 A reduction represents a maximum or a minimum of its
2895 The only reduction type defined by C<isl> is
2896 C<isl_qpolynomial_fold>.
2898 There are currently no functions to directly create such
2899 objects, but they do appear in the piecewise quasipolynomial
2900 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2902 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2904 Reductions can be copied and freed using
2905 the following functions.
2907 #include <isl/polynomial.h>
2908 __isl_give isl_qpolynomial_fold *
2909 isl_qpolynomial_fold_copy(
2910 __isl_keep isl_qpolynomial_fold *fold);
2911 __isl_null isl_qpolynomial_fold *
2912 isl_qpolynomial_fold_free(
2913 __isl_take isl_qpolynomial_fold *fold);
2915 The type of a (union piecewise) reduction
2916 can be obtained using the following functions.
2918 #include <isl/polynomial.h>
2919 enum isl_fold isl_qpolynomial_fold_get_type(
2920 __isl_keep isl_qpolynomial_fold *fold);
2921 enum isl_fold isl_pw_qpolynomial_fold_get_type(
2922 __isl_keep isl_pw_qpolynomial_fold *pwf);
2923 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
2924 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2926 The type may be either C<isl_fold_min> or C<isl_fold_max>
2927 (or C<isl_fold_error> in case of error).
2929 To iterate over all quasipolynomials in a reduction, use
2931 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2932 __isl_keep isl_qpolynomial_fold *fold,
2933 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2934 void *user), void *user);
2936 =head3 Multiple Expressions
2938 A multiple expression represents a sequence of zero or
2939 more base expressions, all defined on the same domain space.
2940 The domain space of the multiple expression is the same
2941 as that of the base expressions, but the range space
2942 can be any space. In case the base expressions have
2943 a set space, the corresponding multiple expression
2944 also has a set space.
2945 Objects of the value or identifier type do not have an associated space.
2946 The space of a multiple value or
2947 multiple identifier is therefore always a set space.
2948 Similarly, the space of a multiple union piecewise
2949 affine expression is always a set space.
2950 If the base expressions are not total, then
2951 a corresponding zero-dimensional multiple expression may
2952 have an explicit domain that keeps track of the domain
2953 outside of any base expressions.
2955 The multiple expression types defined by C<isl>
2956 are C<isl_multi_val>, C<isl_multi_id>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2957 C<isl_multi_union_pw_aff>.
2959 A multiple expression with the value zero for
2960 each output (or set) dimension can be created
2961 using the following functions.
2963 #include <isl/val.h>
2964 __isl_give isl_multi_val *isl_multi_val_zero(
2965 __isl_take isl_space *space);
2967 #include <isl/aff.h>
2968 __isl_give isl_multi_aff *isl_multi_aff_zero(
2969 __isl_take isl_space *space);
2970 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2971 __isl_take isl_space *space);
2972 __isl_give isl_multi_union_pw_aff *
2973 isl_multi_union_pw_aff_zero(
2974 __isl_take isl_space *space);
2976 Since there is no canonical way of representing a zero
2977 value of type C<isl_union_pw_aff>, the space passed
2978 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2980 An identity function can be created using the following
2982 For the first group of functions, the space needs to be that of a set.
2983 For the second group,
2984 the space needs to be that of a relation
2985 with the same number of input and output dimensions.
2986 For the third group, the input function needs to live in a space
2987 with the same number of input and output dimensions and
2988 the identity function is created in that space.
2990 #include <isl/aff.h>
2991 __isl_give isl_multi_aff *
2992 isl_multi_aff_identity_on_domain_space(
2993 __isl_take isl_space *space);
2994 __isl_give isl_multi_pw_aff *
2995 isl_multi_pw_aff_identity_on_domain_space(
2996 __isl_take isl_space *space);
2997 __isl_give isl_multi_aff *isl_multi_aff_identity(
2998 __isl_take isl_space *space);
2999 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3000 __isl_take isl_space *space);
3001 __isl_give isl_multi_aff *
3002 isl_multi_aff_identity_multi_aff(
3003 __isl_take isl_multi_aff *ma);
3004 __isl_give isl_multi_pw_aff *
3005 isl_multi_pw_aff_identity_multi_pw_aff(
3006 __isl_take isl_multi_pw_aff *mpa);
3008 A function that performs a projection on a universe
3009 relation or set can be created using the following functions.
3010 See also the corresponding
3011 projection operations in L</"Unary Operations">.
3013 #include <isl/aff.h>
3014 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
3015 __isl_take isl_space *space);
3016 __isl_give isl_multi_aff *isl_multi_aff_range_map(
3017 __isl_take isl_space *space);
3018 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
3019 __isl_take isl_space *space,
3020 enum isl_dim_type type,
3021 unsigned first, unsigned n);
3023 A multiple expression can be created from a single
3024 base expression using the following functions.
3025 The space of the created multiple expression is the same
3026 as that of the base expression, except for
3027 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
3028 lives in a parameter space and the output lives
3029 in a single-dimensional set space.
3031 #include <isl/aff.h>
3032 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3033 __isl_take isl_aff *aff);
3034 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3035 __isl_take isl_pw_aff *pa);
3036 __isl_give isl_multi_union_pw_aff *
3037 isl_multi_union_pw_aff_from_union_pw_aff(
3038 __isl_take isl_union_pw_aff *upa);
3040 A multiple expression can be created from a list
3041 of base expression in a specified space.
3042 The domain of this space needs to be the same
3043 as the domains of the base expressions in the list.
3044 If the base expressions have a set space (or no associated space),
3045 then this space also needs to be a set space.
3048 __isl_give isl_multi_id *isl_multi_id_from_id_list(
3049 __isl_take isl_space *space,
3050 __isl_take isl_id_list *list);
3052 #include <isl/val.h>
3053 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3054 __isl_take isl_space *space,
3055 __isl_take isl_val_list *list);
3057 #include <isl/aff.h>
3058 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3059 __isl_take isl_space *space,
3060 __isl_take isl_aff_list *list);
3061 __isl_give isl_multi_pw_aff *
3062 isl_multi_pw_aff_from_pw_aff_list(
3063 __isl_take isl_space *space,
3064 __isl_take isl_pw_aff_list *list);
3065 __isl_give isl_multi_union_pw_aff *
3066 isl_multi_union_pw_aff_from_union_pw_aff_list(
3067 __isl_take isl_space *space,
3068 __isl_take isl_union_pw_aff_list *list);
3070 As a convenience, a multiple piecewise expression can
3071 also be created from a multiple expression.
3072 Each piecewise expression in the result has a single
3075 #include <isl/aff.h>
3076 __isl_give isl_multi_pw_aff *
3077 isl_multi_pw_aff_from_multi_aff(
3078 __isl_take isl_multi_aff *ma);
3080 Similarly, a multiple union expression can be
3081 created from a multiple expression.
3083 #include <isl/aff.h>
3084 __isl_give isl_multi_union_pw_aff *
3085 isl_multi_union_pw_aff_from_multi_aff(
3086 __isl_take isl_multi_aff *ma);
3087 __isl_give isl_multi_union_pw_aff *
3088 isl_multi_union_pw_aff_from_multi_pw_aff(
3089 __isl_take isl_multi_pw_aff *mpa);
3091 A multiple quasi-affine expression can be created from
3092 a multiple value with a given domain space using the following
3095 #include <isl/aff.h>
3096 __isl_give isl_multi_aff *
3097 isl_multi_aff_multi_val_on_space(
3098 __isl_take isl_space *space,
3099 __isl_take isl_multi_val *mv);
3102 a multiple union piecewise affine expression can be created from
3103 a multiple value with a given domain or
3104 a (piecewise) multiple affine expression with a given domain
3105 using the following functions.
3107 #include <isl/aff.h>
3108 __isl_give isl_multi_union_pw_aff *
3109 isl_multi_union_pw_aff_multi_val_on_domain(
3110 __isl_take isl_union_set *domain,
3111 __isl_take isl_multi_val *mv);
3112 __isl_give isl_multi_union_pw_aff *
3113 isl_multi_union_pw_aff_multi_aff_on_domain(
3114 __isl_take isl_union_set *domain,
3115 __isl_take isl_multi_aff *ma);
3116 __isl_give isl_multi_union_pw_aff *
3117 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
3118 __isl_take isl_union_set *domain,
3119 __isl_take isl_pw_multi_aff *pma);
3121 Multiple expressions can be copied and freed using
3122 the following functions.
3125 __isl_give isl_multi_id *isl_multi_id_copy(
3126 __isl_keep isl_multi_id *mi);
3127 __isl_null isl_multi_id *isl_multi_id_free(
3128 __isl_take isl_multi_id *mi);
3130 #include <isl/val.h>
3131 __isl_give isl_multi_val *isl_multi_val_copy(
3132 __isl_keep isl_multi_val *mv);
3133 __isl_null isl_multi_val *isl_multi_val_free(
3134 __isl_take isl_multi_val *mv);
3136 #include <isl/aff.h>
3137 __isl_give isl_multi_aff *isl_multi_aff_copy(
3138 __isl_keep isl_multi_aff *maff);
3139 __isl_null isl_multi_aff *isl_multi_aff_free(
3140 __isl_take isl_multi_aff *maff);
3141 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3142 __isl_keep isl_multi_pw_aff *mpa);
3143 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
3144 __isl_take isl_multi_pw_aff *mpa);
3145 __isl_give isl_multi_union_pw_aff *
3146 isl_multi_union_pw_aff_copy(
3147 __isl_keep isl_multi_union_pw_aff *mupa);
3148 __isl_null isl_multi_union_pw_aff *
3149 isl_multi_union_pw_aff_free(
3150 __isl_take isl_multi_union_pw_aff *mupa);
3152 The number of base expressions in a multiple
3153 expression can be obtained using the following functions.
3156 int isl_multi_id_size(__isl_keep isl_multi_id *mi);
3158 #include <isl/val.h>
3159 isl_size isl_multi_val_size(__isl_keep isl_multi_val *mv);
3161 #include <isl/aff.h>
3162 isl_size isl_multi_aff_size(
3163 __isl_keep isl_multi_aff *multi);
3164 isl_size isl_multi_pw_aff_size(
3165 __isl_keep isl_multi_pw_aff *mpa);
3166 isl_size isl_multi_union_pw_aff_size(
3167 __isl_keep isl_multi_union_pw_aff *mupa);
3169 The base expression at a given position of a multiple
3170 expression can be extracted using the following functions.
3173 __isl_give isl_id *isl_multi_id_get_at(
3174 __isl_keep isl_multi_id *mi, int pos);
3175 __isl_give isl_id *isl_multi_id_get_id(
3176 __isl_keep isl_multi_id *mi, int pos);
3178 #include <isl/val.h>
3179 __isl_give isl_val *isl_multi_val_get_at(
3180 __isl_keep isl_multi_val *mv, int pos);
3181 __isl_give isl_val *isl_multi_val_get_val(
3182 __isl_keep isl_multi_val *mv, int pos);
3184 #include <isl/aff.h>
3185 __isl_give isl_aff *isl_multi_aff_get_at(
3186 __isl_keep isl_multi_aff *ma, int pos);
3187 __isl_give isl_aff *isl_multi_aff_get_aff(
3188 __isl_keep isl_multi_aff *multi, int pos);
3189 __isl_give isl_pw_aff *isl_multi_pw_aff_get_at(
3190 __isl_keep isl_multi_pw_aff *mpa, int pos);
3191 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3192 __isl_keep isl_multi_pw_aff *mpa, int pos);
3193 __isl_give isl_union_pw_aff *
3194 isl_multi_union_pw_aff_get_at(
3195 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3196 __isl_give isl_union_pw_aff *
3197 isl_multi_union_pw_aff_get_union_pw_aff(
3198 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3200 C<isl_multi_id_get_id> is an alternative name for C<isl_multi_id_get_at>.
3201 Similarly for the other pairs of functions.
3203 The base expression can be replaced using the following functions.
3206 __isl_give isl_multi_id *isl_multi_id_set_at(
3207 __isl_take isl_multi_id *mi, int pos,
3208 __isl_take isl_id *id);
3209 __isl_give isl_multi_id *isl_multi_id_set_id(
3210 __isl_take isl_multi_id *mi, int pos,
3211 __isl_take isl_id *id);
3213 #include <isl/val.h>
3214 __isl_give isl_multi_val *isl_multi_val_set_at(
3215 __isl_take isl_multi_val *mv, int pos,
3216 __isl_take isl_val *val);
3217 __isl_give isl_multi_val *isl_multi_val_set_val(
3218 __isl_take isl_multi_val *mv, int pos,
3219 __isl_take isl_val *val);
3221 #include <isl/aff.h>
3222 __isl_give isl_multi_aff *isl_multi_aff_set_at(
3223 __isl_take isl_multi_aff *ma, int pos,
3224 __isl_take isl_aff *aff);
3225 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3226 __isl_take isl_multi_aff *multi, int pos,
3227 __isl_take isl_aff *aff);
3228 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_at(
3229 __isl_take isl_multi_pw_aff *mpa, int pos,
3230 __isl_take isl_pw_aff *pa);
3231 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_pw_aff(
3232 __isl_take isl_multi_pw_aff *mpa, int pos,
3233 __isl_take isl_pw_aff *pa);
3234 __isl_give isl_multi_union_pw_aff *
3235 isl_multi_union_pw_aff_set_at(
3236 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3237 __isl_take isl_union_pw_aff *upa);
3238 __isl_give isl_multi_union_pw_aff *
3239 isl_multi_union_pw_aff_set_union_pw_aff(
3240 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3241 __isl_take isl_union_pw_aff *upa);
3243 C<isl_multi_id_set_id> is an alternative name for C<isl_multi_id_set_at>.
3244 Similarly for the other pairs of functions.
3246 A list of all base expressions of a multiple
3247 expression can be extracted using the following functions.
3250 __isl_give isl_id_list *isl_multi_id_get_list(
3251 __isl_keep isl_multi_id *mi);
3253 #include <isl/val.h>
3254 __isl_give isl_val_list *isl_multi_val_get_list(
3255 __isl_keep isl_multi_val *mv);
3257 #include <isl/aff.h>
3258 __isl_give isl_aff_list *isl_multi_aff_get_list(
3259 __isl_keep isl_multi_aff *multi);
3260 __isl_give isl_pw_aff_list *isl_multi_pw_aff_get_list(
3261 __isl_keep isl_multi_pw_aff *mpa);
3262 __isl_give isl_union_pw_aff_list *
3263 isl_multi_union_pw_aff_list(
3264 __isl_keep isl_multi_union_pw_aff *mupa);
3266 The constant terms of the base expressions can be obtained using
3267 the following function.
3269 #include <isl/aff.h>
3270 __isl_give isl_multi_val *
3271 isl_multi_aff_get_constant_multi_val(
3272 __isl_keep isl_multi_aff *ma);
3274 As a convenience, a sequence of base expressions that have
3275 their domains in a given space can be extracted from a sequence
3276 of union expressions using the following function.
3278 #include <isl/aff.h>
3279 __isl_give isl_multi_pw_aff *
3280 isl_multi_union_pw_aff_extract_multi_pw_aff(
3281 __isl_keep isl_multi_union_pw_aff *mupa,
3282 __isl_take isl_space *space);
3284 Note that there is a difference between C<isl_multi_union_pw_aff>
3285 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3286 of unions of piecewise expressions, while the second is a union
3287 of piecewise sequences. In particular, multiple affine expressions
3288 in an C<isl_union_pw_multi_aff> may live in different spaces,
3289 while there is only a single multiple expression in
3290 an C<isl_multi_union_pw_aff>, which can therefore only live
3291 in a single space. This means that not every
3292 C<isl_union_pw_multi_aff> can be converted to
3293 an C<isl_multi_union_pw_aff>. Conversely, the elements
3294 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3295 while each multiple expression inside an C<isl_union_pw_multi_aff>
3296 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3297 of dimension greater than one may therefore not be exact.
3298 The following functions can
3299 be used to perform these conversions when they are possible.
3301 #include <isl/aff.h>
3302 __isl_give isl_multi_union_pw_aff *
3303 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3304 __isl_take isl_union_pw_multi_aff *upma);
3305 __isl_give isl_union_pw_multi_aff *
3306 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3307 __isl_take isl_multi_union_pw_aff *mupa);
3309 =head3 Piecewise Expressions
3311 A piecewise expression is an expression that is described
3312 using zero or more base expression defined over the same
3313 number of cells in the domain space of the base expressions.
3314 All base expressions are defined over the same
3315 domain space and the cells are disjoint.
3316 The space of a piecewise expression is the same as
3317 that of the base expressions.
3318 If the union of the cells is a strict subset of the domain
3319 space, then the value of the piecewise expression outside
3320 this union is different for types derived from quasi-affine
3321 expressions and those derived from quasipolynomials.
3322 Piecewise expressions derived from quasi-affine expressions
3323 are considered to be undefined outside the union of their cells.
3324 Piecewise expressions derived from quasipolynomials
3325 are considered to be zero outside the union of their cells.
3327 Piecewise quasipolynomials are mainly used by the C<barvinok>
3328 library for representing the number of elements in a parametric set or map.
3329 For example, the piecewise quasipolynomial
3331 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3333 represents the number of points in the map
3335 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3337 The piecewise expression types defined by C<isl>
3338 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3339 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3341 A piecewise expression with no cells can be created using
3342 the following functions.
3344 #include <isl/aff.h>
3345 __isl_give isl_pw_aff *isl_pw_aff_empty(
3346 __isl_take isl_space *space);
3347 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3348 __isl_take isl_space *space);
3350 A piecewise expression with a single universe cell can be
3351 created using the following functions.
3353 #include <isl/aff.h>
3354 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3355 __isl_take isl_aff *aff);
3356 __isl_give isl_pw_multi_aff *
3357 isl_pw_multi_aff_from_multi_aff(
3358 __isl_take isl_multi_aff *ma);
3360 #include <isl/polynomial.h>
3361 __isl_give isl_pw_qpolynomial *
3362 isl_pw_qpolynomial_from_qpolynomial(
3363 __isl_take isl_qpolynomial *qp);
3364 __isl_give isl_pw_qpolynomial_fold *
3365 isl_pw_qpolynomial_fold_from_qpolynomial_fold(
3366 __isl_take isl_qpolynomial_fold *fold);
3368 The inverse conversions below can only be used if the input
3369 expression is known to be defined over a single universe domain.
3371 #include <isl/aff.h>
3372 isl_bool isl_pw_aff_isa_aff(__isl_keep isl_pw_aff *pa);
3373 __isl_give isl_aff *isl_pw_aff_as_aff(
3374 __isl_take isl_pw_aff *pa);
3375 isl_bool isl_pw_multi_aff_isa_multi_aff(
3376 __isl_keep isl_pw_multi_aff *pma);
3377 __isl_give isl_multi_aff *isl_pw_multi_aff_as_multi_aff(
3378 __isl_take isl_pw_multi_aff *pma);
3380 #include <isl/polynomial.h>
3381 isl_bool isl_pw_qpolynomial_isa_qpolynomial(
3382 __isl_keep isl_pw_qpolynomial *pwqp);
3383 __isl_give isl_qpolynomial *
3384 isl_pw_qpolynomial_as_qpolynomial(
3385 __isl_take isl_pw_qpolynomial *pwqp);
3386 isl_bool isl_pw_qpolynomial_fold_isa_qpolynomial_fold(
3387 __isl_keep isl_pw_qpolynomial_fold *pwf);
3388 __isl_give isl_qpolynomial_fold *
3389 isl_pw_qpolynomial_fold_as_qpolynomial_fold(
3390 __isl_take isl_pw_qpolynomial_fold *pwf);
3392 A piecewise expression with a single specified cell can be
3393 created using the following functions.
3395 #include <isl/aff.h>
3396 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3397 __isl_take isl_set *set, __isl_take isl_aff *aff);
3398 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3399 __isl_take isl_set *set,
3400 __isl_take isl_multi_aff *maff);
3402 #include <isl/polynomial.h>
3403 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3404 __isl_take isl_set *set,
3405 __isl_take isl_qpolynomial *qp);
3407 The following convenience functions first create a base expression and
3408 then create a piecewise expression over a universe domain.
3410 #include <isl/aff.h>
3411 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3412 __isl_take isl_local_space *ls);
3413 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3414 __isl_take isl_local_space *ls,
3415 enum isl_dim_type type, unsigned pos);
3416 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3417 __isl_take isl_local_space *ls);
3418 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3419 __isl_take isl_space *space);
3420 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3421 __isl_take isl_space *space);
3422 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3423 __isl_take isl_space *space);
3424 __isl_give isl_pw_multi_aff *
3425 isl_pw_multi_aff_project_out_map(
3426 __isl_take isl_space *space,
3427 enum isl_dim_type type,
3428 unsigned first, unsigned n);
3430 #include <isl/polynomial.h>
3431 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3432 __isl_take isl_space *space);
3434 The following convenience functions first create a base expression and
3435 then create a piecewise expression over a given domain.
3437 #include <isl/aff.h>
3438 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3439 __isl_take isl_set *domain,
3440 __isl_take isl_val *v);
3441 __isl_give isl_pw_multi_aff *
3442 isl_pw_multi_aff_multi_val_on_domain(
3443 __isl_take isl_set *domain,
3444 __isl_take isl_multi_val *mv);
3445 __isl_give isl_pw_aff *isl_pw_aff_param_on_domain_id(
3446 __isl_take isl_set *domain,
3447 __isl_take isl_id *id);
3449 As a convenience, a piecewise multiple expression can
3450 also be created from a piecewise expression.
3451 Each multiple expression in the result is derived
3452 from the corresponding base expression.
3454 #include <isl/aff.h>
3455 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3456 __isl_take isl_pw_aff *pa);
3458 Similarly, a piecewise quasipolynomial can be
3459 created from a piecewise quasi-affine expression using
3460 the following function.
3462 #include <isl/polynomial.h>
3463 __isl_give isl_pw_qpolynomial *
3464 isl_pw_qpolynomial_from_pw_aff(
3465 __isl_take isl_pw_aff *pwaff);
3467 Piecewise expressions can be copied and freed using the following functions.
3469 #include <isl/aff.h>
3470 __isl_give isl_pw_aff *isl_pw_aff_copy(
3471 __isl_keep isl_pw_aff *pwaff);
3472 __isl_null isl_pw_aff *isl_pw_aff_free(
3473 __isl_take isl_pw_aff *pwaff);
3474 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3475 __isl_keep isl_pw_multi_aff *pma);
3476 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3477 __isl_take isl_pw_multi_aff *pma);
3479 #include <isl/polynomial.h>
3480 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3481 __isl_keep isl_pw_qpolynomial *pwqp);
3482 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3483 __isl_take isl_pw_qpolynomial *pwqp);
3484 __isl_give isl_pw_qpolynomial_fold *
3485 isl_pw_qpolynomial_fold_copy(
3486 __isl_keep isl_pw_qpolynomial_fold *pwf);
3487 __isl_null isl_pw_qpolynomial_fold *
3488 isl_pw_qpolynomial_fold_free(
3489 __isl_take isl_pw_qpolynomial_fold *pwf);
3491 To iterate over the different cells of a piecewise expression,
3492 use the following functions.
3494 #include <isl/aff.h>
3495 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3496 isl_size isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3497 isl_stat isl_pw_aff_foreach_piece(
3498 __isl_keep isl_pw_aff *pwaff,
3499 isl_stat (*fn)(__isl_take isl_set *set,
3500 __isl_take isl_aff *aff,
3501 void *user), void *user);
3502 isl_bool isl_pw_aff_every_piece(__isl_keep isl_pw_aff *pa,
3503 isl_bool (*test)(__isl_keep isl_set *set,
3504 __isl_keep isl_aff *aff, void *user),
3506 isl_size isl_pw_multi_aff_n_piece(
3507 __isl_keep isl_pw_multi_aff *pma);
3508 isl_stat isl_pw_multi_aff_foreach_piece(
3509 __isl_keep isl_pw_multi_aff *pma,
3510 isl_stat (*fn)(__isl_take isl_set *set,
3511 __isl_take isl_multi_aff *maff,
3512 void *user), void *user);
3513 isl_bool isl_pw_multi_aff_every_piece(
3514 __isl_keep isl_pw_multi_aff *pma,
3515 isl_bool (*test)(__isl_keep isl_set *set,
3516 __isl_keep isl_multi_aff *ma, void *user),
3519 #include <isl/polynomial.h>
3520 isl_size isl_pw_qpolynomial_n_piece(
3521 __isl_keep isl_pw_qpolynomial *pwqp);
3522 isl_stat isl_pw_qpolynomial_foreach_piece(
3523 __isl_keep isl_pw_qpolynomial *pwqp,
3524 isl_stat (*fn)(__isl_take isl_set *set,
3525 __isl_take isl_qpolynomial *qp,
3526 void *user), void *user);
3527 isl_bool isl_pw_qpolynomial_every_piece(
3528 __isl_keep isl_pw_qpolynomial *pwqp,
3529 isl_bool (*test)(__isl_keep isl_set *set,
3530 __isl_keep isl_qpolynomial *qp,
3531 void *user), void *user);
3532 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3533 __isl_keep isl_pw_qpolynomial *pwqp,
3534 isl_stat (*fn)(__isl_take isl_set *set,
3535 __isl_take isl_qpolynomial *qp,
3536 void *user), void *user);
3537 isl_size isl_pw_qpolynomial_fold_n_piece(
3538 __isl_keep isl_pw_qpolynomial_fold *pwf);
3539 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3540 __isl_keep isl_pw_qpolynomial_fold *pwf,
3541 isl_stat (*fn)(__isl_take isl_set *set,
3542 __isl_take isl_qpolynomial_fold *fold,
3543 void *user), void *user);
3544 isl_bool isl_pw_qpolynomial_fold_every_piece(
3545 __isl_keep isl_pw_qpolynomial_fold *pwf,
3546 isl_bool (*test)(__isl_keep isl_set *set,
3547 __isl_keep isl_qpolynomial_fold *fold,
3548 void *user), void *user);
3549 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3550 __isl_keep isl_pw_qpolynomial_fold *pwf,
3551 isl_stat (*fn)(__isl_take isl_set *set,
3552 __isl_take isl_qpolynomial_fold *fold,
3553 void *user), void *user);
3555 As usual, the function C<fn> should return C<isl_stat_ok> on success
3556 and C<isl_stat_error> on failure. The difference between
3557 C<isl_pw_qpolynomial_foreach_piece> and
3558 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3559 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3560 compute unique representations for all existentially quantified
3561 variables and then turn these existentially quantified variables
3562 into extra set variables, adapting the associated quasipolynomial
3563 accordingly. This means that the C<set> passed to C<fn>
3564 will not have any existentially quantified variables, but that
3565 the dimensions of the sets may be different for different
3566 invocations of C<fn>.
3567 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3568 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3569 The function C<isl_pw_aff_every_piece> and its variants
3570 check whether each call to the callback returns true and
3571 stop checking as soon as one of these calls returns false (or error).
3573 A piecewise expression consisting of the expressions at a given
3574 position of a piecewise multiple expression can be extracted
3575 using the following function.
3577 #include <isl/aff.h>
3578 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3579 __isl_keep isl_pw_multi_aff *pma, int pos);
3581 These expressions can be replaced using the following function.
3583 #include <isl/aff.h>
3584 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3585 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3586 __isl_take isl_pw_aff *pa);
3588 Note that there is a difference between C<isl_multi_pw_aff> and
3589 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3590 affine expressions, while the second is a piecewise sequence
3591 of affine expressions. In particular, each of the piecewise
3592 affine expressions in an C<isl_multi_pw_aff> may have a different
3593 domain, while all multiple expressions associated to a cell
3594 in an C<isl_pw_multi_aff> have the same domain.
3595 It is possible to convert between the two, but when converting
3596 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3597 of the result is the intersection of the domains of the input.
3598 The reverse conversion is exact.
3600 #include <isl/aff.h>
3601 __isl_give isl_pw_multi_aff *
3602 isl_pw_multi_aff_from_multi_pw_aff(
3603 __isl_take isl_multi_pw_aff *mpa);
3604 __isl_give isl_multi_pw_aff *
3605 isl_multi_pw_aff_from_pw_multi_aff(
3606 __isl_take isl_pw_multi_aff *pma);
3608 =head3 Union Expressions
3610 A union expression collects base expressions defined
3611 over different domains. The space of a union expression
3612 is that of the shared parameter space.
3614 The union expression types defined by C<isl>
3615 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3616 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3618 C<isl_union_pw_aff>,
3619 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3620 there can be at most one base expression for a given domain space.
3622 C<isl_union_pw_multi_aff>,
3623 there can be multiple such expressions for a given domain space,
3624 but the domains of these expressions need to be disjoint.
3626 An empty union expression can be created using the following functions.
3628 #include <isl/aff.h>
3629 __isl_give isl_union_pw_aff *
3630 isl_union_pw_aff_empty_ctx(
3632 __isl_give isl_union_pw_aff *
3633 isl_union_pw_aff_empty_space(
3634 __isl_take isl_space *space);
3635 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3636 __isl_take isl_space *space);
3637 __isl_give isl_union_pw_multi_aff *
3638 isl_union_pw_multi_aff_empty_ctx(
3640 __isl_give isl_union_pw_multi_aff *
3641 isl_union_pw_multi_aff_empty_space(
3642 __isl_take isl_space *space);
3643 __isl_give isl_union_pw_multi_aff *
3644 isl_union_pw_multi_aff_empty(
3645 __isl_take isl_space *space);
3647 #include <isl/polynomial.h>
3648 __isl_give isl_union_pw_qpolynomial *
3649 isl_union_pw_qpolynomial_zero_ctx(
3651 __isl_give isl_union_pw_qpolynomial *
3652 isl_union_pw_qpolynomial_zero_space(
3653 __isl_take isl_space *space);
3654 __isl_give isl_union_pw_qpolynomial *
3655 isl_union_pw_qpolynomial_zero(
3656 __isl_take isl_space *space);
3658 C<isl_union_pw_aff_empty> is an alternative name for
3659 C<isl_union_pw_aff_empty_space>.
3660 Similarly for the other pairs of functions.
3662 A union expression containing a single base expression
3663 can be created using the following functions.
3665 #include <isl/aff.h>
3666 __isl_give isl_union_pw_aff *
3667 isl_union_pw_aff_from_pw_aff(
3668 __isl_take isl_pw_aff *pa);
3669 __isl_give isl_union_pw_multi_aff *
3670 isl_union_pw_multi_aff_from_aff(
3671 __isl_take isl_aff *aff);
3672 __isl_give isl_union_pw_multi_aff *
3673 isl_union_pw_multi_aff_from_pw_multi_aff(
3674 __isl_take isl_pw_multi_aff *pma);
3676 #include <isl/polynomial.h>
3677 __isl_give isl_union_pw_qpolynomial *
3678 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3679 __isl_take isl_pw_qpolynomial *pwqp);
3681 The inverse conversions below can only be used if the input
3682 expression is known to live in exactly one space.
3684 #include <isl/aff.h>
3685 isl_bool isl_union_pw_multi_aff_isa_pw_multi_aff(
3686 __isl_keep isl_union_pw_multi_aff *upma);
3687 __isl_give isl_pw_multi_aff *
3688 isl_union_pw_multi_aff_as_pw_multi_aff(
3689 __isl_take isl_union_pw_multi_aff *upma);
3691 The following functions create a base expression on each
3692 of the sets in the union set and collect the results.
3694 #include <isl/aff.h>
3695 __isl_give isl_union_pw_multi_aff *
3696 isl_union_pw_multi_aff_from_union_pw_aff(
3697 __isl_take isl_union_pw_aff *upa);
3698 __isl_give isl_union_pw_aff *
3699 isl_union_pw_multi_aff_get_union_pw_aff(
3700 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3701 __isl_give isl_union_pw_aff *
3702 isl_union_pw_aff_val_on_domain(
3703 __isl_take isl_union_set *domain,
3704 __isl_take isl_val *v);
3705 __isl_give isl_union_pw_multi_aff *
3706 isl_union_pw_multi_aff_multi_val_on_domain(
3707 __isl_take isl_union_set *domain,
3708 __isl_take isl_multi_val *mv);
3709 __isl_give isl_union_pw_aff *
3710 isl_union_pw_aff_param_on_domain_id(
3711 __isl_take isl_union_set *domain,
3712 __isl_take isl_id *id);
3714 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3715 is the identifier of a parameter that may or may not already
3716 be present in C<domain>.
3718 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3720 expression on a given domain can be created using the following
3723 #include <isl/aff.h>
3724 __isl_give isl_union_pw_aff *
3725 isl_union_pw_aff_aff_on_domain(
3726 __isl_take isl_union_set *domain,
3727 __isl_take isl_aff *aff);
3728 __isl_give isl_union_pw_aff *
3729 isl_union_pw_aff_pw_aff_on_domain(
3730 __isl_take isl_union_set *domain,
3731 __isl_take isl_pw_aff *pa);
3733 A base expression can be added to a union expression using
3734 the following functions.
3736 #include <isl/aff.h>
3737 __isl_give isl_union_pw_aff *
3738 isl_union_pw_aff_add_pw_aff(
3739 __isl_take isl_union_pw_aff *upa,
3740 __isl_take isl_pw_aff *pa);
3741 __isl_give isl_union_pw_multi_aff *
3742 isl_union_pw_multi_aff_add_pw_multi_aff(
3743 __isl_take isl_union_pw_multi_aff *upma,
3744 __isl_take isl_pw_multi_aff *pma);
3746 #include <isl/polynomial.h>
3747 __isl_give isl_union_pw_qpolynomial *
3748 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3749 __isl_take isl_union_pw_qpolynomial *upwqp,
3750 __isl_take isl_pw_qpolynomial *pwqp);
3752 Union expressions can be copied and freed using
3753 the following functions.
3755 #include <isl/aff.h>
3756 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3757 __isl_keep isl_union_pw_aff *upa);
3758 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3759 __isl_take isl_union_pw_aff *upa);
3760 __isl_give isl_union_pw_multi_aff *
3761 isl_union_pw_multi_aff_copy(
3762 __isl_keep isl_union_pw_multi_aff *upma);
3763 __isl_null isl_union_pw_multi_aff *
3764 isl_union_pw_multi_aff_free(
3765 __isl_take isl_union_pw_multi_aff *upma);
3767 #include <isl/polynomial.h>
3768 __isl_give isl_union_pw_qpolynomial *
3769 isl_union_pw_qpolynomial_copy(
3770 __isl_keep isl_union_pw_qpolynomial *upwqp);
3771 __isl_null isl_union_pw_qpolynomial *
3772 isl_union_pw_qpolynomial_free(
3773 __isl_take isl_union_pw_qpolynomial *upwqp);
3774 __isl_give isl_union_pw_qpolynomial_fold *
3775 isl_union_pw_qpolynomial_fold_copy(
3776 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3777 __isl_null isl_union_pw_qpolynomial_fold *
3778 isl_union_pw_qpolynomial_fold_free(
3779 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3781 To iterate over the base expressions in a union expression,
3782 use the following functions.
3784 #include <isl/aff.h>
3785 isl_size isl_union_pw_aff_n_pw_aff(
3786 __isl_keep isl_union_pw_aff *upa);
3787 isl_stat isl_union_pw_aff_foreach_pw_aff(
3788 __isl_keep isl_union_pw_aff *upa,
3789 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3790 void *user), void *user);
3791 isl_bool isl_union_pw_aff_every_pw_aff(
3792 __isl_keep isl_union_pw_aff *upa,
3793 isl_bool (*test)(__isl_keep isl_pw_aff *pa,
3794 void *user), void *user);
3795 isl_size isl_union_pw_multi_aff_n_pw_multi_aff(
3796 __isl_keep isl_union_pw_multi_aff *upma);
3797 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3798 __isl_keep isl_union_pw_multi_aff *upma,
3799 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3800 void *user), void *user);
3801 isl_bool isl_union_pw_multi_aff_every_pw_multi_aff(
3802 __isl_keep isl_union_pw_multi_aff *upma,
3804 __isl_keep isl_pw_multi_aff *pma,
3805 void *user), void *user);
3807 #include <isl/polynomial.h>
3808 isl_size isl_union_pw_qpolynomial_n_pw_qpolynomial(
3809 __isl_keep isl_union_pw_qpolynomial *upwqp);
3810 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3811 __isl_keep isl_union_pw_qpolynomial *upwqp,
3812 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3813 void *user), void *user);
3814 isl_bool isl_union_pw_qpolynomial_every_pw_qpolynomial(
3815 __isl_keep isl_union_pw_qpolynomial *upwqp,
3817 __isl_keep isl_pw_qpolynomial *pwqp,
3818 void *user), void *user);
3819 isl_size isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3820 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3821 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3822 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3823 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3824 void *user), void *user);
3826 isl_union_pw_qpolynomial_fold_every_pw_qpolynomial_fold(
3827 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3829 __isl_keep isl_pw_qpolynomial_fold *pwf,
3830 void *user), void *user);
3832 To extract the base expression in a given space from a union, use
3833 the following functions.
3835 #include <isl/aff.h>
3836 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3837 __isl_keep isl_union_pw_aff *upa,
3838 __isl_take isl_space *space);
3839 __isl_give isl_pw_multi_aff *
3840 isl_union_pw_multi_aff_extract_pw_multi_aff(
3841 __isl_keep isl_union_pw_multi_aff *upma,
3842 __isl_take isl_space *space);
3844 #include <isl/polynomial.h>
3845 __isl_give isl_pw_qpolynomial *
3846 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3847 __isl_keep isl_union_pw_qpolynomial *upwqp,
3848 __isl_take isl_space *space);
3850 It is also possible to obtain a list of the base expressions using
3851 the following functions.
3853 #include <isl/aff.h>
3854 __isl_give isl_pw_aff_list *
3855 isl_union_pw_aff_get_pw_aff_list(
3856 __isl_keep isl_union_pw_aff *upa);
3857 __isl_give isl_pw_multi_aff_list *
3858 isl_union_pw_multi_aff_get_pw_multi_aff_list(
3859 __isl_keep isl_union_pw_multi_aff *upma);
3861 #include <isl/polynomial.h>
3862 __isl_give isl_pw_qpolynomial_list *
3863 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
3864 __isl_keep isl_union_pw_qpolynomial *upwqp);
3865 __isl_give isl_pw_qpolynomial_fold_list *
3866 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
3867 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3869 The returned list can be manipulated using the functions in L<"Lists">.
3871 =head2 Input and Output
3873 For set and relation,
3874 C<isl> supports its own input/output format, which is similar
3875 to the C<Omega> format, but also supports the C<PolyLib> format
3877 For other object types, typically only an C<isl> format is supported.
3879 =head3 C<isl> format
3881 The C<isl> format is similar to that of C<Omega>, but has a different
3882 syntax for describing the parameters and allows for the definition
3883 of an existentially quantified variable as the integer division
3884 of an affine expression.
3885 For example, the set of integers C<i> between C<0> and C<n>
3886 such that C<i % 10 <= 6> can be described as
3888 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3891 A set or relation can have several disjuncts, separated
3892 by the keyword C<or>. Each disjunct is either a conjunction
3893 of constraints or a projection (C<exists>) of a conjunction
3894 of constraints. The constraints are separated by the keyword
3897 =head3 C<PolyLib> format
3899 If the represented set is a union, then the first line
3900 contains a single number representing the number of disjuncts.
3901 Otherwise, a line containing the number C<1> is optional.
3903 Each disjunct is represented by a matrix of constraints.
3904 The first line contains two numbers representing
3905 the number of rows and columns,
3906 where the number of rows is equal to the number of constraints
3907 and the number of columns is equal to two plus the number of variables.
3908 The following lines contain the actual rows of the constraint matrix.
3909 In each row, the first column indicates whether the constraint
3910 is an equality (C<0>) or inequality (C<1>). The final column
3911 corresponds to the constant term.
3913 If the set is parametric, then the coefficients of the parameters
3914 appear in the last columns before the constant column.
3915 The coefficients of any existentially quantified variables appear
3916 between those of the set variables and those of the parameters.
3918 =head3 Extended C<PolyLib> format
3920 The extended C<PolyLib> format is nearly identical to the
3921 C<PolyLib> format. The only difference is that the line
3922 containing the number of rows and columns of a constraint matrix
3923 also contains four additional numbers:
3924 the number of output dimensions, the number of input dimensions,
3925 the number of local dimensions (i.e., the number of existentially
3926 quantified variables) and the number of parameters.
3927 For sets, the number of ``output'' dimensions is equal
3928 to the number of set dimensions, while the number of ``input''
3933 Objects can be read from input using the following functions.
3936 __isl_give isl_id *isl_id_read_from_str(isl_ctx *ctx,
3938 __isl_give isl_multi_id *isl_multi_id_read_from_str(
3939 isl_ctx *ctx, const char *str);
3941 #include <isl/val.h>
3942 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3944 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3945 isl_ctx *ctx, const char *str);
3947 #include <isl/set.h>
3948 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3949 isl_ctx *ctx, FILE *input);
3950 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3951 isl_ctx *ctx, const char *str);
3952 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3954 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3957 #include <isl/map.h>
3958 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3959 isl_ctx *ctx, FILE *input);
3960 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3961 isl_ctx *ctx, const char *str);
3962 __isl_give isl_map *isl_map_read_from_file(
3963 isl_ctx *ctx, FILE *input);
3964 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3967 #include <isl/union_set.h>
3968 __isl_give isl_union_set *isl_union_set_read_from_file(
3969 isl_ctx *ctx, FILE *input);
3970 __isl_give isl_union_set *isl_union_set_read_from_str(
3971 isl_ctx *ctx, const char *str);
3973 #include <isl/union_map.h>
3974 __isl_give isl_union_map *isl_union_map_read_from_file(
3975 isl_ctx *ctx, FILE *input);
3976 __isl_give isl_union_map *isl_union_map_read_from_str(
3977 isl_ctx *ctx, const char *str);
3979 #include <isl/aff.h>
3980 __isl_give isl_aff *isl_aff_read_from_str(
3981 isl_ctx *ctx, const char *str);
3982 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3983 isl_ctx *ctx, const char *str);
3984 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3985 isl_ctx *ctx, const char *str);
3986 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3987 isl_ctx *ctx, const char *str);
3988 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3989 isl_ctx *ctx, const char *str);
3990 __isl_give isl_union_pw_aff *
3991 isl_union_pw_aff_read_from_str(
3992 isl_ctx *ctx, const char *str);
3993 __isl_give isl_union_pw_multi_aff *
3994 isl_union_pw_multi_aff_read_from_str(
3995 isl_ctx *ctx, const char *str);
3996 __isl_give isl_multi_union_pw_aff *
3997 isl_multi_union_pw_aff_read_from_str(
3998 isl_ctx *ctx, const char *str);
4000 #include <isl/polynomial.h>
4001 __isl_give isl_union_pw_qpolynomial *
4002 isl_union_pw_qpolynomial_read_from_str(
4003 isl_ctx *ctx, const char *str);
4005 For sets and relations,
4006 the input format is autodetected and may be either the C<PolyLib> format
4007 or the C<isl> format.
4011 Before anything can be printed, an C<isl_printer> needs to
4014 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
4016 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
4017 __isl_null isl_printer *isl_printer_free(
4018 __isl_take isl_printer *printer);
4020 C<isl_printer_to_file> prints to the given file, while
4021 C<isl_printer_to_str> prints to a string that can be extracted
4022 using the following function.
4024 #include <isl/printer.h>
4025 __isl_give char *isl_printer_get_str(
4026 __isl_keep isl_printer *printer);
4028 The printer can be inspected using the following functions.
4030 FILE *isl_printer_get_file(
4031 __isl_keep isl_printer *printer);
4032 int isl_printer_get_output_format(
4033 __isl_keep isl_printer *p);
4034 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
4036 The behavior of the printer can be modified in various ways
4038 __isl_give isl_printer *isl_printer_set_output_format(
4039 __isl_take isl_printer *p, int output_format);
4040 __isl_give isl_printer *isl_printer_set_indent(
4041 __isl_take isl_printer *p, int indent);
4042 __isl_give isl_printer *isl_printer_set_indent_prefix(
4043 __isl_take isl_printer *p, const char *prefix);
4044 __isl_give isl_printer *isl_printer_indent(
4045 __isl_take isl_printer *p, int indent);
4046 __isl_give isl_printer *isl_printer_set_prefix(
4047 __isl_take isl_printer *p, const char *prefix);
4048 __isl_give isl_printer *isl_printer_set_suffix(
4049 __isl_take isl_printer *p, const char *suffix);
4050 __isl_give isl_printer *isl_printer_set_yaml_style(
4051 __isl_take isl_printer *p, int yaml_style);
4053 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
4054 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
4055 and defaults to C<ISL_FORMAT_ISL>.
4056 Each line in the output is prefixed by C<indent_prefix>,
4057 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
4058 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
4059 In the C<PolyLib> format output,
4060 the coefficients of the existentially quantified variables
4061 appear between those of the set variables and those
4063 The function C<isl_printer_indent> increases the indentation
4064 by the specified amount (which may be negative).
4065 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
4066 C<ISL_YAML_STYLE_FLOW> and when we are printing something
4069 To actually print something, use
4071 #include <isl/printer.h>
4072 __isl_give isl_printer *isl_printer_print_double(
4073 __isl_take isl_printer *p, double d);
4075 #include <isl/val.h>
4076 __isl_give isl_printer *isl_printer_print_val(
4077 __isl_take isl_printer *p, __isl_keep isl_val *v);
4079 #include <isl/set.h>
4080 __isl_give isl_printer *isl_printer_print_basic_set(
4081 __isl_take isl_printer *printer,
4082 __isl_keep isl_basic_set *bset);
4083 __isl_give isl_printer *isl_printer_print_set(
4084 __isl_take isl_printer *printer,
4085 __isl_keep isl_set *set);
4087 #include <isl/map.h>
4088 __isl_give isl_printer *isl_printer_print_basic_map(
4089 __isl_take isl_printer *printer,
4090 __isl_keep isl_basic_map *bmap);
4091 __isl_give isl_printer *isl_printer_print_map(
4092 __isl_take isl_printer *printer,
4093 __isl_keep isl_map *map);
4095 #include <isl/union_set.h>
4096 __isl_give isl_printer *isl_printer_print_union_set(
4097 __isl_take isl_printer *p,
4098 __isl_keep isl_union_set *uset);
4100 #include <isl/union_map.h>
4101 __isl_give isl_printer *isl_printer_print_union_map(
4102 __isl_take isl_printer *p,
4103 __isl_keep isl_union_map *umap);
4105 #include <isl/val.h>
4106 __isl_give isl_printer *isl_printer_print_multi_val(
4107 __isl_take isl_printer *p,
4108 __isl_keep isl_multi_val *mv);
4111 __isl_give isl_printer *isl_printer_print_multi_id(
4112 __isl_take isl_printer *p,
4113 __isl_keep isl_multi_id *mi);
4115 #include <isl/aff.h>
4116 __isl_give isl_printer *isl_printer_print_aff(
4117 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4118 __isl_give isl_printer *isl_printer_print_multi_aff(
4119 __isl_take isl_printer *p,
4120 __isl_keep isl_multi_aff *maff);
4121 __isl_give isl_printer *isl_printer_print_pw_aff(
4122 __isl_take isl_printer *p,
4123 __isl_keep isl_pw_aff *pwaff);
4124 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4125 __isl_take isl_printer *p,
4126 __isl_keep isl_pw_multi_aff *pma);
4127 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4128 __isl_take isl_printer *p,
4129 __isl_keep isl_multi_pw_aff *mpa);
4130 __isl_give isl_printer *isl_printer_print_union_pw_aff(
4131 __isl_take isl_printer *p,
4132 __isl_keep isl_union_pw_aff *upa);
4133 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4134 __isl_take isl_printer *p,
4135 __isl_keep isl_union_pw_multi_aff *upma);
4136 __isl_give isl_printer *
4137 isl_printer_print_multi_union_pw_aff(
4138 __isl_take isl_printer *p,
4139 __isl_keep isl_multi_union_pw_aff *mupa);
4141 #include <isl/polynomial.h>
4142 __isl_give isl_printer *isl_printer_print_qpolynomial(
4143 __isl_take isl_printer *p,
4144 __isl_keep isl_qpolynomial *qp);
4145 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4146 __isl_take isl_printer *p,
4147 __isl_keep isl_pw_qpolynomial *pwqp);
4148 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4149 __isl_take isl_printer *p,
4150 __isl_keep isl_union_pw_qpolynomial *upwqp);
4152 __isl_give isl_printer *
4153 isl_printer_print_pw_qpolynomial_fold(
4154 __isl_take isl_printer *p,
4155 __isl_keep isl_pw_qpolynomial_fold *pwf);
4156 __isl_give isl_printer *
4157 isl_printer_print_union_pw_qpolynomial_fold(
4158 __isl_take isl_printer *p,
4159 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4161 For C<isl_printer_print_qpolynomial>,
4162 C<isl_printer_print_pw_qpolynomial> and
4163 C<isl_printer_print_pw_qpolynomial_fold>,
4164 the output format of the printer
4165 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4166 For C<isl_printer_print_union_pw_qpolynomial> and
4167 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
4169 In case of printing in C<ISL_FORMAT_C>, the user may want
4170 to set the names of all dimensions first.
4172 C<isl> also provides limited support for printing YAML documents,
4173 just enough for the internal use for printing such documents.
4175 #include <isl/printer.h>
4176 __isl_give isl_printer *isl_printer_yaml_start_mapping(
4177 __isl_take isl_printer *p);
4178 __isl_give isl_printer *isl_printer_yaml_end_mapping(
4179 __isl_take isl_printer *p);
4180 __isl_give isl_printer *isl_printer_yaml_start_sequence(
4181 __isl_take isl_printer *p);
4182 __isl_give isl_printer *isl_printer_yaml_end_sequence(
4183 __isl_take isl_printer *p);
4184 __isl_give isl_printer *isl_printer_yaml_next(
4185 __isl_take isl_printer *p);
4187 A document is started by a call to either
4188 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4189 Anything printed to the printer after such a call belong to the
4190 first key of the mapping or the first element in the sequence.
4191 The function C<isl_printer_yaml_next> moves to the value if
4192 we are currently printing a mapping key, the next key if we
4193 are printing a value or the next element if we are printing
4194 an element in a sequence.
4195 Nested mappings and sequences are initiated by the same
4196 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4197 Each call to these functions needs to have a corresponding call to
4198 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
4200 When called on a file printer, the following function flushes
4201 the file. When called on a string printer, the buffer is cleared.
4203 __isl_give isl_printer *isl_printer_flush(
4204 __isl_take isl_printer *p);
4206 The following functions allow the user to attach
4207 notes to a printer in order to keep track of additional state.
4209 #include <isl/printer.h>
4210 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
4211 __isl_keep isl_id *id);
4212 __isl_give isl_id *isl_printer_get_note(
4213 __isl_keep isl_printer *p, __isl_take isl_id *id);
4214 __isl_give isl_printer *isl_printer_set_note(
4215 __isl_take isl_printer *p,
4216 __isl_take isl_id *id, __isl_take isl_id *note);
4218 C<isl_printer_set_note> associates the given note to the given
4219 identifier in the printer.
4220 C<isl_printer_get_note> retrieves a note associated to an
4222 C<isl_printer_has_note> checks if there is such a note.
4223 C<isl_printer_get_note> fails if the requested note does not exist.
4225 Alternatively, a string representation can be obtained
4226 directly using the following functions, which always print
4230 __isl_give char *isl_id_to_str(
4231 __isl_keep isl_id *id);
4232 __isl_give char *isl_multi_id_to_str(
4233 __isl_keep isl_multi_id *mi);
4235 #include <isl/space.h>
4236 __isl_give char *isl_space_to_str(
4237 __isl_keep isl_space *space);
4239 #include <isl/val.h>
4240 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
4241 __isl_give char *isl_multi_val_to_str(
4242 __isl_keep isl_multi_val *mv);
4244 #include <isl/set.h>
4245 __isl_give char *isl_basic_set_to_str(
4246 __isl_keep isl_basic_set *bset);
4247 __isl_give char *isl_set_to_str(
4248 __isl_keep isl_set *set);
4250 #include <isl/union_set.h>
4251 __isl_give char *isl_union_set_to_str(
4252 __isl_keep isl_union_set *uset);
4254 #include <isl/map.h>
4255 __isl_give char *isl_basic_map_to_str(
4256 __isl_keep isl_basic_map *bmap);
4257 __isl_give char *isl_map_to_str(
4258 __isl_keep isl_map *map);
4260 #include <isl/union_map.h>
4261 __isl_give char *isl_union_map_to_str(
4262 __isl_keep isl_union_map *umap);
4264 #include <isl/aff.h>
4265 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
4266 __isl_give char *isl_pw_aff_to_str(
4267 __isl_keep isl_pw_aff *pa);
4268 __isl_give char *isl_multi_aff_to_str(
4269 __isl_keep isl_multi_aff *ma);
4270 __isl_give char *isl_pw_multi_aff_to_str(
4271 __isl_keep isl_pw_multi_aff *pma);
4272 __isl_give char *isl_multi_pw_aff_to_str(
4273 __isl_keep isl_multi_pw_aff *mpa);
4274 __isl_give char *isl_union_pw_aff_to_str(
4275 __isl_keep isl_union_pw_aff *upa);
4276 __isl_give char *isl_union_pw_multi_aff_to_str(
4277 __isl_keep isl_union_pw_multi_aff *upma);
4278 __isl_give char *isl_multi_union_pw_aff_to_str(
4279 __isl_keep isl_multi_union_pw_aff *mupa);
4281 #include <isl/point.h>
4282 __isl_give char *isl_point_to_str(
4283 __isl_keep isl_point *pnt);
4285 #include <isl/polynomial.h>
4286 __isl_give char *isl_pw_qpolynomial_to_str(
4287 __isl_keep isl_pw_qpolynomial *pwqp);
4288 __isl_give char *isl_union_pw_qpolynomial_to_str(
4289 __isl_keep isl_union_pw_qpolynomial *upwqp);
4293 =head3 Unary Properties
4299 The following functions test whether the given set or relation
4300 contains any integer points. The ``plain'' variants do not perform
4301 any computations, but simply check if the given set or relation
4302 is already known to be empty.
4304 #include <isl/set.h>
4305 isl_bool isl_basic_set_plain_is_empty(
4306 __isl_keep isl_basic_set *bset);
4307 isl_bool isl_basic_set_is_empty(
4308 __isl_keep isl_basic_set *bset);
4309 isl_bool isl_set_plain_is_empty(
4310 __isl_keep isl_set *set);
4311 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
4313 #include <isl/union_set.h>
4314 isl_bool isl_union_set_is_empty(
4315 __isl_keep isl_union_set *uset);
4317 #include <isl/map.h>
4318 isl_bool isl_basic_map_plain_is_empty(
4319 __isl_keep isl_basic_map *bmap);
4320 isl_bool isl_basic_map_is_empty(
4321 __isl_keep isl_basic_map *bmap);
4322 isl_bool isl_map_plain_is_empty(
4323 __isl_keep isl_map *map);
4324 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
4326 #include <isl/union_map.h>
4327 isl_bool isl_union_map_plain_is_empty(
4328 __isl_keep isl_union_map *umap);
4329 isl_bool isl_union_map_is_empty(
4330 __isl_keep isl_union_map *umap);
4332 #include <isl/aff.h>
4333 isl_bool isl_union_pw_multi_aff_plain_is_empty(
4334 __isl_keep isl_union_pw_multi_aff *upma);
4336 =item * Universality
4338 isl_bool isl_basic_set_plain_is_universe(
4339 __isl_keep isl_basic_set *bset);
4340 isl_bool isl_basic_set_is_universe(
4341 __isl_keep isl_basic_set *bset);
4342 isl_bool isl_basic_map_plain_is_universe(
4343 __isl_keep isl_basic_map *bmap);
4344 isl_bool isl_basic_map_is_universe(
4345 __isl_keep isl_basic_map *bmap);
4346 isl_bool isl_set_plain_is_universe(
4347 __isl_keep isl_set *set);
4348 isl_bool isl_map_plain_is_universe(
4349 __isl_keep isl_map *map);
4351 =item * Single-valuedness
4353 #include <isl/set.h>
4354 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
4356 #include <isl/map.h>
4357 isl_bool isl_basic_map_is_single_valued(
4358 __isl_keep isl_basic_map *bmap);
4359 isl_bool isl_map_plain_is_single_valued(
4360 __isl_keep isl_map *map);
4361 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
4363 #include <isl/union_map.h>
4364 isl_bool isl_union_map_is_single_valued(
4365 __isl_keep isl_union_map *umap);
4369 isl_bool isl_map_plain_is_injective(
4370 __isl_keep isl_map *map);
4371 isl_bool isl_map_is_injective(
4372 __isl_keep isl_map *map);
4373 isl_bool isl_union_map_plain_is_injective(
4374 __isl_keep isl_union_map *umap);
4375 isl_bool isl_union_map_is_injective(
4376 __isl_keep isl_union_map *umap);
4380 isl_bool isl_map_is_bijective(
4381 __isl_keep isl_map *map);
4382 isl_bool isl_union_map_is_bijective(
4383 __isl_keep isl_union_map *umap);
4387 The following functions test whether the given relation
4388 only maps elements to themselves.
4390 #include <isl/map.h>
4391 isl_bool isl_map_is_identity(
4392 __isl_keep isl_map *map);
4394 #include <isl/union_map.h>
4395 isl_bool isl_union_map_is_identity(
4396 __isl_keep isl_union_map *umap);
4400 __isl_give isl_val *
4401 isl_basic_map_plain_get_val_if_fixed(
4402 __isl_keep isl_basic_map *bmap,
4403 enum isl_dim_type type, unsigned pos);
4404 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4405 __isl_keep isl_set *set,
4406 enum isl_dim_type type, unsigned pos);
4407 __isl_give isl_multi_val *
4408 isl_set_get_plain_multi_val_if_fixed(
4409 __isl_keep isl_set *set);
4410 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4411 __isl_keep isl_map *map,
4412 enum isl_dim_type type, unsigned pos);
4414 If the set or relation obviously lies on a hyperplane where the given dimension
4415 has a fixed value, then return that value.
4416 Otherwise return NaN.
4417 C<isl_set_get_plain_multi_val_if_fixed> collects the results over
4422 isl_stat isl_set_dim_residue_class_val(
4423 __isl_keep isl_set *set,
4424 int pos, __isl_give isl_val **modulo,
4425 __isl_give isl_val **residue);
4427 Check if the values of the given set dimension are equal to a fixed
4428 value modulo some integer value. If so, assign the modulo to C<*modulo>
4429 and the fixed value to C<*residue>. If the given dimension attains only
4430 a single value, then assign C<0> to C<*modulo> and the fixed value to
4432 If the dimension does not attain only a single value and if no modulo
4433 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4435 #include <isl/set.h>
4436 __isl_give isl_stride_info *isl_set_get_stride_info(
4437 __isl_keep isl_set *set, int pos);
4438 __isl_give isl_val *isl_set_get_stride(
4439 __isl_keep isl_set *set, int pos);
4441 #include <isl/map.h>
4442 __isl_give isl_stride_info *
4443 isl_map_get_range_stride_info(
4444 __isl_keep isl_map *map, int pos);
4446 Check if the values of the given set dimension are equal to
4447 some affine expression of the other dimensions (the offset)
4448 modulo some integer stride or
4449 check if the values of the given output dimensions are equal to
4450 some affine expression of the input dimensions (the offset)
4451 modulo some integer stride.
4452 If no more specific information can be found, then the stride
4453 is taken to be one and the offset is taken to be the zero expression.
4454 The function C<isl_set_get_stride> performs the same
4455 computation as C<isl_set_get_stride_info> but only returns the stride.
4456 For the other functions,
4457 the stride and offset can be extracted from the returned object
4458 using the following functions.
4460 #include <isl/stride_info.h>
4461 __isl_give isl_val *isl_stride_info_get_stride(
4462 __isl_keep isl_stride_info *si);
4463 __isl_give isl_aff *isl_stride_info_get_offset(
4464 __isl_keep isl_stride_info *si);
4466 The stride info object can be copied and released using the following
4469 #include <isl/stride_info.h>
4470 __isl_give isl_stride_info *isl_stride_info_copy(
4471 __isl_keep isl_stride_info *si);
4472 __isl_null isl_stride_info *isl_stride_info_free(
4473 __isl_take isl_stride_info *si);
4477 To check whether a function involves any local variables,
4478 i.e., integer divisions,
4479 the following functions can be used.
4481 #include <isl/set.h>
4482 isl_bool isl_set_involves_locals(
4483 __isl_keep isl_set *set);
4485 #include <isl/aff.h>
4486 isl_bool isl_aff_involves_locals(
4487 __isl_keep isl_aff *aff);
4488 isl_bool isl_multi_aff_involves_locals(
4489 __isl_keep isl_multi_aff *ma);
4490 isl_bool isl_pw_multi_aff_involves_locals(
4491 __isl_keep isl_pw_multi_aff *pma);
4492 isl_bool isl_union_pw_multi_aff_involves_locals(
4493 __isl_keep isl_union_pw_multi_aff *upma);
4495 To check whether the description of a set, relation or function depends
4496 on a parameter or one or more given dimensions,
4497 the following functions can be used.
4499 #include <isl/constraint.h>
4500 isl_bool isl_constraint_involves_dims(
4501 __isl_keep isl_constraint *constraint,
4502 enum isl_dim_type type, unsigned first, unsigned n);
4504 #include <isl/set.h>
4505 isl_bool isl_basic_set_involves_dims(
4506 __isl_keep isl_basic_set *bset,
4507 enum isl_dim_type type, unsigned first, unsigned n);
4508 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4509 enum isl_dim_type type, unsigned first, unsigned n);
4511 #include <isl/map.h>
4512 isl_bool isl_basic_map_involves_dims(
4513 __isl_keep isl_basic_map *bmap,
4514 enum isl_dim_type type, unsigned first, unsigned n);
4515 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4516 enum isl_dim_type type, unsigned first, unsigned n);
4518 #include <isl/union_map.h>
4519 isl_bool isl_union_map_involves_dims(
4520 __isl_keep isl_union_map *umap,
4521 enum isl_dim_type type, unsigned first, unsigned n);
4523 #include <isl/aff.h>
4524 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4525 enum isl_dim_type type, unsigned first, unsigned n);
4526 isl_bool isl_pw_aff_involves_param_id(
4527 __isl_keep isl_pw_aff *pa,
4528 __isl_keep isl_id *id);
4529 isl_bool isl_pw_aff_involves_dims(
4530 __isl_keep isl_pw_aff *pwaff,
4531 enum isl_dim_type type, unsigned first, unsigned n);
4532 isl_bool isl_multi_aff_involves_dims(
4533 __isl_keep isl_multi_aff *ma,
4534 enum isl_dim_type type, unsigned first, unsigned n);
4535 isl_bool isl_pw_multi_aff_involves_param_id(
4536 __isl_keep isl_pw_multi_aff *pma,
4537 __isl_keep isl_id *id);
4538 isl_bool isl_pw_multi_aff_involves_dims(
4539 __isl_keep isl_pw_multi_aff *pma,
4540 enum isl_dim_type type, unsigned first, unsigned n);
4541 isl_bool isl_multi_pw_aff_involves_dims(
4542 __isl_keep isl_multi_pw_aff *mpa,
4543 enum isl_dim_type type, unsigned first, unsigned n);
4544 isl_bool isl_multi_pw_aff_involves_param_id(
4545 __isl_keep isl_multi_pw_aff *mpa,
4546 __isl_keep isl_id *id);
4547 isl_bool isl_multi_pw_aff_involves_param_id_list(
4548 __isl_keep isl_multi_pw_aff *mpa,
4549 __isl_keep isl_id_list *list);
4551 #include <isl/polynomial.h>
4552 isl_bool isl_qpolynomial_involves_dims(
4553 __isl_keep isl_qpolynomial *qp,
4554 enum isl_dim_type type, unsigned first, unsigned n);
4555 isl_bool isl_pw_qpolynomial_involves_param_id(
4556 __isl_keep isl_pw_qpolynomial *pwqp,
4557 __isl_keep isl_id *id);
4558 isl_bool isl_pw_qpolynomial_fold_involves_param_id(
4559 __isl_keep isl_pw_qpolynomial_fold *pwf,
4560 __isl_keep isl_id *id);
4562 Similarly, the following functions can be used to check whether
4563 a given dimension is involved in any lower or upper bound.
4565 #include <isl/set.h>
4566 isl_bool isl_set_dim_has_any_lower_bound(
4567 __isl_keep isl_set *set,
4568 enum isl_dim_type type, unsigned pos);
4569 isl_bool isl_set_dim_has_any_upper_bound(
4570 __isl_keep isl_set *set,
4571 enum isl_dim_type type, unsigned pos);
4573 Note that these functions return true even if there is a bound on
4574 the dimension on only some of the basic sets of C<set>.
4575 To check if they have a bound for all of the basic sets in C<set>,
4576 use the following functions instead.
4578 #include <isl/set.h>
4579 isl_bool isl_set_dim_has_lower_bound(
4580 __isl_keep isl_set *set,
4581 enum isl_dim_type type, unsigned pos);
4582 isl_bool isl_set_dim_has_upper_bound(
4583 __isl_keep isl_set *set,
4584 enum isl_dim_type type, unsigned pos);
4588 To check whether a set is a parameter domain, use this function:
4590 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4591 isl_bool isl_union_set_is_params(
4592 __isl_keep isl_union_set *uset);
4596 The following functions check whether the space of the given
4597 (basic) set or relation domain and/or range is a wrapped relation.
4599 #include <isl/space.h>
4600 isl_bool isl_space_is_wrapping(
4601 __isl_keep isl_space *space);
4602 isl_bool isl_space_domain_is_wrapping(
4603 __isl_keep isl_space *space);
4604 isl_bool isl_space_range_is_wrapping(
4605 __isl_keep isl_space *space);
4606 isl_bool isl_space_is_product(
4607 __isl_keep isl_space *space);
4609 #include <isl/set.h>
4610 isl_bool isl_basic_set_is_wrapping(
4611 __isl_keep isl_basic_set *bset);
4612 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4614 #include <isl/map.h>
4615 isl_bool isl_map_domain_is_wrapping(
4616 __isl_keep isl_map *map);
4617 isl_bool isl_map_range_is_wrapping(
4618 __isl_keep isl_map *map);
4619 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4622 isl_bool isl_multi_id_range_is_wrapping(
4623 __isl_keep isl_multi_id *mi);
4625 #include <isl/val.h>
4626 isl_bool isl_multi_val_range_is_wrapping(
4627 __isl_keep isl_multi_val *mv);
4629 #include <isl/aff.h>
4630 isl_bool isl_multi_aff_range_is_wrapping(
4631 __isl_keep isl_multi_aff *ma);
4632 isl_bool isl_multi_pw_aff_range_is_wrapping(
4633 __isl_keep isl_multi_pw_aff *mpa);
4634 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4635 __isl_keep isl_multi_union_pw_aff *mupa);
4637 The input to C<isl_space_is_wrapping> should
4638 be the space of a set, while that of
4639 C<isl_space_domain_is_wrapping> and
4640 C<isl_space_range_is_wrapping> should be the space of a relation.
4641 The input to C<isl_space_is_product> can be either the space
4642 of a set or that of a binary relation.
4643 In case the input is the space of a binary relation, it checks
4644 whether both domain and range are wrapping.
4646 =item * Internal Product
4648 isl_bool isl_basic_map_can_zip(
4649 __isl_keep isl_basic_map *bmap);
4650 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4652 Check whether the product of domain and range of the given relation
4654 i.e., whether both domain and range are nested relations.
4658 #include <isl/space.h>
4659 isl_bool isl_space_can_curry(
4660 __isl_keep isl_space *space);
4662 #include <isl/map.h>
4663 isl_bool isl_basic_map_can_curry(
4664 __isl_keep isl_basic_map *bmap);
4665 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4667 Check whether the domain of the (basic) relation is a wrapped relation.
4669 #include <isl/space.h>
4670 __isl_give isl_space *isl_space_uncurry(
4671 __isl_take isl_space *space);
4673 #include <isl/map.h>
4674 isl_bool isl_basic_map_can_uncurry(
4675 __isl_keep isl_basic_map *bmap);
4676 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4678 Check whether the range of the (basic) relation is a wrapped relation.
4680 #include <isl/space.h>
4681 isl_bool isl_space_can_range_curry(
4682 __isl_keep isl_space *space);
4684 #include <isl/map.h>
4685 isl_bool isl_map_can_range_curry(
4686 __isl_keep isl_map *map);
4688 Check whether the domain of the relation wrapped in the range of
4689 the input is itself a wrapped relation.
4691 =item * Special Values
4693 #include <isl/aff.h>
4694 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4695 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4696 isl_bool isl_multi_pw_aff_is_cst(
4697 __isl_keep isl_multi_pw_aff *mpa);
4699 Check whether the given expression is a constant.
4701 #include <isl/val.h>
4702 isl_bool isl_multi_val_involves_nan(
4703 __isl_keep isl_multi_val *mv);
4705 #include <isl/aff.h>
4706 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4707 isl_bool isl_multi_aff_involves_nan(
4708 __isl_keep isl_multi_aff *ma);
4709 isl_bool isl_pw_aff_involves_nan(
4710 __isl_keep isl_pw_aff *pa);
4711 isl_bool isl_pw_multi_aff_involves_nan(
4712 __isl_keep isl_pw_multi_aff *pma);
4713 isl_bool isl_multi_pw_aff_involves_nan(
4714 __isl_keep isl_multi_pw_aff *mpa);
4715 isl_bool isl_union_pw_aff_involves_nan(
4716 __isl_keep isl_union_pw_aff *upa);
4717 isl_bool isl_union_pw_multi_aff_involves_nan(
4718 __isl_keep isl_union_pw_multi_aff *upma);
4719 isl_bool isl_multi_union_pw_aff_involves_nan(
4720 __isl_keep isl_multi_union_pw_aff *mupa);
4722 #include <isl/polynomial.h>
4723 isl_bool isl_qpolynomial_is_nan(
4724 __isl_keep isl_qpolynomial *qp);
4725 isl_bool isl_qpolynomial_fold_is_nan(
4726 __isl_keep isl_qpolynomial_fold *fold);
4727 isl_bool isl_pw_qpolynomial_involves_nan(
4728 __isl_keep isl_pw_qpolynomial *pwqp);
4729 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4730 __isl_keep isl_pw_qpolynomial_fold *pwf);
4731 isl_bool isl_union_pw_qpolynomial_involves_nan(
4732 __isl_keep isl_union_pw_qpolynomial *upwqp);
4733 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4734 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4736 Check whether the given expression is equal to or involves NaN.
4738 #include <isl/val.h>
4739 isl_bool isl_multi_val_is_zero(
4740 __isl_keep isl_multi_val *mv);
4742 Check whether the multiple value is zero.
4744 #include <isl/aff.h>
4745 isl_bool isl_aff_plain_is_zero(
4746 __isl_keep isl_aff *aff);
4748 Check whether the affine expression is obviously zero.
4752 =head3 Binary Properties
4758 The following functions check whether two objects
4759 represent the same set, relation or function.
4760 The C<plain> variants only return true if the objects
4761 are obviously the same. That is, they may return false
4762 even if the objects are the same, but they will never
4763 return true if the objects are not the same.
4765 #include <isl/set.h>
4766 isl_bool isl_basic_set_plain_is_equal(
4767 __isl_keep isl_basic_set *bset1,
4768 __isl_keep isl_basic_set *bset2);
4769 isl_bool isl_basic_set_is_equal(
4770 __isl_keep isl_basic_set *bset1,
4771 __isl_keep isl_basic_set *bset2);
4772 isl_bool isl_set_plain_is_equal(
4773 __isl_keep isl_set *set1,
4774 __isl_keep isl_set *set2);
4775 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4776 __isl_keep isl_set *set2);
4778 #include <isl/map.h>
4779 isl_bool isl_basic_map_is_equal(
4780 __isl_keep isl_basic_map *bmap1,
4781 __isl_keep isl_basic_map *bmap2);
4782 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4783 __isl_keep isl_map *map2);
4784 isl_bool isl_map_plain_is_equal(
4785 __isl_keep isl_map *map1,
4786 __isl_keep isl_map *map2);
4788 #include <isl/union_set.h>
4789 isl_bool isl_union_set_is_equal(
4790 __isl_keep isl_union_set *uset1,
4791 __isl_keep isl_union_set *uset2);
4793 #include <isl/union_map.h>
4794 isl_bool isl_union_map_is_equal(
4795 __isl_keep isl_union_map *umap1,
4796 __isl_keep isl_union_map *umap2);
4799 isl_bool isl_multi_id_plain_is_equal(
4800 __isl_keep isl_multi_id *mi1,
4801 __isl_keep isl_multi_id *mi2);
4803 #include <isl/val.h>
4804 isl_bool isl_multi_val_plain_is_equal(
4805 __isl_keep isl_multi_val *mv1,
4806 __isl_keep isl_multi_val *mv2);
4808 #include <isl/aff.h>
4809 isl_bool isl_aff_plain_is_equal(
4810 __isl_keep isl_aff *aff1,
4811 __isl_keep isl_aff *aff2);
4812 isl_bool isl_multi_aff_plain_is_equal(
4813 __isl_keep isl_multi_aff *maff1,
4814 __isl_keep isl_multi_aff *maff2);
4815 isl_bool isl_pw_aff_plain_is_equal(
4816 __isl_keep isl_pw_aff *pwaff1,
4817 __isl_keep isl_pw_aff *pwaff2);
4818 isl_bool isl_pw_aff_is_equal(
4819 __isl_keep isl_pw_aff *pa1,
4820 __isl_keep isl_pw_aff *pa2);
4821 isl_bool isl_pw_multi_aff_plain_is_equal(
4822 __isl_keep isl_pw_multi_aff *pma1,
4823 __isl_keep isl_pw_multi_aff *pma2);
4824 isl_bool isl_pw_multi_aff_is_equal(
4825 __isl_keep isl_pw_multi_aff *pma1,
4826 __isl_keep isl_pw_multi_aff *pma2);
4827 isl_bool isl_multi_pw_aff_plain_is_equal(
4828 __isl_keep isl_multi_pw_aff *mpa1,
4829 __isl_keep isl_multi_pw_aff *mpa2);
4830 isl_bool isl_multi_pw_aff_is_equal(
4831 __isl_keep isl_multi_pw_aff *mpa1,
4832 __isl_keep isl_multi_pw_aff *mpa2);
4833 isl_bool isl_union_pw_aff_plain_is_equal(
4834 __isl_keep isl_union_pw_aff *upa1,
4835 __isl_keep isl_union_pw_aff *upa2);
4836 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4837 __isl_keep isl_union_pw_multi_aff *upma1,
4838 __isl_keep isl_union_pw_multi_aff *upma2);
4839 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4840 __isl_keep isl_multi_union_pw_aff *mupa1,
4841 __isl_keep isl_multi_union_pw_aff *mupa2);
4843 #include <isl/polynomial.h>
4844 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4845 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4846 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4847 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4848 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4849 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4851 =item * Disjointness
4853 #include <isl/set.h>
4854 isl_bool isl_basic_set_is_disjoint(
4855 __isl_keep isl_basic_set *bset1,
4856 __isl_keep isl_basic_set *bset2);
4857 isl_bool isl_set_plain_is_disjoint(
4858 __isl_keep isl_set *set1,
4859 __isl_keep isl_set *set2);
4860 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4861 __isl_keep isl_set *set2);
4863 #include <isl/map.h>
4864 isl_bool isl_basic_map_is_disjoint(
4865 __isl_keep isl_basic_map *bmap1,
4866 __isl_keep isl_basic_map *bmap2);
4867 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4868 __isl_keep isl_map *map2);
4870 #include <isl/union_set.h>
4871 isl_bool isl_union_set_is_disjoint(
4872 __isl_keep isl_union_set *uset1,
4873 __isl_keep isl_union_set *uset2);
4875 #include <isl/union_map.h>
4876 isl_bool isl_union_map_is_disjoint(
4877 __isl_keep isl_union_map *umap1,
4878 __isl_keep isl_union_map *umap2);
4882 isl_bool isl_basic_set_is_subset(
4883 __isl_keep isl_basic_set *bset1,
4884 __isl_keep isl_basic_set *bset2);
4885 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4886 __isl_keep isl_set *set2);
4887 isl_bool isl_set_is_strict_subset(
4888 __isl_keep isl_set *set1,
4889 __isl_keep isl_set *set2);
4890 isl_bool isl_union_set_is_subset(
4891 __isl_keep isl_union_set *uset1,
4892 __isl_keep isl_union_set *uset2);
4893 isl_bool isl_union_set_is_strict_subset(
4894 __isl_keep isl_union_set *uset1,
4895 __isl_keep isl_union_set *uset2);
4896 isl_bool isl_basic_map_is_subset(
4897 __isl_keep isl_basic_map *bmap1,
4898 __isl_keep isl_basic_map *bmap2);
4899 isl_bool isl_basic_map_is_strict_subset(
4900 __isl_keep isl_basic_map *bmap1,
4901 __isl_keep isl_basic_map *bmap2);
4902 isl_bool isl_map_is_subset(
4903 __isl_keep isl_map *map1,
4904 __isl_keep isl_map *map2);
4905 isl_bool isl_map_is_strict_subset(
4906 __isl_keep isl_map *map1,
4907 __isl_keep isl_map *map2);
4908 isl_bool isl_union_map_is_subset(
4909 __isl_keep isl_union_map *umap1,
4910 __isl_keep isl_union_map *umap2);
4911 isl_bool isl_union_map_is_strict_subset(
4912 __isl_keep isl_union_map *umap1,
4913 __isl_keep isl_union_map *umap2);
4915 Check whether the first argument is a (strict) subset of the
4920 Every comparison function returns a negative value if the first
4921 argument is considered smaller than the second, a positive value
4922 if the first argument is considered greater and zero if the two
4923 constraints are considered the same by the comparison criterion.
4925 #include <isl/constraint.h>
4926 int isl_constraint_plain_cmp(
4927 __isl_keep isl_constraint *c1,
4928 __isl_keep isl_constraint *c2);
4930 This function is useful for sorting C<isl_constraint>s.
4931 The order depends on the internal representation of the inputs.
4932 The order is fixed over different calls to the function (assuming
4933 the internal representation of the inputs has not changed), but may
4934 change over different versions of C<isl>.
4936 #include <isl/constraint.h>
4937 int isl_constraint_cmp_last_non_zero(
4938 __isl_keep isl_constraint *c1,
4939 __isl_keep isl_constraint *c2);
4941 This function can be used to sort constraints that live in the same
4942 local space. Constraints that involve ``earlier'' dimensions or
4943 that have a smaller coefficient for the shared latest dimension
4944 are considered smaller than other constraints.
4945 This function only defines a B<partial> order.
4947 #include <isl/set.h>
4948 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4949 __isl_keep isl_set *set2);
4951 This function is useful for sorting C<isl_set>s.
4952 The order depends on the internal representation of the inputs.
4953 The order is fixed over different calls to the function (assuming
4954 the internal representation of the inputs has not changed), but may
4955 change over different versions of C<isl>.
4957 #include <isl/aff.h>
4958 int isl_multi_aff_plain_cmp(
4959 __isl_keep isl_multi_aff *ma1,
4960 __isl_keep isl_multi_aff *ma2);
4961 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4962 __isl_keep isl_pw_aff *pa2);
4964 The functions C<isl_multi_aff_plain_cmp> and
4965 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4966 C<isl_pw_aff>s. The order is not strictly defined.
4967 The current order sorts expressions that only involve
4968 earlier dimensions before those that involve later dimensions.
4972 =head2 Unary Operations
4978 __isl_give isl_set *isl_set_complement(
4979 __isl_take isl_set *set);
4980 __isl_give isl_map *isl_map_complement(
4981 __isl_take isl_map *map);
4985 #include <isl/space.h>
4986 __isl_give isl_space *isl_space_reverse(
4987 __isl_take isl_space *space);
4988 __isl_give isl_space *isl_space_range_reverse(
4989 __isl_take isl_space *space);
4991 #include <isl/map.h>
4992 __isl_give isl_basic_map *isl_basic_map_reverse(
4993 __isl_take isl_basic_map *bmap);
4994 __isl_give isl_map *isl_map_reverse(
4995 __isl_take isl_map *map);
4996 __isl_give isl_map *isl_map_range_reverse(
4997 __isl_take isl_map *map);
4999 #include <isl/union_map.h>
5000 __isl_give isl_union_map *isl_union_map_reverse(
5001 __isl_take isl_union_map *umap);
5002 __isl_give isl_union_map *isl_union_map_range_reverse(
5003 __isl_take isl_union_map *umap);
5005 The function C<isl_space_range_reverse> reverses the relation
5006 that is embedded in the range of the input map space.
5007 The identifier of the range, if any, is only preserved
5008 if this embedded relation has identical input and output tuples.
5010 =item * Tuple binding
5012 The following function binds
5013 a tuple to a sequence of parameter identifiers, equating
5014 the tuple dimensions to the parameters with those identifiers and
5015 subsequently projecting out the tuple.
5016 If the original object did not reference any such parameters,
5017 then this means that the tuple dimensions are reinterpreted
5019 The space of C<tuple> needs to match that of the bound tuple.
5021 #include <isl/set.h>
5022 __isl_give isl_set *isl_set_bind(
5023 __isl_take isl_set *set,
5024 __isl_take isl_multi_id *tuple);
5026 #include <isl/map.h>
5027 __isl_give isl_set *isl_map_bind_domain(
5028 __isl_take isl_map *map,
5029 __isl_take isl_multi_id *tuple);
5030 __isl_give isl_set *isl_map_bind_range(
5031 __isl_take isl_map *map,
5032 __isl_take isl_multi_id *tuple);
5034 #include <isl/union_map.h>
5035 __isl_give isl_union_set *isl_union_map_bind_range(
5036 __isl_take isl_union_map *umap,
5037 __isl_take isl_multi_id *tuple);
5039 #include <isl/aff.h>
5040 __isl_give isl_pw_aff *isl_pw_aff_bind_domain(
5041 __isl_take isl_pw_aff *pa,
5042 __isl_take isl_multi_id *tuple);
5043 __isl_give isl_multi_aff *isl_multi_aff_bind_domain(
5044 __isl_take isl_multi_aff *ma,
5045 __isl_take isl_multi_id *tuple);
5046 __isl_give isl_pw_multi_aff *
5047 isl_pw_multi_aff_bind_domain(
5048 __isl_take isl_pw_multi_aff *pma,
5049 __isl_take isl_multi_id *tuple);
5050 __isl_give isl_multi_pw_aff *
5051 isl_multi_pw_aff_bind_domain(
5052 __isl_take isl_multi_pw_aff *mpa,
5053 __isl_take isl_multi_id *tuple);
5054 __isl_give isl_pw_aff *
5055 isl_pw_aff_bind_domain_wrapped_domain(
5056 __isl_take isl_pw_aff *pa,
5057 __isl_take isl_multi_id *tuple);
5058 __isl_give isl_multi_aff *
5059 isl_multi_aff_bind_domain_wrapped_domain(
5060 __isl_take isl_multi_aff *ma,
5061 __isl_take isl_multi_id *tuple);
5062 __isl_give isl_pw_multi_aff *
5063 isl_pw_multi_aff_bind_domain_wrapped_domain(
5064 __isl_take isl_pw_multi_aff *pma,
5065 __isl_take isl_multi_id *tuple);
5066 __isl_give isl_multi_pw_aff *
5067 isl_multi_pw_aff_bind_domain_wrapped_domain(
5068 __isl_take isl_multi_pw_aff *mpa,
5069 __isl_take isl_multi_id *tuple);
5070 __isl_give isl_basic_set *isl_aff_bind_id(
5071 __isl_take isl_aff *aff,
5072 __isl_take isl_id *id);
5073 __isl_give isl_set *isl_pw_aff_bind_id(
5074 __isl_take isl_pw_aff *pa,
5075 __isl_take isl_id *id);
5076 __isl_give isl_basic_set *isl_multi_aff_bind(
5077 __isl_take isl_multi_aff *ma,
5078 __isl_take isl_multi_id *tuple);
5079 __isl_give isl_set *isl_multi_pw_aff_bind(
5080 __isl_take isl_multi_pw_aff *mpa,
5081 __isl_take isl_multi_id *tuple);
5082 __isl_give isl_union_set *isl_union_pw_aff_bind_id(
5083 __isl_take isl_union_pw_aff *upa,
5084 __isl_take isl_id *id);
5085 __isl_give isl_union_set *
5086 isl_multi_union_pw_aff_bind(
5087 __isl_take isl_multi_union_pw_aff *mupa,
5088 __isl_take isl_multi_id *tuple);
5090 Projecting out the domain of the wrapped relation in the domain
5091 of a function leaves the range of that wrapped relation
5092 in the domain of the resulting function.
5093 In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>,
5094 C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>,
5095 C<isl_union_pw_aff_bind_id> and
5096 C<isl_multi_union_pw_aff_bind>, the parameters
5097 are bound to the function values and the result lives
5098 in the domain of the input function.
5102 #include <isl/space.h>
5103 __isl_give isl_space *isl_space_domain(
5104 __isl_take isl_space *space);
5105 __isl_give isl_space *isl_space_range(
5106 __isl_take isl_space *space);
5107 __isl_give isl_space *isl_space_params(
5108 __isl_take isl_space *space);
5110 #include <isl/local_space.h>
5111 __isl_give isl_local_space *isl_local_space_domain(
5112 __isl_take isl_local_space *ls);
5113 __isl_give isl_local_space *isl_local_space_range(
5114 __isl_take isl_local_space *ls);
5116 #include <isl/set.h>
5117 __isl_give isl_basic_set *isl_basic_set_project_out(
5118 __isl_take isl_basic_set *bset,
5119 enum isl_dim_type type, unsigned first, unsigned n);
5120 __isl_give isl_set *isl_set_project_out_param_id(
5121 __isl_take isl_set *set,
5122 __isl_take isl_id *id);
5123 __isl_give isl_set *
5124 isl_set_project_out_param_id_list(
5125 __isl_take isl_set *set,
5126 __isl_take isl_id_list *list);
5127 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
5128 enum isl_dim_type type, unsigned first, unsigned n);
5129 __isl_give isl_set *isl_set_project_out_all_params(
5130 __isl_take isl_set *set);
5131 __isl_give isl_map *isl_set_project_onto_map(
5132 __isl_take isl_set *set,
5133 enum isl_dim_type type, unsigned first,
5135 __isl_give isl_basic_set *isl_basic_set_params(
5136 __isl_take isl_basic_set *bset);
5137 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
5139 The function C<isl_set_project_onto_map> returns a relation
5140 that projects the input set onto the given set dimensions.
5142 #include <isl/map.h>
5143 __isl_give isl_basic_map *isl_basic_map_project_out(
5144 __isl_take isl_basic_map *bmap,
5145 enum isl_dim_type type, unsigned first, unsigned n);
5146 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
5147 enum isl_dim_type type, unsigned first, unsigned n);
5148 __isl_give isl_map *isl_map_project_out_all_params(
5149 __isl_take isl_map *map);
5150 __isl_give isl_basic_set *isl_basic_map_domain(
5151 __isl_take isl_basic_map *bmap);
5152 __isl_give isl_basic_set *isl_basic_map_range(
5153 __isl_take isl_basic_map *bmap);
5154 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
5155 __isl_give isl_set *isl_map_domain(
5156 __isl_take isl_map *bmap);
5157 __isl_give isl_set *isl_map_range(
5158 __isl_take isl_map *map);
5160 #include <isl/union_set.h>
5161 __isl_give isl_union_set *isl_union_set_project_out(
5162 __isl_take isl_union_set *uset,
5163 enum isl_dim_type type,
5164 unsigned first, unsigned n);
5165 __isl_give isl_union_set *
5166 isl_union_set_project_out_all_params(
5167 __isl_take isl_union_set *uset);
5168 __isl_give isl_set *isl_union_set_params(
5169 __isl_take isl_union_set *uset);
5171 The function C<isl_union_set_project_out> can only project out
5174 #include <isl/union_map.h>
5175 __isl_give isl_union_map *isl_union_map_project_out(
5176 __isl_take isl_union_map *umap,
5177 enum isl_dim_type type, unsigned first, unsigned n);
5178 __isl_give isl_union_map *
5179 isl_union_map_project_out_all_params(
5180 __isl_take isl_union_map *umap);
5181 __isl_give isl_set *isl_union_map_params(
5182 __isl_take isl_union_map *umap);
5183 __isl_give isl_union_set *isl_union_map_domain(
5184 __isl_take isl_union_map *umap);
5185 __isl_give isl_union_set *isl_union_map_range(
5186 __isl_take isl_union_map *umap);
5188 The function C<isl_union_map_project_out> can only project out
5191 #include <isl/aff.h>
5192 __isl_give isl_aff *isl_aff_project_domain_on_params(
5193 __isl_take isl_aff *aff);
5194 __isl_give isl_multi_aff *
5195 isl_multi_aff_project_domain_on_params(
5196 __isl_take isl_multi_aff *ma);
5197 __isl_give isl_pw_aff *
5198 isl_pw_aff_project_domain_on_params(
5199 __isl_take isl_pw_aff *pa);
5200 __isl_give isl_multi_pw_aff *
5201 isl_multi_pw_aff_project_domain_on_params(
5202 __isl_take isl_multi_pw_aff *mpa);
5203 __isl_give isl_pw_multi_aff *
5204 isl_pw_multi_aff_project_domain_on_params(
5205 __isl_take isl_pw_multi_aff *pma);
5206 __isl_give isl_set *isl_pw_aff_domain(
5207 __isl_take isl_pw_aff *pwaff);
5208 __isl_give isl_set *isl_pw_multi_aff_domain(
5209 __isl_take isl_pw_multi_aff *pma);
5210 __isl_give isl_set *isl_multi_pw_aff_domain(
5211 __isl_take isl_multi_pw_aff *mpa);
5212 __isl_give isl_union_set *isl_union_pw_aff_domain(
5213 __isl_take isl_union_pw_aff *upa);
5214 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
5215 __isl_take isl_union_pw_multi_aff *upma);
5216 __isl_give isl_union_set *
5217 isl_multi_union_pw_aff_domain(
5218 __isl_take isl_multi_union_pw_aff *mupa);
5219 __isl_give isl_set *isl_pw_aff_params(
5220 __isl_take isl_pw_aff *pwa);
5222 If no explicit domain was set on a zero-dimensional input to
5223 C<isl_multi_union_pw_aff_domain>, then this function will
5224 return a parameter set.
5226 #include <isl/polynomial.h>
5227 __isl_give isl_qpolynomial *
5228 isl_qpolynomial_project_domain_on_params(
5229 __isl_take isl_qpolynomial *qp);
5230 __isl_give isl_pw_qpolynomial *
5231 isl_pw_qpolynomial_project_domain_on_params(
5232 __isl_take isl_pw_qpolynomial *pwqp);
5233 __isl_give isl_pw_qpolynomial_fold *
5234 isl_pw_qpolynomial_fold_project_domain_on_params(
5235 __isl_take isl_pw_qpolynomial_fold *pwf);
5236 __isl_give isl_set *isl_pw_qpolynomial_domain(
5237 __isl_take isl_pw_qpolynomial *pwqp);
5238 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5239 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5240 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5241 __isl_take isl_union_pw_qpolynomial *upwqp);
5243 #include <isl/space.h>
5244 __isl_give isl_space *isl_space_domain_map(
5245 __isl_take isl_space *space);
5246 __isl_give isl_space *isl_space_range_map(
5247 __isl_take isl_space *space);
5249 #include <isl/map.h>
5250 __isl_give isl_map *isl_set_wrapped_domain_map(
5251 __isl_take isl_set *set);
5252 __isl_give isl_basic_map *isl_basic_map_domain_map(
5253 __isl_take isl_basic_map *bmap);
5254 __isl_give isl_basic_map *isl_basic_map_range_map(
5255 __isl_take isl_basic_map *bmap);
5256 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
5257 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
5259 #include <isl/union_map.h>
5260 __isl_give isl_union_map *isl_union_map_domain_map(
5261 __isl_take isl_union_map *umap);
5262 __isl_give isl_union_pw_multi_aff *
5263 isl_union_map_domain_map_union_pw_multi_aff(
5264 __isl_take isl_union_map *umap);
5265 __isl_give isl_union_map *isl_union_map_range_map(
5266 __isl_take isl_union_map *umap);
5267 __isl_give isl_union_map *
5268 isl_union_set_wrapped_domain_map(
5269 __isl_take isl_union_set *uset);
5271 The functions above construct a (basic, regular or union) relation
5272 that maps (a wrapped version of) the input relation to its domain or range.
5273 C<isl_set_wrapped_domain_map> maps the input set to the domain
5274 of its wrapped relation.
5278 __isl_give isl_basic_set *isl_basic_set_eliminate(
5279 __isl_take isl_basic_set *bset,
5280 enum isl_dim_type type,
5281 unsigned first, unsigned n);
5282 __isl_give isl_set *isl_set_eliminate(
5283 __isl_take isl_set *set, enum isl_dim_type type,
5284 unsigned first, unsigned n);
5285 __isl_give isl_basic_map *isl_basic_map_eliminate(
5286 __isl_take isl_basic_map *bmap,
5287 enum isl_dim_type type,
5288 unsigned first, unsigned n);
5289 __isl_give isl_map *isl_map_eliminate(
5290 __isl_take isl_map *map, enum isl_dim_type type,
5291 unsigned first, unsigned n);
5293 Eliminate the coefficients for the given dimensions from the constraints,
5294 without removing the dimensions.
5296 =item * Constructing a set from a parameter domain
5298 A set space of a given dimension and with an optional name
5299 can be created from a parameter space using the following functions.
5301 #include <isl/space.h>
5302 __isl_give isl_space *isl_space_add_unnamed_tuple_ui(
5303 __isl_take isl_space *space, unsigned dim);
5304 __isl_give isl_space *
5305 isl_space_add_named_tuple_id_ui(
5306 __isl_take isl_space *space,
5307 __isl_take isl_id *tuple_id, unsigned dim);
5309 A set with a given tuple can be created from a parameter domain
5310 using the following function.
5312 #include <isl/set.h>
5313 __isl_give isl_set *isl_set_unbind_params(
5314 __isl_take isl_set *set,
5315 __isl_take isl_multi_id *tuple);
5317 Any parameters with identifiers in C<tuple> are reinterpreted
5318 as the corresponding set dimensions.
5320 A zero-dimensional (local) space or (basic) set can be constructed
5321 on a given parameter domain using the following functions.
5323 #include <isl/space.h>
5324 __isl_give isl_space *isl_space_set_from_params(
5325 __isl_take isl_space *space);
5327 #include <isl/local_space.h>
5328 __isl_give isl_local_space *
5329 isl_local_space_set_from_params(
5330 __isl_take isl_local_space *ls);
5332 #include <isl/set.h>
5333 __isl_give isl_basic_set *isl_basic_set_from_params(
5334 __isl_take isl_basic_set *bset);
5335 __isl_give isl_set *isl_set_from_params(
5336 __isl_take isl_set *set);
5338 =item * Constructing a relation from one or two sets
5340 A map space with a range of a given dimension and with an optional name
5341 can be created from a domain space using the functions
5342 C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui>
5345 A relation with a given domain tuple can be created from a set
5346 that will become the range of the relation
5347 using the following function.
5349 #include <isl/set.h>
5350 __isl_give isl_map *
5351 isl_set_unbind_params_insert_domain(
5352 __isl_take isl_set *set,
5353 __isl_take isl_multi_id *domain);
5355 Any parameters with identifiers in C<domain> are reinterpreted
5356 as the corresponding input dimensions.
5358 Similarly, a function defined over a parameter domain can
5359 be converted into one defined over a set domain
5360 using the following functions.
5362 #include <isl/aff.h>
5363 __isl_give isl_aff *
5364 isl_aff_unbind_params_insert_domain(
5365 __isl_take isl_aff *aff,
5366 __isl_take isl_multi_id *domain);
5367 __isl_give isl_multi_aff *
5368 isl_multi_aff_unbind_params_insert_domain(
5369 __isl_take isl_multi_aff *ma,
5370 __isl_take isl_multi_id *domain);
5371 __isl_give isl_multi_pw_aff *
5372 isl_multi_pw_aff_unbind_params_insert_domain(
5373 __isl_take isl_multi_pw_aff *mpa,
5374 __isl_take isl_multi_id *domain);
5377 any parameters with identifiers in C<domain> are reinterpreted
5378 as the corresponding input dimensions.
5380 Create a relation with the given set(s) as domain and/or range.
5381 If only the domain or the range is specified, then
5382 the range or domain of the created relation is a zero-dimensional
5383 flat anonymous space.
5384 If the case of C<isl_space_map_from_set>, the input space
5385 specifies both the domain and the range of the result.
5387 #include <isl/space.h>
5388 __isl_give isl_space *isl_space_from_domain(
5389 __isl_take isl_space *space);
5390 __isl_give isl_space *isl_space_from_range(
5391 __isl_take isl_space *space);
5392 __isl_give isl_space *isl_space_map_from_set(
5393 __isl_take isl_space *space);
5394 __isl_give isl_space *isl_space_map_from_domain_and_range(
5395 __isl_take isl_space *domain,
5396 __isl_take isl_space *range);
5398 #include <isl/local_space.h>
5399 __isl_give isl_local_space *isl_local_space_from_domain(
5400 __isl_take isl_local_space *ls);
5402 #include <isl/map.h>
5403 __isl_give isl_map *isl_set_insert_domain(
5404 __isl_take isl_set *set,
5405 __isl_take isl_space *domain);
5406 __isl_give isl_map *isl_map_from_domain(
5407 __isl_take isl_set *set);
5408 __isl_give isl_map *isl_map_from_range(
5409 __isl_take isl_set *set);
5411 #include <isl/union_map.h>
5412 __isl_give isl_union_map *isl_union_map_from_domain(
5413 __isl_take isl_union_set *uset);
5414 __isl_give isl_union_map *isl_union_map_from_range(
5415 __isl_take isl_union_set *uset);
5416 __isl_give isl_union_map *
5417 isl_union_map_from_domain_and_range(
5418 __isl_take isl_union_set *domain,
5419 __isl_take isl_union_set *range);
5422 __isl_give isl_multi_id *isl_multi_id_from_range(
5423 __isl_take isl_multi_id *mi);
5425 #include <isl/val.h>
5426 __isl_give isl_multi_val *isl_multi_val_from_range(
5427 __isl_take isl_multi_val *mv);
5429 #include <isl/aff.h>
5430 __isl_give isl_multi_aff *
5431 isl_multi_aff_insert_domain(
5432 __isl_take isl_multi_aff *ma,
5433 __isl_take isl_space *domain);
5434 __isl_give isl_pw_aff *isl_pw_aff_insert_domain(
5435 __isl_take isl_pw_aff *pa,
5436 __isl_take isl_space *domain);
5437 __isl_give isl_pw_multi_aff *
5438 isl_pw_multi_aff_insert_domain(
5439 __isl_take isl_pw_multi_aff *pma,
5440 __isl_take isl_space *domain);
5441 __isl_give isl_multi_pw_aff *
5442 isl_multi_pw_aff_insert_domain(
5443 __isl_take isl_multi_pw_aff *mpa,
5444 __isl_take isl_space *domain);
5445 __isl_give isl_aff *isl_aff_from_range(
5446 __isl_take isl_aff *aff);
5447 __isl_give isl_multi_aff *isl_multi_aff_from_range(
5448 __isl_take isl_multi_aff *ma);
5449 __isl_give isl_pw_aff *isl_pw_aff_from_range(
5450 __isl_take isl_pw_aff *pwa);
5451 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
5452 __isl_take isl_multi_pw_aff *mpa);
5453 __isl_give isl_multi_union_pw_aff *
5454 isl_multi_union_pw_aff_from_range(
5455 __isl_take isl_multi_union_pw_aff *mupa);
5456 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5457 __isl_take isl_set *set);
5458 __isl_give isl_union_pw_multi_aff *
5459 isl_union_pw_multi_aff_from_domain(
5460 __isl_take isl_union_set *uset);
5462 #include <isl/polynomial.h>
5463 __isl_give isl_pw_qpolynomial *
5464 isl_pw_qpolynomial_from_range(
5465 __isl_take isl_pw_qpolynomial *pwqp);
5466 __isl_give isl_pw_qpolynomial_fold *
5467 isl_pw_qpolynomial_fold_from_range(
5468 __isl_take isl_pw_qpolynomial_fold *pwf);
5472 #include <isl/set.h>
5473 __isl_give isl_basic_set *isl_basic_set_fix_si(
5474 __isl_take isl_basic_set *bset,
5475 enum isl_dim_type type, unsigned pos, int value);
5476 __isl_give isl_basic_set *isl_basic_set_fix_val(
5477 __isl_take isl_basic_set *bset,
5478 enum isl_dim_type type, unsigned pos,
5479 __isl_take isl_val *v);
5480 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5481 enum isl_dim_type type, unsigned pos, int value);
5482 __isl_give isl_set *isl_set_fix_val(
5483 __isl_take isl_set *set,
5484 enum isl_dim_type type, unsigned pos,
5485 __isl_take isl_val *v);
5487 #include <isl/map.h>
5488 __isl_give isl_basic_map *isl_basic_map_fix_si(
5489 __isl_take isl_basic_map *bmap,
5490 enum isl_dim_type type, unsigned pos, int value);
5491 __isl_give isl_basic_map *isl_basic_map_fix_val(
5492 __isl_take isl_basic_map *bmap,
5493 enum isl_dim_type type, unsigned pos,
5494 __isl_take isl_val *v);
5495 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
5496 enum isl_dim_type type, unsigned pos, int value);
5497 __isl_give isl_map *isl_map_fix_val(
5498 __isl_take isl_map *map,
5499 enum isl_dim_type type, unsigned pos,
5500 __isl_take isl_val *v);
5502 #include <isl/aff.h>
5503 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
5504 __isl_take isl_pw_multi_aff *pma,
5505 enum isl_dim_type type, unsigned pos, int value);
5507 #include <isl/polynomial.h>
5508 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5509 __isl_take isl_pw_qpolynomial *pwqp,
5510 enum isl_dim_type type, unsigned n,
5511 __isl_take isl_val *v);
5512 __isl_give isl_pw_qpolynomial_fold *
5513 isl_pw_qpolynomial_fold_fix_val(
5514 __isl_take isl_pw_qpolynomial_fold *pwf,
5515 enum isl_dim_type type, unsigned n,
5516 __isl_take isl_val *v);
5518 Intersect the set, relation or function domain
5519 with the hyperplane where the given
5520 dimension has the fixed given value.
5522 #include <isl/set.h>
5523 __isl_give isl_basic_set *
5524 isl_basic_set_lower_bound_val(
5525 __isl_take isl_basic_set *bset,
5526 enum isl_dim_type type, unsigned pos,
5527 __isl_take isl_val *value);
5528 __isl_give isl_basic_set *
5529 isl_basic_set_upper_bound_val(
5530 __isl_take isl_basic_set *bset,
5531 enum isl_dim_type type, unsigned pos,
5532 __isl_take isl_val *value);
5533 __isl_give isl_set *isl_set_lower_bound_si(
5534 __isl_take isl_set *set,
5535 enum isl_dim_type type, unsigned pos, int value);
5536 __isl_give isl_set *isl_set_lower_bound_val(
5537 __isl_take isl_set *set,
5538 enum isl_dim_type type, unsigned pos,
5539 __isl_take isl_val *value);
5540 __isl_give isl_set *isl_set_upper_bound_si(
5541 __isl_take isl_set *set,
5542 enum isl_dim_type type, unsigned pos, int value);
5543 __isl_give isl_set *isl_set_upper_bound_val(
5544 __isl_take isl_set *set,
5545 enum isl_dim_type type, unsigned pos,
5546 __isl_take isl_val *value);
5547 __isl_give isl_set *isl_set_lower_bound_multi_val(
5548 __isl_take isl_set *set,
5549 __isl_take isl_multi_val *lower);
5550 __isl_give isl_set *isl_set_upper_bound_multi_val(
5551 __isl_take isl_set *set,
5552 __isl_take isl_multi_val *upper);
5553 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff(
5554 __isl_take isl_set *set,
5555 __isl_take isl_multi_pw_aff *lower);
5556 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff(
5557 __isl_take isl_set *set,
5558 __isl_take isl_multi_pw_aff *upper);
5560 #include <isl/map.h>
5561 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
5562 __isl_take isl_basic_map *bmap,
5563 enum isl_dim_type type, unsigned pos, int value);
5564 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
5565 __isl_take isl_basic_map *bmap,
5566 enum isl_dim_type type, unsigned pos, int value);
5567 __isl_give isl_map *isl_map_lower_bound_si(
5568 __isl_take isl_map *map,
5569 enum isl_dim_type type, unsigned pos, int value);
5570 __isl_give isl_map *isl_map_upper_bound_si(
5571 __isl_take isl_map *map,
5572 enum isl_dim_type type, unsigned pos, int value);
5573 __isl_give isl_map *isl_map_lower_bound_val(
5574 __isl_take isl_map *map,
5575 enum isl_dim_type type, unsigned pos,
5576 __isl_take isl_val *value);
5577 __isl_give isl_map *isl_map_upper_bound_val(
5578 __isl_take isl_map *map,
5579 enum isl_dim_type type, unsigned pos,
5580 __isl_take isl_val *value);
5581 __isl_give isl_map *isl_map_lower_bound_multi_val(
5582 __isl_take isl_map *map,
5583 __isl_take isl_multi_val *lower);
5584 __isl_give isl_map *isl_map_upper_bound_multi_val(
5585 __isl_take isl_map *map,
5586 __isl_take isl_multi_val *upper);
5587 __isl_give isl_map *isl_map_lower_bound_multi_pw_aff(
5588 __isl_take isl_map *map,
5589 __isl_take isl_multi_pw_aff *lower);
5590 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff(
5591 __isl_take isl_map *map,
5592 __isl_take isl_multi_pw_aff *upper);
5594 Intersect the set or relation with the half-space where the given
5595 dimension has a value bounded by the given fixed integer value or
5596 symbolic constant expression.
5597 For functions taking a multi expression,
5598 this applies to all set dimensions.
5599 Those that bound a map, bound the range of that map.
5601 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
5602 enum isl_dim_type type1, int pos1,
5603 enum isl_dim_type type2, int pos2);
5604 __isl_give isl_basic_map *isl_basic_map_equate(
5605 __isl_take isl_basic_map *bmap,
5606 enum isl_dim_type type1, int pos1,
5607 enum isl_dim_type type2, int pos2);
5608 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
5609 enum isl_dim_type type1, int pos1,
5610 enum isl_dim_type type2, int pos2);
5612 Intersect the set or relation with the hyperplane where the given
5613 dimensions are equal to each other.
5615 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
5616 enum isl_dim_type type1, int pos1,
5617 enum isl_dim_type type2, int pos2);
5619 Intersect the relation with the hyperplane where the given
5620 dimensions have opposite values.
5622 __isl_give isl_map *isl_map_order_le(
5623 __isl_take isl_map *map,
5624 enum isl_dim_type type1, int pos1,
5625 enum isl_dim_type type2, int pos2);
5626 __isl_give isl_basic_map *isl_basic_map_order_ge(
5627 __isl_take isl_basic_map *bmap,
5628 enum isl_dim_type type1, int pos1,
5629 enum isl_dim_type type2, int pos2);
5630 __isl_give isl_map *isl_map_order_ge(
5631 __isl_take isl_map *map,
5632 enum isl_dim_type type1, int pos1,
5633 enum isl_dim_type type2, int pos2);
5634 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
5635 enum isl_dim_type type1, int pos1,
5636 enum isl_dim_type type2, int pos2);
5637 __isl_give isl_basic_map *isl_basic_map_order_gt(
5638 __isl_take isl_basic_map *bmap,
5639 enum isl_dim_type type1, int pos1,
5640 enum isl_dim_type type2, int pos2);
5641 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
5642 enum isl_dim_type type1, int pos1,
5643 enum isl_dim_type type2, int pos2);
5645 Intersect the relation with the half-space where the given
5646 dimensions satisfy the given ordering.
5648 #include <isl/union_set.h>
5649 __isl_give isl_union_map *isl_union_map_remove_map_if(
5650 __isl_take isl_union_map *umap,
5651 isl_bool (*fn)(__isl_keep isl_map *map,
5652 void *user), void *user);
5654 This function calls the callback function once for each
5655 pair of spaces for which there are elements in the input.
5656 If the callback returns C<isl_bool_true>, then all those elements
5657 are removed from the result. The only remaining elements in the output
5658 are then those for which the callback returns C<isl_bool_false>.
5662 #include <isl/aff.h>
5663 __isl_give isl_basic_set *isl_aff_zero_basic_set(
5664 __isl_take isl_aff *aff);
5665 __isl_give isl_basic_set *isl_aff_neg_basic_set(
5666 __isl_take isl_aff *aff);
5667 __isl_give isl_set *isl_pw_aff_pos_set(
5668 __isl_take isl_pw_aff *pa);
5669 __isl_give isl_set *isl_pw_aff_nonneg_set(
5670 __isl_take isl_pw_aff *pwaff);
5671 __isl_give isl_set *isl_pw_aff_zero_set(
5672 __isl_take isl_pw_aff *pwaff);
5673 __isl_give isl_set *isl_pw_aff_non_zero_set(
5674 __isl_take isl_pw_aff *pwaff);
5675 __isl_give isl_union_set *
5676 isl_union_pw_aff_zero_union_set(
5677 __isl_take isl_union_pw_aff *upa);
5678 __isl_give isl_union_set *
5679 isl_multi_union_pw_aff_zero_union_set(
5680 __isl_take isl_multi_union_pw_aff *mupa);
5682 The function C<isl_aff_neg_basic_set> returns a basic set
5683 containing those elements in the domain space
5684 of C<aff> where C<aff> is negative.
5685 The function C<isl_pw_aff_nonneg_set> returns a set
5686 containing those elements in the domain
5687 of C<pwaff> where C<pwaff> is non-negative.
5688 The function C<isl_multi_union_pw_aff_zero_union_set>
5689 returns a union set containing those elements
5690 in the domains of its elements where they are all zero.
5694 __isl_give isl_map *isl_set_identity(
5695 __isl_take isl_set *set);
5696 __isl_give isl_union_map *isl_union_set_identity(
5697 __isl_take isl_union_set *uset);
5698 __isl_give isl_union_pw_multi_aff *
5699 isl_union_set_identity_union_pw_multi_aff(
5700 __isl_take isl_union_set *uset);
5702 Construct an identity relation on the given (union) set.
5704 =item * Function Extraction
5706 A piecewise quasi affine expression that is equal to 1 on a set
5707 and 0 outside the set can be created using the following function.
5709 #include <isl/aff.h>
5710 __isl_give isl_pw_aff *isl_set_indicator_function(
5711 __isl_take isl_set *set);
5713 A piecewise multiple quasi affine expression can be extracted
5714 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
5715 and the C<isl_map> is single-valued.
5716 In case of a conversion from an C<isl_union_map>
5717 to an C<isl_union_pw_multi_aff>, these properties need to hold
5718 in each domain space.
5719 A conversion to a C<isl_multi_union_pw_aff> additionally
5720 requires that the input is non-empty and involves only a single
5723 #include <isl/aff.h>
5724 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
5725 __isl_take isl_set *set);
5726 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
5727 __isl_take isl_map *map);
5729 __isl_give isl_union_pw_multi_aff *
5730 isl_union_pw_multi_aff_from_union_set(
5731 __isl_take isl_union_set *uset);
5732 __isl_give isl_union_pw_multi_aff *
5733 isl_union_pw_multi_aff_from_union_map(
5734 __isl_take isl_union_map *umap);
5736 __isl_give isl_multi_union_pw_aff *
5737 isl_multi_union_pw_aff_from_union_map(
5738 __isl_take isl_union_map *umap);
5742 __isl_give isl_basic_set *isl_basic_map_deltas(
5743 __isl_take isl_basic_map *bmap);
5744 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
5745 __isl_give isl_union_set *isl_union_map_deltas(
5746 __isl_take isl_union_map *umap);
5748 These functions return a (basic) set containing the differences
5749 between image elements and corresponding domain elements in the input.
5751 __isl_give isl_basic_map *isl_basic_map_deltas_map(
5752 __isl_take isl_basic_map *bmap);
5753 __isl_give isl_map *isl_map_deltas_map(
5754 __isl_take isl_map *map);
5755 __isl_give isl_union_map *isl_union_map_deltas_map(
5756 __isl_take isl_union_map *umap);
5758 The functions above construct a (basic, regular or union) relation
5759 that maps (a wrapped version of) the input relation to its delta set.
5763 Simplify the representation of a set, relation or functions by trying
5764 to combine pairs of basic sets or relations into a single
5765 basic set or relation.
5767 #include <isl/set.h>
5768 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
5770 #include <isl/map.h>
5771 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5773 #include <isl/union_set.h>
5774 __isl_give isl_union_set *isl_union_set_coalesce(
5775 __isl_take isl_union_set *uset);
5777 #include <isl/union_map.h>
5778 __isl_give isl_union_map *isl_union_map_coalesce(
5779 __isl_take isl_union_map *umap);
5781 #include <isl/aff.h>
5782 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5783 __isl_take isl_pw_aff *pa);
5784 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5785 __isl_take isl_pw_multi_aff *pma);
5786 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5787 __isl_take isl_multi_pw_aff *mpa);
5788 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5789 __isl_take isl_union_pw_aff *upa);
5790 __isl_give isl_union_pw_multi_aff *
5791 isl_union_pw_multi_aff_coalesce(
5792 __isl_take isl_union_pw_multi_aff *upma);
5793 __isl_give isl_multi_union_pw_aff *
5794 isl_multi_union_pw_aff_coalesce(
5795 __isl_take isl_multi_union_pw_aff *mupa);
5797 #include <isl/polynomial.h>
5798 __isl_give isl_pw_qpolynomial_fold *
5799 isl_pw_qpolynomial_fold_coalesce(
5800 __isl_take isl_pw_qpolynomial_fold *pwf);
5801 __isl_give isl_union_pw_qpolynomial *
5802 isl_union_pw_qpolynomial_coalesce(
5803 __isl_take isl_union_pw_qpolynomial *upwqp);
5804 __isl_give isl_union_pw_qpolynomial_fold *
5805 isl_union_pw_qpolynomial_fold_coalesce(
5806 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5808 One of the methods for combining pairs of basic sets or relations
5809 can result in coefficients that are much larger than those that appear
5810 in the constraints of the input. By default, the coefficients are
5811 not allowed to grow larger, but this can be changed by unsetting
5812 the following option.
5814 isl_stat isl_options_set_coalesce_bounded_wrapping(
5815 isl_ctx *ctx, int val);
5816 int isl_options_get_coalesce_bounded_wrapping(
5819 One of the other methods tries to combine pairs of basic sets
5820 with different local variables, treating them as existentially
5821 quantified variables even if they have known (but different)
5822 integer division expressions. The result may then also have
5823 existentially quantified variables. Turning on the following
5824 option prevents this from happening.
5826 isl_stat isl_options_set_coalesce_preserve_locals(
5827 isl_ctx *ctx, int val);
5828 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
5830 =item * Detecting equalities
5832 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5833 __isl_take isl_basic_set *bset);
5834 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5835 __isl_take isl_basic_map *bmap);
5836 __isl_give isl_set *isl_set_detect_equalities(
5837 __isl_take isl_set *set);
5838 __isl_give isl_map *isl_map_detect_equalities(
5839 __isl_take isl_map *map);
5840 __isl_give isl_union_set *isl_union_set_detect_equalities(
5841 __isl_take isl_union_set *uset);
5842 __isl_give isl_union_map *isl_union_map_detect_equalities(
5843 __isl_take isl_union_map *umap);
5845 Simplify the representation of a set or relation by detecting implicit
5848 =item * Removing redundant constraints
5850 #include <isl/set.h>
5851 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5852 __isl_take isl_basic_set *bset);
5853 __isl_give isl_set *isl_set_remove_redundancies(
5854 __isl_take isl_set *set);
5856 #include <isl/union_set.h>
5857 __isl_give isl_union_set *
5858 isl_union_set_remove_redundancies(
5859 __isl_take isl_union_set *uset);
5861 #include <isl/map.h>
5862 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5863 __isl_take isl_basic_map *bmap);
5864 __isl_give isl_map *isl_map_remove_redundancies(
5865 __isl_take isl_map *map);
5867 #include <isl/union_map.h>
5868 __isl_give isl_union_map *
5869 isl_union_map_remove_redundancies(
5870 __isl_take isl_union_map *umap);
5874 __isl_give isl_basic_set *isl_set_convex_hull(
5875 __isl_take isl_set *set);
5876 __isl_give isl_basic_map *isl_map_convex_hull(
5877 __isl_take isl_map *map);
5879 If the input set or relation has any existentially quantified
5880 variables, then the result of these operations is currently undefined.
5884 #include <isl/set.h>
5885 __isl_give isl_basic_set *
5886 isl_set_unshifted_simple_hull(
5887 __isl_take isl_set *set);
5888 __isl_give isl_basic_set *isl_set_simple_hull(
5889 __isl_take isl_set *set);
5890 __isl_give isl_basic_set *
5891 isl_set_plain_unshifted_simple_hull(
5892 __isl_take isl_set *set);
5893 __isl_give isl_basic_set *
5894 isl_set_unshifted_simple_hull_from_set_list(
5895 __isl_take isl_set *set,
5896 __isl_take isl_set_list *list);
5898 #include <isl/map.h>
5899 __isl_give isl_basic_map *
5900 isl_map_unshifted_simple_hull(
5901 __isl_take isl_map *map);
5902 __isl_give isl_basic_map *isl_map_simple_hull(
5903 __isl_take isl_map *map);
5904 __isl_give isl_basic_map *
5905 isl_map_plain_unshifted_simple_hull(
5906 __isl_take isl_map *map);
5907 __isl_give isl_basic_map *
5908 isl_map_unshifted_simple_hull_from_map_list(
5909 __isl_take isl_map *map,
5910 __isl_take isl_map_list *list);
5912 #include <isl/union_map.h>
5913 __isl_give isl_union_map *isl_union_map_simple_hull(
5914 __isl_take isl_union_map *umap);
5916 These functions compute a single basic set or relation
5917 that contains the whole input set or relation.
5918 In particular, the output is described by translates
5919 of the constraints describing the basic sets or relations in the input.
5920 In case of C<isl_set_unshifted_simple_hull>, only the original
5921 constraints are used, without any translation.
5922 In case of C<isl_set_plain_unshifted_simple_hull> and
5923 C<isl_map_plain_unshifted_simple_hull>, the result is described
5924 by original constraints that are obviously satisfied
5925 by the entire input set or relation.
5926 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5927 C<isl_map_unshifted_simple_hull_from_map_list>, the
5928 constraints are taken from the elements of the second argument.
5932 (See \autoref{s:simple hull}.)
5938 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5939 __isl_take isl_basic_set *bset);
5940 __isl_give isl_basic_set *isl_set_affine_hull(
5941 __isl_take isl_set *set);
5942 __isl_give isl_union_set *isl_union_set_affine_hull(
5943 __isl_take isl_union_set *uset);
5944 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5945 __isl_take isl_basic_map *bmap);
5946 __isl_give isl_basic_map *isl_map_affine_hull(
5947 __isl_take isl_map *map);
5948 __isl_give isl_union_map *isl_union_map_affine_hull(
5949 __isl_take isl_union_map *umap);
5951 In case of union sets and relations, the affine hull is computed
5954 =item * Polyhedral hull
5956 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5957 __isl_take isl_set *set);
5958 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5959 __isl_take isl_map *map);
5960 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5961 __isl_take isl_union_set *uset);
5962 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5963 __isl_take isl_union_map *umap);
5965 These functions compute a single basic set or relation
5966 not involving any existentially quantified variables
5967 that contains the whole input set or relation.
5968 In case of union sets and relations, the polyhedral hull is computed
5973 #include <isl/set.h>
5974 __isl_give isl_fixed_box *
5975 isl_set_get_simple_fixed_box_hull(
5976 __isl_keep isl_set *set)
5978 #include <isl/map.h>
5979 __isl_give isl_fixed_box *
5980 isl_map_get_range_simple_fixed_box_hull(
5981 __isl_keep isl_map *map);
5983 These functions try to approximate the set or
5984 the range of the map by a box of fixed size.
5985 The box is described in terms of an offset living in the same space as
5986 the input and a size living in the set or range space. For any element
5987 in the input map, the range value is greater than or equal to
5988 the offset applied to the domain value and the difference with
5989 this offset is strictly smaller than the size.
5990 The same holds for the elements of the input set, where
5991 the offset is a parametric constant value.
5992 If no fixed-size approximation can be found,
5993 an I<invalid> box is returned, i.e., one for which
5994 C<isl_fixed_box_is_valid> below returns false.
5996 The validity, the offset and the size of the box can be obtained using
5997 the following functions.
5999 #include <isl/fixed_box.h>
6000 isl_bool isl_fixed_box_is_valid(
6001 __isl_keep isl_fixed_box *box);
6002 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
6003 __isl_keep isl_fixed_box *box);
6004 __isl_give isl_multi_val *isl_fixed_box_get_size(
6005 __isl_keep isl_fixed_box *box);
6007 The box can be copied and freed using the following functions.
6009 #include <isl/fixed_box.h>
6010 __isl_give isl_fixed_box *isl_fixed_box_copy(
6011 __isl_keep isl_fixed_box *box);
6012 __isl_null isl_fixed_box *isl_fixed_box_free(
6013 __isl_take isl_fixed_box *box);
6015 A representation of the information contained in an object
6016 of type C<isl_fixed_box> can be obtained using
6018 #include <isl/fixed_box.h>
6019 __isl_give isl_printer *isl_printer_print_fixed_box(
6020 __isl_take isl_printer *p,
6021 __isl_keep isl_fixed_box *box);
6022 __isl_give char *isl_fixed_box_to_str(
6023 __isl_keep isl_fixed_box *box);
6025 C<isl_fixed_box_to_str> prints the information in flow format.
6027 =item * Other approximations
6029 #include <isl/set.h>
6030 __isl_give isl_basic_set *
6031 isl_basic_set_drop_constraints_involving_dims(
6032 __isl_take isl_basic_set *bset,
6033 enum isl_dim_type type,
6034 unsigned first, unsigned n);
6035 __isl_give isl_basic_set *
6036 isl_basic_set_drop_constraints_not_involving_dims(
6037 __isl_take isl_basic_set *bset,
6038 enum isl_dim_type type,
6039 unsigned first, unsigned n);
6040 __isl_give isl_set *
6041 isl_set_drop_constraints_involving_dims(
6042 __isl_take isl_set *set,
6043 enum isl_dim_type type,
6044 unsigned first, unsigned n);
6045 __isl_give isl_set *
6046 isl_set_drop_constraints_not_involving_dims(
6047 __isl_take isl_set *set,
6048 enum isl_dim_type type,
6049 unsigned first, unsigned n);
6051 #include <isl/map.h>
6052 __isl_give isl_basic_map *
6053 isl_basic_map_drop_constraints_involving_dims(
6054 __isl_take isl_basic_map *bmap,
6055 enum isl_dim_type type,
6056 unsigned first, unsigned n);
6057 __isl_give isl_basic_map *
6058 isl_basic_map_drop_constraints_not_involving_dims(
6059 __isl_take isl_basic_map *bmap,
6060 enum isl_dim_type type,
6061 unsigned first, unsigned n);
6062 __isl_give isl_map *
6063 isl_map_drop_constraints_involving_dims(
6064 __isl_take isl_map *map,
6065 enum isl_dim_type type,
6066 unsigned first, unsigned n);
6067 __isl_give isl_map *
6068 isl_map_drop_constraints_not_involving_dims(
6069 __isl_take isl_map *map,
6070 enum isl_dim_type type,
6071 unsigned first, unsigned n);
6073 These functions drop any constraints (not) involving the specified dimensions.
6074 Note that the result depends on the representation of the input.
6076 #include <isl/polynomial.h>
6077 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
6078 __isl_take isl_pw_qpolynomial *pwqp, int sign);
6079 __isl_give isl_union_pw_qpolynomial *
6080 isl_union_pw_qpolynomial_to_polynomial(
6081 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
6083 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
6084 the polynomial will be an overapproximation. If C<sign> is negative,
6085 it will be an underapproximation. If C<sign> is zero, the approximation
6086 will lie somewhere in between.
6090 __isl_give isl_basic_set *isl_basic_set_sample(
6091 __isl_take isl_basic_set *bset);
6092 __isl_give isl_basic_set *isl_set_sample(
6093 __isl_take isl_set *set);
6094 __isl_give isl_basic_map *isl_basic_map_sample(
6095 __isl_take isl_basic_map *bmap);
6096 __isl_give isl_basic_map *isl_map_sample(
6097 __isl_take isl_map *map);
6099 If the input (basic) set or relation is non-empty, then return
6100 a singleton subset of the input. Otherwise, return an empty set.
6102 =item * Optimization
6104 #include <isl/ilp.h>
6105 __isl_give isl_val *isl_basic_set_max_val(
6106 __isl_keep isl_basic_set *bset,
6107 __isl_keep isl_aff *obj);
6108 __isl_give isl_val *isl_set_min_val(
6109 __isl_keep isl_set *set,
6110 __isl_keep isl_aff *obj);
6111 __isl_give isl_val *isl_set_max_val(
6112 __isl_keep isl_set *set,
6113 __isl_keep isl_aff *obj);
6114 __isl_give isl_multi_val *
6115 isl_union_set_min_multi_union_pw_aff(
6116 __isl_keep isl_union_set *uset,
6117 __isl_keep isl_multi_union_pw_aff *obj);
6119 Compute the minimum or maximum of the integer affine expression C<obj>
6120 over the points in C<set>.
6121 The result is C<NULL> in case of an error, the optimal value in case
6122 there is one, negative infinity or infinity if the problem is unbounded and
6123 NaN if the problem is empty.
6125 #include <isl/ilp.h>
6126 __isl_give isl_multi_val *
6127 isl_pw_multi_aff_min_multi_val(
6128 __isl_take isl_pw_multi_aff *pma);
6129 __isl_give isl_multi_val *
6130 isl_pw_multi_aff_max_multi_val(
6131 __isl_take isl_pw_multi_aff *pma);
6132 __isl_give isl_multi_val *
6133 isl_multi_pw_aff_min_multi_val(
6134 __isl_take isl_multi_pw_aff *mpa);
6135 __isl_give isl_multi_val *
6136 isl_multi_pw_aff_max_multi_val(
6137 __isl_take isl_multi_pw_aff *mpa);
6138 __isl_give isl_val *isl_union_pw_aff_min_val(
6139 __isl_take isl_union_pw_aff *upa);
6140 __isl_give isl_val *isl_union_pw_aff_max_val(
6141 __isl_take isl_union_pw_aff *upa);
6142 __isl_give isl_multi_val *
6143 isl_multi_union_pw_aff_min_multi_val(
6144 __isl_take isl_multi_union_pw_aff *mupa);
6145 __isl_give isl_multi_val *
6146 isl_multi_union_pw_aff_max_multi_val(
6147 __isl_take isl_multi_union_pw_aff *mupa);
6149 Compute the minimum or maximum of the integer affine expression
6150 over its definition domain.
6151 The result is C<NULL> in case of an error, the optimal value in case
6152 there is one, negative infinity or infinity if the problem is unbounded and
6153 NaN if the problem is empty.
6155 #include <isl/ilp.h>
6156 __isl_give isl_val *isl_basic_set_dim_max_val(
6157 __isl_take isl_basic_set *bset, int pos);
6158 __isl_give isl_val *isl_set_dim_min_val(
6159 __isl_take isl_set *set, int pos);
6160 __isl_give isl_val *isl_set_dim_max_val(
6161 __isl_take isl_set *set, int pos);
6163 Return the minimal or maximal value attained by the given set dimension,
6164 independently of the parameter values and of any other dimensions.
6165 The result is C<NULL> in case of an error, the optimal value in case
6166 there is one, (negative) infinity if the problem is unbounded and
6167 NaN if the input is empty.
6169 =item * Parametric optimization
6171 __isl_give isl_pw_aff *isl_set_dim_min(
6172 __isl_take isl_set *set, int pos);
6173 __isl_give isl_pw_aff *isl_set_dim_max(
6174 __isl_take isl_set *set, int pos);
6175 __isl_give isl_pw_aff *isl_map_dim_min(
6176 __isl_take isl_map *map, int pos);
6177 __isl_give isl_pw_aff *isl_map_dim_max(
6178 __isl_take isl_map *map, int pos);
6179 __isl_give isl_multi_pw_aff *
6180 isl_set_min_multi_pw_aff(
6181 __isl_take isl_set *set);
6182 __isl_give isl_multi_pw_aff *
6183 isl_set_max_multi_pw_aff(
6184 __isl_take isl_set *set);
6185 __isl_give isl_multi_pw_aff *
6186 isl_map_min_multi_pw_aff(
6187 __isl_take isl_map *map);
6188 __isl_give isl_multi_pw_aff *
6189 isl_map_max_multi_pw_aff(
6190 __isl_take isl_map *map);
6192 Compute the minimum or maximum of the (given) set or output dimension(s)
6193 as a function of the parameters (and input dimensions), but independently
6194 of the other set or output dimensions.
6195 For lexicographic optimization, see L<"Lexicographic Optimization">.
6199 The following functions compute either the set of (rational) coefficient
6200 values of valid constraints for the given set or the set of (rational)
6201 values satisfying the constraints with coefficients from the given set.
6202 Internally, these two sets of functions perform essentially the
6203 same operations, except that the set of coefficients is assumed to
6204 be a cone, while the set of values may be any polyhedron.
6205 The current implementation is based on the Farkas lemma and
6206 Fourier-Motzkin elimination, but this may change or be made optional
6207 in future. In particular, future implementations may use different
6208 dualization algorithms or skip the elimination step.
6210 #include <isl/set.h>
6211 __isl_give isl_basic_set *isl_basic_set_coefficients(
6212 __isl_take isl_basic_set *bset);
6213 __isl_give isl_basic_set_list *
6214 isl_basic_set_list_coefficients(
6215 __isl_take isl_basic_set_list *list);
6216 __isl_give isl_basic_set *isl_set_coefficients(
6217 __isl_take isl_set *set);
6218 __isl_give isl_union_set *isl_union_set_coefficients(
6219 __isl_take isl_union_set *bset);
6220 __isl_give isl_basic_set *isl_basic_set_solutions(
6221 __isl_take isl_basic_set *bset);
6222 __isl_give isl_basic_set *isl_set_solutions(
6223 __isl_take isl_set *set);
6224 __isl_give isl_union_set *isl_union_set_solutions(
6225 __isl_take isl_union_set *bset);
6229 __isl_give isl_map *isl_map_fixed_power_val(
6230 __isl_take isl_map *map,
6231 __isl_take isl_val *exp);
6232 __isl_give isl_union_map *
6233 isl_union_map_fixed_power_val(
6234 __isl_take isl_union_map *umap,
6235 __isl_take isl_val *exp);
6237 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
6238 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
6239 of C<map> is computed.
6241 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
6243 __isl_give isl_union_map *isl_union_map_power(
6244 __isl_take isl_union_map *umap, isl_bool *exact);
6246 Compute a parametric representation for all positive powers I<k> of C<map>.
6247 The result maps I<k> to a nested relation corresponding to the
6248 I<k>th power of C<map>.
6249 The result may be an overapproximation. If the result is known to be exact,
6250 then C<*exact> is set to C<1>.
6252 =item * Transitive closure
6254 __isl_give isl_map *isl_map_transitive_closure(
6255 __isl_take isl_map *map, isl_bool *exact);
6256 __isl_give isl_union_map *isl_union_map_transitive_closure(
6257 __isl_take isl_union_map *umap, isl_bool *exact);
6259 Compute the transitive closure of C<map>.
6260 The result may be an overapproximation. If the result is known to be exact,
6261 then C<*exact> is set to C<1>.
6263 =item * Reaching path lengths
6265 __isl_give isl_map *isl_map_reaching_path_lengths(
6266 __isl_take isl_map *map, isl_bool *exact);
6268 Compute a relation that maps each element in the range of C<map>
6269 to the lengths of all paths composed of edges in C<map> that
6270 end up in the given element.
6271 The result may be an overapproximation. If the result is known to be exact,
6272 then C<*exact> is set to C<1>.
6273 To compute the I<maximal> path length, the resulting relation
6274 should be postprocessed by C<isl_map_lexmax>.
6275 In particular, if the input relation is a dependence relation
6276 (mapping sources to sinks), then the maximal path length corresponds
6277 to the free schedule.
6278 Note, however, that C<isl_map_lexmax> expects the maximum to be
6279 finite, so if the path lengths are unbounded (possibly due to
6280 the overapproximation), then you will get an error message.
6284 #include <isl/space.h>
6285 __isl_give isl_space *isl_space_wrap(
6286 __isl_take isl_space *space);
6287 __isl_give isl_space *isl_space_unwrap(
6288 __isl_take isl_space *space);
6290 #include <isl/local_space.h>
6291 __isl_give isl_local_space *isl_local_space_wrap(
6292 __isl_take isl_local_space *ls);
6294 #include <isl/set.h>
6295 __isl_give isl_basic_map *isl_basic_set_unwrap(
6296 __isl_take isl_basic_set *bset);
6297 __isl_give isl_map *isl_set_unwrap(
6298 __isl_take isl_set *set);
6300 #include <isl/map.h>
6301 __isl_give isl_basic_set *isl_basic_map_wrap(
6302 __isl_take isl_basic_map *bmap);
6303 __isl_give isl_set *isl_map_wrap(
6304 __isl_take isl_map *map);
6306 #include <isl/union_set.h>
6307 __isl_give isl_union_map *isl_union_set_unwrap(
6308 __isl_take isl_union_set *uset);
6310 #include <isl/union_map.h>
6311 __isl_give isl_union_set *isl_union_map_wrap(
6312 __isl_take isl_union_map *umap);
6314 The input to C<isl_space_unwrap> should
6315 be the space of a set, while that of
6316 C<isl_space_wrap> should be the space of a relation.
6317 Conversely, the output of C<isl_space_unwrap> is the space
6318 of a relation, while that of C<isl_space_wrap> is the space of a set.
6322 Remove any internal structure of domain (and range) of the given
6323 set or relation. If there is any such internal structure in the input,
6324 then the name of the space is also removed.
6326 #include <isl/space.h>
6327 __isl_give isl_space *isl_space_flatten_domain(
6328 __isl_take isl_space *space);
6329 __isl_give isl_space *isl_space_flatten_range(
6330 __isl_take isl_space *space);
6332 #include <isl/local_space.h>
6333 __isl_give isl_local_space *
6334 isl_local_space_flatten_domain(
6335 __isl_take isl_local_space *ls);
6336 __isl_give isl_local_space *
6337 isl_local_space_flatten_range(
6338 __isl_take isl_local_space *ls);
6340 #include <isl/set.h>
6341 __isl_give isl_basic_set *isl_basic_set_flatten(
6342 __isl_take isl_basic_set *bset);
6343 __isl_give isl_set *isl_set_flatten(
6344 __isl_take isl_set *set);
6346 #include <isl/map.h>
6347 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
6348 __isl_take isl_basic_map *bmap);
6349 __isl_give isl_basic_map *isl_basic_map_flatten_range(
6350 __isl_take isl_basic_map *bmap);
6351 __isl_give isl_map *isl_map_flatten_range(
6352 __isl_take isl_map *map);
6353 __isl_give isl_map *isl_map_flatten_domain(
6354 __isl_take isl_map *map);
6355 __isl_give isl_basic_map *isl_basic_map_flatten(
6356 __isl_take isl_basic_map *bmap);
6357 __isl_give isl_map *isl_map_flatten(
6358 __isl_take isl_map *map);
6361 __isl_give isl_multi_id *isl_multi_id_flatten_range(
6362 __isl_take isl_multi_id *mi);
6364 #include <isl/val.h>
6365 __isl_give isl_multi_val *isl_multi_val_flatten_range(
6366 __isl_take isl_multi_val *mv);
6368 #include <isl/aff.h>
6369 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
6370 __isl_take isl_multi_aff *ma);
6371 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
6372 __isl_take isl_multi_aff *ma);
6373 __isl_give isl_multi_pw_aff *
6374 isl_multi_pw_aff_flatten_range(
6375 __isl_take isl_multi_pw_aff *mpa);
6376 __isl_give isl_multi_union_pw_aff *
6377 isl_multi_union_pw_aff_flatten_range(
6378 __isl_take isl_multi_union_pw_aff *mupa);
6380 #include <isl/map.h>
6381 __isl_give isl_map *isl_set_flatten_map(
6382 __isl_take isl_set *set);
6384 The function above constructs a relation
6385 that maps the input set to a flattened version of the set.
6389 Lift the input set to a space with extra dimensions corresponding
6390 to the existentially quantified variables in the input.
6391 In particular, the result lives in a wrapped map where the domain
6392 is the original space and the range corresponds to the original
6393 existentially quantified variables.
6395 #include <isl/set.h>
6396 __isl_give isl_basic_set *isl_basic_set_lift(
6397 __isl_take isl_basic_set *bset);
6398 __isl_give isl_set *isl_set_lift(
6399 __isl_take isl_set *set);
6400 __isl_give isl_union_set *isl_union_set_lift(
6401 __isl_take isl_union_set *uset);
6403 Given a local space that contains the existentially quantified
6404 variables of a set, a basic relation that, when applied to
6405 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
6406 can be constructed using the following function.
6408 #include <isl/local_space.h>
6409 __isl_give isl_basic_map *isl_local_space_lifting(
6410 __isl_take isl_local_space *ls);
6412 #include <isl/aff.h>
6413 __isl_give isl_multi_aff *isl_multi_aff_lift(
6414 __isl_take isl_multi_aff *maff,
6415 __isl_give isl_local_space **ls);
6417 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
6418 then it is assigned the local space that lies at the basis of
6419 the lifting applied.
6421 =item * Internal Product
6423 #include <isl/space.h>
6424 __isl_give isl_space *isl_space_zip(
6425 __isl_take isl_space *space);
6427 #include <isl/map.h>
6428 __isl_give isl_basic_map *isl_basic_map_zip(
6429 __isl_take isl_basic_map *bmap);
6430 __isl_give isl_map *isl_map_zip(
6431 __isl_take isl_map *map);
6433 #include <isl/union_map.h>
6434 __isl_give isl_union_map *isl_union_map_zip(
6435 __isl_take isl_union_map *umap);
6437 Given a relation with nested relations for domain and range,
6438 interchange the range of the domain with the domain of the range.
6442 #include <isl/space.h>
6443 __isl_give isl_space *isl_space_curry(
6444 __isl_take isl_space *space);
6445 __isl_give isl_space *isl_space_uncurry(
6446 __isl_take isl_space *space);
6448 #include <isl/map.h>
6449 __isl_give isl_basic_map *isl_basic_map_curry(
6450 __isl_take isl_basic_map *bmap);
6451 __isl_give isl_basic_map *isl_basic_map_uncurry(
6452 __isl_take isl_basic_map *bmap);
6453 __isl_give isl_map *isl_map_curry(
6454 __isl_take isl_map *map);
6455 __isl_give isl_map *isl_map_uncurry(
6456 __isl_take isl_map *map);
6458 #include <isl/union_map.h>
6459 __isl_give isl_union_map *isl_union_map_curry(
6460 __isl_take isl_union_map *umap);
6461 __isl_give isl_union_map *isl_union_map_uncurry(
6462 __isl_take isl_union_map *umap);
6464 Given a relation with a nested relation for domain,
6465 the C<curry> functions
6466 move the range of the nested relation out of the domain
6467 and use it as the domain of a nested relation in the range,
6468 with the original range as range of this nested relation.
6469 The C<uncurry> functions perform the inverse operation.
6471 #include <isl/space.h>
6472 __isl_give isl_space *isl_space_range_curry(
6473 __isl_take isl_space *space);
6475 #include <isl/map.h>
6476 __isl_give isl_map *isl_map_range_curry(
6477 __isl_take isl_map *map);
6479 #include <isl/union_map.h>
6480 __isl_give isl_union_map *isl_union_map_range_curry(
6481 __isl_take isl_union_map *umap);
6483 These functions apply the currying to the relation that
6484 is nested inside the range of the input.
6486 =item * Aligning parameters
6488 Change the order of the parameters of the given set, relation
6490 such that the first parameters match those of C<model>.
6491 This may involve the introduction of extra parameters.
6492 All parameters need to be named.
6494 #include <isl/space.h>
6495 __isl_give isl_space *isl_space_align_params(
6496 __isl_take isl_space *space1,
6497 __isl_take isl_space *space2)
6499 #include <isl/set.h>
6500 __isl_give isl_basic_set *isl_basic_set_align_params(
6501 __isl_take isl_basic_set *bset,
6502 __isl_take isl_space *model);
6503 __isl_give isl_set *isl_set_align_params(
6504 __isl_take isl_set *set,
6505 __isl_take isl_space *model);
6507 #include <isl/map.h>
6508 __isl_give isl_basic_map *isl_basic_map_align_params(
6509 __isl_take isl_basic_map *bmap,
6510 __isl_take isl_space *model);
6511 __isl_give isl_map *isl_map_align_params(
6512 __isl_take isl_map *map,
6513 __isl_take isl_space *model);
6516 __isl_give isl_multi_id *isl_multi_id_align_params(
6517 __isl_take isl_multi_id *mi,
6518 __isl_take isl_space *model);
6520 #include <isl/val.h>
6521 __isl_give isl_multi_val *isl_multi_val_align_params(
6522 __isl_take isl_multi_val *mv,
6523 __isl_take isl_space *model);
6525 #include <isl/aff.h>
6526 __isl_give isl_aff *isl_aff_align_params(
6527 __isl_take isl_aff *aff,
6528 __isl_take isl_space *model);
6529 __isl_give isl_multi_aff *isl_multi_aff_align_params(
6530 __isl_take isl_multi_aff *multi,
6531 __isl_take isl_space *model);
6532 __isl_give isl_pw_aff *isl_pw_aff_align_params(
6533 __isl_take isl_pw_aff *pwaff,
6534 __isl_take isl_space *model);
6535 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
6536 __isl_take isl_pw_multi_aff *pma,
6537 __isl_take isl_space *model);
6538 __isl_give isl_union_pw_aff *
6539 isl_union_pw_aff_align_params(
6540 __isl_take isl_union_pw_aff *upa,
6541 __isl_take isl_space *model);
6542 __isl_give isl_union_pw_multi_aff *
6543 isl_union_pw_multi_aff_align_params(
6544 __isl_take isl_union_pw_multi_aff *upma,
6545 __isl_take isl_space *model);
6546 __isl_give isl_multi_union_pw_aff *
6547 isl_multi_union_pw_aff_align_params(
6548 __isl_take isl_multi_union_pw_aff *mupa,
6549 __isl_take isl_space *model);
6551 #include <isl/polynomial.h>
6552 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
6553 __isl_take isl_qpolynomial *qp,
6554 __isl_take isl_space *model);
6556 =item * Drop unused parameters
6558 Drop parameters that are not referenced by the isl object.
6559 All parameters need to be named.
6561 #include <isl/set.h>
6562 __isl_give isl_basic_set *
6563 isl_basic_set_drop_unused_params(
6564 __isl_take isl_basic_set *bset);
6565 __isl_give isl_set *isl_set_drop_unused_params(
6566 __isl_take isl_set *set);
6568 #include <isl/map.h>
6569 __isl_give isl_basic_map *
6570 isl_basic_map_drop_unused_params(
6571 __isl_take isl_basic_map *bmap);
6572 __isl_give isl_map *isl_map_drop_unused_params(
6573 __isl_take isl_map *map);
6575 #include <isl/aff.h>
6576 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
6577 __isl_take isl_pw_aff *pa);
6578 __isl_give isl_pw_multi_aff *
6579 isl_pw_multi_aff_drop_unused_params(
6580 __isl_take isl_pw_multi_aff *pma);
6582 #include <isl/polynomial.h>
6583 __isl_give isl_pw_qpolynomial *
6584 isl_pw_qpolynomial_drop_unused_params(
6585 __isl_take isl_pw_qpolynomial *pwqp);
6586 __isl_give isl_pw_qpolynomial_fold *
6587 isl_pw_qpolynomial_fold_drop_unused_params(
6588 __isl_take isl_pw_qpolynomial_fold *pwf);
6590 =item * Unary Arithmetic Operations
6592 #include <isl/set.h>
6593 __isl_give isl_set *isl_set_neg(
6594 __isl_take isl_set *set);
6595 #include <isl/map.h>
6596 __isl_give isl_map *isl_map_neg(
6597 __isl_take isl_map *map);
6599 C<isl_set_neg> constructs a set containing the opposites of
6600 the elements in its argument.
6601 The domain of the result of C<isl_map_neg> is the same
6602 as the domain of its argument. The corresponding range
6603 elements are the opposites of the corresponding range
6604 elements in the argument.
6606 #include <isl/val.h>
6607 __isl_give isl_multi_val *isl_multi_val_neg(
6608 __isl_take isl_multi_val *mv);
6610 #include <isl/aff.h>
6611 __isl_give isl_aff *isl_aff_neg(
6612 __isl_take isl_aff *aff);
6613 __isl_give isl_multi_aff *isl_multi_aff_neg(
6614 __isl_take isl_multi_aff *ma);
6615 __isl_give isl_pw_aff *isl_pw_aff_neg(
6616 __isl_take isl_pw_aff *pwaff);
6617 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
6618 __isl_take isl_pw_multi_aff *pma);
6619 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
6620 __isl_take isl_multi_pw_aff *mpa);
6621 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
6622 __isl_take isl_union_pw_aff *upa);
6623 __isl_give isl_union_pw_multi_aff *
6624 isl_union_pw_multi_aff_neg(
6625 __isl_take isl_union_pw_multi_aff *upma);
6626 __isl_give isl_multi_union_pw_aff *
6627 isl_multi_union_pw_aff_neg(
6628 __isl_take isl_multi_union_pw_aff *mupa);
6629 __isl_give isl_aff *isl_aff_ceil(
6630 __isl_take isl_aff *aff);
6631 __isl_give isl_pw_aff *isl_pw_aff_ceil(
6632 __isl_take isl_pw_aff *pwaff);
6633 __isl_give isl_aff *isl_aff_floor(
6634 __isl_take isl_aff *aff);
6635 __isl_give isl_multi_aff *isl_multi_aff_floor(
6636 __isl_take isl_multi_aff *ma);
6637 __isl_give isl_pw_aff *isl_pw_aff_floor(
6638 __isl_take isl_pw_aff *pwaff);
6639 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
6640 __isl_take isl_union_pw_aff *upa);
6641 __isl_give isl_multi_union_pw_aff *
6642 isl_multi_union_pw_aff_floor(
6643 __isl_take isl_multi_union_pw_aff *mupa);
6645 #include <isl/aff.h>
6646 __isl_give isl_pw_aff *isl_pw_aff_list_min(
6647 __isl_take isl_pw_aff_list *list);
6648 __isl_give isl_pw_aff *isl_pw_aff_list_max(
6649 __isl_take isl_pw_aff_list *list);
6651 #include <isl/polynomial.h>
6652 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
6653 __isl_take isl_qpolynomial *qp);
6654 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
6655 __isl_take isl_pw_qpolynomial *pwqp);
6656 __isl_give isl_union_pw_qpolynomial *
6657 isl_union_pw_qpolynomial_neg(
6658 __isl_take isl_union_pw_qpolynomial *upwqp);
6659 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
6660 __isl_take isl_qpolynomial *qp,
6662 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
6663 __isl_take isl_pw_qpolynomial *pwqp,
6668 The following functions evaluate a function in a point.
6670 #include <isl/aff.h>
6671 __isl_give isl_val *isl_aff_eval(
6672 __isl_take isl_aff *aff,
6673 __isl_take isl_point *pnt);
6674 __isl_give isl_val *isl_pw_aff_eval(
6675 __isl_take isl_pw_aff *pa,
6676 __isl_take isl_point *pnt);
6678 #include <isl/polynomial.h>
6679 __isl_give isl_val *isl_pw_qpolynomial_eval(
6680 __isl_take isl_pw_qpolynomial *pwqp,
6681 __isl_take isl_point *pnt);
6682 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
6683 __isl_take isl_pw_qpolynomial_fold *pwf,
6684 __isl_take isl_point *pnt);
6685 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
6686 __isl_take isl_union_pw_qpolynomial *upwqp,
6687 __isl_take isl_point *pnt);
6688 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
6689 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6690 __isl_take isl_point *pnt);
6692 These functions return NaN when evaluated at a void point.
6693 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
6694 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
6695 when the function is evaluated outside its explicit domain.
6697 =item * Dimension manipulation
6699 It is usually not advisable to directly change the (input or output)
6700 space of a set or a relation as this removes the name and the internal
6701 structure of the space. However, the functions below can be useful
6702 to add new parameters, assuming
6703 C<isl_set_align_params> and C<isl_map_align_params>
6706 #include <isl/space.h>
6707 __isl_give isl_space *isl_space_add_dims(
6708 __isl_take isl_space *space,
6709 enum isl_dim_type type, unsigned n);
6710 __isl_give isl_space *isl_space_insert_dims(
6711 __isl_take isl_space *space,
6712 enum isl_dim_type type, unsigned pos, unsigned n);
6713 __isl_give isl_space *isl_space_drop_dims(
6714 __isl_take isl_space *space,
6715 enum isl_dim_type type, unsigned first, unsigned n);
6716 __isl_give isl_space *isl_space_move_dims(
6717 __isl_take isl_space *space,
6718 enum isl_dim_type dst_type, unsigned dst_pos,
6719 enum isl_dim_type src_type, unsigned src_pos,
6722 #include <isl/local_space.h>
6723 __isl_give isl_local_space *isl_local_space_add_dims(
6724 __isl_take isl_local_space *ls,
6725 enum isl_dim_type type, unsigned n);
6726 __isl_give isl_local_space *isl_local_space_insert_dims(
6727 __isl_take isl_local_space *ls,
6728 enum isl_dim_type type, unsigned first, unsigned n);
6729 __isl_give isl_local_space *isl_local_space_drop_dims(
6730 __isl_take isl_local_space *ls,
6731 enum isl_dim_type type, unsigned first, unsigned n);
6733 #include <isl/set.h>
6734 __isl_give isl_basic_set *isl_basic_set_add_dims(
6735 __isl_take isl_basic_set *bset,
6736 enum isl_dim_type type, unsigned n);
6737 __isl_give isl_set *isl_set_add_dims(
6738 __isl_take isl_set *set,
6739 enum isl_dim_type type, unsigned n);
6740 __isl_give isl_basic_set *isl_basic_set_insert_dims(
6741 __isl_take isl_basic_set *bset,
6742 enum isl_dim_type type, unsigned pos,
6744 __isl_give isl_set *isl_set_insert_dims(
6745 __isl_take isl_set *set,
6746 enum isl_dim_type type, unsigned pos, unsigned n);
6747 __isl_give isl_basic_set *isl_basic_set_move_dims(
6748 __isl_take isl_basic_set *bset,
6749 enum isl_dim_type dst_type, unsigned dst_pos,
6750 enum isl_dim_type src_type, unsigned src_pos,
6752 __isl_give isl_set *isl_set_move_dims(
6753 __isl_take isl_set *set,
6754 enum isl_dim_type dst_type, unsigned dst_pos,
6755 enum isl_dim_type src_type, unsigned src_pos,
6758 #include <isl/map.h>
6759 __isl_give isl_basic_map *isl_basic_map_add_dims(
6760 __isl_take isl_basic_map *bmap,
6761 enum isl_dim_type type, unsigned n);
6762 __isl_give isl_map *isl_map_add_dims(
6763 __isl_take isl_map *map,
6764 enum isl_dim_type type, unsigned n);
6765 __isl_give isl_basic_map *isl_basic_map_insert_dims(
6766 __isl_take isl_basic_map *bmap,
6767 enum isl_dim_type type, unsigned pos,
6769 __isl_give isl_map *isl_map_insert_dims(
6770 __isl_take isl_map *map,
6771 enum isl_dim_type type, unsigned pos, unsigned n);
6772 __isl_give isl_basic_map *isl_basic_map_move_dims(
6773 __isl_take isl_basic_map *bmap,
6774 enum isl_dim_type dst_type, unsigned dst_pos,
6775 enum isl_dim_type src_type, unsigned src_pos,
6777 __isl_give isl_map *isl_map_move_dims(
6778 __isl_take isl_map *map,
6779 enum isl_dim_type dst_type, unsigned dst_pos,
6780 enum isl_dim_type src_type, unsigned src_pos,
6783 #include <isl/val.h>
6784 __isl_give isl_multi_val *isl_multi_val_insert_dims(
6785 __isl_take isl_multi_val *mv,
6786 enum isl_dim_type type, unsigned first, unsigned n);
6787 __isl_give isl_multi_val *isl_multi_val_add_dims(
6788 __isl_take isl_multi_val *mv,
6789 enum isl_dim_type type, unsigned n);
6790 __isl_give isl_multi_val *isl_multi_val_drop_dims(
6791 __isl_take isl_multi_val *mv,
6792 enum isl_dim_type type, unsigned first, unsigned n);
6794 #include <isl/aff.h>
6795 __isl_give isl_aff *isl_aff_insert_dims(
6796 __isl_take isl_aff *aff,
6797 enum isl_dim_type type, unsigned first, unsigned n);
6798 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
6799 __isl_take isl_multi_aff *ma,
6800 enum isl_dim_type type, unsigned first, unsigned n);
6801 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
6802 __isl_take isl_pw_aff *pwaff,
6803 enum isl_dim_type type, unsigned first, unsigned n);
6804 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
6805 __isl_take isl_multi_pw_aff *mpa,
6806 enum isl_dim_type type, unsigned first, unsigned n);
6807 __isl_give isl_aff *isl_aff_add_dims(
6808 __isl_take isl_aff *aff,
6809 enum isl_dim_type type, unsigned n);
6810 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
6811 __isl_take isl_multi_aff *ma,
6812 enum isl_dim_type type, unsigned n);
6813 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
6814 __isl_take isl_pw_aff *pwaff,
6815 enum isl_dim_type type, unsigned n);
6816 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
6817 __isl_take isl_multi_pw_aff *mpa,
6818 enum isl_dim_type type, unsigned n);
6819 __isl_give isl_aff *isl_aff_drop_dims(
6820 __isl_take isl_aff *aff,
6821 enum isl_dim_type type, unsigned first, unsigned n);
6822 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
6823 __isl_take isl_multi_aff *maff,
6824 enum isl_dim_type type, unsigned first, unsigned n);
6825 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
6826 __isl_take isl_pw_aff *pwaff,
6827 enum isl_dim_type type, unsigned first, unsigned n);
6828 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
6829 __isl_take isl_pw_multi_aff *pma,
6830 enum isl_dim_type type, unsigned first, unsigned n);
6831 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
6832 __isl_take isl_union_pw_aff *upa,
6833 enum isl_dim_type type, unsigned first, unsigned n);
6834 __isl_give isl_union_pw_multi_aff *
6835 isl_union_pw_multi_aff_drop_dims(
6836 __isl_take isl_union_pw_multi_aff *upma,
6837 enum isl_dim_type type,
6838 unsigned first, unsigned n);
6839 __isl_give isl_multi_union_pw_aff *
6840 isl_multi_union_pw_aff_drop_dims(
6841 __isl_take isl_multi_union_pw_aff *mupa,
6842 enum isl_dim_type type, unsigned first,
6844 __isl_give isl_aff *isl_aff_move_dims(
6845 __isl_take isl_aff *aff,
6846 enum isl_dim_type dst_type, unsigned dst_pos,
6847 enum isl_dim_type src_type, unsigned src_pos,
6849 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
6850 __isl_take isl_multi_aff *ma,
6851 enum isl_dim_type dst_type, unsigned dst_pos,
6852 enum isl_dim_type src_type, unsigned src_pos,
6854 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
6855 __isl_take isl_pw_aff *pa,
6856 enum isl_dim_type dst_type, unsigned dst_pos,
6857 enum isl_dim_type src_type, unsigned src_pos,
6859 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
6860 __isl_take isl_multi_pw_aff *pma,
6861 enum isl_dim_type dst_type, unsigned dst_pos,
6862 enum isl_dim_type src_type, unsigned src_pos,
6865 #include <isl/polynomial.h>
6866 __isl_give isl_union_pw_qpolynomial *
6867 isl_union_pw_qpolynomial_drop_dims(
6868 __isl_take isl_union_pw_qpolynomial *upwqp,
6869 enum isl_dim_type type,
6870 unsigned first, unsigned n);
6871 __isl_give isl_union_pw_qpolynomial_fold *
6872 isl_union_pw_qpolynomial_fold_drop_dims(
6873 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6874 enum isl_dim_type type,
6875 unsigned first, unsigned n);
6877 The operations on union expressions can only manipulate parameters.
6881 =head2 Binary Operations
6883 The two arguments of a binary operation not only need to live
6884 in the same C<isl_ctx>, they currently also need to have
6885 the same (number of) parameters.
6887 =head3 Basic Operations
6891 =item * Intersection
6893 #include <isl/local_space.h>
6894 __isl_give isl_local_space *isl_local_space_intersect(
6895 __isl_take isl_local_space *ls1,
6896 __isl_take isl_local_space *ls2);
6898 #include <isl/set.h>
6899 __isl_give isl_basic_set *isl_basic_set_intersect_params(
6900 __isl_take isl_basic_set *bset1,
6901 __isl_take isl_basic_set *bset2);
6902 __isl_give isl_basic_set *isl_basic_set_intersect(
6903 __isl_take isl_basic_set *bset1,
6904 __isl_take isl_basic_set *bset2);
6905 __isl_give isl_basic_set *isl_basic_set_list_intersect(
6906 __isl_take struct isl_basic_set_list *list);
6907 __isl_give isl_set *isl_set_intersect_params(
6908 __isl_take isl_set *set,
6909 __isl_take isl_set *params);
6910 __isl_give isl_set *isl_set_intersect(
6911 __isl_take isl_set *set1,
6912 __isl_take isl_set *set2);
6913 __isl_give isl_set *isl_set_intersect_factor_domain(
6914 __isl_take isl_set *set,
6915 __isl_take isl_set *domain);
6916 __isl_give isl_set *isl_set_intersect_factor_range(
6917 __isl_take isl_set *set,
6918 __isl_take isl_set *range);
6920 #include <isl/map.h>
6921 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
6922 __isl_take isl_basic_map *bmap,
6923 __isl_take isl_basic_set *bset);
6924 __isl_give isl_basic_map *isl_basic_map_intersect_range(
6925 __isl_take isl_basic_map *bmap,
6926 __isl_take isl_basic_set *bset);
6927 __isl_give isl_basic_map *isl_basic_map_intersect(
6928 __isl_take isl_basic_map *bmap1,
6929 __isl_take isl_basic_map *bmap2);
6930 __isl_give isl_basic_map *isl_basic_map_list_intersect(
6931 __isl_take isl_basic_map_list *list);
6932 __isl_give isl_map *isl_map_intersect_params(
6933 __isl_take isl_map *map,
6934 __isl_take isl_set *params);
6935 __isl_give isl_map *isl_map_intersect_domain(
6936 __isl_take isl_map *map,
6937 __isl_take isl_set *set);
6938 __isl_give isl_map *isl_map_intersect_range(
6939 __isl_take isl_map *map,
6940 __isl_take isl_set *set);
6941 __isl_give isl_map *isl_map_intersect(
6942 __isl_take isl_map *map1,
6943 __isl_take isl_map *map2);
6944 __isl_give isl_map *
6945 isl_map_intersect_domain_factor_range(
6946 __isl_take isl_map *map,
6947 __isl_take isl_map *factor);
6948 __isl_give isl_map *
6949 isl_map_intersect_range_factor_domain(
6950 __isl_take isl_map *map,
6951 __isl_take isl_map *factor);
6952 __isl_give isl_map *
6953 isl_map_intersect_range_factor_range(
6954 __isl_take isl_map *map,
6955 __isl_take isl_map *factor);
6957 #include <isl/union_set.h>
6958 __isl_give isl_union_set *isl_union_set_intersect_params(
6959 __isl_take isl_union_set *uset,
6960 __isl_take isl_set *set);
6961 __isl_give isl_union_set *isl_union_set_intersect(
6962 __isl_take isl_union_set *uset1,
6963 __isl_take isl_union_set *uset2);
6965 #include <isl/union_map.h>
6966 __isl_give isl_union_map *isl_union_map_intersect_params(
6967 __isl_take isl_union_map *umap,
6968 __isl_take isl_set *set);
6969 __isl_give isl_union_map *isl_union_map_intersect_domain(
6970 __isl_take isl_union_map *umap,
6971 __isl_take isl_union_set *uset);
6972 __isl_give isl_union_map *isl_union_map_intersect_range(
6973 __isl_take isl_union_map *umap,
6974 __isl_take isl_union_set *uset);
6975 __isl_give isl_union_map *isl_union_map_intersect(
6976 __isl_take isl_union_map *umap1,
6977 __isl_take isl_union_map *umap2);
6978 __isl_give isl_union_map *
6979 isl_union_map_intersect_domain_factor_range(
6980 __isl_take isl_union_map *umap,
6981 __isl_take isl_union_map *factor);
6982 __isl_give isl_union_map *
6983 isl_union_map_intersect_range_factor_domain(
6984 __isl_take isl_union_map *umap,
6985 __isl_take isl_union_map *factor);
6986 __isl_give isl_union_map *
6987 isl_union_map_intersect_range_factor_range(
6988 __isl_take isl_union_map *umap,
6989 __isl_take isl_union_map *factor);
6991 #include <isl/aff.h>
6992 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6993 __isl_take isl_pw_aff *pa,
6994 __isl_take isl_set *set);
6995 __isl_give isl_multi_pw_aff *
6996 isl_multi_pw_aff_intersect_domain(
6997 __isl_take isl_multi_pw_aff *mpa,
6998 __isl_take isl_set *domain);
6999 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
7000 __isl_take isl_pw_multi_aff *pma,
7001 __isl_take isl_set *set);
7002 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
7003 __isl_take isl_union_pw_aff *upa,
7004 __isl_take isl_union_set *uset);
7005 __isl_give isl_union_pw_multi_aff *
7006 isl_union_pw_multi_aff_intersect_domain(
7007 __isl_take isl_union_pw_multi_aff *upma,
7008 __isl_take isl_union_set *uset);
7009 __isl_give isl_multi_union_pw_aff *
7010 isl_multi_union_pw_aff_intersect_domain(
7011 __isl_take isl_multi_union_pw_aff *mupa,
7012 __isl_take isl_union_set *uset);
7013 __isl_give isl_pw_aff *
7014 isl_pw_aff_intersect_domain_wrapped_domain(
7015 __isl_take isl_pw_aff *pa,
7016 __isl_take isl_set *set);
7017 __isl_give isl_pw_multi_aff *
7018 isl_pw_multi_aff_intersect_domain_wrapped_domain(
7019 __isl_take isl_pw_multi_aff *pma,
7020 __isl_take isl_set *set);
7021 __isl_give isl_union_pw_aff *
7022 isl_union_pw_aff_intersect_domain_wrapped_domain(
7023 __isl_take isl_union_pw_aff *upa,
7024 __isl_take isl_union_set *uset);
7025 __isl_give isl_union_pw_multi_aff *
7026 isl_union_pw_multi_aff_intersect_domain_wrapped_domain(
7027 __isl_take isl_union_pw_multi_aff *upma,
7028 __isl_take isl_union_set *uset);
7029 __isl_give isl_pw_aff *
7030 isl_pw_aff_intersect_domain_wrapped_range(
7031 __isl_take isl_pw_aff *pa,
7032 __isl_take isl_set *set);
7033 __isl_give isl_pw_multi_aff *
7034 isl_pw_multi_aff_intersect_domain_wrapped_range(
7035 __isl_take isl_pw_multi_aff *pma,
7036 __isl_take isl_set *set);
7037 __isl_give isl_union_pw_multi_aff *
7038 isl_union_pw_multi_aff_intersect_domain_wrapped_range(
7039 __isl_take isl_union_pw_multi_aff *upma,
7040 __isl_take isl_union_set *uset);
7041 __isl_give isl_union_pw_aff *
7042 isl_union_pw_aff_intersect_domain_wrapped_range(
7043 __isl_take isl_union_pw_aff *upa,
7044 __isl_take isl_union_set *uset);
7045 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
7046 __isl_take isl_pw_aff *pa,
7047 __isl_take isl_set *set);
7048 __isl_give isl_multi_pw_aff *
7049 isl_multi_pw_aff_intersect_params(
7050 __isl_take isl_multi_pw_aff *mpa,
7051 __isl_take isl_set *set);
7052 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
7053 __isl_take isl_pw_multi_aff *pma,
7054 __isl_take isl_set *set);
7055 __isl_give isl_union_pw_aff *
7056 isl_union_pw_aff_intersect_params(
7057 __isl_take isl_union_pw_aff *upa,
7058 __isl_take isl_set *set);
7059 __isl_give isl_union_pw_multi_aff *
7060 isl_union_pw_multi_aff_intersect_params(
7061 __isl_take isl_union_pw_multi_aff *upma,
7062 __isl_take isl_set *set);
7063 __isl_give isl_multi_union_pw_aff *
7064 isl_multi_union_pw_aff_intersect_params(
7065 __isl_take isl_multi_union_pw_aff *mupa,
7066 __isl_take isl_set *params);
7067 __isl_give isl_multi_union_pw_aff *
7068 isl_multi_union_pw_aff_intersect_range(
7069 __isl_take isl_multi_union_pw_aff *mupa,
7070 __isl_take isl_set *set);
7072 #include <isl/polynomial.h>
7073 __isl_give isl_pw_qpolynomial *
7074 isl_pw_qpolynomial_intersect_domain(
7075 __isl_take isl_pw_qpolynomial *pwpq,
7076 __isl_take isl_set *set);
7077 __isl_give isl_union_pw_qpolynomial *
7078 isl_union_pw_qpolynomial_intersect_domain(
7079 __isl_take isl_union_pw_qpolynomial *upwpq,
7080 __isl_take isl_union_set *uset);
7081 __isl_give isl_union_pw_qpolynomial_fold *
7082 isl_union_pw_qpolynomial_fold_intersect_domain(
7083 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7084 __isl_take isl_union_set *uset);
7085 __isl_give isl_pw_qpolynomial *
7086 isl_pw_qpolynomial_intersect_domain_wrapped_domain(
7087 __isl_take isl_pw_qpolynomial *pwpq,
7088 __isl_take isl_set *set);
7089 __isl_give isl_pw_qpolynomial_fold *
7090 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7091 __isl_take isl_pw_qpolynomial_fold *pwf,
7092 __isl_take isl_set *set);
7093 __isl_give isl_union_pw_qpolynomial *
7094 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain(
7095 __isl_take isl_union_pw_qpolynomial *upwpq,
7096 __isl_take isl_union_set *uset);
7097 __isl_give isl_union_pw_qpolynomial_fold *
7098 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7099 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7100 __isl_take isl_union_set *uset);
7101 __isl_give isl_pw_qpolynomial *
7102 isl_pw_qpolynomial_intersect_domain_wrapped_range(
7103 __isl_take isl_pw_qpolynomial *pwpq,
7104 __isl_take isl_set *set);
7105 __isl_give isl_pw_qpolynomial_fold *
7106 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7107 __isl_take isl_pw_qpolynomial_fold *pwf,
7108 __isl_take isl_set *set);
7109 __isl_give isl_union_pw_qpolynomial *
7110 isl_union_pw_qpolynomial_intersect_domain_wrapped_range(
7111 __isl_take isl_union_pw_qpolynomial *upwpq,
7112 __isl_take isl_union_set *uset);
7113 __isl_give isl_union_pw_qpolynomial_fold *
7114 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7115 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7116 __isl_take isl_union_set *uset);
7117 __isl_give isl_pw_qpolynomial *
7118 isl_pw_qpolynomial_intersect_params(
7119 __isl_take isl_pw_qpolynomial *pwpq,
7120 __isl_take isl_set *set);
7121 __isl_give isl_pw_qpolynomial_fold *
7122 isl_pw_qpolynomial_fold_intersect_params(
7123 __isl_take isl_pw_qpolynomial_fold *pwf,
7124 __isl_take isl_set *set);
7125 __isl_give isl_union_pw_qpolynomial *
7126 isl_union_pw_qpolynomial_intersect_params(
7127 __isl_take isl_union_pw_qpolynomial *upwpq,
7128 __isl_take isl_set *set);
7129 __isl_give isl_union_pw_qpolynomial_fold *
7130 isl_union_pw_qpolynomial_fold_intersect_params(
7131 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7132 __isl_take isl_set *set);
7134 The second argument to the C<_params> functions needs to be
7135 a parametric (basic) set. For the other functions, a parametric set
7136 for either argument is only allowed if the other argument is
7137 a parametric set as well.
7138 The list passed to C<isl_basic_set_list_intersect> needs to have
7139 at least one element and all elements need to live in the same space.
7140 The function C<isl_multi_union_pw_aff_intersect_range>
7141 restricts the input function to those shared domain elements
7142 that map to the specified range.
7146 #include <isl/set.h>
7147 __isl_give isl_set *isl_basic_set_union(
7148 __isl_take isl_basic_set *bset1,
7149 __isl_take isl_basic_set *bset2);
7150 __isl_give isl_set *isl_set_union(
7151 __isl_take isl_set *set1,
7152 __isl_take isl_set *set2);
7153 __isl_give isl_set *isl_set_list_union(
7154 __isl_take isl_set_list *list);
7156 #include <isl/map.h>
7157 __isl_give isl_map *isl_basic_map_union(
7158 __isl_take isl_basic_map *bmap1,
7159 __isl_take isl_basic_map *bmap2);
7160 __isl_give isl_map *isl_map_union(
7161 __isl_take isl_map *map1,
7162 __isl_take isl_map *map2);
7164 #include <isl/union_set.h>
7165 __isl_give isl_union_set *isl_union_set_union(
7166 __isl_take isl_union_set *uset1,
7167 __isl_take isl_union_set *uset2);
7168 __isl_give isl_union_set *isl_union_set_list_union(
7169 __isl_take isl_union_set_list *list);
7171 #include <isl/union_map.h>
7172 __isl_give isl_union_map *isl_union_map_union(
7173 __isl_take isl_union_map *umap1,
7174 __isl_take isl_union_map *umap2);
7176 The list passed to C<isl_set_list_union> needs to have
7177 at least one element and all elements need to live in the same space.
7179 =item * Set difference
7181 #include <isl/set.h>
7182 __isl_give isl_set *isl_set_subtract(
7183 __isl_take isl_set *set1,
7184 __isl_take isl_set *set2);
7186 #include <isl/map.h>
7187 __isl_give isl_map *isl_map_subtract(
7188 __isl_take isl_map *map1,
7189 __isl_take isl_map *map2);
7190 __isl_give isl_map *isl_map_subtract_domain(
7191 __isl_take isl_map *map,
7192 __isl_take isl_set *dom);
7193 __isl_give isl_map *isl_map_subtract_range(
7194 __isl_take isl_map *map,
7195 __isl_take isl_set *dom);
7197 #include <isl/union_set.h>
7198 __isl_give isl_union_set *isl_union_set_subtract(
7199 __isl_take isl_union_set *uset1,
7200 __isl_take isl_union_set *uset2);
7202 #include <isl/union_map.h>
7203 __isl_give isl_union_map *isl_union_map_subtract(
7204 __isl_take isl_union_map *umap1,
7205 __isl_take isl_union_map *umap2);
7206 __isl_give isl_union_map *isl_union_map_subtract_domain(
7207 __isl_take isl_union_map *umap,
7208 __isl_take isl_union_set *dom);
7209 __isl_give isl_union_map *isl_union_map_subtract_range(
7210 __isl_take isl_union_map *umap,
7211 __isl_take isl_union_set *dom);
7213 #include <isl/aff.h>
7214 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
7215 __isl_take isl_pw_aff *pa,
7216 __isl_take isl_set *set);
7217 __isl_give isl_pw_multi_aff *
7218 isl_pw_multi_aff_subtract_domain(
7219 __isl_take isl_pw_multi_aff *pma,
7220 __isl_take isl_set *set);
7221 __isl_give isl_union_pw_aff *
7222 isl_union_pw_aff_subtract_domain(
7223 __isl_take isl_union_pw_aff *upa,
7224 __isl_take isl_union_set *uset);
7225 __isl_give isl_union_pw_multi_aff *
7226 isl_union_pw_multi_aff_subtract_domain(
7227 __isl_take isl_union_pw_multi_aff *upma,
7228 __isl_take isl_union_set *uset);
7230 #include <isl/polynomial.h>
7231 __isl_give isl_pw_qpolynomial *
7232 isl_pw_qpolynomial_subtract_domain(
7233 __isl_take isl_pw_qpolynomial *pwpq,
7234 __isl_take isl_set *set);
7235 __isl_give isl_pw_qpolynomial_fold *
7236 isl_pw_qpolynomial_fold_subtract_domain(
7237 __isl_take isl_pw_qpolynomial_fold *pwf,
7238 __isl_take isl_set *set);
7239 __isl_give isl_union_pw_qpolynomial *
7240 isl_union_pw_qpolynomial_subtract_domain(
7241 __isl_take isl_union_pw_qpolynomial *upwpq,
7242 __isl_take isl_union_set *uset);
7243 __isl_give isl_union_pw_qpolynomial_fold *
7244 isl_union_pw_qpolynomial_fold_subtract_domain(
7245 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7246 __isl_take isl_union_set *uset);
7250 #include <isl/space.h>
7251 __isl_give isl_space *isl_space_join(
7252 __isl_take isl_space *left,
7253 __isl_take isl_space *right);
7255 #include <isl/set.h>
7256 __isl_give isl_basic_set *isl_basic_set_apply(
7257 __isl_take isl_basic_set *bset,
7258 __isl_take isl_basic_map *bmap);
7259 __isl_give isl_set *isl_set_apply(
7260 __isl_take isl_set *set,
7261 __isl_take isl_map *map);
7263 #include <isl/union_set.h>
7264 __isl_give isl_union_set *isl_union_set_apply(
7265 __isl_take isl_union_set *uset,
7266 __isl_take isl_union_map *umap);
7268 #include <isl/map.h>
7269 __isl_give isl_basic_map *isl_basic_map_apply_domain(
7270 __isl_take isl_basic_map *bmap1,
7271 __isl_take isl_basic_map *bmap2);
7272 __isl_give isl_basic_map *isl_basic_map_apply_range(
7273 __isl_take isl_basic_map *bmap1,
7274 __isl_take isl_basic_map *bmap2);
7275 __isl_give isl_map *isl_map_apply_domain(
7276 __isl_take isl_map *map1,
7277 __isl_take isl_map *map2);
7278 __isl_give isl_map *isl_map_apply_range(
7279 __isl_take isl_map *map1,
7280 __isl_take isl_map *map2);
7282 #include <isl/union_map.h>
7283 __isl_give isl_union_map *isl_union_map_apply_domain(
7284 __isl_take isl_union_map *umap1,
7285 __isl_take isl_union_map *umap2);
7286 __isl_give isl_union_map *isl_union_map_apply_range(
7287 __isl_take isl_union_map *umap1,
7288 __isl_take isl_union_map *umap2);
7290 #include <isl/aff.h>
7291 __isl_give isl_union_pw_aff *
7292 isl_multi_union_pw_aff_apply_aff(
7293 __isl_take isl_multi_union_pw_aff *mupa,
7294 __isl_take isl_aff *aff);
7295 __isl_give isl_union_pw_aff *
7296 isl_multi_union_pw_aff_apply_pw_aff(
7297 __isl_take isl_multi_union_pw_aff *mupa,
7298 __isl_take isl_pw_aff *pa);
7299 __isl_give isl_multi_union_pw_aff *
7300 isl_multi_union_pw_aff_apply_multi_aff(
7301 __isl_take isl_multi_union_pw_aff *mupa,
7302 __isl_take isl_multi_aff *ma);
7303 __isl_give isl_multi_union_pw_aff *
7304 isl_multi_union_pw_aff_apply_pw_multi_aff(
7305 __isl_take isl_multi_union_pw_aff *mupa,
7306 __isl_take isl_pw_multi_aff *pma);
7308 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
7309 over the shared domain of the elements of the input. The dimension is
7310 required to be greater than zero.
7311 The C<isl_multi_union_pw_aff> argument of
7312 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
7313 but only if the range of the C<isl_multi_aff> argument
7314 is also zero-dimensional.
7315 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
7317 #include <isl/polynomial.h>
7318 __isl_give isl_pw_qpolynomial_fold *
7319 isl_set_apply_pw_qpolynomial_fold(
7320 __isl_take isl_set *set,
7321 __isl_take isl_pw_qpolynomial_fold *pwf,
7323 __isl_give isl_pw_qpolynomial_fold *
7324 isl_map_apply_pw_qpolynomial_fold(
7325 __isl_take isl_map *map,
7326 __isl_take isl_pw_qpolynomial_fold *pwf,
7328 __isl_give isl_union_pw_qpolynomial_fold *
7329 isl_union_set_apply_union_pw_qpolynomial_fold(
7330 __isl_take isl_union_set *uset,
7331 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7333 __isl_give isl_union_pw_qpolynomial_fold *
7334 isl_union_map_apply_union_pw_qpolynomial_fold(
7335 __isl_take isl_union_map *umap,
7336 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7339 The functions taking a map
7340 compose the given map with the given piecewise quasipolynomial reduction.
7341 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
7342 over all elements in the intersection of the range of the map
7343 and the domain of the piecewise quasipolynomial reduction
7344 as a function of an element in the domain of the map.
7345 The functions taking a set compute a bound over all elements in the
7346 intersection of the set and the domain of the
7347 piecewise quasipolynomial reduction.
7351 #include <isl/set.h>
7352 __isl_give isl_basic_set *
7353 isl_basic_set_preimage_multi_aff(
7354 __isl_take isl_basic_set *bset,
7355 __isl_take isl_multi_aff *ma);
7356 __isl_give isl_set *isl_set_preimage_multi_aff(
7357 __isl_take isl_set *set,
7358 __isl_take isl_multi_aff *ma);
7359 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
7360 __isl_take isl_set *set,
7361 __isl_take isl_pw_multi_aff *pma);
7362 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
7363 __isl_take isl_set *set,
7364 __isl_take isl_multi_pw_aff *mpa);
7366 #include <isl/union_set.h>
7367 __isl_give isl_union_set *
7368 isl_union_set_preimage_multi_aff(
7369 __isl_take isl_union_set *uset,
7370 __isl_take isl_multi_aff *ma);
7371 __isl_give isl_union_set *
7372 isl_union_set_preimage_pw_multi_aff(
7373 __isl_take isl_union_set *uset,
7374 __isl_take isl_pw_multi_aff *pma);
7375 __isl_give isl_union_set *
7376 isl_union_set_preimage_union_pw_multi_aff(
7377 __isl_take isl_union_set *uset,
7378 __isl_take isl_union_pw_multi_aff *upma);
7380 #include <isl/map.h>
7381 __isl_give isl_basic_map *
7382 isl_basic_map_preimage_domain_multi_aff(
7383 __isl_take isl_basic_map *bmap,
7384 __isl_take isl_multi_aff *ma);
7385 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
7386 __isl_take isl_map *map,
7387 __isl_take isl_multi_aff *ma);
7388 __isl_give isl_map *isl_map_preimage_range_multi_aff(
7389 __isl_take isl_map *map,
7390 __isl_take isl_multi_aff *ma);
7391 __isl_give isl_map *
7392 isl_map_preimage_domain_pw_multi_aff(
7393 __isl_take isl_map *map,
7394 __isl_take isl_pw_multi_aff *pma);
7395 __isl_give isl_map *
7396 isl_map_preimage_range_pw_multi_aff(
7397 __isl_take isl_map *map,
7398 __isl_take isl_pw_multi_aff *pma);
7399 __isl_give isl_map *
7400 isl_map_preimage_domain_multi_pw_aff(
7401 __isl_take isl_map *map,
7402 __isl_take isl_multi_pw_aff *mpa);
7403 __isl_give isl_basic_map *
7404 isl_basic_map_preimage_range_multi_aff(
7405 __isl_take isl_basic_map *bmap,
7406 __isl_take isl_multi_aff *ma);
7408 #include <isl/union_map.h>
7409 __isl_give isl_union_map *
7410 isl_union_map_preimage_domain_multi_aff(
7411 __isl_take isl_union_map *umap,
7412 __isl_take isl_multi_aff *ma);
7413 __isl_give isl_union_map *
7414 isl_union_map_preimage_range_multi_aff(
7415 __isl_take isl_union_map *umap,
7416 __isl_take isl_multi_aff *ma);
7417 __isl_give isl_union_map *
7418 isl_union_map_preimage_domain_pw_multi_aff(
7419 __isl_take isl_union_map *umap,
7420 __isl_take isl_pw_multi_aff *pma);
7421 __isl_give isl_union_map *
7422 isl_union_map_preimage_range_pw_multi_aff(
7423 __isl_take isl_union_map *umap,
7424 __isl_take isl_pw_multi_aff *pma);
7425 __isl_give isl_union_map *
7426 isl_union_map_preimage_domain_union_pw_multi_aff(
7427 __isl_take isl_union_map *umap,
7428 __isl_take isl_union_pw_multi_aff *upma);
7429 __isl_give isl_union_map *
7430 isl_union_map_preimage_range_union_pw_multi_aff(
7431 __isl_take isl_union_map *umap,
7432 __isl_take isl_union_pw_multi_aff *upma);
7434 These functions compute the preimage of the given set or map domain/range under
7435 the given function. In other words, the expression is plugged
7436 into the set description or into the domain/range of the map.
7440 #include <isl/aff.h>
7441 __isl_give isl_aff *isl_aff_pullback_aff(
7442 __isl_take isl_aff *aff1,
7443 __isl_take isl_aff *aff2);
7444 __isl_give isl_aff *isl_aff_pullback_multi_aff(
7445 __isl_take isl_aff *aff,
7446 __isl_take isl_multi_aff *ma);
7447 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
7448 __isl_take isl_pw_aff *pa,
7449 __isl_take isl_multi_aff *ma);
7450 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
7451 __isl_take isl_pw_aff *pa,
7452 __isl_take isl_pw_multi_aff *pma);
7453 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
7454 __isl_take isl_pw_aff *pa,
7455 __isl_take isl_multi_pw_aff *mpa);
7456 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
7457 __isl_take isl_multi_aff *ma1,
7458 __isl_take isl_multi_aff *ma2);
7459 __isl_give isl_pw_multi_aff *
7460 isl_pw_multi_aff_pullback_multi_aff(
7461 __isl_take isl_pw_multi_aff *pma,
7462 __isl_take isl_multi_aff *ma);
7463 __isl_give isl_multi_pw_aff *
7464 isl_multi_pw_aff_pullback_multi_aff(
7465 __isl_take isl_multi_pw_aff *mpa,
7466 __isl_take isl_multi_aff *ma);
7467 __isl_give isl_pw_multi_aff *
7468 isl_pw_multi_aff_pullback_pw_multi_aff(
7469 __isl_take isl_pw_multi_aff *pma1,
7470 __isl_take isl_pw_multi_aff *pma2);
7471 __isl_give isl_multi_pw_aff *
7472 isl_multi_pw_aff_pullback_pw_multi_aff(
7473 __isl_take isl_multi_pw_aff *mpa,
7474 __isl_take isl_pw_multi_aff *pma);
7475 __isl_give isl_multi_pw_aff *
7476 isl_multi_pw_aff_pullback_multi_pw_aff(
7477 __isl_take isl_multi_pw_aff *mpa1,
7478 __isl_take isl_multi_pw_aff *mpa2);
7479 __isl_give isl_union_pw_aff *
7480 isl_union_pw_aff_pullback_union_pw_multi_aff(
7481 __isl_take isl_union_pw_aff *upa,
7482 __isl_take isl_union_pw_multi_aff *upma);
7483 __isl_give isl_union_pw_multi_aff *
7484 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
7485 __isl_take isl_union_pw_multi_aff *upma1,
7486 __isl_take isl_union_pw_multi_aff *upma2);
7487 __isl_give isl_multi_union_pw_aff *
7488 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
7489 __isl_take isl_multi_union_pw_aff *mupa,
7490 __isl_take isl_union_pw_multi_aff *upma);
7492 These functions precompose the first expression by the second function.
7493 In other words, the second function is plugged
7494 into the first expression.
7498 #include <isl/aff.h>
7499 __isl_give isl_basic_set *isl_aff_eq_basic_set(
7500 __isl_take isl_aff *aff1,
7501 __isl_take isl_aff *aff2);
7502 __isl_give isl_set *isl_aff_eq_set(
7503 __isl_take isl_aff *aff1,
7504 __isl_take isl_aff *aff2);
7505 __isl_give isl_set *isl_aff_ne_set(
7506 __isl_take isl_aff *aff1,
7507 __isl_take isl_aff *aff2);
7508 __isl_give isl_basic_set *isl_aff_le_basic_set(
7509 __isl_take isl_aff *aff1,
7510 __isl_take isl_aff *aff2);
7511 __isl_give isl_set *isl_aff_le_set(
7512 __isl_take isl_aff *aff1,
7513 __isl_take isl_aff *aff2);
7514 __isl_give isl_basic_set *isl_aff_lt_basic_set(
7515 __isl_take isl_aff *aff1,
7516 __isl_take isl_aff *aff2);
7517 __isl_give isl_set *isl_aff_lt_set(
7518 __isl_take isl_aff *aff1,
7519 __isl_take isl_aff *aff2);
7520 __isl_give isl_basic_set *isl_aff_ge_basic_set(
7521 __isl_take isl_aff *aff1,
7522 __isl_take isl_aff *aff2);
7523 __isl_give isl_set *isl_aff_ge_set(
7524 __isl_take isl_aff *aff1,
7525 __isl_take isl_aff *aff2);
7526 __isl_give isl_basic_set *isl_aff_gt_basic_set(
7527 __isl_take isl_aff *aff1,
7528 __isl_take isl_aff *aff2);
7529 __isl_give isl_set *isl_aff_gt_set(
7530 __isl_take isl_aff *aff1,
7531 __isl_take isl_aff *aff2);
7532 __isl_give isl_set *isl_pw_aff_eq_set(
7533 __isl_take isl_pw_aff *pwaff1,
7534 __isl_take isl_pw_aff *pwaff2);
7535 __isl_give isl_set *isl_pw_aff_ne_set(
7536 __isl_take isl_pw_aff *pwaff1,
7537 __isl_take isl_pw_aff *pwaff2);
7538 __isl_give isl_set *isl_pw_aff_le_set(
7539 __isl_take isl_pw_aff *pwaff1,
7540 __isl_take isl_pw_aff *pwaff2);
7541 __isl_give isl_set *isl_pw_aff_lt_set(
7542 __isl_take isl_pw_aff *pwaff1,
7543 __isl_take isl_pw_aff *pwaff2);
7544 __isl_give isl_set *isl_pw_aff_ge_set(
7545 __isl_take isl_pw_aff *pwaff1,
7546 __isl_take isl_pw_aff *pwaff2);
7547 __isl_give isl_set *isl_pw_aff_gt_set(
7548 __isl_take isl_pw_aff *pwaff1,
7549 __isl_take isl_pw_aff *pwaff2);
7551 __isl_give isl_set *isl_multi_aff_lex_le_set(
7552 __isl_take isl_multi_aff *ma1,
7553 __isl_take isl_multi_aff *ma2);
7554 __isl_give isl_set *isl_multi_aff_lex_lt_set(
7555 __isl_take isl_multi_aff *ma1,
7556 __isl_take isl_multi_aff *ma2);
7557 __isl_give isl_set *isl_multi_aff_lex_ge_set(
7558 __isl_take isl_multi_aff *ma1,
7559 __isl_take isl_multi_aff *ma2);
7560 __isl_give isl_set *isl_multi_aff_lex_gt_set(
7561 __isl_take isl_multi_aff *ma1,
7562 __isl_take isl_multi_aff *ma2);
7564 __isl_give isl_set *isl_pw_aff_list_eq_set(
7565 __isl_take isl_pw_aff_list *list1,
7566 __isl_take isl_pw_aff_list *list2);
7567 __isl_give isl_set *isl_pw_aff_list_ne_set(
7568 __isl_take isl_pw_aff_list *list1,
7569 __isl_take isl_pw_aff_list *list2);
7570 __isl_give isl_set *isl_pw_aff_list_le_set(
7571 __isl_take isl_pw_aff_list *list1,
7572 __isl_take isl_pw_aff_list *list2);
7573 __isl_give isl_set *isl_pw_aff_list_lt_set(
7574 __isl_take isl_pw_aff_list *list1,
7575 __isl_take isl_pw_aff_list *list2);
7576 __isl_give isl_set *isl_pw_aff_list_ge_set(
7577 __isl_take isl_pw_aff_list *list1,
7578 __isl_take isl_pw_aff_list *list2);
7579 __isl_give isl_set *isl_pw_aff_list_gt_set(
7580 __isl_take isl_pw_aff_list *list1,
7581 __isl_take isl_pw_aff_list *list2);
7583 The function C<isl_aff_ge_basic_set> returns a basic set
7584 containing those elements in the shared space
7585 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
7586 The function C<isl_pw_aff_ge_set> returns a set
7587 containing those elements in the shared domain
7588 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
7589 greater than or equal to C<pwaff2>.
7590 The function C<isl_multi_aff_lex_le_set> returns a set
7591 containing those elements in the shared domain space
7592 where C<ma1> is lexicographically smaller than or
7594 The functions operating on C<isl_pw_aff_list> apply the corresponding
7595 C<isl_pw_aff> function to each pair of elements in the two lists.
7597 #include <isl/aff.h>
7598 __isl_give isl_map *isl_pw_aff_eq_map(
7599 __isl_take isl_pw_aff *pa1,
7600 __isl_take isl_pw_aff *pa2);
7601 __isl_give isl_map *isl_pw_aff_le_map(
7602 __isl_take isl_pw_aff *pa1,
7603 __isl_take isl_pw_aff *pa2);
7604 __isl_give isl_map *isl_pw_aff_lt_map(
7605 __isl_take isl_pw_aff *pa1,
7606 __isl_take isl_pw_aff *pa2);
7607 __isl_give isl_map *isl_pw_aff_ge_map(
7608 __isl_take isl_pw_aff *pa1,
7609 __isl_take isl_pw_aff *pa2);
7610 __isl_give isl_map *isl_pw_aff_gt_map(
7611 __isl_take isl_pw_aff *pa1,
7612 __isl_take isl_pw_aff *pa2);
7614 __isl_give isl_map *isl_multi_pw_aff_eq_map(
7615 __isl_take isl_multi_pw_aff *mpa1,
7616 __isl_take isl_multi_pw_aff *mpa2);
7617 __isl_give isl_map *isl_multi_pw_aff_lex_le_map(
7618 __isl_take isl_multi_pw_aff *mpa1,
7619 __isl_take isl_multi_pw_aff *mpa2);
7620 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
7621 __isl_take isl_multi_pw_aff *mpa1,
7622 __isl_take isl_multi_pw_aff *mpa2);
7623 __isl_give isl_map *isl_multi_pw_aff_lex_ge_map(
7624 __isl_take isl_multi_pw_aff *mpa1,
7625 __isl_take isl_multi_pw_aff *mpa2);
7626 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
7627 __isl_take isl_multi_pw_aff *mpa1,
7628 __isl_take isl_multi_pw_aff *mpa2);
7630 These functions return a map between domain elements of the arguments
7631 where the function values satisfy the given relation.
7633 #include <isl/map.h>
7634 __isl_give isl_map *isl_map_eq_at_multi_pw_aff(
7635 __isl_take isl_map *map,
7636 __isl_take isl_multi_pw_aff *mpa);
7637 __isl_give isl_map *isl_map_lex_lt_at_multi_pw_aff(
7638 __isl_take isl_map *map,
7639 __isl_take isl_multi_pw_aff *mpa);
7640 __isl_give isl_map *isl_map_lex_le_at_multi_pw_aff(
7641 __isl_take isl_map *map,
7642 __isl_take isl_multi_pw_aff *mpa);
7643 __isl_give isl_map *isl_map_lex_gt_at_multi_pw_aff(
7644 __isl_take isl_map *map,
7645 __isl_take isl_multi_pw_aff *mpa);
7646 __isl_give isl_map *isl_map_lex_ge_at_multi_pw_aff(
7647 __isl_take isl_map *map,
7648 __isl_take isl_multi_pw_aff *mpa);
7650 #include <isl/union_map.h>
7651 __isl_give isl_union_map *
7652 isl_union_map_eq_at_multi_union_pw_aff(
7653 __isl_take isl_union_map *umap,
7654 __isl_take isl_multi_union_pw_aff *mupa);
7655 __isl_give isl_union_map *
7656 isl_union_map_lex_lt_at_multi_union_pw_aff(
7657 __isl_take isl_union_map *umap,
7658 __isl_take isl_multi_union_pw_aff *mupa);
7659 __isl_give isl_union_map *
7660 isl_union_map_lex_gt_at_multi_union_pw_aff(
7661 __isl_take isl_union_map *umap,
7662 __isl_take isl_multi_union_pw_aff *mupa);
7664 These functions select the subset of elements in the union map
7665 that have an equal or lexicographically smaller function value.
7667 =item * Cartesian Product
7669 #include <isl/space.h>
7670 __isl_give isl_space *isl_space_product(
7671 __isl_take isl_space *space1,
7672 __isl_take isl_space *space2);
7673 __isl_give isl_space *isl_space_domain_product(
7674 __isl_take isl_space *space1,
7675 __isl_take isl_space *space2);
7676 __isl_give isl_space *isl_space_range_product(
7677 __isl_take isl_space *space1,
7678 __isl_take isl_space *space2);
7681 C<isl_space_product>, C<isl_space_domain_product>
7682 and C<isl_space_range_product> take pairs or relation spaces and
7683 produce a single relations space, where either the domain, the range
7684 or both domain and range are wrapped spaces of relations between
7685 the domains and/or ranges of the input spaces.
7686 If the product is only constructed over the domain or the range
7687 then the ranges or the domains of the inputs should be the same.
7688 The function C<isl_space_product> also accepts a pair of set spaces,
7689 in which case it returns a wrapped space of a relation between the
7692 #include <isl/set.h>
7693 __isl_give isl_set *isl_set_product(
7694 __isl_take isl_set *set1,
7695 __isl_take isl_set *set2);
7697 #include <isl/map.h>
7698 __isl_give isl_basic_map *isl_basic_map_domain_product(
7699 __isl_take isl_basic_map *bmap1,
7700 __isl_take isl_basic_map *bmap2);
7701 __isl_give isl_basic_map *isl_basic_map_range_product(
7702 __isl_take isl_basic_map *bmap1,
7703 __isl_take isl_basic_map *bmap2);
7704 __isl_give isl_basic_map *isl_basic_map_product(
7705 __isl_take isl_basic_map *bmap1,
7706 __isl_take isl_basic_map *bmap2);
7707 __isl_give isl_map *isl_map_domain_product(
7708 __isl_take isl_map *map1,
7709 __isl_take isl_map *map2);
7710 __isl_give isl_map *isl_map_range_product(
7711 __isl_take isl_map *map1,
7712 __isl_take isl_map *map2);
7713 __isl_give isl_map *isl_map_product(
7714 __isl_take isl_map *map1,
7715 __isl_take isl_map *map2);
7717 #include <isl/union_set.h>
7718 __isl_give isl_union_set *isl_union_set_product(
7719 __isl_take isl_union_set *uset1,
7720 __isl_take isl_union_set *uset2);
7722 #include <isl/union_map.h>
7723 __isl_give isl_union_map *isl_union_map_domain_product(
7724 __isl_take isl_union_map *umap1,
7725 __isl_take isl_union_map *umap2);
7726 __isl_give isl_union_map *isl_union_map_range_product(
7727 __isl_take isl_union_map *umap1,
7728 __isl_take isl_union_map *umap2);
7729 __isl_give isl_union_map *isl_union_map_product(
7730 __isl_take isl_union_map *umap1,
7731 __isl_take isl_union_map *umap2);
7734 __isl_give isl_multi_id *isl_multi_id_range_product(
7735 __isl_take isl_multi_id *mi1,
7736 __isl_take isl_multi_id *mi2);
7738 #include <isl/val.h>
7739 __isl_give isl_multi_val *isl_multi_val_range_product(
7740 __isl_take isl_multi_val *mv1,
7741 __isl_take isl_multi_val *mv2);
7742 __isl_give isl_multi_val *isl_multi_val_product(
7743 __isl_take isl_multi_val *mv1,
7744 __isl_take isl_multi_val *mv2);
7746 #include <isl/aff.h>
7747 __isl_give isl_multi_aff *isl_multi_aff_range_product(
7748 __isl_take isl_multi_aff *ma1,
7749 __isl_take isl_multi_aff *ma2);
7750 __isl_give isl_multi_aff *isl_multi_aff_product(
7751 __isl_take isl_multi_aff *ma1,
7752 __isl_take isl_multi_aff *ma2);
7753 __isl_give isl_multi_pw_aff *
7754 isl_multi_pw_aff_range_product(
7755 __isl_take isl_multi_pw_aff *mpa1,
7756 __isl_take isl_multi_pw_aff *mpa2);
7757 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
7758 __isl_take isl_multi_pw_aff *mpa1,
7759 __isl_take isl_multi_pw_aff *mpa2);
7760 __isl_give isl_pw_multi_aff *
7761 isl_pw_multi_aff_range_product(
7762 __isl_take isl_pw_multi_aff *pma1,
7763 __isl_take isl_pw_multi_aff *pma2);
7764 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
7765 __isl_take isl_pw_multi_aff *pma1,
7766 __isl_take isl_pw_multi_aff *pma2);
7767 __isl_give isl_union_pw_multi_aff *
7768 isl_union_pw_multi_aff_range_product(
7769 __isl_take isl_union_pw_multi_aff *upma1,
7770 __isl_take isl_union_pw_multi_aff *upma2);
7771 __isl_give isl_multi_union_pw_aff *
7772 isl_multi_union_pw_aff_range_product(
7773 __isl_take isl_multi_union_pw_aff *mupa1,
7774 __isl_take isl_multi_union_pw_aff *mupa2);
7776 The above functions compute the cross product of the given
7777 sets, relations or functions. The domains and ranges of the results
7778 are wrapped maps between domains and ranges of the inputs.
7779 To obtain a ``flat'' product, use the following functions
7782 #include <isl/set.h>
7783 __isl_give isl_basic_set *isl_basic_set_flat_product(
7784 __isl_take isl_basic_set *bset1,
7785 __isl_take isl_basic_set *bset2);
7786 __isl_give isl_set *isl_set_flat_product(
7787 __isl_take isl_set *set1,
7788 __isl_take isl_set *set2);
7790 #include <isl/map.h>
7791 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
7792 __isl_take isl_basic_map *bmap1,
7793 __isl_take isl_basic_map *bmap2);
7794 __isl_give isl_map *isl_map_flat_domain_product(
7795 __isl_take isl_map *map1,
7796 __isl_take isl_map *map2);
7797 __isl_give isl_map *isl_map_flat_range_product(
7798 __isl_take isl_map *map1,
7799 __isl_take isl_map *map2);
7800 __isl_give isl_basic_map *isl_basic_map_flat_product(
7801 __isl_take isl_basic_map *bmap1,
7802 __isl_take isl_basic_map *bmap2);
7803 __isl_give isl_map *isl_map_flat_product(
7804 __isl_take isl_map *map1,
7805 __isl_take isl_map *map2);
7807 #include <isl/union_map.h>
7808 __isl_give isl_union_map *
7809 isl_union_map_flat_domain_product(
7810 __isl_take isl_union_map *umap1,
7811 __isl_take isl_union_map *umap2);
7812 __isl_give isl_union_map *
7813 isl_union_map_flat_range_product(
7814 __isl_take isl_union_map *umap1,
7815 __isl_take isl_union_map *umap2);
7818 __isl_give isl_multi_id *
7819 isl_multi_id_flat_range_product(
7820 __isl_take isl_multi_id *mi1,
7821 __isl_take isl_multi_id *mi2);
7823 #include <isl/val.h>
7824 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
7825 __isl_take isl_multi_val *mv1,
7826 __isl_take isl_multi_val *mv2);
7828 #include <isl/aff.h>
7829 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
7830 __isl_take isl_multi_aff *ma1,
7831 __isl_take isl_multi_aff *ma2);
7832 __isl_give isl_pw_multi_aff *
7833 isl_pw_multi_aff_flat_range_product(
7834 __isl_take isl_pw_multi_aff *pma1,
7835 __isl_take isl_pw_multi_aff *pma2);
7836 __isl_give isl_multi_pw_aff *
7837 isl_multi_pw_aff_flat_range_product(
7838 __isl_take isl_multi_pw_aff *mpa1,
7839 __isl_take isl_multi_pw_aff *mpa2);
7840 __isl_give isl_union_pw_multi_aff *
7841 isl_union_pw_multi_aff_flat_range_product(
7842 __isl_take isl_union_pw_multi_aff *upma1,
7843 __isl_take isl_union_pw_multi_aff *upma2);
7844 __isl_give isl_multi_union_pw_aff *
7845 isl_multi_union_pw_aff_flat_range_product(
7846 __isl_take isl_multi_union_pw_aff *mupa1,
7847 __isl_take isl_multi_union_pw_aff *mupa2);
7849 #include <isl/space.h>
7850 __isl_give isl_space *isl_space_factor_domain(
7851 __isl_take isl_space *space);
7852 __isl_give isl_space *isl_space_factor_range(
7853 __isl_take isl_space *space);
7854 __isl_give isl_space *isl_space_domain_factor_domain(
7855 __isl_take isl_space *space);
7856 __isl_give isl_space *isl_space_domain_factor_range(
7857 __isl_take isl_space *space);
7858 __isl_give isl_space *isl_space_range_factor_domain(
7859 __isl_take isl_space *space);
7860 __isl_give isl_space *isl_space_range_factor_range(
7861 __isl_take isl_space *space);
7863 The functions C<isl_space_range_factor_domain> and
7864 C<isl_space_range_factor_range> extract the two arguments from
7865 the result of a call to C<isl_space_range_product>.
7867 The arguments of a call to a product can be extracted
7868 from the result using the following functions.
7870 #include <isl/map.h>
7871 __isl_give isl_map *isl_map_factor_domain(
7872 __isl_take isl_map *map);
7873 __isl_give isl_map *isl_map_factor_range(
7874 __isl_take isl_map *map);
7875 __isl_give isl_map *isl_map_domain_factor_domain(
7876 __isl_take isl_map *map);
7877 __isl_give isl_map *isl_map_domain_factor_range(
7878 __isl_take isl_map *map);
7879 __isl_give isl_map *isl_map_range_factor_domain(
7880 __isl_take isl_map *map);
7881 __isl_give isl_map *isl_map_range_factor_range(
7882 __isl_take isl_map *map);
7884 #include <isl/union_map.h>
7885 __isl_give isl_union_map *isl_union_map_factor_domain(
7886 __isl_take isl_union_map *umap);
7887 __isl_give isl_union_map *isl_union_map_factor_range(
7888 __isl_take isl_union_map *umap);
7889 __isl_give isl_union_map *
7890 isl_union_map_domain_factor_domain(
7891 __isl_take isl_union_map *umap);
7892 __isl_give isl_union_map *
7893 isl_union_map_domain_factor_range(
7894 __isl_take isl_union_map *umap);
7895 __isl_give isl_union_map *
7896 isl_union_map_range_factor_domain(
7897 __isl_take isl_union_map *umap);
7898 __isl_give isl_union_map *
7899 isl_union_map_range_factor_range(
7900 __isl_take isl_union_map *umap);
7903 __isl_give isl_multi_id *isl_multi_id_factor_range(
7904 __isl_take isl_multi_id *mi);
7905 __isl_give isl_multi_id *
7906 isl_multi_id_range_factor_domain(
7907 __isl_take isl_multi_id *mi);
7908 __isl_give isl_multi_id *
7909 isl_multi_id_range_factor_range(
7910 __isl_take isl_multi_id *mi);
7912 #include <isl/val.h>
7913 __isl_give isl_multi_val *isl_multi_val_factor_range(
7914 __isl_take isl_multi_val *mv);
7915 __isl_give isl_multi_val *
7916 isl_multi_val_range_factor_domain(
7917 __isl_take isl_multi_val *mv);
7918 __isl_give isl_multi_val *
7919 isl_multi_val_range_factor_range(
7920 __isl_take isl_multi_val *mv);
7922 #include <isl/aff.h>
7923 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
7924 __isl_take isl_multi_aff *ma);
7925 __isl_give isl_multi_aff *
7926 isl_multi_aff_range_factor_domain(
7927 __isl_take isl_multi_aff *ma);
7928 __isl_give isl_multi_aff *
7929 isl_multi_aff_range_factor_range(
7930 __isl_take isl_multi_aff *ma);
7931 __isl_give isl_multi_pw_aff *
7932 isl_multi_pw_aff_factor_range(
7933 __isl_take isl_multi_pw_aff *mpa);
7934 __isl_give isl_multi_pw_aff *
7935 isl_multi_pw_aff_range_factor_domain(
7936 __isl_take isl_multi_pw_aff *mpa);
7937 __isl_give isl_multi_pw_aff *
7938 isl_multi_pw_aff_range_factor_range(
7939 __isl_take isl_multi_pw_aff *mpa);
7940 __isl_give isl_pw_multi_aff *
7941 isl_pw_multi_aff_range_factor_domain(
7942 __isl_take isl_pw_multi_aff *pma);
7943 __isl_give isl_pw_multi_aff *
7944 isl_pw_multi_aff_range_factor_range(
7945 __isl_take isl_pw_multi_aff *pma);
7946 __isl_give isl_union_pw_multi_aff *
7947 isl_union_pw_multi_aff_range_factor_domain(
7948 __isl_take isl_union_pw_multi_aff *upma);
7949 __isl_give isl_union_pw_multi_aff *
7950 isl_union_pw_multi_aff_range_factor_range(
7951 __isl_take isl_union_pw_multi_aff *upma);
7952 __isl_give isl_multi_union_pw_aff *
7953 isl_multi_union_pw_aff_factor_range(
7954 __isl_take isl_multi_union_pw_aff *mupa);
7955 __isl_give isl_multi_union_pw_aff *
7956 isl_multi_union_pw_aff_range_factor_domain(
7957 __isl_take isl_multi_union_pw_aff *mupa);
7958 __isl_give isl_multi_union_pw_aff *
7959 isl_multi_union_pw_aff_range_factor_range(
7960 __isl_take isl_multi_union_pw_aff *mupa);
7962 The splice functions are a generalization of the flat product functions,
7963 where the second argument may be inserted at any position inside
7964 the first argument rather than being placed at the end.
7965 The functions C<isl_multi_val_factor_range>,
7966 C<isl_multi_aff_factor_range>,
7967 C<isl_multi_pw_aff_factor_range> and
7968 C<isl_multi_union_pw_aff_factor_range>
7969 take functions that live in a set space.
7972 __isl_give isl_multi_id *isl_multi_id_range_splice(
7973 __isl_take isl_multi_id *mi1, unsigned pos,
7974 __isl_take isl_multi_id *mi2);
7976 #include <isl/val.h>
7977 __isl_give isl_multi_val *isl_multi_val_range_splice(
7978 __isl_take isl_multi_val *mv1, unsigned pos,
7979 __isl_take isl_multi_val *mv2);
7981 #include <isl/aff.h>
7982 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
7983 __isl_take isl_multi_aff *ma1, unsigned pos,
7984 __isl_take isl_multi_aff *ma2);
7985 __isl_give isl_multi_aff *isl_multi_aff_splice(
7986 __isl_take isl_multi_aff *ma1,
7987 unsigned in_pos, unsigned out_pos,
7988 __isl_take isl_multi_aff *ma2);
7989 __isl_give isl_multi_pw_aff *
7990 isl_multi_pw_aff_range_splice(
7991 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
7992 __isl_take isl_multi_pw_aff *mpa2);
7993 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
7994 __isl_take isl_multi_pw_aff *mpa1,
7995 unsigned in_pos, unsigned out_pos,
7996 __isl_take isl_multi_pw_aff *mpa2);
7997 __isl_give isl_multi_union_pw_aff *
7998 isl_multi_union_pw_aff_range_splice(
7999 __isl_take isl_multi_union_pw_aff *mupa1,
8001 __isl_take isl_multi_union_pw_aff *mupa2);
8003 =item * Simplification
8005 When applied to a set or relation,
8006 the gist operation returns a set or relation that has the
8007 same intersection with the context as the input set or relation.
8008 Any implicit equality in the intersection is made explicit in the result,
8009 while all inequalities that are redundant with respect to the intersection
8011 In case of union sets and relations, the gist operation is performed
8014 When applied to a function,
8015 the gist operation applies the set gist operation to each of
8016 the cells in the domain of the input piecewise expression.
8017 The context is also exploited
8018 to simplify the expression associated to each cell.
8020 #include <isl/set.h>
8021 __isl_give isl_basic_set *isl_basic_set_gist(
8022 __isl_take isl_basic_set *bset,
8023 __isl_take isl_basic_set *context);
8024 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
8025 __isl_take isl_set *context);
8026 __isl_give isl_set *isl_set_gist_params(
8027 __isl_take isl_set *set,
8028 __isl_take isl_set *context);
8030 #include <isl/map.h>
8031 __isl_give isl_basic_map *isl_basic_map_gist(
8032 __isl_take isl_basic_map *bmap,
8033 __isl_take isl_basic_map *context);
8034 __isl_give isl_basic_map *isl_basic_map_gist_domain(
8035 __isl_take isl_basic_map *bmap,
8036 __isl_take isl_basic_set *context);
8037 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
8038 __isl_take isl_map *context);
8039 __isl_give isl_map *isl_map_gist_params(
8040 __isl_take isl_map *map,
8041 __isl_take isl_set *context);
8042 __isl_give isl_map *isl_map_gist_domain(
8043 __isl_take isl_map *map,
8044 __isl_take isl_set *context);
8045 __isl_give isl_map *isl_map_gist_range(
8046 __isl_take isl_map *map,
8047 __isl_take isl_set *context);
8049 #include <isl/union_set.h>
8050 __isl_give isl_union_set *isl_union_set_gist(
8051 __isl_take isl_union_set *uset,
8052 __isl_take isl_union_set *context);
8053 __isl_give isl_union_set *isl_union_set_gist_params(
8054 __isl_take isl_union_set *uset,
8055 __isl_take isl_set *set);
8057 #include <isl/union_map.h>
8058 __isl_give isl_union_map *isl_union_map_gist(
8059 __isl_take isl_union_map *umap,
8060 __isl_take isl_union_map *context);
8061 __isl_give isl_union_map *isl_union_map_gist_params(
8062 __isl_take isl_union_map *umap,
8063 __isl_take isl_set *set);
8064 __isl_give isl_union_map *isl_union_map_gist_domain(
8065 __isl_take isl_union_map *umap,
8066 __isl_take isl_union_set *uset);
8067 __isl_give isl_union_map *isl_union_map_gist_range(
8068 __isl_take isl_union_map *umap,
8069 __isl_take isl_union_set *uset);
8071 #include <isl/aff.h>
8072 __isl_give isl_aff *isl_aff_gist_params(
8073 __isl_take isl_aff *aff,
8074 __isl_take isl_set *context);
8075 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
8076 __isl_take isl_set *context);
8077 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
8078 __isl_take isl_multi_aff *maff,
8079 __isl_take isl_set *context);
8080 __isl_give isl_multi_aff *isl_multi_aff_gist(
8081 __isl_take isl_multi_aff *maff,
8082 __isl_take isl_set *context);
8083 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
8084 __isl_take isl_pw_aff *pwaff,
8085 __isl_take isl_set *context);
8086 __isl_give isl_pw_aff *isl_pw_aff_gist(
8087 __isl_take isl_pw_aff *pwaff,
8088 __isl_take isl_set *context);
8089 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
8090 __isl_take isl_pw_multi_aff *pma,
8091 __isl_take isl_set *set);
8092 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
8093 __isl_take isl_pw_multi_aff *pma,
8094 __isl_take isl_set *set);
8095 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
8096 __isl_take isl_multi_pw_aff *mpa,
8097 __isl_take isl_set *set);
8098 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
8099 __isl_take isl_multi_pw_aff *mpa,
8100 __isl_take isl_set *set);
8101 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
8102 __isl_take isl_union_pw_aff *upa,
8103 __isl_take isl_union_set *context);
8104 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
8105 __isl_take isl_union_pw_aff *upa,
8106 __isl_take isl_set *context);
8107 __isl_give isl_union_pw_multi_aff *
8108 isl_union_pw_multi_aff_gist_params(
8109 __isl_take isl_union_pw_multi_aff *upma,
8110 __isl_take isl_set *context);
8111 __isl_give isl_union_pw_multi_aff *
8112 isl_union_pw_multi_aff_gist(
8113 __isl_take isl_union_pw_multi_aff *upma,
8114 __isl_take isl_union_set *context);
8115 __isl_give isl_multi_union_pw_aff *
8116 isl_multi_union_pw_aff_gist_params(
8117 __isl_take isl_multi_union_pw_aff *mupa,
8118 __isl_take isl_set *context);
8119 __isl_give isl_multi_union_pw_aff *
8120 isl_multi_union_pw_aff_gist(
8121 __isl_take isl_multi_union_pw_aff *mupa,
8122 __isl_take isl_union_set *context);
8124 #include <isl/polynomial.h>
8125 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
8126 __isl_take isl_qpolynomial *qp,
8127 __isl_take isl_set *context);
8128 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
8129 __isl_take isl_qpolynomial *qp,
8130 __isl_take isl_set *context);
8131 __isl_give isl_qpolynomial_fold *
8132 isl_qpolynomial_fold_gist_params(
8133 __isl_take isl_qpolynomial_fold *fold,
8134 __isl_take isl_set *context);
8135 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
8136 __isl_take isl_qpolynomial_fold *fold,
8137 __isl_take isl_set *context);
8138 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
8139 __isl_take isl_pw_qpolynomial *pwqp,
8140 __isl_take isl_set *context);
8141 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
8142 __isl_take isl_pw_qpolynomial *pwqp,
8143 __isl_take isl_set *context);
8144 __isl_give isl_pw_qpolynomial_fold *
8145 isl_pw_qpolynomial_fold_gist(
8146 __isl_take isl_pw_qpolynomial_fold *pwf,
8147 __isl_take isl_set *context);
8148 __isl_give isl_pw_qpolynomial_fold *
8149 isl_pw_qpolynomial_fold_gist_params(
8150 __isl_take isl_pw_qpolynomial_fold *pwf,
8151 __isl_take isl_set *context);
8152 __isl_give isl_union_pw_qpolynomial *
8153 isl_union_pw_qpolynomial_gist_params(
8154 __isl_take isl_union_pw_qpolynomial *upwqp,
8155 __isl_take isl_set *context);
8156 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
8157 __isl_take isl_union_pw_qpolynomial *upwqp,
8158 __isl_take isl_union_set *context);
8159 __isl_give isl_union_pw_qpolynomial_fold *
8160 isl_union_pw_qpolynomial_fold_gist(
8161 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8162 __isl_take isl_union_set *context);
8163 __isl_give isl_union_pw_qpolynomial_fold *
8164 isl_union_pw_qpolynomial_fold_gist_params(
8165 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8166 __isl_take isl_set *context);
8168 =item * Binary Arithmetic Operations
8170 #include <isl/set.h>
8171 __isl_give isl_set *isl_set_sum(
8172 __isl_take isl_set *set1,
8173 __isl_take isl_set *set2);
8174 #include <isl/map.h>
8175 __isl_give isl_map *isl_map_sum(
8176 __isl_take isl_map *map1,
8177 __isl_take isl_map *map2);
8179 C<isl_set_sum> computes the Minkowski sum of its two arguments,
8180 i.e., the set containing the sums of pairs of elements from
8181 C<set1> and C<set2>.
8182 The domain of the result of C<isl_map_sum> is the intersection
8183 of the domains of its two arguments. The corresponding range
8184 elements are the sums of the corresponding range elements
8185 in the two arguments.
8187 #include <isl/val.h>
8188 __isl_give isl_multi_val *isl_multi_val_add(
8189 __isl_take isl_multi_val *mv1,
8190 __isl_take isl_multi_val *mv2);
8191 __isl_give isl_multi_val *isl_multi_val_sub(
8192 __isl_take isl_multi_val *mv1,
8193 __isl_take isl_multi_val *mv2);
8194 __isl_give isl_multi_val *isl_multi_val_min(
8195 __isl_take isl_multi_val *mv1,
8196 __isl_take isl_multi_val *mv2);
8197 __isl_give isl_multi_val *isl_multi_val_max(
8198 __isl_take isl_multi_val *mv1,
8199 __isl_take isl_multi_val *mv2);
8201 #include <isl/aff.h>
8202 __isl_give isl_aff *isl_aff_add(
8203 __isl_take isl_aff *aff1,
8204 __isl_take isl_aff *aff2);
8205 __isl_give isl_multi_aff *isl_multi_aff_add(
8206 __isl_take isl_multi_aff *maff1,
8207 __isl_take isl_multi_aff *maff2);
8208 __isl_give isl_pw_aff *isl_pw_aff_add(
8209 __isl_take isl_pw_aff *pwaff1,
8210 __isl_take isl_pw_aff *pwaff2);
8211 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
8212 __isl_take isl_multi_pw_aff *mpa1,
8213 __isl_take isl_multi_pw_aff *mpa2);
8214 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
8215 __isl_take isl_pw_multi_aff *pma1,
8216 __isl_take isl_pw_multi_aff *pma2);
8217 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
8218 __isl_take isl_union_pw_aff *upa1,
8219 __isl_take isl_union_pw_aff *upa2);
8220 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
8221 __isl_take isl_union_pw_multi_aff *upma1,
8222 __isl_take isl_union_pw_multi_aff *upma2);
8223 __isl_give isl_multi_union_pw_aff *
8224 isl_multi_union_pw_aff_add(
8225 __isl_take isl_multi_union_pw_aff *mupa1,
8226 __isl_take isl_multi_union_pw_aff *mupa2);
8227 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val(
8228 __isl_take isl_pw_aff *pa,
8229 __isl_take isl_val *v);
8230 __isl_give isl_multi_aff *
8231 isl_multi_aff_add_constant_val(
8232 __isl_take isl_multi_aff *pa,
8233 __isl_take isl_val *v);
8234 __isl_give isl_pw_multi_aff *
8235 isl_pw_multi_aff_add_constant_val(
8236 __isl_take isl_pw_multi_aff *pma,
8237 __isl_take isl_val *v);
8238 __isl_give isl_pw_multi_aff *
8239 isl_pw_multi_aff_add_constant_multi_val(
8240 __isl_take isl_pw_multi_aff *pma,
8241 __isl_take isl_multi_val *mv);
8242 __isl_give isl_multi_pw_aff *
8243 isl_multi_pw_aff_add_constant_val(
8244 __isl_take isl_multi_pw_aff *mpa,
8245 __isl_take isl_val *v);
8246 __isl_give isl_multi_aff *
8247 isl_multi_aff_add_constant_multi_val(
8248 __isl_take isl_multi_aff *pa,
8249 __isl_take isl_multi_val *mv);
8250 __isl_give isl_multi_pw_aff *
8251 isl_multi_pw_aff_add_constant_multi_val(
8252 __isl_take isl_multi_pw_aff *mpa,
8253 __isl_take isl_multi_val *mv);
8254 __isl_give isl_pw_aff *isl_pw_aff_min(
8255 __isl_take isl_pw_aff *pwaff1,
8256 __isl_take isl_pw_aff *pwaff2);
8257 __isl_give isl_pw_aff *isl_pw_aff_max(
8258 __isl_take isl_pw_aff *pwaff1,
8259 __isl_take isl_pw_aff *pwaff2);
8260 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min(
8261 __isl_take isl_multi_pw_aff *mpa1,
8262 __isl_take isl_multi_pw_aff *mpa2);
8263 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max(
8264 __isl_take isl_multi_pw_aff *mpa1,
8265 __isl_take isl_multi_pw_aff *mpa2);
8266 __isl_give isl_aff *isl_aff_sub(
8267 __isl_take isl_aff *aff1,
8268 __isl_take isl_aff *aff2);
8269 __isl_give isl_multi_aff *isl_multi_aff_sub(
8270 __isl_take isl_multi_aff *ma1,
8271 __isl_take isl_multi_aff *ma2);
8272 __isl_give isl_pw_aff *isl_pw_aff_sub(
8273 __isl_take isl_pw_aff *pwaff1,
8274 __isl_take isl_pw_aff *pwaff2);
8275 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
8276 __isl_take isl_multi_pw_aff *mpa1,
8277 __isl_take isl_multi_pw_aff *mpa2);
8278 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
8279 __isl_take isl_pw_multi_aff *pma1,
8280 __isl_take isl_pw_multi_aff *pma2);
8281 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
8282 __isl_take isl_union_pw_aff *upa1,
8283 __isl_take isl_union_pw_aff *upa2);
8284 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
8285 __isl_take isl_union_pw_multi_aff *upma1,
8286 __isl_take isl_union_pw_multi_aff *upma2);
8287 __isl_give isl_multi_union_pw_aff *
8288 isl_multi_union_pw_aff_sub(
8289 __isl_take isl_multi_union_pw_aff *mupa1,
8290 __isl_take isl_multi_union_pw_aff *mupa2);
8292 C<isl_aff_sub> subtracts the second argument from the first.
8294 #include <isl/polynomial.h>
8295 __isl_give isl_qpolynomial *isl_qpolynomial_add(
8296 __isl_take isl_qpolynomial *qp1,
8297 __isl_take isl_qpolynomial *qp2);
8298 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
8299 __isl_take isl_pw_qpolynomial *pwqp1,
8300 __isl_take isl_pw_qpolynomial *pwqp2);
8301 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
8302 __isl_take isl_pw_qpolynomial *pwqp1,
8303 __isl_take isl_pw_qpolynomial *pwqp2);
8304 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
8305 __isl_take isl_pw_qpolynomial_fold *pwf1,
8306 __isl_take isl_pw_qpolynomial_fold *pwf2);
8307 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
8308 __isl_take isl_union_pw_qpolynomial *upwqp1,
8309 __isl_take isl_union_pw_qpolynomial *upwqp2);
8310 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
8311 __isl_take isl_qpolynomial *qp1,
8312 __isl_take isl_qpolynomial *qp2);
8313 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
8314 __isl_take isl_pw_qpolynomial *pwqp1,
8315 __isl_take isl_pw_qpolynomial *pwqp2);
8316 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
8317 __isl_take isl_union_pw_qpolynomial *upwqp1,
8318 __isl_take isl_union_pw_qpolynomial *upwqp2);
8319 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
8320 __isl_take isl_pw_qpolynomial_fold *pwf1,
8321 __isl_take isl_pw_qpolynomial_fold *pwf2);
8322 __isl_give isl_union_pw_qpolynomial_fold *
8323 isl_union_pw_qpolynomial_fold_fold(
8324 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
8325 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
8327 #include <isl/aff.h>
8328 __isl_give isl_pw_aff *isl_pw_aff_union_add(
8329 __isl_take isl_pw_aff *pwaff1,
8330 __isl_take isl_pw_aff *pwaff2);
8331 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add(
8332 __isl_take isl_multi_pw_aff *mpa1,
8333 __isl_take isl_multi_pw_aff *mpa2);
8334 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
8335 __isl_take isl_pw_multi_aff *pma1,
8336 __isl_take isl_pw_multi_aff *pma2);
8337 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
8338 __isl_take isl_union_pw_aff *upa1,
8339 __isl_take isl_union_pw_aff *upa2);
8340 __isl_give isl_union_pw_multi_aff *
8341 isl_union_pw_multi_aff_union_add(
8342 __isl_take isl_union_pw_multi_aff *upma1,
8343 __isl_take isl_union_pw_multi_aff *upma2);
8344 __isl_give isl_multi_union_pw_aff *
8345 isl_multi_union_pw_aff_union_add(
8346 __isl_take isl_multi_union_pw_aff *mupa1,
8347 __isl_take isl_multi_union_pw_aff *mupa2);
8348 __isl_give isl_pw_aff *isl_pw_aff_union_min(
8349 __isl_take isl_pw_aff *pwaff1,
8350 __isl_take isl_pw_aff *pwaff2);
8351 __isl_give isl_pw_aff *isl_pw_aff_union_max(
8352 __isl_take isl_pw_aff *pwaff1,
8353 __isl_take isl_pw_aff *pwaff2);
8355 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
8356 expression with a domain that is the union of those of C<pwaff1> and
8357 C<pwaff2> and such that on each cell, the quasi-affine expression is
8358 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
8359 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
8360 associated expression is the defined one.
8361 This in contrast to the C<isl_pw_aff_max> function, which is
8362 only defined on the shared definition domain of the arguments.
8364 #include <isl/val.h>
8365 __isl_give isl_multi_val *isl_multi_val_add_val(
8366 __isl_take isl_multi_val *mv,
8367 __isl_take isl_val *v);
8368 __isl_give isl_multi_val *isl_multi_val_mod_val(
8369 __isl_take isl_multi_val *mv,
8370 __isl_take isl_val *v);
8371 __isl_give isl_multi_val *isl_multi_val_scale_val(
8372 __isl_take isl_multi_val *mv,
8373 __isl_take isl_val *v);
8374 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
8375 __isl_take isl_multi_val *mv,
8376 __isl_take isl_val *v);
8378 #include <isl/aff.h>
8379 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
8380 __isl_take isl_val *mod);
8381 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
8382 __isl_take isl_pw_aff *pa,
8383 __isl_take isl_val *mod);
8384 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
8385 __isl_take isl_union_pw_aff *upa,
8386 __isl_take isl_val *f);
8387 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
8388 __isl_take isl_val *v);
8389 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
8390 __isl_take isl_multi_aff *ma,
8391 __isl_take isl_val *v);
8392 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
8393 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
8394 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
8395 __isl_take isl_multi_pw_aff *mpa,
8396 __isl_take isl_val *v);
8397 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
8398 __isl_take isl_pw_multi_aff *pma,
8399 __isl_take isl_val *v);
8400 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
8401 __isl_take isl_union_pw_aff *upa,
8402 __isl_take isl_val *f);
8403 __isl_give isl_union_pw_multi_aff *
8404 isl_union_pw_multi_aff_scale_val(
8405 __isl_take isl_union_pw_multi_aff *upma,
8406 __isl_take isl_val *val);
8407 __isl_give isl_multi_union_pw_aff *
8408 isl_multi_union_pw_aff_scale_val(
8409 __isl_take isl_multi_union_pw_aff *mupa,
8410 __isl_take isl_val *v);
8411 __isl_give isl_aff *isl_aff_scale_down_ui(
8412 __isl_take isl_aff *aff, unsigned f);
8413 __isl_give isl_aff *isl_aff_scale_down_val(
8414 __isl_take isl_aff *aff, __isl_take isl_val *v);
8415 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
8416 __isl_take isl_multi_aff *ma,
8417 __isl_take isl_val *v);
8418 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
8419 __isl_take isl_pw_aff *pa,
8420 __isl_take isl_val *f);
8421 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
8422 __isl_take isl_multi_pw_aff *mpa,
8423 __isl_take isl_val *v);
8424 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
8425 __isl_take isl_pw_multi_aff *pma,
8426 __isl_take isl_val *v);
8427 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
8428 __isl_take isl_union_pw_aff *upa,
8429 __isl_take isl_val *v);
8430 __isl_give isl_union_pw_multi_aff *
8431 isl_union_pw_multi_aff_scale_down_val(
8432 __isl_take isl_union_pw_multi_aff *upma,
8433 __isl_take isl_val *val);
8434 __isl_give isl_multi_union_pw_aff *
8435 isl_multi_union_pw_aff_scale_down_val(
8436 __isl_take isl_multi_union_pw_aff *mupa,
8437 __isl_take isl_val *v);
8439 #include <isl/polynomial.h>
8440 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
8441 __isl_take isl_qpolynomial *qp,
8442 __isl_take isl_val *v);
8443 __isl_give isl_qpolynomial_fold *
8444 isl_qpolynomial_fold_scale_val(
8445 __isl_take isl_qpolynomial_fold *fold,
8446 __isl_take isl_val *v);
8447 __isl_give isl_pw_qpolynomial *
8448 isl_pw_qpolynomial_scale_val(
8449 __isl_take isl_pw_qpolynomial *pwqp,
8450 __isl_take isl_val *v);
8451 __isl_give isl_pw_qpolynomial_fold *
8452 isl_pw_qpolynomial_fold_scale_val(
8453 __isl_take isl_pw_qpolynomial_fold *pwf,
8454 __isl_take isl_val *v);
8455 __isl_give isl_union_pw_qpolynomial *
8456 isl_union_pw_qpolynomial_scale_val(
8457 __isl_take isl_union_pw_qpolynomial *upwqp,
8458 __isl_take isl_val *v);
8459 __isl_give isl_union_pw_qpolynomial_fold *
8460 isl_union_pw_qpolynomial_fold_scale_val(
8461 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8462 __isl_take isl_val *v);
8463 __isl_give isl_qpolynomial *
8464 isl_qpolynomial_scale_down_val(
8465 __isl_take isl_qpolynomial *qp,
8466 __isl_take isl_val *v);
8467 __isl_give isl_qpolynomial_fold *
8468 isl_qpolynomial_fold_scale_down_val(
8469 __isl_take isl_qpolynomial_fold *fold,
8470 __isl_take isl_val *v);
8471 __isl_give isl_pw_qpolynomial *
8472 isl_pw_qpolynomial_scale_down_val(
8473 __isl_take isl_pw_qpolynomial *pwqp,
8474 __isl_take isl_val *v);
8475 __isl_give isl_pw_qpolynomial_fold *
8476 isl_pw_qpolynomial_fold_scale_down_val(
8477 __isl_take isl_pw_qpolynomial_fold *pwf,
8478 __isl_take isl_val *v);
8479 __isl_give isl_union_pw_qpolynomial *
8480 isl_union_pw_qpolynomial_scale_down_val(
8481 __isl_take isl_union_pw_qpolynomial *upwqp,
8482 __isl_take isl_val *v);
8483 __isl_give isl_union_pw_qpolynomial_fold *
8484 isl_union_pw_qpolynomial_fold_scale_down_val(
8485 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8486 __isl_take isl_val *v);
8488 #include <isl/val.h>
8489 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
8490 __isl_take isl_multi_val *mv1,
8491 __isl_take isl_multi_val *mv2);
8492 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
8493 __isl_take isl_multi_val *mv1,
8494 __isl_take isl_multi_val *mv2);
8495 __isl_give isl_multi_val *
8496 isl_multi_val_scale_down_multi_val(
8497 __isl_take isl_multi_val *mv1,
8498 __isl_take isl_multi_val *mv2);
8500 #include <isl/aff.h>
8501 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
8502 __isl_take isl_multi_aff *ma,
8503 __isl_take isl_multi_val *mv);
8504 __isl_give isl_multi_union_pw_aff *
8505 isl_multi_union_pw_aff_mod_multi_val(
8506 __isl_take isl_multi_union_pw_aff *upma,
8507 __isl_take isl_multi_val *mv);
8508 __isl_give isl_multi_pw_aff *
8509 isl_multi_pw_aff_mod_multi_val(
8510 __isl_take isl_multi_pw_aff *mpa,
8511 __isl_take isl_multi_val *mv);
8512 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
8513 __isl_take isl_multi_aff *ma,
8514 __isl_take isl_multi_val *mv);
8515 __isl_give isl_pw_multi_aff *
8516 isl_pw_multi_aff_scale_multi_val(
8517 __isl_take isl_pw_multi_aff *pma,
8518 __isl_take isl_multi_val *mv);
8519 __isl_give isl_multi_pw_aff *
8520 isl_multi_pw_aff_scale_multi_val(
8521 __isl_take isl_multi_pw_aff *mpa,
8522 __isl_take isl_multi_val *mv);
8523 __isl_give isl_multi_union_pw_aff *
8524 isl_multi_union_pw_aff_scale_multi_val(
8525 __isl_take isl_multi_union_pw_aff *mupa,
8526 __isl_take isl_multi_val *mv);
8527 __isl_give isl_union_pw_multi_aff *
8528 isl_union_pw_multi_aff_scale_multi_val(
8529 __isl_take isl_union_pw_multi_aff *upma,
8530 __isl_take isl_multi_val *mv);
8531 __isl_give isl_multi_aff *
8532 isl_multi_aff_scale_down_multi_val(
8533 __isl_take isl_multi_aff *ma,
8534 __isl_take isl_multi_val *mv);
8535 __isl_give isl_multi_pw_aff *
8536 isl_multi_pw_aff_scale_down_multi_val(
8537 __isl_take isl_multi_pw_aff *mpa,
8538 __isl_take isl_multi_val *mv);
8539 __isl_give isl_multi_union_pw_aff *
8540 isl_multi_union_pw_aff_scale_down_multi_val(
8541 __isl_take isl_multi_union_pw_aff *mupa,
8542 __isl_take isl_multi_val *mv);
8544 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
8545 by the corresponding elements of C<mv>.
8547 #include <isl/aff.h>
8548 __isl_give isl_aff *isl_aff_mul(
8549 __isl_take isl_aff *aff1,
8550 __isl_take isl_aff *aff2);
8551 __isl_give isl_aff *isl_aff_div(
8552 __isl_take isl_aff *aff1,
8553 __isl_take isl_aff *aff2);
8554 __isl_give isl_pw_aff *isl_pw_aff_mul(
8555 __isl_take isl_pw_aff *pwaff1,
8556 __isl_take isl_pw_aff *pwaff2);
8557 __isl_give isl_pw_aff *isl_pw_aff_div(
8558 __isl_take isl_pw_aff *pa1,
8559 __isl_take isl_pw_aff *pa2);
8560 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
8561 __isl_take isl_pw_aff *pa1,
8562 __isl_take isl_pw_aff *pa2);
8563 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
8564 __isl_take isl_pw_aff *pa1,
8565 __isl_take isl_pw_aff *pa2);
8567 When multiplying two affine expressions, at least one of the two needs
8568 to be a constant. Similarly, when dividing an affine expression by another,
8569 the second expression needs to be a constant.
8570 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
8571 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
8574 #include <isl/polynomial.h>
8575 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
8576 __isl_take isl_qpolynomial *qp1,
8577 __isl_take isl_qpolynomial *qp2);
8578 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
8579 __isl_take isl_pw_qpolynomial *pwqp1,
8580 __isl_take isl_pw_qpolynomial *pwqp2);
8581 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
8582 __isl_take isl_union_pw_qpolynomial *upwqp1,
8583 __isl_take isl_union_pw_qpolynomial *upwqp2);
8587 =head3 Lexicographic Optimization
8589 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
8590 the following functions
8591 compute a set that contains the lexicographic minimum or maximum
8592 of the elements in C<set> (or C<bset>) for those values of the parameters
8593 that satisfy C<dom>.
8594 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
8595 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
8597 In other words, the union of the parameter values
8598 for which the result is non-empty and of C<*empty>
8601 #include <isl/set.h>
8602 __isl_give isl_set *isl_basic_set_partial_lexmin(
8603 __isl_take isl_basic_set *bset,
8604 __isl_take isl_basic_set *dom,
8605 __isl_give isl_set **empty);
8606 __isl_give isl_set *isl_basic_set_partial_lexmax(
8607 __isl_take isl_basic_set *bset,
8608 __isl_take isl_basic_set *dom,
8609 __isl_give isl_set **empty);
8610 __isl_give isl_set *isl_set_partial_lexmin(
8611 __isl_take isl_set *set, __isl_take isl_set *dom,
8612 __isl_give isl_set **empty);
8613 __isl_give isl_set *isl_set_partial_lexmax(
8614 __isl_take isl_set *set, __isl_take isl_set *dom,
8615 __isl_give isl_set **empty);
8617 Given a (basic) set C<set> (or C<bset>), the following functions simply
8618 return a set containing the lexicographic minimum or maximum
8619 of the elements in C<set> (or C<bset>).
8620 In case of union sets, the optimum is computed per space.
8622 #include <isl/set.h>
8623 __isl_give isl_set *isl_basic_set_lexmin(
8624 __isl_take isl_basic_set *bset);
8625 __isl_give isl_set *isl_basic_set_lexmax(
8626 __isl_take isl_basic_set *bset);
8627 __isl_give isl_set *isl_set_lexmin(
8628 __isl_take isl_set *set);
8629 __isl_give isl_set *isl_set_lexmax(
8630 __isl_take isl_set *set);
8631 __isl_give isl_union_set *isl_union_set_lexmin(
8632 __isl_take isl_union_set *uset);
8633 __isl_give isl_union_set *isl_union_set_lexmax(
8634 __isl_take isl_union_set *uset);
8636 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
8637 the following functions
8638 compute a relation that maps each element of C<dom>
8639 to the single lexicographic minimum or maximum
8640 of the elements that are associated to that same
8641 element in C<map> (or C<bmap>).
8642 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
8643 that contains the elements in C<dom> that do not map
8644 to any elements in C<map> (or C<bmap>).
8645 In other words, the union of the domain of the result and of C<*empty>
8648 #include <isl/map.h>
8649 __isl_give isl_map *isl_basic_map_partial_lexmax(
8650 __isl_take isl_basic_map *bmap,
8651 __isl_take isl_basic_set *dom,
8652 __isl_give isl_set **empty);
8653 __isl_give isl_map *isl_basic_map_partial_lexmin(
8654 __isl_take isl_basic_map *bmap,
8655 __isl_take isl_basic_set *dom,
8656 __isl_give isl_set **empty);
8657 __isl_give isl_map *isl_map_partial_lexmax(
8658 __isl_take isl_map *map, __isl_take isl_set *dom,
8659 __isl_give isl_set **empty);
8660 __isl_give isl_map *isl_map_partial_lexmin(
8661 __isl_take isl_map *map, __isl_take isl_set *dom,
8662 __isl_give isl_set **empty);
8664 Given a (basic) map C<map> (or C<bmap>), the following functions simply
8665 return a map mapping each element in the domain of
8666 C<map> (or C<bmap>) to the lexicographic minimum or maximum
8667 of all elements associated to that element.
8668 In case of union relations, the optimum is computed per space.
8670 #include <isl/map.h>
8671 __isl_give isl_map *isl_basic_map_lexmin(
8672 __isl_take isl_basic_map *bmap);
8673 __isl_give isl_map *isl_basic_map_lexmax(
8674 __isl_take isl_basic_map *bmap);
8675 __isl_give isl_map *isl_map_lexmin(
8676 __isl_take isl_map *map);
8677 __isl_give isl_map *isl_map_lexmax(
8678 __isl_take isl_map *map);
8679 __isl_give isl_union_map *isl_union_map_lexmin(
8680 __isl_take isl_union_map *umap);
8681 __isl_give isl_union_map *isl_union_map_lexmax(
8682 __isl_take isl_union_map *umap);
8684 The following functions return their result in the form of
8685 a piecewise multi-affine expression,
8686 but are otherwise equivalent to the corresponding functions
8687 returning a basic set or relation.
8689 #include <isl/set.h>
8690 __isl_give isl_pw_multi_aff *
8691 isl_basic_set_partial_lexmin_pw_multi_aff(
8692 __isl_take isl_basic_set *bset,
8693 __isl_take isl_basic_set *dom,
8694 __isl_give isl_set **empty);
8695 __isl_give isl_pw_multi_aff *
8696 isl_basic_set_partial_lexmax_pw_multi_aff(
8697 __isl_take isl_basic_set *bset,
8698 __isl_take isl_basic_set *dom,
8699 __isl_give isl_set **empty);
8700 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
8701 __isl_take isl_set *set);
8702 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
8703 __isl_take isl_set *set);
8705 #include <isl/map.h>
8706 __isl_give isl_pw_multi_aff *
8707 isl_basic_map_lexmin_pw_multi_aff(
8708 __isl_take isl_basic_map *bmap);
8709 __isl_give isl_pw_multi_aff *
8710 isl_basic_map_partial_lexmin_pw_multi_aff(
8711 __isl_take isl_basic_map *bmap,
8712 __isl_take isl_basic_set *dom,
8713 __isl_give isl_set **empty);
8714 __isl_give isl_pw_multi_aff *
8715 isl_basic_map_partial_lexmax_pw_multi_aff(
8716 __isl_take isl_basic_map *bmap,
8717 __isl_take isl_basic_set *dom,
8718 __isl_give isl_set **empty);
8719 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
8720 __isl_take isl_map *map);
8721 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
8722 __isl_take isl_map *map);
8724 The following functions return the lexicographic minimum or maximum
8725 on the shared domain of the inputs and the single defined function
8726 on those parts of the domain where only a single function is defined.
8728 #include <isl/aff.h>
8729 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
8730 __isl_take isl_pw_multi_aff *pma1,
8731 __isl_take isl_pw_multi_aff *pma2);
8732 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
8733 __isl_take isl_pw_multi_aff *pma1,
8734 __isl_take isl_pw_multi_aff *pma2);
8736 If the input to a lexicographic optimization problem has
8737 multiple constraints with the same coefficients for the optimized
8738 variables, then, by default, this symmetry is exploited by
8739 replacing those constraints by a single constraint with
8740 an abstract bound, which is in turn bounded by the corresponding terms
8741 in the original constraints.
8742 Without this optimization, the solver would typically consider
8743 all possible orderings of those original bounds, resulting in a needless
8744 decomposition of the domain.
8745 However, the optimization can also result in slowdowns since
8746 an extra parameter is introduced that may get used in additional
8748 The following option determines whether symmetry detection is applied
8749 during lexicographic optimization.
8751 #include <isl/options.h>
8752 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
8754 int isl_options_get_pip_symmetry(isl_ctx *ctx);
8758 See also \autoref{s:offline}.
8762 =head2 Ternary Operations
8764 #include <isl/aff.h>
8765 __isl_give isl_pw_aff *isl_pw_aff_cond(
8766 __isl_take isl_pw_aff *cond,
8767 __isl_take isl_pw_aff *pwaff_true,
8768 __isl_take isl_pw_aff *pwaff_false);
8770 The function C<isl_pw_aff_cond> performs a conditional operator
8771 and returns an expression that is equal to C<pwaff_true>
8772 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
8773 where C<cond> is zero.
8777 Lists are defined over several element types, including
8778 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
8779 C<isl_union_pw_aff>,
8780 C<isl_union_pw_multi_aff>,
8781 C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
8783 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
8784 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
8785 Here we take lists of C<isl_set>s as an example.
8786 Lists can be created, copied, modified and freed using the following functions.
8788 #include <isl/set.h>
8789 __isl_give isl_set_list *isl_set_list_from_set(
8790 __isl_take isl_set *el);
8791 __isl_give isl_set_list *isl_set_list_alloc(
8792 isl_ctx *ctx, int n);
8793 __isl_give isl_set_list *isl_set_list_copy(
8794 __isl_keep isl_set_list *list);
8795 __isl_give isl_set_list *isl_set_list_insert(
8796 __isl_take isl_set_list *list, unsigned pos,
8797 __isl_take isl_set *el);
8798 __isl_give isl_set_list *isl_set_list_add(
8799 __isl_take isl_set_list *list,
8800 __isl_take isl_set *el);
8801 __isl_give isl_set_list *isl_set_list_drop(
8802 __isl_take isl_set_list *list,
8803 unsigned first, unsigned n);
8804 __isl_give isl_set_list *isl_set_list_clear(
8805 __isl_take isl_set_list *list);
8806 __isl_give isl_set_list *isl_set_list_swap(
8807 __isl_take isl_set_list *list,
8808 unsigned pos1, unsigned pos2);
8809 __isl_give isl_set_list *isl_set_list_reverse(
8810 __isl_take isl_set_list *list);
8811 __isl_give isl_set_list *isl_set_list_set_set(
8812 __isl_take isl_set_list *list, int index,
8813 __isl_take isl_set *set);
8814 __isl_give isl_set_list *isl_set_list_concat(
8815 __isl_take isl_set_list *list1,
8816 __isl_take isl_set_list *list2);
8817 __isl_give isl_set_list *isl_set_list_map(
8818 __isl_take isl_set_list *list,
8819 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
8822 __isl_give isl_set_list *isl_set_list_sort(
8823 __isl_take isl_set_list *list,
8824 int (*cmp)(__isl_keep isl_set *a,
8825 __isl_keep isl_set *b, void *user),
8827 __isl_null isl_set_list *isl_set_list_free(
8828 __isl_take isl_set_list *list);
8830 C<isl_set_list_alloc> creates an empty list with an initial capacity
8831 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
8832 add elements to a list, increasing its capacity as needed.
8833 C<isl_set_list_from_set> creates a list with a single element.
8834 C<isl_set_list_clear> removes all elements from a list.
8835 C<isl_set_list_swap> swaps the elements at the specified locations.
8836 C<isl_set_list_reverse> reverses the elements in the list.
8838 Lists can be inspected using the following functions.
8840 #include <isl/set.h>
8841 isl_size isl_set_list_size(__isl_keep isl_set_list *list);
8842 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list);
8843 __isl_give isl_set *isl_set_list_get_at(
8844 __isl_keep isl_set_list *list, int index);
8845 __isl_give isl_set *isl_set_list_get_set(
8846 __isl_keep isl_set_list *list, int index);
8847 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
8848 isl_stat (*fn)(__isl_take isl_set *el, void *user),
8850 isl_bool isl_set_list_every(__isl_keep isl_set_list *list,
8851 isl_bool (*test)(__isl_take isl_set *el,
8854 isl_stat isl_set_list_foreach_scc(
8855 __isl_keep isl_set_list *list,
8856 isl_bool (*follows)(__isl_keep isl_set *a,
8857 __isl_keep isl_set *b, void *user),
8859 isl_stat (*fn)(__isl_take isl_set *el, void *user),
8862 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
8864 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
8865 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
8866 strongly connected components of the graph with as vertices the elements
8867 of C<list> and a directed edge from vertex C<b> to vertex C<a>
8868 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
8869 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
8871 Lists can be printed using
8873 #include <isl/set.h>
8874 __isl_give isl_printer *isl_printer_print_set_list(
8875 __isl_take isl_printer *p,
8876 __isl_keep isl_set_list *list);
8878 Alternatively, a string representation can be obtained
8879 directly using the following function, which always prints
8882 #include <isl/set.h>
8883 __isl_give char *isl_set_list_to_str(
8884 __isl_keep isl_set_list *list);
8886 =head2 Associative arrays
8888 Associative arrays map isl objects of a specific type to isl objects
8889 of some (other) specific type. They are defined for several pairs
8890 of types, including (C<isl_map>, C<isl_basic_set>),
8891 (C<isl_id>, C<isl_ast_expr>),
8892 (C<isl_id>, C<isl_id>) and
8893 (C<isl_id>, C<isl_pw_aff>).
8894 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
8897 Associative arrays can be created, copied and freed using
8898 the following functions.
8900 #include <isl/id_to_ast_expr.h>
8901 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
8902 isl_ctx *ctx, int min_size);
8903 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
8904 __isl_keep isl_id_to_ast_expr *id2expr);
8905 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
8906 __isl_take isl_id_to_ast_expr *id2expr);
8908 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
8909 to specify the expected size of the associative array.
8910 The associative array will be grown automatically as needed.
8912 Associative arrays can be inspected using the following functions.
8914 #include <isl/id_to_ast_expr.h>
8915 __isl_give isl_maybe_isl_ast_expr
8916 isl_id_to_ast_expr_try_get(
8917 __isl_keep isl_id_to_ast_expr *id2expr,
8918 __isl_keep isl_id *key);
8919 isl_bool isl_id_to_ast_expr_has(
8920 __isl_keep isl_id_to_ast_expr *id2expr,
8921 __isl_keep isl_id *key);
8922 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
8923 __isl_keep isl_id_to_ast_expr *id2expr,
8924 __isl_take isl_id *key);
8925 isl_stat isl_id_to_ast_expr_foreach(
8926 __isl_keep isl_id_to_ast_expr *id2expr,
8927 isl_stat (*fn)(__isl_take isl_id *key,
8928 __isl_take isl_ast_expr *val, void *user),
8931 The function C<isl_id_to_ast_expr_try_get> returns a structure
8932 containing two elements, C<valid> and C<value>.
8933 If there is a value associated to the key, then C<valid>
8934 is set to C<isl_bool_true> and C<value> contains a copy of
8935 the associated value. Otherwise C<value> is C<NULL> and
8936 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
8937 on whether some error has occurred or there simply is no associated value.
8938 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
8939 in the structure and
8940 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
8942 Associative arrays can be modified using the following functions.
8944 #include <isl/id_to_ast_expr.h>
8945 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
8946 __isl_take isl_id_to_ast_expr *id2expr,
8947 __isl_take isl_id *key,
8948 __isl_take isl_ast_expr *val);
8949 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
8950 __isl_take isl_id_to_ast_expr *id2expr,
8951 __isl_take isl_id *key);
8953 Associative arrays can be printed using the following function.
8955 #include <isl/id_to_ast_expr.h>
8956 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
8957 __isl_take isl_printer *p,
8958 __isl_keep isl_id_to_ast_expr *id2expr);
8962 Vectors can be created, copied and freed using the following functions.
8964 #include <isl/vec.h>
8965 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
8967 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
8969 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
8970 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
8972 Note that the elements of a vector created by C<isl_vec_alloc>
8973 may have arbitrary values.
8974 A vector created by C<isl_vec_zero> has elements with value zero.
8975 The elements can be changed and inspected using the following functions.
8977 isl_size isl_vec_size(__isl_keep isl_vec *vec);
8978 __isl_give isl_val *isl_vec_get_element_val(
8979 __isl_keep isl_vec *vec, int pos);
8980 __isl_give isl_vec *isl_vec_set_element_si(
8981 __isl_take isl_vec *vec, int pos, int v);
8982 __isl_give isl_vec *isl_vec_set_element_val(
8983 __isl_take isl_vec *vec, int pos,
8984 __isl_take isl_val *v);
8985 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
8987 __isl_give isl_vec *isl_vec_set_val(
8988 __isl_take isl_vec *vec, __isl_take isl_val *v);
8989 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
8990 __isl_keep isl_vec *vec2, int pos);
8992 C<isl_vec_get_element> will return a negative value if anything went wrong.
8993 In that case, the value of C<*v> is undefined.
8995 The following function can be used to concatenate two vectors.
8997 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
8998 __isl_take isl_vec *vec2);
9002 Matrices can be created, copied and freed using the following functions.
9004 #include <isl/mat.h>
9005 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
9006 unsigned n_row, unsigned n_col);
9007 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
9008 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
9010 Note that the elements of a newly created matrix may have arbitrary values.
9011 The elements can be changed and inspected using the following functions.
9013 isl_size isl_mat_rows(__isl_keep isl_mat *mat);
9014 isl_size isl_mat_cols(__isl_keep isl_mat *mat);
9015 __isl_give isl_val *isl_mat_get_element_val(
9016 __isl_keep isl_mat *mat, int row, int col);
9017 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
9018 int row, int col, int v);
9019 __isl_give isl_mat *isl_mat_set_element_val(
9020 __isl_take isl_mat *mat, int row, int col,
9021 __isl_take isl_val *v);
9023 The following function computes the rank of a matrix.
9024 The return value may be -1 if some error occurred.
9026 #include <isl/mat.h>
9027 isl_size isl_mat_rank(__isl_keep isl_mat *mat);
9029 The following function can be used to compute the (right) inverse
9030 of a matrix, i.e., a matrix such that the product of the original
9031 and the inverse (in that order) is a multiple of the identity matrix.
9032 The input matrix is assumed to be of full row-rank.
9034 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
9036 The following function can be used to compute the (right) kernel
9037 (or null space) of a matrix, i.e., a matrix such that the product of
9038 the original and the kernel (in that order) is the zero matrix.
9040 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
9042 The following function computes a basis for the space spanned
9043 by the rows of a matrix.
9045 __isl_give isl_mat *isl_mat_row_basis(
9046 __isl_take isl_mat *mat);
9048 The following function computes rows that extend a basis of C<mat1>
9049 to a basis that also covers C<mat2>.
9051 __isl_give isl_mat *isl_mat_row_basis_extension(
9052 __isl_take isl_mat *mat1,
9053 __isl_take isl_mat *mat2);
9055 The following function checks whether there is no linear dependence
9056 among the combined rows of "mat1" and "mat2" that is not already present
9057 in "mat1" or "mat2" individually.
9058 If "mat1" and "mat2" have linearly independent rows by themselves,
9059 then this means that there is no linear dependence among all rows together.
9061 isl_bool isl_mat_has_linearly_independent_rows(
9062 __isl_keep isl_mat *mat1,
9063 __isl_keep isl_mat *mat2);
9065 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
9067 The following functions determine
9068 an upper or lower bound on a quasipolynomial over its domain.
9070 __isl_give isl_pw_qpolynomial_fold *
9071 isl_pw_qpolynomial_bound(
9072 __isl_take isl_pw_qpolynomial *pwqp,
9073 enum isl_fold type, isl_bool *tight);
9075 __isl_give isl_union_pw_qpolynomial_fold *
9076 isl_union_pw_qpolynomial_bound(
9077 __isl_take isl_union_pw_qpolynomial *upwqp,
9078 enum isl_fold type, isl_bool *tight);
9080 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
9081 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
9082 is the returned bound is known be tight, i.e., for each value
9083 of the parameters there is at least
9084 one element in the domain that reaches the bound.
9085 If the domain of C<pwqp> is not wrapping, then the bound is computed
9086 over all elements in that domain and the result has a purely parametric
9087 domain. If the domain of C<pwqp> is wrapping, then the bound is
9088 computed over the range of the wrapped relation. The domain of the
9089 wrapped relation becomes the domain of the result.
9091 =head2 Parametric Vertex Enumeration
9093 The parametric vertex enumeration described in this section
9094 is mainly intended to be used internally and by the C<barvinok>
9097 #include <isl/vertices.h>
9098 __isl_give isl_vertices *isl_basic_set_compute_vertices(
9099 __isl_keep isl_basic_set *bset);
9101 The function C<isl_basic_set_compute_vertices> performs the
9102 actual computation of the parametric vertices and the chamber
9103 decomposition and stores the result in an C<isl_vertices> object.
9104 This information can be queried by either iterating over all
9105 the vertices or iterating over all the chambers or cells
9106 and then iterating over all vertices that are active on the chamber.
9108 isl_stat isl_vertices_foreach_vertex(
9109 __isl_keep isl_vertices *vertices,
9110 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9111 void *user), void *user);
9113 isl_stat isl_vertices_foreach_cell(
9114 __isl_keep isl_vertices *vertices,
9115 isl_stat (*fn)(__isl_take isl_cell *cell,
9116 void *user), void *user);
9117 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
9118 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9119 void *user), void *user);
9121 Other operations that can be performed on an C<isl_vertices> object are
9124 isl_size isl_vertices_get_n_vertices(
9125 __isl_keep isl_vertices *vertices);
9126 __isl_null isl_vertices *isl_vertices_free(
9127 __isl_take isl_vertices *vertices);
9129 Vertices can be inspected and destroyed using the following functions.
9131 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex);
9132 __isl_give isl_basic_set *isl_vertex_get_domain(
9133 __isl_keep isl_vertex *vertex);
9134 __isl_give isl_multi_aff *isl_vertex_get_expr(
9135 __isl_keep isl_vertex *vertex);
9136 __isl_null isl_vertex *isl_vertex_free(
9137 __isl_take isl_vertex *vertex);
9139 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
9140 describing the vertex in terms of the parameters,
9141 while C<isl_vertex_get_domain> returns the activity domain
9144 Chambers can be inspected and destroyed using the following functions.
9146 __isl_give isl_basic_set *isl_cell_get_domain(
9147 __isl_keep isl_cell *cell);
9148 __isl_null isl_cell *isl_cell_free(
9149 __isl_take isl_cell *cell);
9151 =head1 Polyhedral Compilation Library
9153 This section collects functionality in C<isl> that has been specifically
9154 designed for use during polyhedral compilation.
9156 =head2 Schedule Trees
9158 A schedule tree is a structured representation of a schedule,
9159 assigning a relative order to a set of domain elements.
9160 The relative order expressed by the schedule tree is
9161 defined recursively. In particular, the order between
9162 two domain elements is determined by the node that is closest
9163 to the root that refers to both elements and that orders them apart.
9164 Each node in the tree is of one of several types.
9165 The root node is always of type C<isl_schedule_node_domain>
9166 (or C<isl_schedule_node_extension>)
9167 and it describes the (extra) domain elements to which the schedule applies.
9168 The other types of nodes are as follows.
9172 =item C<isl_schedule_node_band>
9174 A band of schedule dimensions. Each schedule dimension is represented
9175 by a union piecewise quasi-affine expression. If this expression
9176 assigns a different value to two domain elements, while all previous
9177 schedule dimensions in the same band assign them the same value,
9178 then the two domain elements are ordered according to these two
9180 Each expression is required to be total in the domain elements
9181 that reach the band node.
9183 =item C<isl_schedule_node_expansion>
9185 An expansion node maps each of the domain elements that reach the node
9186 to one or more domain elements. The image of this mapping forms
9187 the set of domain elements that reach the child of the expansion node.
9188 The function that maps each of the expanded domain elements
9189 to the original domain element from which it was expanded
9190 is called the contraction.
9192 =item C<isl_schedule_node_filter>
9194 A filter node does not impose any ordering, but rather intersects
9195 the set of domain elements that the current subtree refers to
9196 with a given union set. The subtree of the filter node only
9197 refers to domain elements in the intersection.
9198 A filter node is typically only used as a child of a sequence or
9201 =item C<isl_schedule_node_leaf>
9203 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
9205 =item C<isl_schedule_node_mark>
9207 A mark node can be used to attach any kind of information to a subtree
9208 of the schedule tree.
9210 =item C<isl_schedule_node_sequence>
9212 A sequence node has one or more children, each of which is a filter node.
9213 The filters on these filter nodes form a partition of
9214 the domain elements that the current subtree refers to.
9215 If two domain elements appear in distinct filters then the sequence
9216 node orders them according to the child positions of the corresponding
9219 =item C<isl_schedule_node_set>
9221 A set node is similar to a sequence node, except that
9222 it expresses that domain elements appearing in distinct filters
9223 may have any order. The order of the children of a set node
9224 is therefore also immaterial.
9228 The following node types are only supported by the AST generator.
9232 =item C<isl_schedule_node_context>
9234 The context describes constraints on the parameters and
9235 the schedule dimensions of outer
9236 bands that the AST generator may assume to hold. It is also the only
9237 kind of node that may introduce additional parameters.
9238 The space of the context is that of the flat product of the outer
9239 band nodes. In particular, if there are no outer band nodes, then
9240 this space is the unnamed zero-dimensional space.
9241 Since a context node references the outer band nodes, any tree
9242 containing a context node is considered to be anchored.
9244 =item C<isl_schedule_node_extension>
9246 An extension node instructs the AST generator to add additional
9247 domain elements that need to be scheduled.
9248 The additional domain elements are described by the range of
9249 the extension map in terms of the outer schedule dimensions,
9250 i.e., the flat product of the outer band nodes.
9251 Note that domain elements are added whenever the AST generator
9252 reaches the extension node, meaning that there are still some
9253 active domain elements for which an AST needs to be generated.
9254 The conditions under which some domain elements are still active
9255 may however not be completely described by the outer AST nodes
9256 generated at that point.
9257 Since an extension node references the outer band nodes, any tree
9258 containing an extension node is considered to be anchored.
9260 An extension node may also appear as the root of a schedule tree,
9261 when it is intended to be inserted into another tree
9262 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
9263 In this case, the domain of the extension node should
9264 correspond to the flat product of the outer band nodes
9265 in this other schedule tree at the point where the extension tree
9268 =item C<isl_schedule_node_guard>
9270 The guard describes constraints on the parameters and
9271 the schedule dimensions of outer
9272 bands that need to be enforced by the outer nodes
9273 in the generated AST.
9274 That is, the part of the AST that is generated from descendants
9275 of the guard node can assume that these constraints are satisfied.
9276 The space of the guard is that of the flat product of the outer
9277 band nodes. In particular, if there are no outer band nodes, then
9278 this space is the unnamed zero-dimensional space.
9279 Since a guard node references the outer band nodes, any tree
9280 containing a guard node is considered to be anchored.
9284 Except for the C<isl_schedule_node_context> nodes,
9285 none of the nodes may introduce any parameters that were not
9286 already present in the root domain node.
9288 A schedule tree is encapsulated in an C<isl_schedule> object.
9289 The simplest such objects, those with a tree consisting of single domain node,
9290 can be created using the following functions with either an empty
9291 domain or a given domain.
9293 #include <isl/schedule.h>
9294 __isl_give isl_schedule *isl_schedule_empty(
9295 __isl_take isl_space *space);
9296 __isl_give isl_schedule *isl_schedule_from_domain(
9297 __isl_take isl_union_set *domain);
9299 The function C<isl_schedule_constraints_compute_schedule> described
9300 in L</"Scheduling"> can also be used to construct schedules.
9302 C<isl_schedule> objects may be copied and freed using the following functions.
9304 #include <isl/schedule.h>
9305 __isl_give isl_schedule *isl_schedule_copy(
9306 __isl_keep isl_schedule *sched);
9307 __isl_null isl_schedule *isl_schedule_free(
9308 __isl_take isl_schedule *sched);
9310 The following functions checks whether two C<isl_schedule> objects
9311 are obviously the same.
9313 #include <isl/schedule.h>
9314 isl_bool isl_schedule_plain_is_equal(
9315 __isl_keep isl_schedule *schedule1,
9316 __isl_keep isl_schedule *schedule2);
9318 The domain of the schedule, i.e., the domain described by the root node,
9319 can be obtained using the following function.
9321 #include <isl/schedule.h>
9322 __isl_give isl_union_set *isl_schedule_get_domain(
9323 __isl_keep isl_schedule *schedule);
9325 An extra top-level band node (right underneath the domain node) can
9326 be introduced into the schedule using the following function.
9327 The schedule tree is assumed not to have any anchored nodes.
9329 #include <isl/schedule.h>
9330 __isl_give isl_schedule *
9331 isl_schedule_insert_partial_schedule(
9332 __isl_take isl_schedule *schedule,
9333 __isl_take isl_multi_union_pw_aff *partial);
9335 A top-level context node (right underneath the domain node) can
9336 be introduced into the schedule using the following function.
9338 #include <isl/schedule.h>
9339 __isl_give isl_schedule *isl_schedule_insert_context(
9340 __isl_take isl_schedule *schedule,
9341 __isl_take isl_set *context)
9343 A top-level guard node (right underneath the domain node) can
9344 be introduced into the schedule using the following function.
9346 #include <isl/schedule.h>
9347 __isl_give isl_schedule *isl_schedule_insert_guard(
9348 __isl_take isl_schedule *schedule,
9349 __isl_take isl_set *guard)
9351 A schedule that combines two schedules either in the given
9352 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
9353 or an C<isl_schedule_node_set> node,
9354 can be created using the following functions.
9356 #include <isl/schedule.h>
9357 __isl_give isl_schedule *isl_schedule_sequence(
9358 __isl_take isl_schedule *schedule1,
9359 __isl_take isl_schedule *schedule2);
9360 __isl_give isl_schedule *isl_schedule_set(
9361 __isl_take isl_schedule *schedule1,
9362 __isl_take isl_schedule *schedule2);
9364 The domains of the two input schedules need to be disjoint.
9366 The following function can be used to restrict the domain
9367 of a schedule with a domain node as root to be a subset of the given union set.
9368 This operation may remove nodes in the tree that have become
9371 #include <isl/schedule.h>
9372 __isl_give isl_schedule *isl_schedule_intersect_domain(
9373 __isl_take isl_schedule *schedule,
9374 __isl_take isl_union_set *domain);
9376 The following function can be used to simplify the domain
9377 of a schedule with a domain node as root with respect to the given
9380 #include <isl/schedule.h>
9381 __isl_give isl_schedule *isl_schedule_gist_domain_params(
9382 __isl_take isl_schedule *schedule,
9383 __isl_take isl_set *context);
9385 The following function resets the user pointers on all parameter
9386 and tuple identifiers referenced by the nodes of the given schedule.
9388 #include <isl/schedule.h>
9389 __isl_give isl_schedule *isl_schedule_reset_user(
9390 __isl_take isl_schedule *schedule);
9392 The following function aligns the parameters of all nodes
9393 in the given schedule to the given space.
9395 #include <isl/schedule.h>
9396 __isl_give isl_schedule *isl_schedule_align_params(
9397 __isl_take isl_schedule *schedule,
9398 __isl_take isl_space *space);
9400 The following function allows the user to plug in a given function
9401 in the iteration domains. The input schedule is not allowed to contain
9402 any expansion nodes.
9404 #include <isl/schedule.h>
9405 __isl_give isl_schedule *
9406 isl_schedule_pullback_union_pw_multi_aff(
9407 __isl_take isl_schedule *schedule,
9408 __isl_take isl_union_pw_multi_aff *upma);
9410 The following function can be used to plug in the schedule C<expansion>
9411 in the leaves of C<schedule>, where C<contraction> describes how
9412 the domain elements of C<expansion> map to the domain elements
9413 at the original leaves of C<schedule>.
9414 The resulting schedule will contain expansion nodes, unless
9415 C<contraction> is an identity function.
9417 #include <isl/schedule.h>
9418 __isl_give isl_schedule *isl_schedule_expand(
9419 __isl_take isl_schedule *schedule,
9420 __isl_take isl_union_pw_multi_aff *contraction,
9421 __isl_take isl_schedule *expansion);
9423 An C<isl_union_map> representation of the schedule can be obtained
9424 from an C<isl_schedule> using the following function.
9426 #include <isl/schedule.h>
9427 __isl_give isl_union_map *isl_schedule_get_map(
9428 __isl_keep isl_schedule *sched);
9430 The resulting relation encodes the same relative ordering as
9431 the schedule by mapping the domain elements to a common schedule space.
9432 If the schedule_separate_components option is set, then the order
9433 of the children of a set node is explicitly encoded in the result.
9434 If the tree contains any expansion nodes, then the relation
9435 is formulated in terms of the expanded domain elements.
9437 Schedules can be read from input using the following functions.
9439 #include <isl/schedule.h>
9440 __isl_give isl_schedule *isl_schedule_read_from_file(
9441 isl_ctx *ctx, FILE *input);
9442 __isl_give isl_schedule *isl_schedule_read_from_str(
9443 isl_ctx *ctx, const char *str);
9445 A representation of the schedule can be printed using
9447 #include <isl/schedule.h>
9448 __isl_give isl_printer *isl_printer_print_schedule(
9449 __isl_take isl_printer *p,
9450 __isl_keep isl_schedule *schedule);
9451 __isl_give char *isl_schedule_to_str(
9452 __isl_keep isl_schedule *schedule);
9454 C<isl_schedule_to_str> prints the schedule in flow format.
9456 The schedule tree can be traversed through the use of
9457 C<isl_schedule_node> objects that point to a particular
9458 position in the schedule tree. Whenever a C<isl_schedule_node>
9459 is used to modify a node in the schedule tree, the original schedule
9460 tree is left untouched and the modifications are performed to a copy
9461 of the tree. The returned C<isl_schedule_node> then points to
9462 this modified copy of the tree.
9464 The root of the schedule tree can be obtained using the following function.
9466 #include <isl/schedule.h>
9467 __isl_give isl_schedule_node *isl_schedule_get_root(
9468 __isl_keep isl_schedule *schedule);
9470 A pointer to a newly created schedule tree with a single domain
9471 node can be created using the following functions.
9473 #include <isl/schedule_node.h>
9474 __isl_give isl_schedule_node *
9475 isl_schedule_node_from_domain(
9476 __isl_take isl_union_set *domain);
9477 __isl_give isl_schedule_node *
9478 isl_schedule_node_from_extension(
9479 __isl_take isl_union_map *extension);
9481 C<isl_schedule_node_from_extension> creates a tree with an extension
9484 Schedule nodes can be copied and freed using the following functions.
9486 #include <isl/schedule_node.h>
9487 __isl_give isl_schedule_node *isl_schedule_node_copy(
9488 __isl_keep isl_schedule_node *node);
9489 __isl_null isl_schedule_node *isl_schedule_node_free(
9490 __isl_take isl_schedule_node *node);
9492 The following functions can be used to check if two schedule
9493 nodes point to the same position in the same schedule.
9495 #include <isl/schedule_node.h>
9496 isl_bool isl_schedule_node_is_equal(
9497 __isl_keep isl_schedule_node *node1,
9498 __isl_keep isl_schedule_node *node2);
9500 The following properties can be obtained from a schedule node.
9502 #include <isl/schedule_node.h>
9503 enum isl_schedule_node_type isl_schedule_node_get_type(
9504 __isl_keep isl_schedule_node *node);
9505 enum isl_schedule_node_type
9506 isl_schedule_node_get_parent_type(
9507 __isl_keep isl_schedule_node *node);
9508 __isl_give isl_schedule *isl_schedule_node_get_schedule(
9509 __isl_keep isl_schedule_node *node);
9511 The function C<isl_schedule_node_get_type> returns the type of
9512 the node, while C<isl_schedule_node_get_parent_type> returns
9513 type of the parent of the node, which is required to exist.
9514 The function C<isl_schedule_node_get_schedule> returns a copy
9515 to the schedule to which the node belongs.
9517 The following functions can be used to move the schedule node
9518 to a different position in the tree or to check if such a position
9521 #include <isl/schedule_node.h>
9522 isl_bool isl_schedule_node_has_parent(
9523 __isl_keep isl_schedule_node *node);
9524 __isl_give isl_schedule_node *isl_schedule_node_parent(
9525 __isl_take isl_schedule_node *node);
9526 __isl_give isl_schedule_node *isl_schedule_node_root(
9527 __isl_take isl_schedule_node *node);
9528 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
9529 __isl_take isl_schedule_node *node,
9531 isl_size isl_schedule_node_n_children(
9532 __isl_keep isl_schedule_node *node);
9533 __isl_give isl_schedule_node *isl_schedule_node_child(
9534 __isl_take isl_schedule_node *node, int pos);
9535 isl_bool isl_schedule_node_has_children(
9536 __isl_keep isl_schedule_node *node);
9537 __isl_give isl_schedule_node *isl_schedule_node_first_child(
9538 __isl_take isl_schedule_node *node);
9539 isl_bool isl_schedule_node_has_previous_sibling(
9540 __isl_keep isl_schedule_node *node);
9541 __isl_give isl_schedule_node *
9542 isl_schedule_node_previous_sibling(
9543 __isl_take isl_schedule_node *node);
9544 isl_bool isl_schedule_node_has_next_sibling(
9545 __isl_keep isl_schedule_node *node);
9546 __isl_give isl_schedule_node *
9547 isl_schedule_node_next_sibling(
9548 __isl_take isl_schedule_node *node);
9550 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
9551 is the node itself, the ancestor of generation 1 is its parent and so on.
9553 It is also possible to query the number of ancestors of a node,
9554 the position of the current node
9555 within the children of its parent, the position of the subtree
9556 containing a node within the children of an ancestor
9557 or to obtain a copy of a given
9558 child without destroying the current node.
9559 Given two nodes that point to the same schedule, their closest
9560 shared ancestor can be obtained using
9561 C<isl_schedule_node_get_shared_ancestor>.
9563 #include <isl/schedule_node.h>
9564 isl_size isl_schedule_node_get_tree_depth(
9565 __isl_keep isl_schedule_node *node);
9566 isl_size isl_schedule_node_get_child_position(
9567 __isl_keep isl_schedule_node *node);
9568 isl_size isl_schedule_node_get_ancestor_child_position(
9569 __isl_keep isl_schedule_node *node,
9570 __isl_keep isl_schedule_node *ancestor);
9571 __isl_give isl_schedule_node *isl_schedule_node_get_child(
9572 __isl_keep isl_schedule_node *node, int pos);
9573 __isl_give isl_schedule_node *
9574 isl_schedule_node_get_shared_ancestor(
9575 __isl_keep isl_schedule_node *node1,
9576 __isl_keep isl_schedule_node *node2);
9578 All nodes in a schedule tree or
9579 all descendants of a specific node (including the node) can be visited
9580 in depth-first pre-order using the following functions.
9582 #include <isl/schedule.h>
9583 isl_stat isl_schedule_foreach_schedule_node_top_down(
9584 __isl_keep isl_schedule *sched,
9585 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
9586 void *user), void *user);
9588 #include <isl/schedule_node.h>
9589 isl_stat isl_schedule_node_foreach_descendant_top_down(
9590 __isl_keep isl_schedule_node *node,
9591 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
9592 void *user), void *user);
9594 The callback function is slightly different from the usual
9595 callbacks in that it not only indicates success (non-negative result)
9596 or failure (negative result), but also indicates whether the children
9597 of the given node should be visited. In particular, if the callback
9598 returns a positive value, then the children are visited, but if
9599 the callback returns zero, then the children are not visited.
9601 The following functions checks whether
9602 all descendants of a specific node (including the node itself)
9603 satisfy a user-specified test.
9605 #include <isl/schedule_node.h>
9606 isl_bool isl_schedule_node_every_descendant(
9607 __isl_keep isl_schedule_node *node,
9608 isl_bool (*test)(__isl_keep isl_schedule_node *node,
9609 void *user), void *user)
9611 The ancestors of a node in a schedule tree can be visited from
9612 the root down to and including the parent of the node using
9613 the following function.
9615 #include <isl/schedule_node.h>
9616 isl_stat isl_schedule_node_foreach_ancestor_top_down(
9617 __isl_keep isl_schedule_node *node,
9618 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
9619 void *user), void *user);
9621 The following functions allows for a depth-first post-order
9622 traversal of the nodes in a schedule tree or
9623 of the descendants of a specific node (including the node
9624 itself), where the user callback is allowed to modify the
9627 #include <isl/schedule.h>
9628 __isl_give isl_schedule *
9629 isl_schedule_map_schedule_node_bottom_up(
9630 __isl_take isl_schedule *schedule,
9631 __isl_give isl_schedule_node *(*fn)(
9632 __isl_take isl_schedule_node *node,
9633 void *user), void *user);
9635 #include <isl/schedule_node.h>
9636 __isl_give isl_schedule_node *
9637 isl_schedule_node_map_descendant_bottom_up(
9638 __isl_take isl_schedule_node *node,
9639 __isl_give isl_schedule_node *(*fn)(
9640 __isl_take isl_schedule_node *node,
9641 void *user), void *user);
9643 The traversal continues from the node returned by the callback function.
9644 It is the responsibility of the user to ensure that this does not
9645 lead to an infinite loop. It is safest to always return a pointer
9646 to the same position (same ancestors and child positions) as the input node.
9648 The following function removes a node (along with its descendants)
9649 from a schedule tree and returns a pointer to the leaf at the
9650 same position in the updated tree.
9651 It is not allowed to remove the root of a schedule tree or
9652 a child of a set or sequence node.
9654 #include <isl/schedule_node.h>
9655 __isl_give isl_schedule_node *isl_schedule_node_cut(
9656 __isl_take isl_schedule_node *node);
9658 The following function removes a single node
9659 from a schedule tree and returns a pointer to the child
9660 of the node, now located at the position of the original node
9661 or to a leaf node at that position if there was no child.
9662 It is not allowed to remove the root of a schedule tree,
9663 a set or sequence node, a child of a set or sequence node or
9664 a band node with an anchored subtree.
9666 #include <isl/schedule_node.h>
9667 __isl_give isl_schedule_node *isl_schedule_node_delete(
9668 __isl_take isl_schedule_node *node);
9670 Most nodes in a schedule tree only contain local information.
9671 In some cases, however, a node may also refer to the schedule dimensions
9672 of its outer band nodes.
9673 This means that the position of the node within the tree should
9674 not be changed, or at least that no changes are performed to the
9675 outer band nodes. The following function can be used to test
9676 whether the subtree rooted at a given node contains any such nodes.
9678 #include <isl/schedule_node.h>
9679 isl_bool isl_schedule_node_is_subtree_anchored(
9680 __isl_keep isl_schedule_node *node);
9682 The following function resets the user pointers on all parameter
9683 and tuple identifiers referenced by the given schedule node.
9685 #include <isl/schedule_node.h>
9686 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
9687 __isl_take isl_schedule_node *node);
9689 The following function aligns the parameters of the given schedule
9690 node to the given space.
9692 #include <isl/schedule_node.h>
9693 __isl_give isl_schedule_node *
9694 isl_schedule_node_align_params(
9695 __isl_take isl_schedule_node *node,
9696 __isl_take isl_space *space);
9698 Several node types have their own functions for querying
9699 (and in some cases setting) some node type specific properties.
9701 #include <isl/schedule_node.h>
9702 __isl_give isl_space *isl_schedule_node_band_get_space(
9703 __isl_keep isl_schedule_node *node);
9704 __isl_give isl_multi_union_pw_aff *
9705 isl_schedule_node_band_get_partial_schedule(
9706 __isl_keep isl_schedule_node *node);
9707 __isl_give isl_union_map *
9708 isl_schedule_node_band_get_partial_schedule_union_map(
9709 __isl_keep isl_schedule_node *node);
9710 isl_size isl_schedule_node_band_n_member(
9711 __isl_keep isl_schedule_node *node);
9712 isl_bool isl_schedule_node_band_member_get_coincident(
9713 __isl_keep isl_schedule_node *node, int pos);
9714 __isl_give isl_schedule_node *
9715 isl_schedule_node_band_member_set_coincident(
9716 __isl_take isl_schedule_node *node, int pos,
9718 isl_bool isl_schedule_node_band_get_permutable(
9719 __isl_keep isl_schedule_node *node);
9720 __isl_give isl_schedule_node *
9721 isl_schedule_node_band_set_permutable(
9722 __isl_take isl_schedule_node *node, int permutable);
9723 enum isl_ast_loop_type
9724 isl_schedule_node_band_member_get_ast_loop_type(
9725 __isl_keep isl_schedule_node *node, int pos);
9726 __isl_give isl_schedule_node *
9727 isl_schedule_node_band_member_set_ast_loop_type(
9728 __isl_take isl_schedule_node *node, int pos,
9729 enum isl_ast_loop_type type);
9730 enum isl_ast_loop_type
9731 isl_schedule_node_band_member_get_isolate_ast_loop_type(
9732 __isl_keep isl_schedule_node *node, int pos);
9733 __isl_give isl_schedule_node *
9734 isl_schedule_node_band_member_set_isolate_ast_loop_type(
9735 __isl_take isl_schedule_node *node, int pos,
9736 enum isl_ast_loop_type type);
9737 __isl_give isl_union_set *
9738 isl_schedule_node_band_get_ast_build_options(
9739 __isl_keep isl_schedule_node *node);
9740 __isl_give isl_schedule_node *
9741 isl_schedule_node_band_set_ast_build_options(
9742 __isl_take isl_schedule_node *node,
9743 __isl_take isl_union_set *options);
9744 __isl_give isl_set *
9745 isl_schedule_node_band_get_ast_isolate_option(
9746 __isl_keep isl_schedule_node *node);
9748 The function C<isl_schedule_node_band_get_space> returns the space
9749 of the partial schedule of the band.
9750 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
9751 returns a representation of the partial schedule of the band node
9752 in the form of an C<isl_union_map>.
9753 The coincident and permutable properties are set by
9754 C<isl_schedule_constraints_compute_schedule> on the schedule tree
9756 A scheduling dimension is considered to be ``coincident''
9757 if it satisfies the coincidence constraints within its band.
9758 That is, if the dependence distances of the coincidence
9759 constraints are all zero in that direction (for fixed
9760 iterations of outer bands).
9761 A band is marked permutable if it was produced using the Pluto-like scheduler.
9762 Note that the scheduler may have to resort to a Feautrier style scheduling
9763 step even if the default scheduler is used.
9764 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
9765 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
9766 For the meaning of these loop AST generation types and the difference
9767 between the regular loop AST generation type and the isolate
9768 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
9769 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
9770 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
9771 may return C<isl_ast_loop_error> if an error occurs.
9772 The AST build options govern how an AST is generated for
9773 the individual schedule dimensions during AST generation.
9774 See L</"AST Generation Options (Schedule Tree)">.
9775 The isolate option for the given node can be extracted from these
9776 AST build options using the function
9777 C<isl_schedule_node_band_get_ast_isolate_option>.
9779 #include <isl/schedule_node.h>
9780 __isl_give isl_set *
9781 isl_schedule_node_context_get_context(
9782 __isl_keep isl_schedule_node *node);
9784 #include <isl/schedule_node.h>
9785 __isl_give isl_union_set *
9786 isl_schedule_node_domain_get_domain(
9787 __isl_keep isl_schedule_node *node);
9789 #include <isl/schedule_node.h>
9790 __isl_give isl_union_map *
9791 isl_schedule_node_expansion_get_expansion(
9792 __isl_keep isl_schedule_node *node);
9793 __isl_give isl_union_pw_multi_aff *
9794 isl_schedule_node_expansion_get_contraction(
9795 __isl_keep isl_schedule_node *node);
9797 #include <isl/schedule_node.h>
9798 __isl_give isl_union_map *
9799 isl_schedule_node_extension_get_extension(
9800 __isl_keep isl_schedule_node *node);
9802 #include <isl/schedule_node.h>
9803 __isl_give isl_union_set *
9804 isl_schedule_node_filter_get_filter(
9805 __isl_keep isl_schedule_node *node);
9807 #include <isl/schedule_node.h>
9808 __isl_give isl_set *isl_schedule_node_guard_get_guard(
9809 __isl_keep isl_schedule_node *node);
9811 #include <isl/schedule_node.h>
9812 __isl_give isl_id *isl_schedule_node_mark_get_id(
9813 __isl_keep isl_schedule_node *node);
9815 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
9816 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
9817 partial schedules related to the node.
9819 #include <isl/schedule_node.h>
9820 __isl_give isl_multi_union_pw_aff *
9821 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
9822 __isl_keep isl_schedule_node *node);
9823 __isl_give isl_union_pw_multi_aff *
9824 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
9825 __isl_keep isl_schedule_node *node);
9826 __isl_give isl_union_map *
9827 isl_schedule_node_get_prefix_schedule_union_map(
9828 __isl_keep isl_schedule_node *node);
9829 __isl_give isl_union_map *
9830 isl_schedule_node_get_prefix_schedule_relation(
9831 __isl_keep isl_schedule_node *node);
9832 __isl_give isl_union_map *
9833 isl_schedule_node_get_subtree_schedule_union_map(
9834 __isl_keep isl_schedule_node *node);
9836 In particular, the functions
9837 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
9838 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
9839 and C<isl_schedule_node_get_prefix_schedule_union_map>
9840 return a relative ordering on the domain elements that reach the given
9841 node determined by its ancestors.
9842 The function C<isl_schedule_node_get_prefix_schedule_relation>
9843 additionally includes the domain constraints in the result.
9844 The function C<isl_schedule_node_get_subtree_schedule_union_map>
9845 returns a representation of the partial schedule defined by the
9846 subtree rooted at the given node.
9847 If the tree contains any expansion nodes, then the subtree schedule
9848 is formulated in terms of the expanded domain elements.
9849 The tree passed to functions returning a prefix schedule
9850 may only contain extension nodes if these would not affect
9851 the result of these functions. That is, if one of the ancestors
9852 is an extension node, then all of the domain elements that were
9853 added by the extension node need to have been filtered out
9854 by filter nodes between the extension node and the input node.
9855 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
9856 may not contain in extension nodes in the selected subtree.
9858 The expansion/contraction defined by an entire subtree, combining
9859 the expansions/contractions
9860 on the expansion nodes in the subtree, can be obtained using
9861 the following functions.
9863 #include <isl/schedule_node.h>
9864 __isl_give isl_union_map *
9865 isl_schedule_node_get_subtree_expansion(
9866 __isl_keep isl_schedule_node *node);
9867 __isl_give isl_union_pw_multi_aff *
9868 isl_schedule_node_get_subtree_contraction(
9869 __isl_keep isl_schedule_node *node);
9871 The total number of outer band members of given node, i.e.,
9872 the shared output dimension of the maps in the result
9873 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
9874 using the following function.
9876 #include <isl/schedule_node.h>
9877 isl_size isl_schedule_node_get_schedule_depth(
9878 __isl_keep isl_schedule_node *node);
9880 The following functions return the elements that reach the given node
9881 or the union of universes in the spaces that contain these elements.
9883 #include <isl/schedule_node.h>
9884 __isl_give isl_union_set *
9885 isl_schedule_node_get_domain(
9886 __isl_keep isl_schedule_node *node);
9887 __isl_give isl_union_set *
9888 isl_schedule_node_get_universe_domain(
9889 __isl_keep isl_schedule_node *node);
9891 The input tree of C<isl_schedule_node_get_domain>
9892 may only contain extension nodes if these would not affect
9893 the result of this function. That is, if one of the ancestors
9894 is an extension node, then all of the domain elements that were
9895 added by the extension node need to have been filtered out
9896 by filter nodes between the extension node and the input node.
9898 The following functions can be used to introduce additional nodes
9899 in the schedule tree. The new node is introduced at the point
9900 in the tree where the C<isl_schedule_node> points to and
9901 the results points to the new node.
9903 #include <isl/schedule_node.h>
9904 __isl_give isl_schedule_node *
9905 isl_schedule_node_insert_partial_schedule(
9906 __isl_take isl_schedule_node *node,
9907 __isl_take isl_multi_union_pw_aff *schedule);
9909 This function inserts a new band node with (the greatest integer
9910 part of) the given partial schedule.
9911 The subtree rooted at the given node is assumed not to have
9914 #include <isl/schedule_node.h>
9915 __isl_give isl_schedule_node *
9916 isl_schedule_node_insert_context(
9917 __isl_take isl_schedule_node *node,
9918 __isl_take isl_set *context);
9920 This function inserts a new context node with the given context constraints.
9922 #include <isl/schedule_node.h>
9923 __isl_give isl_schedule_node *
9924 isl_schedule_node_insert_filter(
9925 __isl_take isl_schedule_node *node,
9926 __isl_take isl_union_set *filter);
9928 This function inserts a new filter node with the given filter.
9929 If the original node already pointed to a filter node, then the
9930 two filter nodes are merged into one.
9932 #include <isl/schedule_node.h>
9933 __isl_give isl_schedule_node *
9934 isl_schedule_node_insert_guard(
9935 __isl_take isl_schedule_node *node,
9936 __isl_take isl_set *guard);
9938 This function inserts a new guard node with the given guard constraints.
9940 #include <isl/schedule_node.h>
9941 __isl_give isl_schedule_node *
9942 isl_schedule_node_insert_mark(
9943 __isl_take isl_schedule_node *node,
9944 __isl_take isl_id *mark);
9946 This function inserts a new mark node with the give mark identifier.
9948 #include <isl/schedule_node.h>
9949 __isl_give isl_schedule_node *
9950 isl_schedule_node_insert_sequence(
9951 __isl_take isl_schedule_node *node,
9952 __isl_take isl_union_set_list *filters);
9953 __isl_give isl_schedule_node *
9954 isl_schedule_node_insert_set(
9955 __isl_take isl_schedule_node *node,
9956 __isl_take isl_union_set_list *filters);
9958 These functions insert a new sequence or set node with the given
9959 filters as children.
9961 #include <isl/schedule_node.h>
9962 __isl_give isl_schedule_node *isl_schedule_node_group(
9963 __isl_take isl_schedule_node *node,
9964 __isl_take isl_id *group_id);
9966 This function introduces an expansion node in between the current
9967 node and its parent that expands instances of a space with tuple
9968 identifier C<group_id> to the original domain elements that reach
9969 the node. The group instances are identified by the prefix schedule
9970 of those domain elements. The ancestors of the node are adjusted
9971 to refer to the group instances instead of the original domain
9972 elements. The return value points to the same node in the updated
9973 schedule tree as the input node, i.e., to the child of the newly
9974 introduced expansion node. Grouping instances of different statements
9975 ensures that they will be treated as a single statement by the
9976 AST generator up to the point of the expansion node.
9978 The following function can be used to flatten a nested
9981 #include <isl/schedule_node.h>
9982 __isl_give isl_schedule_node *
9983 isl_schedule_node_sequence_splice_child(
9984 __isl_take isl_schedule_node *node, int pos);
9986 That is, given a sequence node C<node> that has another sequence node
9987 in its child at position C<pos> (in particular, the child of that filter
9988 node is a sequence node), attach the children of that other sequence
9989 node as children of C<node>, replacing the original child at position
9992 The partial schedule of a band node can be scaled (down) or reduced using
9993 the following functions.
9995 #include <isl/schedule_node.h>
9996 __isl_give isl_schedule_node *
9997 isl_schedule_node_band_scale(
9998 __isl_take isl_schedule_node *node,
9999 __isl_take isl_multi_val *mv);
10000 __isl_give isl_schedule_node *
10001 isl_schedule_node_band_scale_down(
10002 __isl_take isl_schedule_node *node,
10003 __isl_take isl_multi_val *mv);
10004 __isl_give isl_schedule_node *
10005 isl_schedule_node_band_mod(
10006 __isl_take isl_schedule_node *node,
10007 __isl_take isl_multi_val *mv);
10009 The spaces of the two arguments need to match.
10010 After scaling, the partial schedule is replaced by its greatest
10011 integer part to ensure that the schedule remains integral.
10013 The partial schedule of a band node can be shifted by an
10014 C<isl_multi_union_pw_aff> with a domain that is a superset
10015 of the domain of the partial schedule using
10016 the following function.
10018 #include <isl/schedule_node.h>
10019 __isl_give isl_schedule_node *
10020 isl_schedule_node_band_shift(
10021 __isl_take isl_schedule_node *node,
10022 __isl_take isl_multi_union_pw_aff *shift);
10024 A band node can be tiled using the following function.
10026 #include <isl/schedule_node.h>
10027 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
10028 __isl_take isl_schedule_node *node,
10029 __isl_take isl_multi_val *sizes);
10031 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
10033 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
10034 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
10036 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
10038 The C<isl_schedule_node_band_tile> function tiles
10039 the band using the given tile sizes inside its schedule.
10040 A new child band node is created to represent the point loops and it is
10041 inserted between the modified band and its children.
10042 The subtree rooted at the given node is assumed not to have
10043 any anchored nodes.
10044 The C<tile_scale_tile_loops> option specifies whether the tile
10045 loops iterators should be scaled by the tile sizes.
10046 If the C<tile_shift_point_loops> option is set, then the point loops
10047 are shifted to start at zero.
10049 A band node can be split into two nested band nodes
10050 using the following function.
10052 #include <isl/schedule_node.h>
10053 __isl_give isl_schedule_node *isl_schedule_node_band_split(
10054 __isl_take isl_schedule_node *node, int pos);
10056 The resulting outer band node contains the first C<pos> dimensions of
10057 the schedule of C<node> while the inner band contains the remaining dimensions.
10058 The schedules of the two band nodes live in anonymous spaces.
10059 The loop AST generation type options and the isolate option
10060 are split over the two band nodes.
10062 A band node can be moved down to the leaves of the subtree rooted
10063 at the band node using the following function.
10065 #include <isl/schedule_node.h>
10066 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
10067 __isl_take isl_schedule_node *node);
10069 The subtree rooted at the given node is assumed not to have
10070 any anchored nodes.
10071 The result points to the node in the resulting tree that is in the same
10072 position as the node pointed to by C<node> in the original tree.
10074 #include <isl/schedule_node.h>
10075 __isl_give isl_schedule_node *
10076 isl_schedule_node_order_before(
10077 __isl_take isl_schedule_node *node,
10078 __isl_take isl_union_set *filter);
10079 __isl_give isl_schedule_node *
10080 isl_schedule_node_order_after(
10081 __isl_take isl_schedule_node *node,
10082 __isl_take isl_union_set *filter);
10084 These functions split the domain elements that reach C<node>
10085 into those that satisfy C<filter> and those that do not and
10086 arranges for the elements that do satisfy the filter to be
10087 executed before (in case of C<isl_schedule_node_order_before>)
10088 or after (in case of C<isl_schedule_node_order_after>)
10089 those that do not. The order is imposed by
10090 a sequence node, possibly reusing the grandparent of C<node>
10091 on two copies of the subtree attached to the original C<node>.
10092 Both copies are simplified with respect to their filter.
10094 Return a pointer to the copy of the subtree that does not
10095 satisfy C<filter>. If there is no such copy (because all
10096 reaching domain elements satisfy the filter), then return
10097 the original pointer.
10099 #include <isl/schedule_node.h>
10100 __isl_give isl_schedule_node *
10101 isl_schedule_node_graft_before(
10102 __isl_take isl_schedule_node *node,
10103 __isl_take isl_schedule_node *graft);
10104 __isl_give isl_schedule_node *
10105 isl_schedule_node_graft_after(
10106 __isl_take isl_schedule_node *node,
10107 __isl_take isl_schedule_node *graft);
10109 This function inserts the C<graft> tree into the tree containing C<node>
10110 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
10111 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
10112 The root node of C<graft>
10113 should be an extension node where the domain of the extension
10114 is the flat product of all outer band nodes of C<node>.
10115 The root node may also be a domain node.
10116 The elements of the domain or the range of the extension may not
10117 intersect with the domain elements that reach "node".
10118 The schedule tree of C<graft> may not be anchored.
10120 The schedule tree of C<node> is modified to include an extension node
10121 corresponding to the root node of C<graft> as a child of the original
10122 parent of C<node>. The original node that C<node> points to and the
10123 child of the root node of C<graft> are attached to this extension node
10124 through a sequence, with appropriate filters and with the child
10125 of C<graft> appearing before or after the original C<node>.
10127 If C<node> already appears inside a sequence that is the child of
10128 an extension node and if the spaces of the new domain elements
10129 do not overlap with those of the original domain elements,
10130 then that extension node is extended with the new extension
10131 rather than introducing a new segment of extension and sequence nodes.
10133 Return a pointer to the same node in the modified tree that
10134 C<node> pointed to in the original tree.
10136 A representation of the schedule node can be printed using
10138 #include <isl/schedule_node.h>
10139 __isl_give isl_printer *isl_printer_print_schedule_node(
10140 __isl_take isl_printer *p,
10141 __isl_keep isl_schedule_node *node);
10142 __isl_give char *isl_schedule_node_to_str(
10143 __isl_keep isl_schedule_node *node);
10145 C<isl_schedule_node_to_str> prints the schedule node in block format.
10147 =head2 Dependence Analysis
10149 C<isl> contains specialized functionality for performing
10150 array dataflow analysis. That is, given a I<sink> access relation,
10151 a collection of possible I<source> accesses and
10152 a collection of I<kill> accesses,
10153 C<isl> can compute relations that describe
10154 for each iteration of the sink access, which iterations
10155 of which of the source access relations may have
10156 accessed the same data element before the given iteration
10157 of the sink access without any intermediate kill of that data element.
10158 The resulting dependence relations map source iterations
10159 to either the corresponding sink iterations or
10160 pairs of corresponding sink iterations and accessed data elements.
10161 To compute standard flow dependences, the sink should be
10162 a read, while the sources should be writes.
10163 If no kills are specified,
10164 then memory based dependence analysis is performed.
10165 If, on the other hand, all sources are also kills,
10166 then value based dependence analysis is performed.
10167 If any of the source accesses are marked as being I<must>
10168 accesses, then they are also treated as kills.
10169 Furthermore, the specification of must-sources results
10170 in the computation of must-dependences.
10171 Only dependences originating in a must access not coscheduled
10172 with any other access to the same element and without
10173 any may accesses between the must access and the sink access
10174 are considered to be must dependences.
10176 =head3 High-level Interface
10178 A high-level interface to dependence analysis is provided
10179 by the following function.
10181 #include <isl/flow.h>
10182 __isl_give isl_union_flow *
10183 isl_union_access_info_compute_flow(
10184 __isl_take isl_union_access_info *access);
10186 The input C<isl_union_access_info> object describes the sink
10187 access relations, the source access relations and a schedule,
10188 while the output C<isl_union_flow> object describes
10189 the resulting dependence relations and the subsets of the
10190 sink relations for which no source was found.
10192 An C<isl_union_access_info> is created, modified, copied and freed using
10193 the following functions.
10195 #include <isl/flow.h>
10196 __isl_give isl_union_access_info *
10197 isl_union_access_info_from_sink(
10198 __isl_take isl_union_map *sink);
10199 __isl_give isl_union_access_info *
10200 isl_union_access_info_set_kill(
10201 __isl_take isl_union_access_info *access,
10202 __isl_take isl_union_map *kill);
10203 __isl_give isl_union_access_info *
10204 isl_union_access_info_set_may_source(
10205 __isl_take isl_union_access_info *access,
10206 __isl_take isl_union_map *may_source);
10207 __isl_give isl_union_access_info *
10208 isl_union_access_info_set_must_source(
10209 __isl_take isl_union_access_info *access,
10210 __isl_take isl_union_map *must_source);
10211 __isl_give isl_union_access_info *
10212 isl_union_access_info_set_schedule(
10213 __isl_take isl_union_access_info *access,
10214 __isl_take isl_schedule *schedule);
10215 __isl_give isl_union_access_info *
10216 isl_union_access_info_set_schedule_map(
10217 __isl_take isl_union_access_info *access,
10218 __isl_take isl_union_map *schedule_map);
10219 __isl_give isl_union_access_info *
10220 isl_union_access_info_copy(
10221 __isl_keep isl_union_access_info *access);
10222 __isl_null isl_union_access_info *
10223 isl_union_access_info_free(
10224 __isl_take isl_union_access_info *access);
10226 The may sources set by C<isl_union_access_info_set_may_source>
10227 do not need to include the must sources set by
10228 C<isl_union_access_info_set_must_source> as a subset.
10229 The kills set by C<isl_union_access_info_set_kill> may overlap
10230 with the may-sources and/or must-sources.
10231 The user is free not to call one (or more) of these functions,
10232 in which case the corresponding set is kept to its empty default.
10233 Similarly, the default schedule initialized by
10234 C<isl_union_access_info_from_sink> is empty.
10235 The current schedule is determined by the last call to either
10236 C<isl_union_access_info_set_schedule> or
10237 C<isl_union_access_info_set_schedule_map>.
10238 The domain of the schedule corresponds to the domains of
10239 the access relations. In particular, the domains of the access
10240 relations are effectively intersected with the domain of the schedule
10241 and only the resulting accesses are considered by the dependence analysis.
10243 An C<isl_union_access_info> object can be read from input
10244 using the following function.
10246 #include <isl/flow.h>
10247 __isl_give isl_union_access_info *
10248 isl_union_access_info_read_from_file(isl_ctx *ctx,
10251 A representation of the information contained in an object
10252 of type C<isl_union_access_info> can be obtained using
10254 #include <isl/flow.h>
10255 __isl_give isl_printer *
10256 isl_printer_print_union_access_info(
10257 __isl_take isl_printer *p,
10258 __isl_keep isl_union_access_info *access);
10259 __isl_give char *isl_union_access_info_to_str(
10260 __isl_keep isl_union_access_info *access);
10262 C<isl_union_access_info_to_str> prints the information in flow format.
10264 The output of C<isl_union_access_info_compute_flow> can be examined,
10265 copied, and freed using the following functions.
10267 #include <isl/flow.h>
10268 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
10269 __isl_keep isl_union_flow *flow);
10270 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
10271 __isl_keep isl_union_flow *flow);
10272 __isl_give isl_union_map *
10273 isl_union_flow_get_full_must_dependence(
10274 __isl_keep isl_union_flow *flow);
10275 __isl_give isl_union_map *
10276 isl_union_flow_get_full_may_dependence(
10277 __isl_keep isl_union_flow *flow);
10278 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
10279 __isl_keep isl_union_flow *flow);
10280 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
10281 __isl_keep isl_union_flow *flow);
10282 __isl_give isl_union_flow *isl_union_flow_copy(
10283 __isl_keep isl_union_flow *flow);
10284 __isl_null isl_union_flow *isl_union_flow_free(
10285 __isl_take isl_union_flow *flow);
10287 The relation returned by C<isl_union_flow_get_must_dependence>
10288 relates domain elements of must sources to domain elements of the sink.
10289 The relation returned by C<isl_union_flow_get_may_dependence>
10290 relates domain elements of must or may sources to domain elements of the sink
10291 and includes the previous relation as a subset.
10292 The relation returned by C<isl_union_flow_get_full_must_dependence>
10293 relates domain elements of must sources to pairs of domain elements of the sink
10294 and accessed data elements.
10295 The relation returned by C<isl_union_flow_get_full_may_dependence>
10296 relates domain elements of must or may sources to pairs of
10297 domain elements of the sink and accessed data elements.
10298 This relation includes the previous relation as a subset.
10299 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
10300 of the sink relation for which no dependences have been found.
10301 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
10302 of the sink relation for which no definite dependences have been found.
10303 That is, it contains those sink access that do not contribute to any
10304 of the elements in the relation returned
10305 by C<isl_union_flow_get_must_dependence>.
10307 A representation of the information contained in an object
10308 of type C<isl_union_flow> can be obtained using
10310 #include <isl/flow.h>
10311 __isl_give isl_printer *isl_printer_print_union_flow(
10312 __isl_take isl_printer *p,
10313 __isl_keep isl_union_flow *flow);
10314 __isl_give char *isl_union_flow_to_str(
10315 __isl_keep isl_union_flow *flow);
10317 C<isl_union_flow_to_str> prints the information in flow format.
10319 =head3 Low-level Interface
10321 A lower-level interface is provided by the following functions.
10323 #include <isl/flow.h>
10325 typedef int (*isl_access_level_before)(void *first, void *second);
10327 __isl_give isl_access_info *isl_access_info_alloc(
10328 __isl_take isl_map *sink,
10329 void *sink_user, isl_access_level_before fn,
10331 __isl_give isl_access_info *isl_access_info_add_source(
10332 __isl_take isl_access_info *acc,
10333 __isl_take isl_map *source, int must,
10334 void *source_user);
10335 __isl_null isl_access_info *isl_access_info_free(
10336 __isl_take isl_access_info *acc);
10338 __isl_give isl_flow *isl_access_info_compute_flow(
10339 __isl_take isl_access_info *acc);
10341 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
10342 isl_stat (*fn)(__isl_take isl_map *dep, int must,
10343 void *dep_user, void *user),
10345 __isl_give isl_map *isl_flow_get_no_source(
10346 __isl_keep isl_flow *deps, int must);
10347 __isl_null isl_flow *isl_flow_free(
10348 __isl_take isl_flow *deps);
10350 The function C<isl_access_info_compute_flow> performs the actual
10351 dependence analysis. The other functions are used to construct
10352 the input for this function or to read off the output.
10354 The input is collected in an C<isl_access_info>, which can
10355 be created through a call to C<isl_access_info_alloc>.
10356 The arguments to this functions are the sink access relation
10357 C<sink>, a token C<sink_user> used to identify the sink
10358 access to the user, a callback function for specifying the
10359 relative order of source and sink accesses, and the number
10360 of source access relations that will be added.
10362 The callback function has type C<int (*)(void *first, void *second)>.
10363 The function is called with two user supplied tokens identifying
10364 either a source or the sink and it should return the shared nesting
10365 level and the relative order of the two accesses.
10366 In particular, let I<n> be the number of loops shared by
10367 the two accesses. If C<first> precedes C<second> textually,
10368 then the function should return I<2 * n + 1>; otherwise,
10369 it should return I<2 * n>.
10370 The low-level interface assumes that no sources are coscheduled.
10371 If the information returned by the callback does not allow
10372 the relative order to be determined, then one of the sources
10373 is arbitrarily taken to be executed after the other(s).
10375 The sources can be added to the C<isl_access_info> object by performing
10376 (at most) C<max_source> calls to C<isl_access_info_add_source>.
10377 C<must> indicates whether the source is a I<must> access
10378 or a I<may> access. Note that a multi-valued access relation
10379 should only be marked I<must> if every iteration in the domain
10380 of the relation accesses I<all> elements in its image.
10381 The C<source_user> token is again used to identify
10382 the source access. The range of the source access relation
10383 C<source> should have the same dimension as the range
10384 of the sink access relation.
10385 The C<isl_access_info_free> function should usually not be
10386 called explicitly, because it is already called implicitly by
10387 C<isl_access_info_compute_flow>.
10389 The result of the dependence analysis is collected in an
10390 C<isl_flow>. There may be elements of
10391 the sink access for which no preceding source access could be
10392 found or for which all preceding sources are I<may> accesses.
10393 The relations containing these elements can be obtained through
10394 calls to C<isl_flow_get_no_source>, the first with C<must> set
10395 and the second with C<must> unset.
10396 In the case of standard flow dependence analysis,
10397 with the sink a read and the sources I<must> writes,
10398 the first relation corresponds to the reads from uninitialized
10399 array elements and the second relation is empty.
10400 The actual flow dependences can be extracted using
10401 C<isl_flow_foreach>. This function will call the user-specified
10402 callback function C<fn> for each B<non-empty> dependence between
10403 a source and the sink. The callback function is called
10404 with four arguments, the actual flow dependence relation
10405 mapping source iterations to sink iterations, a boolean that
10406 indicates whether it is a I<must> or I<may> dependence, a token
10407 identifying the source and an additional C<void *> with value
10408 equal to the third argument of the C<isl_flow_foreach> call.
10409 A dependence is marked I<must> if it originates from a I<must>
10410 source and if it is not followed by any I<may> sources.
10412 After finishing with an C<isl_flow>, the user should call
10413 C<isl_flow_free> to free all associated memory.
10415 =head3 Interaction with the Low-level Interface
10417 During the dependence analysis, we frequently need to perform
10418 the following operation. Given a relation between sink iterations
10419 and potential source iterations from a particular source domain,
10420 what is the last potential source iteration corresponding to each
10421 sink iteration. It can sometimes be convenient to adjust
10422 the set of potential source iterations before or after each such operation.
10423 The prototypical example is fuzzy array dataflow analysis,
10424 where we need to analyze if, based on data-dependent constraints,
10425 the sink iteration can ever be executed without one or more of
10426 the corresponding potential source iterations being executed.
10427 If so, we can introduce extra parameters and select an unknown
10428 but fixed source iteration from the potential source iterations.
10429 To be able to perform such manipulations, C<isl> provides the following
10432 #include <isl/flow.h>
10434 typedef __isl_give isl_restriction *(*isl_access_restrict)(
10435 __isl_keep isl_map *source_map,
10436 __isl_keep isl_set *sink, void *source_user,
10438 __isl_give isl_access_info *isl_access_info_set_restrict(
10439 __isl_take isl_access_info *acc,
10440 isl_access_restrict fn, void *user);
10442 The function C<isl_access_info_set_restrict> should be called
10443 before calling C<isl_access_info_compute_flow> and registers a callback function
10444 that will be called any time C<isl> is about to compute the last
10445 potential source. The first argument is the (reverse) proto-dependence,
10446 mapping sink iterations to potential source iterations.
10447 The second argument represents the sink iterations for which
10448 we want to compute the last source iteration.
10449 The third argument is the token corresponding to the source
10450 and the final argument is the token passed to C<isl_access_info_set_restrict>.
10451 The callback is expected to return a restriction on either the input or
10452 the output of the operation computing the last potential source.
10453 If the input needs to be restricted then restrictions are needed
10454 for both the source and the sink iterations. The sink iterations
10455 and the potential source iterations will be intersected with these sets.
10456 If the output needs to be restricted then only a restriction on the source
10457 iterations is required.
10458 If any error occurs, the callback should return C<NULL>.
10459 An C<isl_restriction> object can be created, freed and inspected
10460 using the following functions.
10462 #include <isl/flow.h>
10464 __isl_give isl_restriction *isl_restriction_input(
10465 __isl_take isl_set *source_restr,
10466 __isl_take isl_set *sink_restr);
10467 __isl_give isl_restriction *isl_restriction_output(
10468 __isl_take isl_set *source_restr);
10469 __isl_give isl_restriction *isl_restriction_none(
10470 __isl_take isl_map *source_map);
10471 __isl_give isl_restriction *isl_restriction_empty(
10472 __isl_take isl_map *source_map);
10473 __isl_null isl_restriction *isl_restriction_free(
10474 __isl_take isl_restriction *restr);
10476 C<isl_restriction_none> and C<isl_restriction_empty> are special
10477 cases of C<isl_restriction_input>. C<isl_restriction_none>
10478 is essentially equivalent to
10480 isl_restriction_input(isl_set_universe(
10481 isl_space_range(isl_map_get_space(source_map))),
10483 isl_space_domain(isl_map_get_space(source_map))));
10485 whereas C<isl_restriction_empty> is essentially equivalent to
10487 isl_restriction_input(isl_set_empty(
10488 isl_space_range(isl_map_get_space(source_map))),
10490 isl_space_domain(isl_map_get_space(source_map))));
10494 #include <isl/schedule.h>
10495 __isl_give isl_schedule *
10496 isl_schedule_constraints_compute_schedule(
10497 __isl_take isl_schedule_constraints *sc);
10499 The function C<isl_schedule_constraints_compute_schedule> can be
10500 used to compute a schedule that satisfies the given schedule constraints.
10501 These schedule constraints include the iteration domain for which
10502 a schedule should be computed and dependences between pairs of
10503 iterations. In particular, these dependences include
10504 I<validity> dependences and I<proximity> dependences.
10505 By default, the algorithm used to construct the schedule is similar
10506 to that of C<Pluto>.
10507 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
10509 The generated schedule respects all validity dependences.
10510 That is, all dependence distances over these dependences in the
10511 scheduled space are lexicographically positive.
10513 The default algorithm tries to ensure that the dependence distances
10514 over coincidence constraints are zero and to minimize the
10515 dependence distances over proximity dependences.
10516 Moreover, it tries to obtain sequences (bands) of schedule dimensions
10517 for groups of domains where the dependence distances over validity
10518 dependences have only non-negative values.
10519 Note that when minimizing the maximal dependence distance
10520 over proximity dependences, a single affine expression in the parameters
10521 is constructed that bounds all dependence distances. If no such expression
10522 exists, then the algorithm will fail and resort to an alternative
10523 scheduling algorithm. In particular, this means that adding proximity
10524 dependences may eliminate valid solutions. A typical example where this
10525 phenomenon may occur is when some subset of the proximity dependences
10526 has no restriction on some parameter, forcing the coefficient of that
10527 parameter to be zero, while some other subset forces the dependence
10528 distance to depend on that parameter, requiring the same coefficient
10530 When using Feautrier's algorithm, the coincidence and proximity constraints
10531 are only taken into account during the extension to a
10532 full-dimensional schedule.
10534 An C<isl_schedule_constraints> object can be constructed
10535 and manipulated using the following functions.
10537 #include <isl/schedule.h>
10538 __isl_give isl_schedule_constraints *
10539 isl_schedule_constraints_copy(
10540 __isl_keep isl_schedule_constraints *sc);
10541 __isl_give isl_schedule_constraints *
10542 isl_schedule_constraints_on_domain(
10543 __isl_take isl_union_set *domain);
10544 __isl_give isl_schedule_constraints *
10545 isl_schedule_constraints_set_context(
10546 __isl_take isl_schedule_constraints *sc,
10547 __isl_take isl_set *context);
10548 __isl_give isl_schedule_constraints *
10549 isl_schedule_constraints_set_validity(
10550 __isl_take isl_schedule_constraints *sc,
10551 __isl_take isl_union_map *validity);
10552 __isl_give isl_schedule_constraints *
10553 isl_schedule_constraints_set_coincidence(
10554 __isl_take isl_schedule_constraints *sc,
10555 __isl_take isl_union_map *coincidence);
10556 __isl_give isl_schedule_constraints *
10557 isl_schedule_constraints_set_proximity(
10558 __isl_take isl_schedule_constraints *sc,
10559 __isl_take isl_union_map *proximity);
10560 __isl_give isl_schedule_constraints *
10561 isl_schedule_constraints_set_conditional_validity(
10562 __isl_take isl_schedule_constraints *sc,
10563 __isl_take isl_union_map *condition,
10564 __isl_take isl_union_map *validity);
10565 __isl_give isl_schedule_constraints *
10566 isl_schedule_constraints_apply(
10567 __isl_take isl_schedule_constraints *sc,
10568 __isl_take isl_union_map *umap);
10569 __isl_null isl_schedule_constraints *
10570 isl_schedule_constraints_free(
10571 __isl_take isl_schedule_constraints *sc);
10573 The initial C<isl_schedule_constraints> object created by
10574 C<isl_schedule_constraints_on_domain> does not impose any constraints.
10575 That is, it has an empty set of dependences.
10576 The function C<isl_schedule_constraints_set_context> allows the user
10577 to specify additional constraints on the parameters that may
10578 be assumed to hold during the construction of the schedule.
10579 The function C<isl_schedule_constraints_set_validity> replaces the
10580 validity dependences, mapping domain elements I<i> to domain
10581 elements that should be scheduled after I<i>.
10582 The function C<isl_schedule_constraints_set_coincidence> replaces the
10583 coincidence dependences, mapping domain elements I<i> to domain
10584 elements that should be scheduled together with I<I>, if possible.
10585 The function C<isl_schedule_constraints_set_proximity> replaces the
10586 proximity dependences, mapping domain elements I<i> to domain
10587 elements that should be scheduled either before I<I>
10588 or as early as possible after I<i>.
10590 The function C<isl_schedule_constraints_set_conditional_validity>
10591 replaces the conditional validity constraints.
10592 A conditional validity constraint is only imposed when any of the corresponding
10593 conditions is satisfied, i.e., when any of them is non-zero.
10594 That is, the scheduler ensures that within each band if the dependence
10595 distances over the condition constraints are not all zero
10596 then all corresponding conditional validity constraints are respected.
10597 A conditional validity constraint corresponds to a condition
10598 if the two are adjacent, i.e., if the domain of one relation intersect
10599 the range of the other relation.
10600 The typical use case of conditional validity constraints is
10601 to allow order constraints between live ranges to be violated
10602 as long as the live ranges themselves are local to the band.
10603 To allow more fine-grained control over which conditions correspond
10604 to which conditional validity constraints, the domains and ranges
10605 of these relations may include I<tags>. That is, the domains and
10606 ranges of those relation may themselves be wrapped relations
10607 where the iteration domain appears in the domain of those wrapped relations
10608 and the range of the wrapped relations can be arbitrarily chosen
10609 by the user. Conditions and conditional validity constraints are only
10610 considered adjacent to each other if the entire wrapped relation matches.
10611 In particular, a relation with a tag will never be considered adjacent
10612 to a relation without a tag.
10614 The function C<isl_schedule_constraints_apply> takes
10615 schedule constraints that are defined on some set of domain elements
10616 and transforms them to schedule constraints on the elements
10617 to which these domain elements are mapped by the given transformation.
10619 An C<isl_schedule_constraints> object can be inspected
10620 using the following functions.
10622 #include <isl/schedule.h>
10623 __isl_give isl_union_set *
10624 isl_schedule_constraints_get_domain(
10625 __isl_keep isl_schedule_constraints *sc);
10626 __isl_give isl_set *isl_schedule_constraints_get_context(
10627 __isl_keep isl_schedule_constraints *sc);
10628 __isl_give isl_union_map *
10629 isl_schedule_constraints_get_validity(
10630 __isl_keep isl_schedule_constraints *sc);
10631 __isl_give isl_union_map *
10632 isl_schedule_constraints_get_coincidence(
10633 __isl_keep isl_schedule_constraints *sc);
10634 __isl_give isl_union_map *
10635 isl_schedule_constraints_get_proximity(
10636 __isl_keep isl_schedule_constraints *sc);
10637 __isl_give isl_union_map *
10638 isl_schedule_constraints_get_conditional_validity(
10639 __isl_keep isl_schedule_constraints *sc);
10640 __isl_give isl_union_map *
10641 isl_schedule_constraints_get_conditional_validity_condition(
10642 __isl_keep isl_schedule_constraints *sc);
10644 An C<isl_schedule_constraints> object can be read from input
10645 using the following functions.
10647 #include <isl/schedule.h>
10648 __isl_give isl_schedule_constraints *
10649 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
10651 __isl_give isl_schedule_constraints *
10652 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
10655 The contents of an C<isl_schedule_constraints> object can be printed
10656 using the following functions.
10658 #include <isl/schedule.h>
10659 __isl_give isl_printer *
10660 isl_printer_print_schedule_constraints(
10661 __isl_take isl_printer *p,
10662 __isl_keep isl_schedule_constraints *sc);
10663 __isl_give char *isl_schedule_constraints_to_str(
10664 __isl_keep isl_schedule_constraints *sc);
10666 The following function computes a schedule directly from
10667 an iteration domain and validity and proximity dependences
10668 and is implemented in terms of the functions described above.
10669 The use of C<isl_union_set_compute_schedule> is discouraged.
10671 #include <isl/schedule.h>
10672 __isl_give isl_schedule *isl_union_set_compute_schedule(
10673 __isl_take isl_union_set *domain,
10674 __isl_take isl_union_map *validity,
10675 __isl_take isl_union_map *proximity);
10677 The generated schedule represents a schedule tree.
10678 For more information on schedule trees, see
10679 L</"Schedule Trees">.
10683 #include <isl/schedule.h>
10684 isl_stat isl_options_set_schedule_max_coefficient(
10685 isl_ctx *ctx, int val);
10686 int isl_options_get_schedule_max_coefficient(
10688 isl_stat isl_options_set_schedule_max_constant_term(
10689 isl_ctx *ctx, int val);
10690 int isl_options_get_schedule_max_constant_term(
10692 isl_stat isl_options_set_schedule_serialize_sccs(
10693 isl_ctx *ctx, int val);
10694 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
10695 isl_stat isl_options_set_schedule_whole_component(
10696 isl_ctx *ctx, int val);
10697 int isl_options_get_schedule_whole_component(
10699 isl_stat isl_options_set_schedule_maximize_band_depth(
10700 isl_ctx *ctx, int val);
10701 int isl_options_get_schedule_maximize_band_depth(
10703 isl_stat isl_options_set_schedule_maximize_coincidence(
10704 isl_ctx *ctx, int val);
10705 int isl_options_get_schedule_maximize_coincidence(
10707 isl_stat isl_options_set_schedule_outer_coincidence(
10708 isl_ctx *ctx, int val);
10709 int isl_options_get_schedule_outer_coincidence(
10711 isl_stat isl_options_set_schedule_split_scaled(
10712 isl_ctx *ctx, int val);
10713 int isl_options_get_schedule_split_scaled(
10715 isl_stat isl_options_set_schedule_treat_coalescing(
10716 isl_ctx *ctx, int val);
10717 int isl_options_get_schedule_treat_coalescing(
10719 isl_stat isl_options_set_schedule_algorithm(
10720 isl_ctx *ctx, int val);
10721 int isl_options_get_schedule_algorithm(
10723 isl_stat isl_options_set_schedule_carry_self_first(
10724 isl_ctx *ctx, int val);
10725 int isl_options_get_schedule_carry_self_first(
10727 isl_stat isl_options_set_schedule_separate_components(
10728 isl_ctx *ctx, int val);
10729 int isl_options_get_schedule_separate_components(
10734 =item * schedule_max_coefficient
10736 This option enforces that the coefficients for variable and parameter
10737 dimensions in the calculated schedule are not larger than the specified value.
10738 This option can significantly increase the speed of the scheduling calculation
10739 and may also prevent fusing of unrelated dimensions. A value of -1 means that
10740 this option does not introduce bounds on the variable or parameter
10742 This option has no effect on the Feautrier style scheduler.
10744 =item * schedule_max_constant_term
10746 This option enforces that the constant coefficients in the calculated schedule
10747 are not larger than the maximal constant term. This option can significantly
10748 increase the speed of the scheduling calculation and may also prevent fusing of
10749 unrelated dimensions. A value of -1 means that this option does not introduce
10750 bounds on the constant coefficients.
10752 =item * schedule_serialize_sccs
10754 If this option is set, then all strongly connected components
10755 in the dependence graph are serialized as soon as they are detected.
10756 This means in particular that instances of statements will only
10757 appear in the same band node if these statements belong
10758 to the same strongly connected component at the point where
10759 the band node is constructed.
10761 =item * schedule_whole_component
10763 If this option is set, then entire (weakly) connected
10764 components in the dependence graph are scheduled together
10766 Otherwise, each strongly connected component within
10767 such a weakly connected component is first scheduled separately
10768 and then combined with other strongly connected components.
10769 This option has no effect if C<schedule_serialize_sccs> is set.
10771 =item * schedule_maximize_band_depth
10773 If this option is set, then the scheduler tries to maximize
10774 the width of the bands. Wider bands give more possibilities for tiling.
10775 In particular, if the C<schedule_whole_component> option is set,
10776 then bands are split if this might result in wider bands.
10777 Otherwise, the effect of this option is to only allow
10778 strongly connected components to be combined if this does
10779 not reduce the width of the bands.
10780 Note that if the C<schedule_serialize_sccs> options is set, then
10781 the C<schedule_maximize_band_depth> option therefore has no effect.
10783 =item * schedule_maximize_coincidence
10785 This option is only effective if the C<schedule_whole_component>
10786 option is turned off.
10787 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
10788 strongly connected components are only combined with each other
10789 if this does not reduce the number of coincident band members.
10791 =item * schedule_outer_coincidence
10793 If this option is set, then we try to construct schedules
10794 where the outermost scheduling dimension in each band
10795 satisfies the coincidence constraints.
10797 =item * schedule_algorithm
10799 Selects the scheduling algorithm to be used.
10800 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
10801 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
10803 =item * schedule_split_scaled
10805 If this option is set, then we try to construct schedules in which the
10806 constant term is split off from the linear part if the linear parts of
10807 the scheduling rows for all nodes in the graph have a common non-trivial
10809 The constant term is then dropped and the linear
10811 This option is only effective when the Feautrier style scheduler is
10812 being used, either as the main scheduler or as a fallback for the
10813 Pluto-like scheduler.
10815 =item * schedule_treat_coalescing
10817 If this option is set, then the scheduler will try and avoid
10818 producing schedules that perform loop coalescing.
10819 In particular, for the Pluto-like scheduler, this option places
10820 bounds on the schedule coefficients based on the sizes of the instance sets.
10821 For the Feautrier style scheduler, this option detects potentially
10822 coalescing schedules and then tries to adjust the schedule to avoid
10825 =item * schedule_carry_self_first
10827 If this option is set, then the Feautrier style scheduler
10828 (when used as a fallback for the Pluto-like scheduler) will
10829 first try to only carry self-dependences.
10831 =item * schedule_separate_components
10833 If this option is set then the function C<isl_schedule_get_map>
10834 will treat set nodes in the same way as sequence nodes.
10838 =head2 AST Generation
10840 This section describes the C<isl> functionality for generating
10841 ASTs that visit all the elements
10842 in a domain in an order specified by a schedule tree or
10844 In case the schedule given as a C<isl_union_map>, an AST is generated
10845 that visits all the elements in the domain of the C<isl_union_map>
10846 according to the lexicographic order of the corresponding image
10847 element(s). If the range of the C<isl_union_map> consists of
10848 elements in more than one space, then each of these spaces is handled
10849 separately in an arbitrary order.
10850 It should be noted that the schedule tree or the image elements
10851 in a schedule map only specify the I<order>
10852 in which the corresponding domain elements should be visited.
10853 No direct relation between the partial schedule values
10854 or the image elements on the one hand and the loop iterators
10855 in the generated AST on the other hand should be assumed.
10857 Each AST is generated within a build. The initial build
10858 simply specifies the constraints on the parameters (if any)
10859 and can be created, inspected, copied and freed using the following functions.
10861 #include <isl/ast_build.h>
10862 __isl_give isl_ast_build *isl_ast_build_alloc(
10864 __isl_give isl_ast_build *isl_ast_build_from_context(
10865 __isl_take isl_set *set);
10866 __isl_give isl_ast_build *isl_ast_build_copy(
10867 __isl_keep isl_ast_build *build);
10868 __isl_null isl_ast_build *isl_ast_build_free(
10869 __isl_take isl_ast_build *build);
10871 The C<set> argument is usually a parameter set with zero or more parameters.
10872 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
10873 this set is required to be a parameter set.
10874 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
10875 specify any parameter constraints.
10876 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
10877 and L</"Fine-grained Control over AST Generation">.
10878 Finally, the AST itself can be constructed using one of the following
10881 #include <isl/ast_build.h>
10882 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
10883 __isl_keep isl_ast_build *build,
10884 __isl_take isl_schedule *schedule);
10885 __isl_give isl_ast_node *
10886 isl_ast_build_node_from_schedule_map(
10887 __isl_keep isl_ast_build *build,
10888 __isl_take isl_union_map *schedule);
10890 =head3 Inspecting the AST
10892 The basic properties of an AST node can be obtained as follows.
10894 #include <isl/ast.h>
10895 enum isl_ast_node_type isl_ast_node_get_type(
10896 __isl_keep isl_ast_node *node);
10898 The type of an AST node is one of
10899 C<isl_ast_node_for>,
10900 C<isl_ast_node_if>,
10901 C<isl_ast_node_block>,
10902 C<isl_ast_node_mark> or
10903 C<isl_ast_node_user>.
10904 An C<isl_ast_node_for> represents a for node.
10905 An C<isl_ast_node_if> represents an if node.
10906 An C<isl_ast_node_block> represents a compound node.
10907 An C<isl_ast_node_mark> introduces a mark in the AST.
10908 An C<isl_ast_node_user> represents an expression statement.
10909 An expression statement typically corresponds to a domain element, i.e.,
10910 one of the elements that is visited by the AST.
10912 Each type of node has its own additional properties.
10914 #include <isl/ast.h>
10915 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
10916 __isl_keep isl_ast_node *node);
10917 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
10918 __isl_keep isl_ast_node *node);
10919 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
10920 __isl_keep isl_ast_node *node);
10921 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
10922 __isl_keep isl_ast_node *node);
10923 __isl_give isl_ast_node *isl_ast_node_for_get_body(
10924 __isl_keep isl_ast_node *node);
10925 isl_bool isl_ast_node_for_is_degenerate(
10926 __isl_keep isl_ast_node *node);
10928 An C<isl_ast_for> is considered degenerate if it is known to execute
10931 #include <isl/ast.h>
10932 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
10933 __isl_keep isl_ast_node *node);
10934 __isl_give isl_ast_node *isl_ast_node_if_get_then_node(
10935 __isl_keep isl_ast_node *node);
10936 __isl_give isl_ast_node *isl_ast_node_if_get_then(
10937 __isl_keep isl_ast_node *node);
10938 isl_bool isl_ast_node_if_has_else_node(
10939 __isl_keep isl_ast_node *node);
10940 isl_bool isl_ast_node_if_has_else(
10941 __isl_keep isl_ast_node *node);
10942 __isl_give isl_ast_node *isl_ast_node_if_get_else_node(
10943 __isl_keep isl_ast_node *node);
10944 __isl_give isl_ast_node *isl_ast_node_if_get_else(
10945 __isl_keep isl_ast_node *node);
10947 C<isl_ast_node_if_get_then>,
10948 C<isl_ast_node_if_has_else> and
10949 C<isl_ast_node_if_get_else>
10950 are alternative names for
10951 C<isl_ast_node_if_get_then_node>,
10952 C<isl_ast_node_if_has_else_node> and
10953 C<isl_ast_node_if_get_else_node>, respectively.
10955 __isl_give isl_ast_node_list *
10956 isl_ast_node_block_get_children(
10957 __isl_keep isl_ast_node *node);
10959 __isl_give isl_id *isl_ast_node_mark_get_id(
10960 __isl_keep isl_ast_node *node);
10961 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
10962 __isl_keep isl_ast_node *node);
10964 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
10965 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
10967 #include <isl/ast.h>
10968 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
10969 __isl_keep isl_ast_node *node);
10971 All descendants of a specific node in the AST (including the node itself)
10973 in depth-first pre-order using the following function.
10975 #include <isl/ast.h>
10976 isl_stat isl_ast_node_foreach_descendant_top_down(
10977 __isl_keep isl_ast_node *node,
10978 isl_bool (*fn)(__isl_keep isl_ast_node *node,
10979 void *user), void *user);
10981 The callback function should return C<isl_bool_true> if the children
10982 of the given node should be visited and C<isl_bool_false> if they should not.
10983 It should return C<isl_bool_error> in case of failure, in which case
10984 the entire traversal is aborted.
10986 Each of the returned C<isl_ast_expr>s can in turn be inspected using
10987 the following functions.
10989 #include <isl/ast.h>
10990 enum isl_ast_expr_type isl_ast_expr_get_type(
10991 __isl_keep isl_ast_expr *expr);
10993 The type of an AST expression is one of
10994 C<isl_ast_expr_op>,
10995 C<isl_ast_expr_id> or
10996 C<isl_ast_expr_int>.
10997 An C<isl_ast_expr_op> represents the result of an operation.
10998 An C<isl_ast_expr_id> represents an identifier.
10999 An C<isl_ast_expr_int> represents an integer value.
11001 Each type of expression has its own additional properties.
11003 #include <isl/ast.h>
11004 enum isl_ast_expr_op_type isl_ast_expr_op_get_type(
11005 __isl_keep isl_ast_expr *expr);
11006 enum isl_ast_expr_op_type isl_ast_expr_get_op_type(
11007 __isl_keep isl_ast_expr *expr);
11008 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr);
11009 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
11010 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg(
11011 __isl_keep isl_ast_expr *expr, int pos);
11012 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
11013 __isl_keep isl_ast_expr *expr, int pos);
11014 isl_stat isl_ast_expr_foreach_ast_expr_op_type(
11015 __isl_keep isl_ast_expr *expr,
11016 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11017 void *user), void *user);
11018 isl_stat isl_ast_expr_foreach_ast_op_type(
11019 __isl_keep isl_ast_expr *expr,
11020 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11021 void *user), void *user);
11022 isl_stat isl_ast_node_foreach_ast_expr_op_type(
11023 __isl_keep isl_ast_node *node,
11024 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11025 void *user), void *user);
11026 isl_stat isl_ast_node_foreach_ast_op_type(
11027 __isl_keep isl_ast_node *node,
11028 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11029 void *user), void *user);
11031 C<isl_ast_expr_op_get_type> returns the type of the operation
11032 performed. C<isl_ast_expr_op_get_n_arg> returns the number of
11033 arguments. C<isl_ast_expr_get_op_arg> returns the specified
11035 C<isl_ast_expr_get_op_type> is an alternative name for
11036 C<isl_ast_expr_op_get_type>.
11038 C<isl_ast_expr_get_op_n_arg> is an alternative name for
11039 C<isl_ast_expr_op_get_n_arg> and
11040 C<isl_ast_expr_get_op_arg> is an alternative name for
11041 C<isl_ast_expr_op_get_arg>.
11043 C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct
11044 C<isl_ast_expr_op_type> that appears in C<expr>.
11045 C<isl_ast_expr_foreach_ast_op_type> is an alternative name for
11046 C<isl_ast_expr_foreach_ast_expr_op_type>.
11047 C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct
11048 C<isl_ast_expr_op_type> that appears in C<node>.
11049 C<isl_ast_node_foreach_ast_op_type> is an alternative name for
11050 C<isl_ast_node_foreach_ast_expr_op_type>.
11051 The operation type is one of the following.
11055 =item C<isl_ast_expr_op_and>
11057 Logical I<and> of two arguments.
11058 Both arguments can be evaluated.
11060 =item C<isl_ast_expr_op_and_then>
11062 Logical I<and> of two arguments.
11063 The second argument can only be evaluated if the first evaluates to true.
11065 =item C<isl_ast_expr_op_or>
11067 Logical I<or> of two arguments.
11068 Both arguments can be evaluated.
11070 =item C<isl_ast_expr_op_or_else>
11072 Logical I<or> of two arguments.
11073 The second argument can only be evaluated if the first evaluates to false.
11075 =item C<isl_ast_expr_op_max>
11077 Maximum of two or more arguments.
11079 =item C<isl_ast_expr_op_min>
11081 Minimum of two or more arguments.
11083 =item C<isl_ast_expr_op_minus>
11087 =item C<isl_ast_expr_op_add>
11089 Sum of two arguments.
11091 =item C<isl_ast_expr_op_sub>
11093 Difference of two arguments.
11095 =item C<isl_ast_expr_op_mul>
11097 Product of two arguments.
11099 =item C<isl_ast_expr_op_div>
11101 Exact division. That is, the result is known to be an integer.
11103 =item C<isl_ast_expr_op_fdiv_q>
11105 Result of integer division, rounded towards negative
11107 The divisor is known to be positive.
11109 =item C<isl_ast_expr_op_pdiv_q>
11111 Result of integer division, where dividend is known to be non-negative.
11112 The divisor is known to be positive.
11114 =item C<isl_ast_expr_op_pdiv_r>
11116 Remainder of integer division, where dividend is known to be non-negative.
11117 The divisor is known to be positive.
11119 =item C<isl_ast_expr_op_zdiv_r>
11121 Equal to zero iff the remainder on integer division is zero.
11122 The divisor is known to be positive.
11124 =item C<isl_ast_expr_op_cond>
11126 Conditional operator defined on three arguments.
11127 If the first argument evaluates to true, then the result
11128 is equal to the second argument. Otherwise, the result
11129 is equal to the third argument.
11130 The second and third argument may only be evaluated if
11131 the first argument evaluates to true and false, respectively.
11132 Corresponds to C<a ? b : c> in C.
11134 =item C<isl_ast_expr_op_select>
11136 Conditional operator defined on three arguments.
11137 If the first argument evaluates to true, then the result
11138 is equal to the second argument. Otherwise, the result
11139 is equal to the third argument.
11140 The second and third argument may be evaluated independently
11141 of the value of the first argument.
11142 Corresponds to C<a * b + (1 - a) * c> in C.
11144 =item C<isl_ast_expr_op_eq>
11148 =item C<isl_ast_expr_op_le>
11150 Less than or equal relation.
11152 =item C<isl_ast_expr_op_lt>
11154 Less than relation.
11156 =item C<isl_ast_expr_op_ge>
11158 Greater than or equal relation.
11160 =item C<isl_ast_expr_op_gt>
11162 Greater than relation.
11164 =item C<isl_ast_expr_op_call>
11167 The number of arguments of the C<isl_ast_expr> is one more than
11168 the number of arguments in the function call, the first argument
11169 representing the function being called.
11171 =item C<isl_ast_expr_op_access>
11174 The number of arguments of the C<isl_ast_expr> is one more than
11175 the number of index expressions in the array access, the first argument
11176 representing the array being accessed.
11178 =item C<isl_ast_expr_op_member>
11181 This operation has two arguments, a structure and the name of
11182 the member of the structure being accessed.
11186 #include <isl/ast.h>
11187 __isl_give isl_id *isl_ast_expr_id_get_id(
11188 __isl_keep isl_ast_expr *expr);
11189 __isl_give isl_id *isl_ast_expr_get_id(
11190 __isl_keep isl_ast_expr *expr);
11192 Return the identifier represented by the AST expression.
11193 C<isl_ast_expr_get_id> is an alternative name for
11194 C<isl_ast_expr_id_get_id>.
11196 #include <isl/ast.h>
11197 __isl_give isl_val *isl_ast_expr_int_get_val(
11198 __isl_keep isl_ast_expr *expr);
11199 __isl_give isl_val *isl_ast_expr_get_val(
11200 __isl_keep isl_ast_expr *expr);
11202 Return the integer represented by the AST expression.
11203 C<isl_ast_expr_get_val> is an alternative name for
11204 C<isl_ast_expr_int_get_val>.
11206 =head3 Properties of ASTs
11208 #include <isl/ast.h>
11209 isl_bool isl_ast_expr_is_equal(
11210 __isl_keep isl_ast_expr *expr1,
11211 __isl_keep isl_ast_expr *expr2);
11213 Check if two C<isl_ast_expr>s are equal to each other.
11215 =head3 Manipulating and printing the AST
11217 AST nodes can be copied and freed using the following functions.
11219 #include <isl/ast.h>
11220 __isl_give isl_ast_node *isl_ast_node_copy(
11221 __isl_keep isl_ast_node *node);
11222 __isl_null isl_ast_node *isl_ast_node_free(
11223 __isl_take isl_ast_node *node);
11225 AST expressions can be copied and freed using the following functions.
11227 #include <isl/ast.h>
11228 __isl_give isl_ast_expr *isl_ast_expr_copy(
11229 __isl_keep isl_ast_expr *expr);
11230 __isl_null isl_ast_expr *isl_ast_expr_free(
11231 __isl_take isl_ast_expr *expr);
11233 New AST expressions can be created either directly or within
11234 the context of an C<isl_ast_build>.
11236 #include <isl/ast.h>
11237 __isl_give isl_ast_expr *isl_ast_expr_from_val(
11238 __isl_take isl_val *v);
11239 __isl_give isl_ast_expr *isl_ast_expr_from_id(
11240 __isl_take isl_id *id);
11241 __isl_give isl_ast_expr *isl_ast_expr_neg(
11242 __isl_take isl_ast_expr *expr);
11243 __isl_give isl_ast_expr *isl_ast_expr_address_of(
11244 __isl_take isl_ast_expr *expr);
11245 __isl_give isl_ast_expr *isl_ast_expr_add(
11246 __isl_take isl_ast_expr *expr1,
11247 __isl_take isl_ast_expr *expr2);
11248 __isl_give isl_ast_expr *isl_ast_expr_sub(
11249 __isl_take isl_ast_expr *expr1,
11250 __isl_take isl_ast_expr *expr2);
11251 __isl_give isl_ast_expr *isl_ast_expr_mul(
11252 __isl_take isl_ast_expr *expr1,
11253 __isl_take isl_ast_expr *expr2);
11254 __isl_give isl_ast_expr *isl_ast_expr_div(
11255 __isl_take isl_ast_expr *expr1,
11256 __isl_take isl_ast_expr *expr2);
11257 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
11258 __isl_take isl_ast_expr *expr1,
11259 __isl_take isl_ast_expr *expr2);
11260 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
11261 __isl_take isl_ast_expr *expr1,
11262 __isl_take isl_ast_expr *expr2);
11263 __isl_give isl_ast_expr *isl_ast_expr_and(
11264 __isl_take isl_ast_expr *expr1,
11265 __isl_take isl_ast_expr *expr2)
11266 __isl_give isl_ast_expr *isl_ast_expr_and_then(
11267 __isl_take isl_ast_expr *expr1,
11268 __isl_take isl_ast_expr *expr2)
11269 __isl_give isl_ast_expr *isl_ast_expr_or(
11270 __isl_take isl_ast_expr *expr1,
11271 __isl_take isl_ast_expr *expr2)
11272 __isl_give isl_ast_expr *isl_ast_expr_or_else(
11273 __isl_take isl_ast_expr *expr1,
11274 __isl_take isl_ast_expr *expr2)
11275 __isl_give isl_ast_expr *isl_ast_expr_eq(
11276 __isl_take isl_ast_expr *expr1,
11277 __isl_take isl_ast_expr *expr2);
11278 __isl_give isl_ast_expr *isl_ast_expr_le(
11279 __isl_take isl_ast_expr *expr1,
11280 __isl_take isl_ast_expr *expr2);
11281 __isl_give isl_ast_expr *isl_ast_expr_lt(
11282 __isl_take isl_ast_expr *expr1,
11283 __isl_take isl_ast_expr *expr2);
11284 __isl_give isl_ast_expr *isl_ast_expr_ge(
11285 __isl_take isl_ast_expr *expr1,
11286 __isl_take isl_ast_expr *expr2);
11287 __isl_give isl_ast_expr *isl_ast_expr_gt(
11288 __isl_take isl_ast_expr *expr1,
11289 __isl_take isl_ast_expr *expr2);
11290 __isl_give isl_ast_expr *isl_ast_expr_access(
11291 __isl_take isl_ast_expr *array,
11292 __isl_take isl_ast_expr_list *indices);
11293 __isl_give isl_ast_expr *isl_ast_expr_call(
11294 __isl_take isl_ast_expr *function,
11295 __isl_take isl_ast_expr_list *arguments);
11297 The function C<isl_ast_expr_address_of> can be applied to an
11298 C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant
11299 to represent the address of the C<isl_ast_expr_access>.
11300 The second argument of the functions C<isl_ast_expr_pdiv_q> and
11301 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
11303 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
11304 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
11306 #include <isl/ast_build.h>
11307 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
11308 __isl_keep isl_ast_build *build,
11309 __isl_take isl_set *set);
11310 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
11311 __isl_keep isl_ast_build *build,
11312 __isl_take isl_pw_aff *pa);
11313 __isl_give isl_ast_expr *
11314 isl_ast_build_access_from_pw_multi_aff(
11315 __isl_keep isl_ast_build *build,
11316 __isl_take isl_pw_multi_aff *pma);
11317 __isl_give isl_ast_expr *
11318 isl_ast_build_access_from_multi_pw_aff(
11319 __isl_keep isl_ast_build *build,
11320 __isl_take isl_multi_pw_aff *mpa);
11321 __isl_give isl_ast_expr *
11322 isl_ast_build_call_from_pw_multi_aff(
11323 __isl_keep isl_ast_build *build,
11324 __isl_take isl_pw_multi_aff *pma);
11325 __isl_give isl_ast_expr *
11326 isl_ast_build_call_from_multi_pw_aff(
11327 __isl_keep isl_ast_build *build,
11328 __isl_take isl_multi_pw_aff *mpa);
11331 the domains of C<pa>, C<mpa> and C<pma> should correspond
11332 to the schedule space of C<build>.
11333 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
11334 the function being called.
11335 If the accessed space is a nested relation, then it is taken
11336 to represent an access of the member specified by the range
11337 of this nested relation of the structure specified by the domain
11338 of the nested relation.
11340 The following functions can be used to modify an C<isl_ast_expr>.
11342 #include <isl/ast.h>
11343 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
11344 __isl_take isl_ast_expr *expr, int pos,
11345 __isl_take isl_ast_expr *arg);
11347 Replace the argument of C<expr> at position C<pos> by C<arg>.
11349 #include <isl/ast.h>
11350 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
11351 __isl_take isl_ast_expr *expr,
11352 __isl_take isl_id_to_ast_expr *id2expr);
11354 The function C<isl_ast_expr_substitute_ids> replaces the
11355 subexpressions of C<expr> of type C<isl_ast_expr_id>
11356 by the corresponding expression in C<id2expr>, if there is any.
11359 User specified data can be attached to an C<isl_ast_node> and obtained
11360 from the same C<isl_ast_node> using the following functions.
11362 #include <isl/ast.h>
11363 __isl_give isl_ast_node *isl_ast_node_set_annotation(
11364 __isl_take isl_ast_node *node,
11365 __isl_take isl_id *annotation);
11366 __isl_give isl_id *isl_ast_node_get_annotation(
11367 __isl_keep isl_ast_node *node);
11369 Basic printing can be performed using the following functions.
11371 #include <isl/ast.h>
11372 __isl_give isl_printer *isl_printer_print_ast_expr(
11373 __isl_take isl_printer *p,
11374 __isl_keep isl_ast_expr *expr);
11375 __isl_give isl_printer *isl_printer_print_ast_node(
11376 __isl_take isl_printer *p,
11377 __isl_keep isl_ast_node *node);
11378 __isl_give char *isl_ast_expr_to_str(
11379 __isl_keep isl_ast_expr *expr);
11380 __isl_give char *isl_ast_node_to_str(
11381 __isl_keep isl_ast_node *node);
11382 __isl_give char *isl_ast_expr_to_C_str(
11383 __isl_keep isl_ast_expr *expr);
11384 __isl_give char *isl_ast_node_to_C_str(
11385 __isl_keep isl_ast_node *node);
11387 The functions C<isl_ast_expr_to_C_str> and
11388 C<isl_ast_node_to_C_str> are convenience functions
11389 that return a string representation of the input in C format.
11391 More advanced printing can be performed using the following functions.
11393 #include <isl/ast.h>
11394 __isl_give isl_printer *
11395 isl_ast_expr_op_type_set_print_name(
11396 __isl_take isl_printer *p,
11397 enum isl_ast_expr_op_type type,
11398 __isl_keep const char *name);
11399 __isl_give isl_printer *isl_ast_op_type_set_print_name(
11400 __isl_take isl_printer *p,
11401 enum isl_ast_expr_op_type type,
11402 __isl_keep const char *name);
11403 isl_stat isl_options_set_ast_print_macro_once(
11404 isl_ctx *ctx, int val);
11405 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
11406 __isl_give isl_printer *isl_ast_expr_op_type_print_macro(
11407 enum isl_ast_expr_op_type type,
11408 __isl_take isl_printer *p);
11409 __isl_give isl_printer *isl_ast_op_type_print_macro(
11410 enum isl_ast_expr_op_type type,
11411 __isl_take isl_printer *p);
11412 __isl_give isl_printer *isl_ast_expr_print_macros(
11413 __isl_keep isl_ast_expr *expr,
11414 __isl_take isl_printer *p);
11415 __isl_give isl_printer *isl_ast_node_print_macros(
11416 __isl_keep isl_ast_node *node,
11417 __isl_take isl_printer *p);
11418 __isl_give isl_printer *isl_ast_node_print(
11419 __isl_keep isl_ast_node *node,
11420 __isl_take isl_printer *p,
11421 __isl_take isl_ast_print_options *options);
11422 __isl_give isl_printer *isl_ast_node_for_print(
11423 __isl_keep isl_ast_node *node,
11424 __isl_take isl_printer *p,
11425 __isl_take isl_ast_print_options *options);
11426 __isl_give isl_printer *isl_ast_node_if_print(
11427 __isl_keep isl_ast_node *node,
11428 __isl_take isl_printer *p,
11429 __isl_take isl_ast_print_options *options);
11431 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
11432 C<isl> may print out an AST that makes use of macros such
11433 as C<floord>, C<min> and C<max>.
11434 The names of these macros may be modified by a call
11435 to C<isl_ast_expr_op_type_set_print_name>. The user-specified
11436 names are associated to the printer object.
11437 C<isl_ast_op_type_set_print_name> is an alternative name for
11438 C<isl_ast_expr_op_type_set_print_name>.
11439 C<isl_ast_expr_op_type_print_macro> prints out the macro
11440 corresponding to a specific C<isl_ast_expr_op_type>.
11441 If the print-macro-once option is set, then a given macro definition
11442 is only printed once to any given printer object.
11443 C<isl_ast_op_type_print_macro> is an alternative name for
11444 C<isl_ast_expr_op_type_print_macro>.
11445 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
11446 for subexpressions where these macros would be used and prints
11447 out the required macro definitions.
11448 Essentially, C<isl_ast_expr_print_macros> calls
11449 C<isl_ast_expr_foreach_ast_expr_op_type> with
11450 C<isl_ast_expr_op_type_print_macro>
11451 as function argument.
11452 C<isl_ast_node_print_macros> does the same
11453 for expressions in its C<isl_ast_node> argument.
11454 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
11455 C<isl_ast_node_if_print> print an C<isl_ast_node>
11456 in C<ISL_FORMAT_C>, but allow for some extra control
11457 through an C<isl_ast_print_options> object.
11458 This object can be created using the following functions.
11460 #include <isl/ast.h>
11461 __isl_give isl_ast_print_options *
11462 isl_ast_print_options_alloc(isl_ctx *ctx);
11463 __isl_give isl_ast_print_options *
11464 isl_ast_print_options_copy(
11465 __isl_keep isl_ast_print_options *options);
11466 __isl_null isl_ast_print_options *
11467 isl_ast_print_options_free(
11468 __isl_take isl_ast_print_options *options);
11470 __isl_give isl_ast_print_options *
11471 isl_ast_print_options_set_print_user(
11472 __isl_take isl_ast_print_options *options,
11473 __isl_give isl_printer *(*print_user)(
11474 __isl_take isl_printer *p,
11475 __isl_take isl_ast_print_options *options,
11476 __isl_keep isl_ast_node *node, void *user),
11478 __isl_give isl_ast_print_options *
11479 isl_ast_print_options_set_print_for(
11480 __isl_take isl_ast_print_options *options,
11481 __isl_give isl_printer *(*print_for)(
11482 __isl_take isl_printer *p,
11483 __isl_take isl_ast_print_options *options,
11484 __isl_keep isl_ast_node *node, void *user),
11487 The callback set by C<isl_ast_print_options_set_print_user>
11488 is called whenever a node of type C<isl_ast_node_user> needs to
11490 The callback set by C<isl_ast_print_options_set_print_for>
11491 is called whenever a node of type C<isl_ast_node_for> needs to
11493 Note that C<isl_ast_node_for_print> will I<not> call the
11494 callback set by C<isl_ast_print_options_set_print_for> on the node
11495 on which C<isl_ast_node_for_print> is called, but only on nested
11496 nodes of type C<isl_ast_node_for>. It is therefore safe to
11497 call C<isl_ast_node_for_print> from within the callback set by
11498 C<isl_ast_print_options_set_print_for>.
11500 The following option determines the type to be used for iterators
11501 while printing the AST.
11503 isl_stat isl_options_set_ast_iterator_type(
11504 isl_ctx *ctx, const char *val);
11505 const char *isl_options_get_ast_iterator_type(
11508 The AST printer only prints body nodes of C<if> and C<for> nodes
11510 blocks cannot be safely omitted.
11511 For example, a C<for> node with one body node will not be
11512 surrounded with braces in C<ISL_FORMAT_C>.
11513 A block will always be printed by setting the following option.
11515 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
11517 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
11519 Explicit block nodes that appear inside the AST are always printed as blocks.
11520 If the block node appears as the outermost node,
11521 then it is only printed if the following option is set.
11523 isl_stat isl_options_set_ast_print_outermost_block(
11524 isl_ctx *ctx, int val);
11525 int isl_options_get_ast_print_outermost_block(
11530 #include <isl/ast_build.h>
11531 isl_stat isl_options_set_ast_build_atomic_upper_bound(
11532 isl_ctx *ctx, int val);
11533 int isl_options_get_ast_build_atomic_upper_bound(
11535 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
11537 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
11538 isl_stat isl_options_set_ast_build_detect_min_max(
11539 isl_ctx *ctx, int val);
11540 int isl_options_get_ast_build_detect_min_max(
11542 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
11543 isl_ctx *ctx, int val);
11544 int isl_options_get_ast_build_exploit_nested_bounds(
11546 isl_stat isl_options_set_ast_build_group_coscheduled(
11547 isl_ctx *ctx, int val);
11548 int isl_options_get_ast_build_group_coscheduled(
11550 isl_stat isl_options_set_ast_build_separation_bounds(
11551 isl_ctx *ctx, int val);
11552 int isl_options_get_ast_build_separation_bounds(
11554 isl_stat isl_options_set_ast_build_scale_strides(
11555 isl_ctx *ctx, int val);
11556 int isl_options_get_ast_build_scale_strides(
11558 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
11560 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
11561 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
11563 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
11567 =item * ast_build_atomic_upper_bound
11569 Generate loop upper bounds that consist of the current loop iterator,
11570 an operator and an expression not involving the iterator.
11571 If this option is not set, then the current loop iterator may appear
11572 several times in the upper bound.
11573 For example, when this option is turned off, AST generation
11576 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
11580 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
11583 When the option is turned on, the following AST is generated
11585 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
11588 =item * ast_build_prefer_pdiv
11590 If this option is turned off, then the AST generation will
11591 produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q>
11592 operators, but no C<isl_ast_expr_op_pdiv_q> or
11593 C<isl_ast_expr_op_pdiv_r> operators.
11594 If this option is turned on, then C<isl> will try to convert
11595 some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing)
11596 C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators.
11598 =item * ast_build_detect_min_max
11600 If this option is turned on, then C<isl> will try and detect
11601 min or max-expressions when building AST expressions from
11602 piecewise affine expressions.
11604 =item * ast_build_exploit_nested_bounds
11606 Simplify conditions based on bounds of nested for loops.
11607 In particular, remove conditions that are implied by the fact
11608 that one or more nested loops have at least one iteration,
11609 meaning that the upper bound is at least as large as the lower bound.
11610 For example, when this option is turned off, AST generation
11613 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
11619 for (int c0 = 0; c0 <= N; c0 += 1)
11620 for (int c1 = 0; c1 <= M; c1 += 1)
11623 When the option is turned on, the following AST is generated
11625 for (int c0 = 0; c0 <= N; c0 += 1)
11626 for (int c1 = 0; c1 <= M; c1 += 1)
11629 =item * ast_build_group_coscheduled
11631 If two domain elements are assigned the same schedule point, then
11632 they may be executed in any order and they may even appear in different
11633 loops. If this options is set, then the AST generator will make
11634 sure that coscheduled domain elements do not appear in separate parts
11635 of the AST. This is useful in case of nested AST generation
11636 if the outer AST generation is given only part of a schedule
11637 and the inner AST generation should handle the domains that are
11638 coscheduled by this initial part of the schedule together.
11639 For example if an AST is generated for a schedule
11641 { A[i] -> [0]; B[i] -> [0] }
11643 then the C<isl_ast_build_set_create_leaf> callback described
11644 below may get called twice, once for each domain.
11645 Setting this option ensures that the callback is only called once
11646 on both domains together.
11648 =item * ast_build_separation_bounds
11650 This option specifies which bounds to use during separation.
11651 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
11652 then all (possibly implicit) bounds on the current dimension will
11653 be used during separation.
11654 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
11655 then only those bounds that are explicitly available will
11656 be used during separation.
11658 =item * ast_build_scale_strides
11660 This option specifies whether the AST generator is allowed
11661 to scale down iterators of strided loops.
11663 =item * ast_build_allow_else
11665 This option specifies whether the AST generator is allowed
11666 to construct if statements with else branches.
11668 =item * ast_build_allow_or
11670 This option specifies whether the AST generator is allowed
11671 to construct if conditions with disjunctions.
11675 =head3 AST Generation Options (Schedule Tree)
11677 In case of AST construction from a schedule tree, the options
11678 that control how an AST is created from the individual schedule
11679 dimensions are stored in the band nodes of the tree
11680 (see L</"Schedule Trees">).
11682 In particular, a schedule dimension can be handled in four
11683 different ways, atomic, separate, unroll or the default.
11684 This loop AST generation type can be set using
11685 C<isl_schedule_node_band_member_set_ast_loop_type>.
11687 the first three can be selected by including a one-dimensional
11688 element with as value the position of the schedule dimension
11689 within the band and as name one of C<atomic>, C<separate>
11690 or C<unroll> in the options
11691 set by C<isl_schedule_node_band_set_ast_build_options>.
11692 Only one of these three may be specified for
11693 any given schedule dimension within a band node.
11694 If none of these is specified, then the default
11695 is used. The meaning of the options is as follows.
11701 When this option is specified, the AST generator will make
11702 sure that a given domains space only appears in a single
11703 loop at the specified level.
11705 For example, for the schedule tree
11707 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
11709 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
11710 options: "{ atomic[x] }"
11712 the following AST will be generated
11714 for (int c0 = 0; c0 <= 10; c0 += 1) {
11721 On the other hand, for the schedule tree
11723 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
11725 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
11726 options: "{ separate[x] }"
11728 the following AST will be generated
11732 for (int c0 = 1; c0 <= 9; c0 += 1) {
11739 If neither C<atomic> nor C<separate> is specified, then the AST generator
11740 may produce either of these two results or some intermediate form.
11744 When this option is specified, the AST generator will
11745 split the domain of the specified schedule dimension
11746 into pieces with a fixed set of statements for which
11747 instances need to be executed by the iterations in
11748 the schedule domain part. This option tends to avoid
11749 the generation of guards inside the corresponding loops.
11750 See also the C<atomic> option.
11754 When this option is specified, the AST generator will
11755 I<completely> unroll the corresponding schedule dimension.
11756 It is the responsibility of the user to ensure that such
11757 unrolling is possible.
11758 To obtain a partial unrolling, the user should apply an additional
11759 strip-mining to the schedule and fully unroll the inner schedule
11764 The C<isolate> option is a bit more involved. It allows the user
11765 to isolate a range of schedule dimension values from smaller and
11766 greater values. Additionally, the user may specify a different
11767 atomic/separate/unroll choice for the isolated part and the remaining
11768 parts. The typical use case of the C<isolate> option is to isolate
11769 full tiles from partial tiles.
11770 The part that needs to be isolated may depend on outer schedule dimensions.
11771 The option therefore needs to be able to reference those outer schedule
11772 dimensions. In particular, the space of the C<isolate> option is that
11773 of a wrapped map with as domain the flat product of all outer band nodes
11774 and as range the space of the current band node.
11775 The atomic/separate/unroll choice for the isolated part is determined
11776 by an option that lives in an unnamed wrapped space with as domain
11777 a zero-dimensional C<isolate> space and as range the regular
11778 C<atomic>, C<separate> or C<unroll> space.
11779 This option may also be set directly using
11780 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
11781 The atomic/separate/unroll choice for the remaining part is determined
11782 by the regular C<atomic>, C<separate> or C<unroll> option.
11783 Since the C<isolate> option references outer schedule dimensions,
11784 its use in a band node causes any tree containing the node
11785 to be considered anchored.
11787 As an example, consider the isolation of full tiles from partial tiles
11788 in a tiling of a triangular domain. The original schedule is as follows.
11790 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
11792 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
11793 { A[i,j] -> [floor(j/10)] }, \
11794 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
11798 for (int c0 = 0; c0 <= 10; c0 += 1)
11799 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
11800 for (int c2 = 10 * c0;
11801 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
11802 for (int c3 = 10 * c1;
11803 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
11806 Isolating the full tiles, we have the following input
11808 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
11810 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
11811 { A[i,j] -> [floor(j/10)] }, \
11812 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
11813 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
11814 10a+9+10b+9 <= 100 }"
11819 for (int c0 = 0; c0 <= 8; c0 += 1) {
11820 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
11821 for (int c2 = 10 * c0;
11822 c2 <= 10 * c0 + 9; c2 += 1)
11823 for (int c3 = 10 * c1;
11824 c3 <= 10 * c1 + 9; c3 += 1)
11826 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
11827 for (int c2 = 10 * c0;
11828 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
11829 for (int c3 = 10 * c1;
11830 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
11833 for (int c0 = 9; c0 <= 10; c0 += 1)
11834 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
11835 for (int c2 = 10 * c0;
11836 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
11837 for (int c3 = 10 * c1;
11838 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
11842 We may then additionally unroll the innermost loop of the isolated part
11844 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
11846 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
11847 { A[i,j] -> [floor(j/10)] }, \
11848 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
11849 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
11850 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
11855 for (int c0 = 0; c0 <= 8; c0 += 1) {
11856 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
11857 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
11859 A(c2, 10 * c1 + 1);
11860 A(c2, 10 * c1 + 2);
11861 A(c2, 10 * c1 + 3);
11862 A(c2, 10 * c1 + 4);
11863 A(c2, 10 * c1 + 5);
11864 A(c2, 10 * c1 + 6);
11865 A(c2, 10 * c1 + 7);
11866 A(c2, 10 * c1 + 8);
11867 A(c2, 10 * c1 + 9);
11869 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
11870 for (int c2 = 10 * c0;
11871 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
11872 for (int c3 = 10 * c1;
11873 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
11876 for (int c0 = 9; c0 <= 10; c0 += 1)
11877 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
11878 for (int c2 = 10 * c0;
11879 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
11880 for (int c3 = 10 * c1;
11881 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
11886 =head3 AST Generation Options (Schedule Map)
11888 In case of AST construction using
11889 C<isl_ast_build_node_from_schedule_map>, the options
11890 that control how an AST is created from the individual schedule
11891 dimensions are stored in the C<isl_ast_build>.
11892 They can be set using the following function.
11894 #include <isl/ast_build.h>
11895 __isl_give isl_ast_build *
11896 isl_ast_build_set_options(
11897 __isl_take isl_ast_build *build,
11898 __isl_take isl_union_map *options);
11900 The options are encoded in an C<isl_union_map>.
11901 The domain of this union relation refers to the schedule domain,
11902 i.e., the range of the schedule passed
11903 to C<isl_ast_build_node_from_schedule_map>.
11904 In the case of nested AST generation (see L</"Nested AST Generation">),
11905 the domain of C<options> should refer to the extra piece of the schedule.
11906 That is, it should be equal to the range of the wrapped relation in the
11907 range of the schedule.
11908 The range of the options can consist of elements in one or more spaces,
11909 the names of which determine the effect of the option.
11910 The values of the range typically also refer to the schedule dimension
11911 to which the option applies, with value C<0> representing
11912 the outermost schedule dimension. In case of nested AST generation
11913 (see L</"Nested AST Generation">), these values refer to the position
11914 of the schedule dimension within the innermost AST generation.
11915 The constraints on the domain elements of
11916 the option should only refer to this dimension and earlier dimensions.
11917 We consider the following spaces.
11921 =item C<separation_class>
11923 B<This option has been deprecated. Use the isolate option on
11924 schedule trees instead.>
11926 This space is a wrapped relation between two one dimensional spaces.
11927 The input space represents the schedule dimension to which the option
11928 applies and the output space represents the separation class.
11929 While constructing a loop corresponding to the specified schedule
11930 dimension(s), the AST generator will try to generate separate loops
11931 for domain elements that are assigned different classes.
11932 If only some of the elements are assigned a class, then those elements
11933 that are not assigned any class will be treated as belonging to a class
11934 that is separate from the explicitly assigned classes.
11935 The typical use case for this option is to separate full tiles from
11937 The other options, described below, are applied after the separation
11940 As an example, consider the separation into full and partial tiles
11941 of a tiling of a triangular domain.
11942 Take, for example, the domain
11944 { A[i,j] : 0 <= i,j and i + j <= 100 }
11946 and a tiling into tiles of 10 by 10. The input to the AST generator
11947 is then the schedule
11949 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
11952 Without any options, the following AST is generated
11954 for (int c0 = 0; c0 <= 10; c0 += 1)
11955 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
11956 for (int c2 = 10 * c0;
11957 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
11959 for (int c3 = 10 * c1;
11960 c3 <= min(10 * c1 + 9, -c2 + 100);
11964 Separation into full and partial tiles can be obtained by assigning
11965 a class, say C<0>, to the full tiles. The full tiles are represented by those
11966 values of the first and second schedule dimensions for which there are
11967 values of the third and fourth dimensions to cover an entire tile.
11968 That is, we need to specify the following option
11970 { [a,b,c,d] -> separation_class[[0]->[0]] :
11971 exists b': 0 <= 10a,10b' and
11972 10a+9+10b'+9 <= 100;
11973 [a,b,c,d] -> separation_class[[1]->[0]] :
11974 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
11976 which simplifies to
11978 { [a, b, c, d] -> separation_class[[1] -> [0]] :
11979 a >= 0 and b >= 0 and b <= 8 - a;
11980 [a, b, c, d] -> separation_class[[0] -> [0]] :
11981 a >= 0 and a <= 8 }
11983 With this option, the generated AST is as follows
11986 for (int c0 = 0; c0 <= 8; c0 += 1) {
11987 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
11988 for (int c2 = 10 * c0;
11989 c2 <= 10 * c0 + 9; c2 += 1)
11990 for (int c3 = 10 * c1;
11991 c3 <= 10 * c1 + 9; c3 += 1)
11993 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
11994 for (int c2 = 10 * c0;
11995 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
11997 for (int c3 = 10 * c1;
11998 c3 <= min(-c2 + 100, 10 * c1 + 9);
12002 for (int c0 = 9; c0 <= 10; c0 += 1)
12003 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12004 for (int c2 = 10 * c0;
12005 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12007 for (int c3 = 10 * c1;
12008 c3 <= min(10 * c1 + 9, -c2 + 100);
12015 This is a single-dimensional space representing the schedule dimension(s)
12016 to which ``separation'' should be applied. Separation tries to split
12017 a loop into several pieces if this can avoid the generation of guards
12019 See also the C<atomic> option.
12023 This is a single-dimensional space representing the schedule dimension(s)
12024 for which the domains should be considered ``atomic''. That is, the
12025 AST generator will make sure that any given domain space will only appear
12026 in a single loop at the specified level.
12028 Consider the following schedule
12030 { a[i] -> [i] : 0 <= i < 10;
12031 b[i] -> [i+1] : 0 <= i < 10 }
12033 If the following option is specified
12035 { [i] -> separate[x] }
12037 then the following AST will be generated
12041 for (int c0 = 1; c0 <= 9; c0 += 1) {
12048 If, on the other hand, the following option is specified
12050 { [i] -> atomic[x] }
12052 then the following AST will be generated
12054 for (int c0 = 0; c0 <= 10; c0 += 1) {
12061 If neither C<atomic> nor C<separate> is specified, then the AST generator
12062 may produce either of these two results or some intermediate form.
12066 This is a single-dimensional space representing the schedule dimension(s)
12067 that should be I<completely> unrolled.
12068 To obtain a partial unrolling, the user should apply an additional
12069 strip-mining to the schedule and fully unroll the inner loop.
12073 =head3 Fine-grained Control over AST Generation
12075 Besides specifying the constraints on the parameters,
12076 an C<isl_ast_build> object can be used to control
12077 various aspects of the AST generation process.
12078 In case of AST construction using
12079 C<isl_ast_build_node_from_schedule_map>,
12080 the most prominent way of control is through ``options'',
12081 as explained above.
12083 Additional control is available through the following functions.
12085 #include <isl/ast_build.h>
12086 __isl_give isl_ast_build *
12087 isl_ast_build_set_iterators(
12088 __isl_take isl_ast_build *build,
12089 __isl_take isl_id_list *iterators);
12091 The function C<isl_ast_build_set_iterators> allows the user to
12092 specify a list of iterator C<isl_id>s to be used as iterators.
12093 If the input schedule is injective, then
12094 the number of elements in this list should be as large as the dimension
12095 of the schedule space, but no direct correspondence should be assumed
12096 between dimensions and elements.
12097 If the input schedule is not injective, then an additional number
12098 of C<isl_id>s equal to the largest dimension of the input domains
12100 If the number of provided C<isl_id>s is insufficient, then additional
12101 names are automatically generated.
12103 #include <isl/ast_build.h>
12104 __isl_give isl_ast_build *
12105 isl_ast_build_set_create_leaf(
12106 __isl_take isl_ast_build *build,
12107 __isl_give isl_ast_node *(*fn)(
12108 __isl_take isl_ast_build *build,
12109 void *user), void *user);
12112 C<isl_ast_build_set_create_leaf> function allows for the
12113 specification of a callback that should be called whenever the AST
12114 generator arrives at an element of the schedule domain.
12115 The callback should return an AST node that should be inserted
12116 at the corresponding position of the AST. The default action (when
12117 the callback is not set) is to continue generating parts of the AST to scan
12118 all the domain elements associated to the schedule domain element
12119 and to insert user nodes, ``calling'' the domain element, for each of them.
12120 The C<build> argument contains the current state of the C<isl_ast_build>.
12121 To ease nested AST generation (see L</"Nested AST Generation">),
12122 all control information that is
12123 specific to the current AST generation such as the options and
12124 the callbacks has been removed from this C<isl_ast_build>.
12125 The callback would typically return the result of a nested
12126 AST generation or a
12127 user defined node created using the following function.
12129 #include <isl/ast.h>
12130 __isl_give isl_ast_node *isl_ast_node_alloc_user(
12131 __isl_take isl_ast_expr *expr);
12133 #include <isl/ast_build.h>
12134 __isl_give isl_ast_build *
12135 isl_ast_build_set_at_each_domain(
12136 __isl_take isl_ast_build *build,
12137 __isl_give isl_ast_node *(*fn)(
12138 __isl_take isl_ast_node *node,
12139 __isl_keep isl_ast_build *build,
12140 void *user), void *user);
12141 __isl_give isl_ast_build *
12142 isl_ast_build_set_before_each_for(
12143 __isl_take isl_ast_build *build,
12144 __isl_give isl_id *(*fn)(
12145 __isl_keep isl_ast_build *build,
12146 void *user), void *user);
12147 __isl_give isl_ast_build *
12148 isl_ast_build_set_after_each_for(
12149 __isl_take isl_ast_build *build,
12150 __isl_give isl_ast_node *(*fn)(
12151 __isl_take isl_ast_node *node,
12152 __isl_keep isl_ast_build *build,
12153 void *user), void *user);
12154 __isl_give isl_ast_build *
12155 isl_ast_build_set_before_each_mark(
12156 __isl_take isl_ast_build *build,
12157 isl_stat (*fn)(__isl_keep isl_id *mark,
12158 __isl_keep isl_ast_build *build,
12159 void *user), void *user);
12160 __isl_give isl_ast_build *
12161 isl_ast_build_set_after_each_mark(
12162 __isl_take isl_ast_build *build,
12163 __isl_give isl_ast_node *(*fn)(
12164 __isl_take isl_ast_node *node,
12165 __isl_keep isl_ast_build *build,
12166 void *user), void *user);
12168 The callback set by C<isl_ast_build_set_at_each_domain> will
12169 be called for each domain AST node.
12170 The callbacks set by C<isl_ast_build_set_before_each_for>
12171 and C<isl_ast_build_set_after_each_for> will be called
12172 for each for AST node. The first will be called in depth-first
12173 pre-order, while the second will be called in depth-first post-order.
12174 Since C<isl_ast_build_set_before_each_for> is called before the for
12175 node is actually constructed, it is only passed an C<isl_ast_build>.
12176 The returned C<isl_id> will be added as an annotation (using
12177 C<isl_ast_node_set_annotation>) to the constructed for node.
12178 In particular, if the user has also specified an C<after_each_for>
12179 callback, then the annotation can be retrieved from the node passed to
12180 that callback using C<isl_ast_node_get_annotation>.
12181 The callbacks set by C<isl_ast_build_set_before_each_mark>
12182 and C<isl_ast_build_set_after_each_mark> will be called for each
12183 mark AST node that is created, i.e., for each mark schedule node
12184 in the input schedule tree. The first will be called in depth-first
12185 pre-order, while the second will be called in depth-first post-order.
12186 Since the callback set by C<isl_ast_build_set_before_each_mark>
12187 is called before the mark AST node is actually constructed, it is passed
12188 the identifier of the mark node.
12189 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
12190 The given C<isl_ast_build> can be used to create new
12191 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
12192 or C<isl_ast_build_call_from_pw_multi_aff>.
12194 =head3 Nested AST Generation
12196 C<isl> allows the user to create an AST within the context
12197 of another AST. These nested ASTs are created using the
12198 same C<isl_ast_build_node_from_schedule_map> function that is used to create
12199 the outer AST. The C<build> argument should be an C<isl_ast_build>
12200 passed to a callback set by
12201 C<isl_ast_build_set_create_leaf>.
12202 The space of the range of the C<schedule> argument should refer
12203 to this build. In particular, the space should be a wrapped
12204 relation and the domain of this wrapped relation should be the
12205 same as that of the range of the schedule returned by
12206 C<isl_ast_build_get_schedule> below.
12207 In practice, the new schedule is typically
12208 created by calling C<isl_union_map_range_product> on the old schedule
12209 and some extra piece of the schedule.
12210 The space of the schedule domain is also available from
12211 the C<isl_ast_build>.
12213 #include <isl/ast_build.h>
12214 __isl_give isl_union_map *isl_ast_build_get_schedule(
12215 __isl_keep isl_ast_build *build);
12216 __isl_give isl_space *isl_ast_build_get_schedule_space(
12217 __isl_keep isl_ast_build *build);
12218 __isl_give isl_ast_build *isl_ast_build_restrict(
12219 __isl_take isl_ast_build *build,
12220 __isl_take isl_set *set);
12222 The C<isl_ast_build_get_schedule> function returns a (partial)
12223 schedule for the domains elements for which part of the AST still needs to
12224 be generated in the current build.
12225 In particular, the domain elements are mapped to those iterations of the loops
12226 enclosing the current point of the AST generation inside which
12227 the domain elements are executed.
12228 No direct correspondence between
12229 the input schedule and this schedule should be assumed.
12230 The space obtained from C<isl_ast_build_get_schedule_space> can be used
12231 to create a set for C<isl_ast_build_restrict> to intersect
12232 with the current build. In particular, the set passed to
12233 C<isl_ast_build_restrict> can have additional parameters.
12234 The ids of the set dimensions in the space returned by
12235 C<isl_ast_build_get_schedule_space> correspond to the
12236 iterators of the already generated loops.
12237 The user should not rely on the ids of the output dimensions
12238 of the relations in the union relation returned by
12239 C<isl_ast_build_get_schedule> having any particular value.
12241 =head1 Applications
12243 Although C<isl> is mainly meant to be used as a library,
12244 it also contains some basic applications that use some
12245 of the functionality of C<isl>.
12246 For applications that take one or more polytopes or polyhedra
12247 as input, this input may be specified in either the L<isl format>
12248 or the L<PolyLib format>.
12250 =head2 C<isl_polyhedron_sample>
12252 C<isl_polyhedron_sample> takes a polyhedron as input and prints
12253 an integer element of the polyhedron, if there is any.
12254 The first column in the output is the denominator and is always
12255 equal to 1. If the polyhedron contains no integer points,
12256 then a vector of length zero is printed.
12260 C<isl_pip> takes the same input as the C<example> program
12261 from the C<piplib> distribution, i.e., a set of constraints
12262 on the parameters, a line containing only -1 and finally a set
12263 of constraints on a parametric polyhedron.
12264 The coefficients of the parameters appear in the last columns
12265 (but before the final constant column).
12266 The output is the lexicographic minimum of the parametric polyhedron.
12267 As C<isl> currently does not have its own output format, the output
12268 is just a dump of the internal state.
12270 =head2 C<isl_polyhedron_minimize>
12272 C<isl_polyhedron_minimize> computes the minimum of some linear
12273 or affine objective function over the integer points in a polyhedron.
12274 If an affine objective function
12275 is given, then the constant should appear in the last column.
12277 =head2 C<isl_polytope_scan>
12279 Given a polytope, C<isl_polytope_scan> prints
12280 all integer points in the polytope.
12284 Given an C<isl_union_access_info> object as input,
12285 C<isl_flow> prints out the corresponding dependences,
12286 as computed by C<isl_union_access_info_compute_flow>.
12288 =head2 C<isl_codegen>
12290 Given either a schedule tree or a sequence consisting of
12291 a schedule map, a context set and an options relation,
12292 C<isl_codegen> prints out an AST that scans the domain elements
12293 of the schedule in the order of their image(s) taking into account
12294 the constraints in the context set.
12296 =head2 C<isl_schedule>
12298 Given an C<isl_schedule_constraints> object as input,
12299 C<isl_schedule> prints out a schedule that satisfies the given