3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
273 =head3 Changes since isl-0.19
277 =item * Zero-dimensional objects of type C<isl_multi_pw_aff> or
278 C<isl_multi_union_pw_aff> can now keep track of an explicit domain.
279 This explicit domain, if present, is taken into account
280 by various operations that take such objects as input.
286 C<isl> is released under the MIT license.
290 Permission is hereby granted, free of charge, to any person obtaining a copy of
291 this software and associated documentation files (the "Software"), to deal in
292 the Software without restriction, including without limitation the rights to
293 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
294 of the Software, and to permit persons to whom the Software is furnished to do
295 so, subject to the following conditions:
297 The above copyright notice and this permission notice shall be included in all
298 copies or substantial portions of the Software.
300 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
301 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
302 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
303 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
304 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
305 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
310 Note that by default C<isl> requires C<GMP>, which is released
311 under the GNU Lesser General Public License (LGPL). This means
312 that code linked against C<isl> is also linked against LGPL code.
314 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
315 will link against C<imath>, a library for exact integer arithmetic released
316 under the MIT license.
320 The source of C<isl> can be obtained either as a tarball
321 or from the git repository. Both are available from
322 L<http://isl.gforge.inria.fr/>.
323 The installation process depends on how you obtained
326 =head2 Installation from the git repository
330 =item 1 Clone or update the repository
332 The first time the source is obtained, you need to clone
335 git clone git://repo.or.cz/isl.git
337 To obtain updates, you need to pull in the latest changes
341 =item 2 Optionally get C<imath> submodule
343 To build C<isl> with C<imath>, you need to obtain the C<imath>
344 submodule by running in the git source tree of C<isl>
349 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
351 =item 2 Generate C<configure>
357 After performing the above steps, continue
358 with the L<Common installation instructions>.
360 =head2 Common installation instructions
364 =item 1 Obtain C<GMP>
366 By default, building C<isl> requires C<GMP>, including its headers files.
367 Your distribution may not provide these header files by default
368 and you may need to install a package called C<gmp-devel> or something
369 similar. Alternatively, C<GMP> can be built from
370 source, available from L<http://gmplib.org/>.
371 C<GMP> is not needed if you build C<isl> with C<imath>.
375 C<isl> uses the standard C<autoconf> C<configure> script.
380 optionally followed by some configure options.
381 A complete list of options can be obtained by running
385 Below we discuss some of the more common options.
391 Installation prefix for C<isl>
393 =item C<--with-int=[gmp|imath|imath-32]>
395 Select the integer library to be used by C<isl>, the default is C<gmp>.
396 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
397 for values out of the 32 bit range. In most applications, C<isl> will run
398 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
401 =item C<--with-gmp-prefix>
403 Installation prefix for C<GMP> (architecture-independent files).
405 =item C<--with-gmp-exec-prefix>
407 Installation prefix for C<GMP> (architecture-dependent files).
415 =item 4 Install (optional)
421 =head1 Integer Set Library
423 =head2 Memory Management
425 Since a high-level operation on isl objects usually involves
426 several substeps and since the user is usually not interested in
427 the intermediate results, most functions that return a new object
428 will also release all the objects passed as arguments.
429 If the user still wants to use one or more of these arguments
430 after the function call, she should pass along a copy of the
431 object rather than the object itself.
432 The user is then responsible for making sure that the original
433 object gets used somewhere else or is explicitly freed.
435 The arguments and return values of all documented functions are
436 annotated to make clear which arguments are released and which
437 arguments are preserved. In particular, the following annotations
444 C<__isl_give> means that a new object is returned.
445 The user should make sure that the returned pointer is
446 used exactly once as a value for an C<__isl_take> argument.
447 In between, it can be used as a value for as many
448 C<__isl_keep> arguments as the user likes.
449 There is one exception, and that is the case where the
450 pointer returned is C<NULL>. Is this case, the user
451 is free to use it as an C<__isl_take> argument or not.
452 When applied to a C<char *>, the returned pointer needs to be
457 C<__isl_null> means that a C<NULL> value is returned.
461 C<__isl_take> means that the object the argument points to
462 is taken over by the function and may no longer be used
463 by the user as an argument to any other function.
464 The pointer value must be one returned by a function
465 returning an C<__isl_give> pointer.
466 If the user passes in a C<NULL> value, then this will
467 be treated as an error in the sense that the function will
468 not perform its usual operation. However, it will still
469 make sure that all the other C<__isl_take> arguments
474 C<__isl_keep> means that the function will only use the object
475 temporarily. After the function has finished, the user
476 can still use it as an argument to other functions.
477 A C<NULL> value will be treated in the same way as
478 a C<NULL> value for an C<__isl_take> argument.
479 This annotation may also be used on return values of
480 type C<const char *>, in which case the returned pointer should
481 not be freed by the user and is only valid until the object
482 from which it was derived is updated or freed.
486 =head2 Initialization
488 All manipulations of integer sets and relations occur within
489 the context of an C<isl_ctx>.
490 A given C<isl_ctx> can only be used within a single thread.
491 All arguments of a function are required to have been allocated
492 within the same context.
493 There are currently no functions available for moving an object
494 from one C<isl_ctx> to another C<isl_ctx>. This means that
495 there is currently no way of safely moving an object from one
496 thread to another, unless the whole C<isl_ctx> is moved.
498 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
499 freed using C<isl_ctx_free>.
500 All objects allocated within an C<isl_ctx> should be freed
501 before the C<isl_ctx> itself is freed.
503 isl_ctx *isl_ctx_alloc();
504 void isl_ctx_free(isl_ctx *ctx);
506 The user can impose a bound on the number of low-level I<operations>
507 that can be performed by an C<isl_ctx>. This bound can be set and
508 retrieved using the following functions. A bound of zero means that
509 no bound is imposed. The number of operations performed can be
510 reset using C<isl_ctx_reset_operations>. Note that the number
511 of low-level operations needed to perform a high-level computation
512 may differ significantly across different versions
513 of C<isl>, but it should be the same across different platforms
514 for the same version of C<isl>.
516 Warning: This feature is experimental. C<isl> has good support to abort and
517 bail out during the computation, but this feature may exercise error code paths
518 that are normally not used that much. Consequently, it is not unlikely that
519 hidden bugs will be exposed.
521 void isl_ctx_set_max_operations(isl_ctx *ctx,
522 unsigned long max_operations);
523 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
524 void isl_ctx_reset_operations(isl_ctx *ctx);
526 In order to be able to create an object in the same context
527 as another object, most object types (described later in
528 this document) provide a function to obtain the context
529 in which the object was created.
532 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
533 isl_ctx *isl_multi_val_get_ctx(
534 __isl_keep isl_multi_val *mv);
537 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
539 #include <isl/local_space.h>
540 isl_ctx *isl_local_space_get_ctx(
541 __isl_keep isl_local_space *ls);
544 isl_ctx *isl_set_list_get_ctx(
545 __isl_keep isl_set_list *list);
548 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
549 isl_ctx *isl_multi_aff_get_ctx(
550 __isl_keep isl_multi_aff *maff);
551 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
552 isl_ctx *isl_pw_multi_aff_get_ctx(
553 __isl_keep isl_pw_multi_aff *pma);
554 isl_ctx *isl_multi_pw_aff_get_ctx(
555 __isl_keep isl_multi_pw_aff *mpa);
556 isl_ctx *isl_union_pw_aff_get_ctx(
557 __isl_keep isl_union_pw_aff *upa);
558 isl_ctx *isl_union_pw_multi_aff_get_ctx(
559 __isl_keep isl_union_pw_multi_aff *upma);
560 isl_ctx *isl_multi_union_pw_aff_get_ctx(
561 __isl_keep isl_multi_union_pw_aff *mupa);
563 #include <isl/id_to_ast_expr.h>
564 isl_ctx *isl_id_to_ast_expr_get_ctx(
565 __isl_keep isl_id_to_ast_expr *id2expr);
567 #include <isl/point.h>
568 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
571 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
574 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
576 #include <isl/vertices.h>
577 isl_ctx *isl_vertices_get_ctx(
578 __isl_keep isl_vertices *vertices);
579 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
580 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
582 #include <isl/flow.h>
583 isl_ctx *isl_restriction_get_ctx(
584 __isl_keep isl_restriction *restr);
585 isl_ctx *isl_union_access_info_get_ctx(
586 __isl_keep isl_union_access_info *access);
587 isl_ctx *isl_union_flow_get_ctx(
588 __isl_keep isl_union_flow *flow);
590 #include <isl/schedule.h>
591 isl_ctx *isl_schedule_get_ctx(
592 __isl_keep isl_schedule *sched);
593 isl_ctx *isl_schedule_constraints_get_ctx(
594 __isl_keep isl_schedule_constraints *sc);
596 #include <isl/schedule_node.h>
597 isl_ctx *isl_schedule_node_get_ctx(
598 __isl_keep isl_schedule_node *node);
600 #include <isl/ast_build.h>
601 isl_ctx *isl_ast_build_get_ctx(
602 __isl_keep isl_ast_build *build);
605 isl_ctx *isl_ast_expr_get_ctx(
606 __isl_keep isl_ast_expr *expr);
607 isl_ctx *isl_ast_node_get_ctx(
608 __isl_keep isl_ast_node *node);
610 #include <isl/stride_info.h>
611 isl_ctx *isl_stride_info_get_ctx(
612 __isl_keep isl_stride_info *si);
614 #include <isl/fixed_box.h>
615 isl_ctx *isl_fixed_box_get_ctx(
616 __isl_keep isl_fixed_box *box);
620 C<isl> uses two special return types for functions that either return
621 a boolean or that in principle do not return anything.
622 In particular, the C<isl_bool> type has three possible values:
623 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
624 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
625 C<isl_bool_error> (a negative integer value), indicating that something
626 went wrong. The following function can be used to negate an C<isl_bool>,
627 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
630 isl_bool isl_bool_not(isl_bool b);
632 The C<isl_stat> type has two possible values:
633 C<isl_stat_ok> (the integer value zero), indicating a successful
635 C<isl_stat_error> (a negative integer value), indicating that something
637 See L</"Error Handling"> for more information on
638 C<isl_bool_error> and C<isl_stat_error>.
642 An C<isl_val> represents an integer value, a rational value
643 or one of three special values, infinity, negative infinity and NaN.
644 Some predefined values can be created using the following functions.
647 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
648 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
649 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
650 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
651 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
652 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
654 Specific integer values can be created using the following functions.
657 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
659 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
661 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
662 size_t n, size_t size, const void *chunks);
664 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
665 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
666 The least significant digit is assumed to be stored first.
668 Value objects can be copied and freed using the following functions.
671 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
672 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
674 They can be inspected using the following functions.
677 long isl_val_get_num_si(__isl_keep isl_val *v);
678 long isl_val_get_den_si(__isl_keep isl_val *v);
679 __isl_give isl_val *isl_val_get_den_val(
680 __isl_keep isl_val *v);
681 double isl_val_get_d(__isl_keep isl_val *v);
682 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
684 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
685 size_t size, void *chunks);
687 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
688 of C<size> bytes needed to store the absolute value of the
690 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
691 which is assumed to have been preallocated by the caller.
692 The least significant digit is stored first.
693 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
694 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
695 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
697 An C<isl_val> can be modified using the following function.
700 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
703 The following unary properties are defined on C<isl_val>s.
706 int isl_val_sgn(__isl_keep isl_val *v);
707 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
708 isl_bool isl_val_is_one(__isl_keep isl_val *v);
709 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
710 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
711 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
712 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
713 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
714 isl_bool isl_val_is_int(__isl_keep isl_val *v);
715 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
716 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
717 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
718 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
720 Note that the sign of NaN is undefined.
722 The following binary properties are defined on pairs of C<isl_val>s.
725 isl_bool isl_val_lt(__isl_keep isl_val *v1,
726 __isl_keep isl_val *v2);
727 isl_bool isl_val_le(__isl_keep isl_val *v1,
728 __isl_keep isl_val *v2);
729 isl_bool isl_val_gt(__isl_keep isl_val *v1,
730 __isl_keep isl_val *v2);
731 isl_bool isl_val_ge(__isl_keep isl_val *v1,
732 __isl_keep isl_val *v2);
733 isl_bool isl_val_eq(__isl_keep isl_val *v1,
734 __isl_keep isl_val *v2);
735 isl_bool isl_val_ne(__isl_keep isl_val *v1,
736 __isl_keep isl_val *v2);
737 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
738 __isl_keep isl_val *v2);
740 Comparisons to NaN always return false.
741 That is, a NaN is not considered to hold any relative position
742 with respect to any value. In particular, a NaN
743 is neither considered to be equal to nor to be different from
744 any value (including another NaN).
745 The function C<isl_val_abs_eq> checks whether its two arguments
746 are equal in absolute value.
748 For integer C<isl_val>s we additionally have the following binary property.
751 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
752 __isl_keep isl_val *v2);
754 An C<isl_val> can also be compared to an integer using the following
755 functions. The result of C<isl_val_cmp_si> undefined for NaN.
758 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
759 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
761 The following unary operations are available on C<isl_val>s.
764 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
765 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
766 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
767 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
768 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
769 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
770 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
772 The following binary operations are available on C<isl_val>s.
775 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
776 __isl_take isl_val *v2);
777 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
778 __isl_take isl_val *v2);
779 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
780 __isl_take isl_val *v2);
781 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
783 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
784 __isl_take isl_val *v2);
785 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
787 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
788 __isl_take isl_val *v2);
789 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
791 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
792 __isl_take isl_val *v2);
793 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
796 On integer values, we additionally have the following operations.
799 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
800 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
801 __isl_take isl_val *v2);
802 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
803 __isl_take isl_val *v2);
804 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
805 __isl_take isl_val *v2, __isl_give isl_val **x,
806 __isl_give isl_val **y);
808 The function C<isl_val_gcdext> returns the greatest common divisor g
809 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
810 that C<*x> * C<v1> + C<*y> * C<v2> = g.
812 =head3 GMP specific functions
814 These functions are only available if C<isl> has been compiled with C<GMP>
817 Specific integer and rational values can be created from C<GMP> values using
818 the following functions.
820 #include <isl/val_gmp.h>
821 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
823 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
824 const mpz_t n, const mpz_t d);
826 The numerator and denominator of a rational value can be extracted as
827 C<GMP> values using the following functions.
829 #include <isl/val_gmp.h>
830 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
831 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
833 =head2 Sets and Relations
835 C<isl> uses six types of objects for representing sets and relations,
836 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
837 C<isl_union_set> and C<isl_union_map>.
838 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
839 can be described as a conjunction of affine constraints, while
840 C<isl_set> and C<isl_map> represent unions of
841 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
842 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
843 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
844 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
845 where spaces are considered different if they have a different number
846 of dimensions and/or different names (see L<"Spaces">).
847 The difference between sets and relations (maps) is that sets have
848 one set of variables, while relations have two sets of variables,
849 input variables and output variables.
851 =head2 Error Handling
853 C<isl> supports different ways to react in case a runtime error is triggered.
854 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
855 with two maps that have incompatible spaces. There are three possible ways
856 to react on error: to warn, to continue or to abort.
858 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
859 the last error in the corresponding C<isl_ctx> and the function in which the
860 error was triggered returns a value indicating that some error has
861 occurred. In case of functions returning a pointer, this value is
862 C<NULL>. In case of functions returning an C<isl_bool> or an
863 C<isl_stat>, this value is C<isl_bool_error> or C<isl_stat_error>.
864 An error does not corrupt internal state,
865 such that isl can continue to be used. C<isl> also provides functions to
866 read the last error, including the specific error message,
867 the isl source file where the error occurred and the line number,
868 and to reset all information about the last error. The
869 last error is only stored for information purposes. Its presence does not
870 change the behavior of C<isl>. Hence, resetting an error is not required to
871 continue to use isl, but only to observe new errors.
874 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
875 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
876 const char *isl_ctx_last_error_file(isl_ctx *ctx);
877 int isl_ctx_last_error_line(isl_ctx *ctx);
878 void isl_ctx_reset_error(isl_ctx *ctx);
880 If no error has occurred since the last call to C<isl_ctx_reset_error>,
881 then the functions C<isl_ctx_last_error_msg> and
882 C<isl_ctx_last_error_file> return C<NULL>.
884 Another option is to continue on error. This is similar to warn on error mode,
885 except that C<isl> does not print any warning. This allows a program to
886 implement its own error reporting.
888 The last option is to directly abort the execution of the program from within
889 the isl library. This makes it obviously impossible to recover from an error,
890 but it allows to directly spot the error location. By aborting on error,
891 debuggers break at the location the error occurred and can provide a stack
892 trace. Other tools that automatically provide stack traces on abort or that do
893 not want to continue execution after an error was triggered may also prefer to
896 The on error behavior of isl can be specified by calling
897 C<isl_options_set_on_error> or by setting the command line option
898 C<--isl-on-error>. Valid arguments for the function call are
899 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
900 choices for the command line option are C<warn>, C<continue> and C<abort>.
901 It is also possible to query the current error mode.
903 #include <isl/options.h>
904 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
905 int isl_options_get_on_error(isl_ctx *ctx);
909 Identifiers are used to identify both individual dimensions
910 and tuples of dimensions. They consist of an optional name and an optional
911 user pointer. The name and the user pointer cannot both be C<NULL>, however.
912 Identifiers with the same name but different pointer values
913 are considered to be distinct.
914 Similarly, identifiers with different names but the same pointer value
915 are also considered to be distinct.
916 Equal identifiers are represented using the same object.
917 Pairs of identifiers can therefore be tested for equality using the
919 Identifiers can be constructed, copied, freed, inspected and printed
920 using the following functions.
923 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
924 __isl_keep const char *name, void *user);
925 __isl_give isl_id *isl_id_set_free_user(
926 __isl_take isl_id *id,
927 void (*free_user)(void *user));
928 __isl_give isl_id *isl_id_copy(isl_id *id);
929 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
931 void *isl_id_get_user(__isl_keep isl_id *id);
932 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
934 __isl_give isl_printer *isl_printer_print_id(
935 __isl_take isl_printer *p, __isl_keep isl_id *id);
937 The callback set by C<isl_id_set_free_user> is called on the user
938 pointer when the last reference to the C<isl_id> is freed.
939 Note that C<isl_id_get_name> returns a pointer to some internal
940 data structure, so the result can only be used while the
941 corresponding C<isl_id> is alive.
945 Whenever a new set, relation or similar object is created from scratch,
946 the space in which it lives needs to be specified using an C<isl_space>.
947 Each space involves zero or more parameters and zero, one or two
948 tuples of set or input/output dimensions. The parameters and dimensions
949 are identified by an C<isl_dim_type> and a position.
950 The type C<isl_dim_param> refers to parameters,
951 the type C<isl_dim_set> refers to set dimensions (for spaces
952 with a single tuple of dimensions) and the types C<isl_dim_in>
953 and C<isl_dim_out> refer to input and output dimensions
954 (for spaces with two tuples of dimensions).
955 Local spaces (see L</"Local Spaces">) also contain dimensions
956 of type C<isl_dim_div>.
957 Note that parameters are only identified by their position within
958 a given object. Across different objects, parameters are (usually)
959 identified by their names or identifiers. Only unnamed parameters
960 are identified by their positions across objects. The use of unnamed
961 parameters is discouraged.
963 #include <isl/space.h>
964 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
965 unsigned nparam, unsigned n_in, unsigned n_out);
966 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
968 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
969 unsigned nparam, unsigned dim);
970 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
971 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
973 The space used for creating a parameter domain
974 needs to be created using C<isl_space_params_alloc>.
975 For other sets, the space
976 needs to be created using C<isl_space_set_alloc>, while
977 for a relation, the space
978 needs to be created using C<isl_space_alloc>.
980 To check whether a given space is that of a set or a map
981 or whether it is a parameter space, use these functions:
983 #include <isl/space.h>
984 isl_bool isl_space_is_params(__isl_keep isl_space *space);
985 isl_bool isl_space_is_set(__isl_keep isl_space *space);
986 isl_bool isl_space_is_map(__isl_keep isl_space *space);
988 Spaces can be compared using the following functions:
990 #include <isl/space.h>
991 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
992 __isl_keep isl_space *space2);
993 isl_bool isl_space_has_equal_params(
994 __isl_keep isl_space *space1,
995 __isl_keep isl_space *space2);
996 isl_bool isl_space_has_equal_tuples(
997 __isl_keep isl_space *space1,
998 __isl_keep isl_space *space2);
999 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
1000 __isl_keep isl_space *space2);
1001 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
1002 __isl_keep isl_space *space2);
1003 isl_bool isl_space_tuple_is_equal(
1004 __isl_keep isl_space *space1,
1005 enum isl_dim_type type1,
1006 __isl_keep isl_space *space2,
1007 enum isl_dim_type type2);
1009 C<isl_space_is_domain> checks whether the first argument is equal
1010 to the domain of the second argument. This requires in particular that
1011 the first argument is a set space and that the second argument
1012 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1013 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1014 spaces are the same. That is, it checks if they have the same
1015 identifier (if any), the same dimension and the same internal structure
1018 C<isl_space_has_equal_params> checks whether two spaces
1019 have the same parameters in the same order.
1020 C<isl_space_has_equal_tuples> check whether two spaces have
1021 the same tuples. In contrast to C<isl_space_is_equal> below,
1022 it does not check the
1023 parameters. This is useful because many C<isl> functions align the
1024 parameters before they perform their operations, such that equivalence
1026 C<isl_space_is_equal> checks whether two spaces are identical,
1027 meaning that they have the same parameters and the same tuples.
1028 That is, it checks whether both C<isl_space_has_equal_params> and
1029 C<isl_space_has_equal_tuples> hold.
1031 It is often useful to create objects that live in the
1032 same space as some other object. This can be accomplished
1033 by creating the new objects
1034 (see L</"Creating New Sets and Relations"> or
1035 L</"Functions">) based on the space
1036 of the original object.
1038 #include <isl/set.h>
1039 __isl_give isl_space *isl_basic_set_get_space(
1040 __isl_keep isl_basic_set *bset);
1041 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1043 #include <isl/union_set.h>
1044 __isl_give isl_space *isl_union_set_get_space(
1045 __isl_keep isl_union_set *uset);
1047 #include <isl/map.h>
1048 __isl_give isl_space *isl_basic_map_get_space(
1049 __isl_keep isl_basic_map *bmap);
1050 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1052 #include <isl/union_map.h>
1053 __isl_give isl_space *isl_union_map_get_space(
1054 __isl_keep isl_union_map *umap);
1056 #include <isl/constraint.h>
1057 __isl_give isl_space *isl_constraint_get_space(
1058 __isl_keep isl_constraint *constraint);
1060 #include <isl/polynomial.h>
1061 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1062 __isl_keep isl_qpolynomial *qp);
1063 __isl_give isl_space *isl_qpolynomial_get_space(
1064 __isl_keep isl_qpolynomial *qp);
1065 __isl_give isl_space *
1066 isl_qpolynomial_fold_get_domain_space(
1067 __isl_keep isl_qpolynomial_fold *fold);
1068 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1069 __isl_keep isl_qpolynomial_fold *fold);
1070 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1071 __isl_keep isl_pw_qpolynomial *pwqp);
1072 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1073 __isl_keep isl_pw_qpolynomial *pwqp);
1074 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1075 __isl_keep isl_pw_qpolynomial_fold *pwf);
1076 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1077 __isl_keep isl_pw_qpolynomial_fold *pwf);
1078 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1079 __isl_keep isl_union_pw_qpolynomial *upwqp);
1080 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1081 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1083 #include <isl/val.h>
1084 __isl_give isl_space *isl_multi_val_get_space(
1085 __isl_keep isl_multi_val *mv);
1087 #include <isl/aff.h>
1088 __isl_give isl_space *isl_aff_get_domain_space(
1089 __isl_keep isl_aff *aff);
1090 __isl_give isl_space *isl_aff_get_space(
1091 __isl_keep isl_aff *aff);
1092 __isl_give isl_space *isl_pw_aff_get_domain_space(
1093 __isl_keep isl_pw_aff *pwaff);
1094 __isl_give isl_space *isl_pw_aff_get_space(
1095 __isl_keep isl_pw_aff *pwaff);
1096 __isl_give isl_space *isl_multi_aff_get_domain_space(
1097 __isl_keep isl_multi_aff *maff);
1098 __isl_give isl_space *isl_multi_aff_get_space(
1099 __isl_keep isl_multi_aff *maff);
1100 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1101 __isl_keep isl_pw_multi_aff *pma);
1102 __isl_give isl_space *isl_pw_multi_aff_get_space(
1103 __isl_keep isl_pw_multi_aff *pma);
1104 __isl_give isl_space *isl_union_pw_aff_get_space(
1105 __isl_keep isl_union_pw_aff *upa);
1106 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1107 __isl_keep isl_union_pw_multi_aff *upma);
1108 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1109 __isl_keep isl_multi_pw_aff *mpa);
1110 __isl_give isl_space *isl_multi_pw_aff_get_space(
1111 __isl_keep isl_multi_pw_aff *mpa);
1112 __isl_give isl_space *
1113 isl_multi_union_pw_aff_get_domain_space(
1114 __isl_keep isl_multi_union_pw_aff *mupa);
1115 __isl_give isl_space *
1116 isl_multi_union_pw_aff_get_space(
1117 __isl_keep isl_multi_union_pw_aff *mupa);
1119 #include <isl/point.h>
1120 __isl_give isl_space *isl_point_get_space(
1121 __isl_keep isl_point *pnt);
1123 #include <isl/fixed_box.h>
1124 __isl_give isl_space *isl_fixed_box_get_space(
1125 __isl_keep isl_fixed_box *box);
1127 The number of dimensions of a given type of space
1128 may be read off from a space or an object that lives
1129 in a space using the following functions.
1130 In case of C<isl_space_dim>, type may be
1131 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1132 C<isl_dim_out> (only for relations), C<isl_dim_set>
1133 (only for sets) or C<isl_dim_all>.
1135 #include <isl/space.h>
1136 unsigned isl_space_dim(__isl_keep isl_space *space,
1137 enum isl_dim_type type);
1139 #include <isl/local_space.h>
1140 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1141 enum isl_dim_type type);
1143 #include <isl/set.h>
1144 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1145 enum isl_dim_type type);
1146 unsigned isl_set_dim(__isl_keep isl_set *set,
1147 enum isl_dim_type type);
1149 #include <isl/union_set.h>
1150 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1151 enum isl_dim_type type);
1153 #include <isl/map.h>
1154 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1155 enum isl_dim_type type);
1156 unsigned isl_map_dim(__isl_keep isl_map *map,
1157 enum isl_dim_type type);
1159 #include <isl/union_map.h>
1160 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1161 enum isl_dim_type type);
1163 #include <isl/val.h>
1164 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1165 enum isl_dim_type type);
1167 #include <isl/aff.h>
1168 int isl_aff_dim(__isl_keep isl_aff *aff,
1169 enum isl_dim_type type);
1170 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1171 enum isl_dim_type type);
1172 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1173 enum isl_dim_type type);
1174 unsigned isl_pw_multi_aff_dim(
1175 __isl_keep isl_pw_multi_aff *pma,
1176 enum isl_dim_type type);
1177 unsigned isl_multi_pw_aff_dim(
1178 __isl_keep isl_multi_pw_aff *mpa,
1179 enum isl_dim_type type);
1180 unsigned isl_union_pw_aff_dim(
1181 __isl_keep isl_union_pw_aff *upa,
1182 enum isl_dim_type type);
1183 unsigned isl_union_pw_multi_aff_dim(
1184 __isl_keep isl_union_pw_multi_aff *upma,
1185 enum isl_dim_type type);
1186 unsigned isl_multi_union_pw_aff_dim(
1187 __isl_keep isl_multi_union_pw_aff *mupa,
1188 enum isl_dim_type type);
1190 #include <isl/polynomial.h>
1191 unsigned isl_union_pw_qpolynomial_dim(
1192 __isl_keep isl_union_pw_qpolynomial *upwqp,
1193 enum isl_dim_type type);
1194 unsigned isl_union_pw_qpolynomial_fold_dim(
1195 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1196 enum isl_dim_type type);
1198 Note that an C<isl_union_set>, an C<isl_union_map>,
1199 an C<isl_union_pw_multi_aff>,
1200 an C<isl_union_pw_qpolynomial> and
1201 an C<isl_union_pw_qpolynomial_fold>
1202 only have parameters.
1204 Additional parameters can be added to a space using the following function.
1206 #include <isl/space.h>
1207 __isl_give isl_space *isl_space_add_param_id(
1208 __isl_take isl_space *space,
1209 __isl_take isl_id *id);
1211 If a parameter with the given identifier already appears in the space,
1212 then it is not added again.
1214 The identifiers or names of the individual dimensions of spaces
1215 may be set or read off using the following functions on spaces
1216 or objects that live in spaces.
1217 These functions are mostly useful to obtain the identifiers, positions
1218 or names of the parameters. Identifiers of individual dimensions are
1219 essentially only useful for printing. They are ignored by all other
1220 operations and may not be preserved across those operations.
1222 #include <isl/space.h>
1223 __isl_give isl_space *isl_space_set_dim_id(
1224 __isl_take isl_space *space,
1225 enum isl_dim_type type, unsigned pos,
1226 __isl_take isl_id *id);
1227 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1228 enum isl_dim_type type, unsigned pos);
1229 __isl_give isl_id *isl_space_get_dim_id(
1230 __isl_keep isl_space *space,
1231 enum isl_dim_type type, unsigned pos);
1232 __isl_give isl_space *isl_space_set_dim_name(
1233 __isl_take isl_space *space,
1234 enum isl_dim_type type, unsigned pos,
1235 __isl_keep const char *name);
1236 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1237 enum isl_dim_type type, unsigned pos);
1238 __isl_keep const char *isl_space_get_dim_name(
1239 __isl_keep isl_space *space,
1240 enum isl_dim_type type, unsigned pos);
1242 #include <isl/local_space.h>
1243 __isl_give isl_local_space *isl_local_space_set_dim_id(
1244 __isl_take isl_local_space *ls,
1245 enum isl_dim_type type, unsigned pos,
1246 __isl_take isl_id *id);
1247 isl_bool isl_local_space_has_dim_id(
1248 __isl_keep isl_local_space *ls,
1249 enum isl_dim_type type, unsigned pos);
1250 __isl_give isl_id *isl_local_space_get_dim_id(
1251 __isl_keep isl_local_space *ls,
1252 enum isl_dim_type type, unsigned pos);
1253 __isl_give isl_local_space *isl_local_space_set_dim_name(
1254 __isl_take isl_local_space *ls,
1255 enum isl_dim_type type, unsigned pos, const char *s);
1256 isl_bool isl_local_space_has_dim_name(
1257 __isl_keep isl_local_space *ls,
1258 enum isl_dim_type type, unsigned pos)
1259 const char *isl_local_space_get_dim_name(
1260 __isl_keep isl_local_space *ls,
1261 enum isl_dim_type type, unsigned pos);
1263 #include <isl/constraint.h>
1264 const char *isl_constraint_get_dim_name(
1265 __isl_keep isl_constraint *constraint,
1266 enum isl_dim_type type, unsigned pos);
1268 #include <isl/set.h>
1269 __isl_give isl_id *isl_basic_set_get_dim_id(
1270 __isl_keep isl_basic_set *bset,
1271 enum isl_dim_type type, unsigned pos);
1272 __isl_give isl_set *isl_set_set_dim_id(
1273 __isl_take isl_set *set, enum isl_dim_type type,
1274 unsigned pos, __isl_take isl_id *id);
1275 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1276 enum isl_dim_type type, unsigned pos);
1277 __isl_give isl_id *isl_set_get_dim_id(
1278 __isl_keep isl_set *set, enum isl_dim_type type,
1280 const char *isl_basic_set_get_dim_name(
1281 __isl_keep isl_basic_set *bset,
1282 enum isl_dim_type type, unsigned pos);
1283 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1284 enum isl_dim_type type, unsigned pos);
1285 const char *isl_set_get_dim_name(
1286 __isl_keep isl_set *set,
1287 enum isl_dim_type type, unsigned pos);
1289 #include <isl/map.h>
1290 __isl_give isl_map *isl_map_set_dim_id(
1291 __isl_take isl_map *map, enum isl_dim_type type,
1292 unsigned pos, __isl_take isl_id *id);
1293 isl_bool isl_basic_map_has_dim_id(
1294 __isl_keep isl_basic_map *bmap,
1295 enum isl_dim_type type, unsigned pos);
1296 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1297 enum isl_dim_type type, unsigned pos);
1298 __isl_give isl_id *isl_map_get_dim_id(
1299 __isl_keep isl_map *map, enum isl_dim_type type,
1301 __isl_give isl_id *isl_union_map_get_dim_id(
1302 __isl_keep isl_union_map *umap,
1303 enum isl_dim_type type, unsigned pos);
1304 const char *isl_basic_map_get_dim_name(
1305 __isl_keep isl_basic_map *bmap,
1306 enum isl_dim_type type, unsigned pos);
1307 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1308 enum isl_dim_type type, unsigned pos);
1309 const char *isl_map_get_dim_name(
1310 __isl_keep isl_map *map,
1311 enum isl_dim_type type, unsigned pos);
1313 #include <isl/val.h>
1314 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1315 __isl_take isl_multi_val *mv,
1316 enum isl_dim_type type, unsigned pos,
1317 __isl_take isl_id *id);
1318 __isl_give isl_id *isl_multi_val_get_dim_id(
1319 __isl_keep isl_multi_val *mv,
1320 enum isl_dim_type type, unsigned pos);
1321 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1322 __isl_take isl_multi_val *mv,
1323 enum isl_dim_type type, unsigned pos, const char *s);
1325 #include <isl/aff.h>
1326 __isl_give isl_aff *isl_aff_set_dim_id(
1327 __isl_take isl_aff *aff, enum isl_dim_type type,
1328 unsigned pos, __isl_take isl_id *id);
1329 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1330 __isl_take isl_multi_aff *maff,
1331 enum isl_dim_type type, unsigned pos,
1332 __isl_take isl_id *id);
1333 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1334 __isl_take isl_pw_aff *pma,
1335 enum isl_dim_type type, unsigned pos,
1336 __isl_take isl_id *id);
1337 __isl_give isl_multi_pw_aff *
1338 isl_multi_pw_aff_set_dim_id(
1339 __isl_take isl_multi_pw_aff *mpa,
1340 enum isl_dim_type type, unsigned pos,
1341 __isl_take isl_id *id);
1342 __isl_give isl_multi_union_pw_aff *
1343 isl_multi_union_pw_aff_set_dim_id(
1344 __isl_take isl_multi_union_pw_aff *mupa,
1345 enum isl_dim_type type, unsigned pos,
1346 __isl_take isl_id *id);
1347 __isl_give isl_id *isl_multi_aff_get_dim_id(
1348 __isl_keep isl_multi_aff *ma,
1349 enum isl_dim_type type, unsigned pos);
1350 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1351 enum isl_dim_type type, unsigned pos);
1352 __isl_give isl_id *isl_pw_aff_get_dim_id(
1353 __isl_keep isl_pw_aff *pa,
1354 enum isl_dim_type type, unsigned pos);
1355 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1356 __isl_keep isl_pw_multi_aff *pma,
1357 enum isl_dim_type type, unsigned pos);
1358 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1359 __isl_keep isl_multi_pw_aff *mpa,
1360 enum isl_dim_type type, unsigned pos);
1361 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1362 __isl_keep isl_multi_union_pw_aff *mupa,
1363 enum isl_dim_type type, unsigned pos);
1364 __isl_give isl_aff *isl_aff_set_dim_name(
1365 __isl_take isl_aff *aff, enum isl_dim_type type,
1366 unsigned pos, const char *s);
1367 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1368 __isl_take isl_multi_aff *maff,
1369 enum isl_dim_type type, unsigned pos, const char *s);
1370 __isl_give isl_multi_pw_aff *
1371 isl_multi_pw_aff_set_dim_name(
1372 __isl_take isl_multi_pw_aff *mpa,
1373 enum isl_dim_type type, unsigned pos, const char *s);
1374 __isl_give isl_union_pw_aff *
1375 isl_union_pw_aff_set_dim_name(
1376 __isl_take isl_union_pw_aff *upa,
1377 enum isl_dim_type type, unsigned pos,
1379 __isl_give isl_union_pw_multi_aff *
1380 isl_union_pw_multi_aff_set_dim_name(
1381 __isl_take isl_union_pw_multi_aff *upma,
1382 enum isl_dim_type type, unsigned pos,
1384 __isl_give isl_multi_union_pw_aff *
1385 isl_multi_union_pw_aff_set_dim_name(
1386 __isl_take isl_multi_union_pw_aff *mupa,
1387 enum isl_dim_type type, unsigned pos,
1388 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1389 enum isl_dim_type type, unsigned pos);
1390 const char *isl_pw_aff_get_dim_name(
1391 __isl_keep isl_pw_aff *pa,
1392 enum isl_dim_type type, unsigned pos);
1393 const char *isl_pw_multi_aff_get_dim_name(
1394 __isl_keep isl_pw_multi_aff *pma,
1395 enum isl_dim_type type, unsigned pos);
1397 #include <isl/polynomial.h>
1398 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1399 __isl_take isl_qpolynomial *qp,
1400 enum isl_dim_type type, unsigned pos,
1402 __isl_give isl_pw_qpolynomial *
1403 isl_pw_qpolynomial_set_dim_name(
1404 __isl_take isl_pw_qpolynomial *pwqp,
1405 enum isl_dim_type type, unsigned pos,
1407 __isl_give isl_pw_qpolynomial_fold *
1408 isl_pw_qpolynomial_fold_set_dim_name(
1409 __isl_take isl_pw_qpolynomial_fold *pwf,
1410 enum isl_dim_type type, unsigned pos,
1412 __isl_give isl_union_pw_qpolynomial *
1413 isl_union_pw_qpolynomial_set_dim_name(
1414 __isl_take isl_union_pw_qpolynomial *upwqp,
1415 enum isl_dim_type type, unsigned pos,
1417 __isl_give isl_union_pw_qpolynomial_fold *
1418 isl_union_pw_qpolynomial_fold_set_dim_name(
1419 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1420 enum isl_dim_type type, unsigned pos,
1423 Note that C<isl_space_get_name> returns a pointer to some internal
1424 data structure, so the result can only be used while the
1425 corresponding C<isl_space> is alive.
1426 Also note that every function that operates on two sets or relations
1427 requires that both arguments have the same parameters. This also
1428 means that if one of the arguments has named parameters, then the
1429 other needs to have named parameters too and the names need to match.
1430 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1431 arguments may have different parameters (as long as they are named),
1432 in which case the result will have as parameters the union of the parameters of
1435 Given the identifier or name of a dimension (typically a parameter),
1436 its position can be obtained from the following functions.
1438 #include <isl/space.h>
1439 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1440 enum isl_dim_type type, __isl_keep isl_id *id);
1441 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1442 enum isl_dim_type type, const char *name);
1444 #include <isl/local_space.h>
1445 int isl_local_space_find_dim_by_name(
1446 __isl_keep isl_local_space *ls,
1447 enum isl_dim_type type, const char *name);
1449 #include <isl/val.h>
1450 int isl_multi_val_find_dim_by_id(
1451 __isl_keep isl_multi_val *mv,
1452 enum isl_dim_type type, __isl_keep isl_id *id);
1453 int isl_multi_val_find_dim_by_name(
1454 __isl_keep isl_multi_val *mv,
1455 enum isl_dim_type type, const char *name);
1457 #include <isl/set.h>
1458 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1459 enum isl_dim_type type, __isl_keep isl_id *id);
1460 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1461 enum isl_dim_type type, const char *name);
1463 #include <isl/map.h>
1464 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1465 enum isl_dim_type type, __isl_keep isl_id *id);
1466 int isl_basic_map_find_dim_by_name(
1467 __isl_keep isl_basic_map *bmap,
1468 enum isl_dim_type type, const char *name);
1469 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1470 enum isl_dim_type type, const char *name);
1471 int isl_union_map_find_dim_by_name(
1472 __isl_keep isl_union_map *umap,
1473 enum isl_dim_type type, const char *name);
1475 #include <isl/aff.h>
1476 int isl_multi_aff_find_dim_by_id(
1477 __isl_keep isl_multi_aff *ma,
1478 enum isl_dim_type type, __isl_keep isl_id *id);
1479 int isl_multi_pw_aff_find_dim_by_id(
1480 __isl_keep isl_multi_pw_aff *mpa,
1481 enum isl_dim_type type, __isl_keep isl_id *id);
1482 int isl_multi_union_pw_aff_find_dim_by_id(
1483 __isl_keep isl_union_multi_pw_aff *mupa,
1484 enum isl_dim_type type, __isl_keep isl_id *id);
1485 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1486 enum isl_dim_type type, const char *name);
1487 int isl_multi_aff_find_dim_by_name(
1488 __isl_keep isl_multi_aff *ma,
1489 enum isl_dim_type type, const char *name);
1490 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1491 enum isl_dim_type type, const char *name);
1492 int isl_multi_pw_aff_find_dim_by_name(
1493 __isl_keep isl_multi_pw_aff *mpa,
1494 enum isl_dim_type type, const char *name);
1495 int isl_pw_multi_aff_find_dim_by_name(
1496 __isl_keep isl_pw_multi_aff *pma,
1497 enum isl_dim_type type, const char *name);
1498 int isl_union_pw_aff_find_dim_by_name(
1499 __isl_keep isl_union_pw_aff *upa,
1500 enum isl_dim_type type, const char *name);
1501 int isl_union_pw_multi_aff_find_dim_by_name(
1502 __isl_keep isl_union_pw_multi_aff *upma,
1503 enum isl_dim_type type, const char *name);
1504 int isl_multi_union_pw_aff_find_dim_by_name(
1505 __isl_keep isl_multi_union_pw_aff *mupa,
1506 enum isl_dim_type type, const char *name);
1508 #include <isl/polynomial.h>
1509 int isl_pw_qpolynomial_find_dim_by_name(
1510 __isl_keep isl_pw_qpolynomial *pwqp,
1511 enum isl_dim_type type, const char *name);
1512 int isl_pw_qpolynomial_fold_find_dim_by_name(
1513 __isl_keep isl_pw_qpolynomial_fold *pwf,
1514 enum isl_dim_type type, const char *name);
1515 int isl_union_pw_qpolynomial_find_dim_by_name(
1516 __isl_keep isl_union_pw_qpolynomial *upwqp,
1517 enum isl_dim_type type, const char *name);
1518 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1519 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1520 enum isl_dim_type type, const char *name);
1522 The identifiers or names of entire spaces may be set or read off
1523 using the following functions.
1525 #include <isl/space.h>
1526 __isl_give isl_space *isl_space_set_tuple_id(
1527 __isl_take isl_space *space,
1528 enum isl_dim_type type, __isl_take isl_id *id);
1529 __isl_give isl_space *isl_space_reset_tuple_id(
1530 __isl_take isl_space *space, enum isl_dim_type type);
1531 isl_bool isl_space_has_tuple_id(
1532 __isl_keep isl_space *space,
1533 enum isl_dim_type type);
1534 __isl_give isl_id *isl_space_get_tuple_id(
1535 __isl_keep isl_space *space, enum isl_dim_type type);
1536 __isl_give isl_space *isl_space_set_tuple_name(
1537 __isl_take isl_space *space,
1538 enum isl_dim_type type, const char *s);
1539 isl_bool isl_space_has_tuple_name(
1540 __isl_keep isl_space *space,
1541 enum isl_dim_type type);
1542 __isl_keep const char *isl_space_get_tuple_name(
1543 __isl_keep isl_space *space,
1544 enum isl_dim_type type);
1546 #include <isl/local_space.h>
1547 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1548 __isl_take isl_local_space *ls,
1549 enum isl_dim_type type, __isl_take isl_id *id);
1551 #include <isl/set.h>
1552 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1553 __isl_take isl_basic_set *bset,
1554 __isl_take isl_id *id);
1555 __isl_give isl_set *isl_set_set_tuple_id(
1556 __isl_take isl_set *set, __isl_take isl_id *id);
1557 __isl_give isl_set *isl_set_reset_tuple_id(
1558 __isl_take isl_set *set);
1559 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1560 __isl_give isl_id *isl_set_get_tuple_id(
1561 __isl_keep isl_set *set);
1562 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1563 __isl_take isl_basic_set *set, const char *s);
1564 __isl_give isl_set *isl_set_set_tuple_name(
1565 __isl_take isl_set *set, const char *s);
1566 const char *isl_basic_set_get_tuple_name(
1567 __isl_keep isl_basic_set *bset);
1568 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1569 const char *isl_set_get_tuple_name(
1570 __isl_keep isl_set *set);
1572 #include <isl/map.h>
1573 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1574 __isl_take isl_basic_map *bmap,
1575 enum isl_dim_type type, __isl_take isl_id *id);
1576 __isl_give isl_map *isl_map_set_tuple_id(
1577 __isl_take isl_map *map, enum isl_dim_type type,
1578 __isl_take isl_id *id);
1579 __isl_give isl_map *isl_map_reset_tuple_id(
1580 __isl_take isl_map *map, enum isl_dim_type type);
1581 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1582 enum isl_dim_type type);
1583 __isl_give isl_id *isl_map_get_tuple_id(
1584 __isl_keep isl_map *map, enum isl_dim_type type);
1585 __isl_give isl_map *isl_map_set_tuple_name(
1586 __isl_take isl_map *map,
1587 enum isl_dim_type type, const char *s);
1588 const char *isl_basic_map_get_tuple_name(
1589 __isl_keep isl_basic_map *bmap,
1590 enum isl_dim_type type);
1591 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1592 __isl_take isl_basic_map *bmap,
1593 enum isl_dim_type type, const char *s);
1594 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1595 enum isl_dim_type type);
1596 const char *isl_map_get_tuple_name(
1597 __isl_keep isl_map *map,
1598 enum isl_dim_type type);
1600 #include <isl/val.h>
1601 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1602 __isl_take isl_multi_val *mv,
1603 enum isl_dim_type type, __isl_take isl_id *id);
1604 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1605 __isl_take isl_multi_val *mv,
1606 enum isl_dim_type type);
1607 isl_bool isl_multi_val_has_tuple_id(
1608 __isl_keep isl_multi_val *mv,
1609 enum isl_dim_type type);
1610 __isl_give isl_id *isl_multi_val_get_tuple_id(
1611 __isl_keep isl_multi_val *mv,
1612 enum isl_dim_type type);
1613 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1614 __isl_take isl_multi_val *mv,
1615 enum isl_dim_type type, const char *s);
1616 const char *isl_multi_val_get_tuple_name(
1617 __isl_keep isl_multi_val *mv,
1618 enum isl_dim_type type);
1620 #include <isl/aff.h>
1621 __isl_give isl_aff *isl_aff_set_tuple_id(
1622 __isl_take isl_aff *aff,
1623 enum isl_dim_type type, __isl_take isl_id *id);
1624 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1625 __isl_take isl_multi_aff *maff,
1626 enum isl_dim_type type, __isl_take isl_id *id);
1627 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1628 __isl_take isl_pw_aff *pwaff,
1629 enum isl_dim_type type, __isl_take isl_id *id);
1630 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1631 __isl_take isl_pw_multi_aff *pma,
1632 enum isl_dim_type type, __isl_take isl_id *id);
1633 __isl_give isl_multi_union_pw_aff *
1634 isl_multi_union_pw_aff_set_tuple_id(
1635 __isl_take isl_multi_union_pw_aff *mupa,
1636 enum isl_dim_type type, __isl_take isl_id *id);
1637 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1638 __isl_take isl_multi_aff *ma,
1639 enum isl_dim_type type);
1640 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1641 __isl_take isl_pw_aff *pa,
1642 enum isl_dim_type type);
1643 __isl_give isl_multi_pw_aff *
1644 isl_multi_pw_aff_reset_tuple_id(
1645 __isl_take isl_multi_pw_aff *mpa,
1646 enum isl_dim_type type);
1647 __isl_give isl_pw_multi_aff *
1648 isl_pw_multi_aff_reset_tuple_id(
1649 __isl_take isl_pw_multi_aff *pma,
1650 enum isl_dim_type type);
1651 __isl_give isl_multi_union_pw_aff *
1652 isl_multi_union_pw_aff_reset_tuple_id(
1653 __isl_take isl_multi_union_pw_aff *mupa,
1654 enum isl_dim_type type);
1655 isl_bool isl_multi_aff_has_tuple_id(
1656 __isl_keep isl_multi_aff *ma,
1657 enum isl_dim_type type);
1658 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1659 __isl_keep isl_multi_aff *ma,
1660 enum isl_dim_type type);
1661 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1662 enum isl_dim_type type);
1663 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1664 __isl_keep isl_pw_aff *pa,
1665 enum isl_dim_type type);
1666 isl_bool isl_pw_multi_aff_has_tuple_id(
1667 __isl_keep isl_pw_multi_aff *pma,
1668 enum isl_dim_type type);
1669 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1670 __isl_keep isl_pw_multi_aff *pma,
1671 enum isl_dim_type type);
1672 isl_bool isl_multi_pw_aff_has_tuple_id(
1673 __isl_keep isl_multi_pw_aff *mpa,
1674 enum isl_dim_type type);
1675 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1676 __isl_keep isl_multi_pw_aff *mpa,
1677 enum isl_dim_type type);
1678 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1679 __isl_keep isl_multi_union_pw_aff *mupa,
1680 enum isl_dim_type type);
1681 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1682 __isl_keep isl_multi_union_pw_aff *mupa,
1683 enum isl_dim_type type);
1684 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1685 __isl_take isl_multi_aff *maff,
1686 enum isl_dim_type type, const char *s);
1687 __isl_give isl_multi_pw_aff *
1688 isl_multi_pw_aff_set_tuple_name(
1689 __isl_take isl_multi_pw_aff *mpa,
1690 enum isl_dim_type type, const char *s);
1691 __isl_give isl_multi_union_pw_aff *
1692 isl_multi_union_pw_aff_set_tuple_name(
1693 __isl_take isl_multi_union_pw_aff *mupa,
1694 enum isl_dim_type type, const char *s);
1695 const char *isl_multi_aff_get_tuple_name(
1696 __isl_keep isl_multi_aff *multi,
1697 enum isl_dim_type type);
1698 isl_bool isl_pw_multi_aff_has_tuple_name(
1699 __isl_keep isl_pw_multi_aff *pma,
1700 enum isl_dim_type type);
1701 const char *isl_pw_multi_aff_get_tuple_name(
1702 __isl_keep isl_pw_multi_aff *pma,
1703 enum isl_dim_type type);
1704 const char *isl_multi_union_pw_aff_get_tuple_name(
1705 __isl_keep isl_multi_union_pw_aff *mupa,
1706 enum isl_dim_type type);
1708 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1709 or C<isl_dim_set>. As with C<isl_space_get_name>,
1710 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1712 Binary operations require the corresponding spaces of their arguments
1713 to have the same name.
1715 To keep the names of all parameters and tuples, but reset the user pointers
1716 of all the corresponding identifiers, use the following function.
1718 #include <isl/space.h>
1719 __isl_give isl_space *isl_space_reset_user(
1720 __isl_take isl_space *space);
1722 #include <isl/set.h>
1723 __isl_give isl_set *isl_set_reset_user(
1724 __isl_take isl_set *set);
1726 #include <isl/map.h>
1727 __isl_give isl_map *isl_map_reset_user(
1728 __isl_take isl_map *map);
1730 #include <isl/union_set.h>
1731 __isl_give isl_union_set *isl_union_set_reset_user(
1732 __isl_take isl_union_set *uset);
1734 #include <isl/union_map.h>
1735 __isl_give isl_union_map *isl_union_map_reset_user(
1736 __isl_take isl_union_map *umap);
1738 #include <isl/val.h>
1739 __isl_give isl_multi_val *isl_multi_val_reset_user(
1740 __isl_take isl_multi_val *mv);
1742 #include <isl/aff.h>
1743 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1744 __isl_take isl_multi_aff *ma);
1745 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1746 __isl_take isl_pw_aff *pa);
1747 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1748 __isl_take isl_multi_pw_aff *mpa);
1749 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1750 __isl_take isl_pw_multi_aff *pma);
1751 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1752 __isl_take isl_union_pw_aff *upa);
1753 __isl_give isl_multi_union_pw_aff *
1754 isl_multi_union_pw_aff_reset_user(
1755 __isl_take isl_multi_union_pw_aff *mupa);
1756 __isl_give isl_union_pw_multi_aff *
1757 isl_union_pw_multi_aff_reset_user(
1758 __isl_take isl_union_pw_multi_aff *upma);
1760 #include <isl/polynomial.h>
1761 __isl_give isl_pw_qpolynomial *
1762 isl_pw_qpolynomial_reset_user(
1763 __isl_take isl_pw_qpolynomial *pwqp);
1764 __isl_give isl_union_pw_qpolynomial *
1765 isl_union_pw_qpolynomial_reset_user(
1766 __isl_take isl_union_pw_qpolynomial *upwqp);
1767 __isl_give isl_pw_qpolynomial_fold *
1768 isl_pw_qpolynomial_fold_reset_user(
1769 __isl_take isl_pw_qpolynomial_fold *pwf);
1770 __isl_give isl_union_pw_qpolynomial_fold *
1771 isl_union_pw_qpolynomial_fold_reset_user(
1772 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1774 Spaces can be nested. In particular, the domain of a set or
1775 the domain or range of a relation can be a nested relation.
1776 This process is also called I<wrapping>.
1777 The functions for detecting, constructing and deconstructing
1778 such nested spaces can be found in the wrapping properties
1779 of L</"Unary Properties">, the wrapping operations
1780 of L</"Unary Operations"> and the Cartesian product operations
1781 of L</"Basic Operations">.
1783 Spaces can be created from other spaces
1784 using the functions described in L</"Unary Operations">
1785 and L</"Binary Operations">.
1789 A local space is essentially a space with
1790 zero or more existentially quantified variables.
1791 The local space of various objects can be obtained
1792 using the following functions.
1794 #include <isl/constraint.h>
1795 __isl_give isl_local_space *isl_constraint_get_local_space(
1796 __isl_keep isl_constraint *constraint);
1798 #include <isl/set.h>
1799 __isl_give isl_local_space *isl_basic_set_get_local_space(
1800 __isl_keep isl_basic_set *bset);
1802 #include <isl/map.h>
1803 __isl_give isl_local_space *isl_basic_map_get_local_space(
1804 __isl_keep isl_basic_map *bmap);
1806 #include <isl/aff.h>
1807 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1808 __isl_keep isl_aff *aff);
1809 __isl_give isl_local_space *isl_aff_get_local_space(
1810 __isl_keep isl_aff *aff);
1812 A new local space can be created from a space using
1814 #include <isl/local_space.h>
1815 __isl_give isl_local_space *isl_local_space_from_space(
1816 __isl_take isl_space *space);
1818 They can be inspected, modified, copied and freed using the following functions.
1820 #include <isl/local_space.h>
1821 isl_bool isl_local_space_is_params(
1822 __isl_keep isl_local_space *ls);
1823 isl_bool isl_local_space_is_set(
1824 __isl_keep isl_local_space *ls);
1825 __isl_give isl_space *isl_local_space_get_space(
1826 __isl_keep isl_local_space *ls);
1827 __isl_give isl_aff *isl_local_space_get_div(
1828 __isl_keep isl_local_space *ls, int pos);
1829 __isl_give isl_local_space *isl_local_space_copy(
1830 __isl_keep isl_local_space *ls);
1831 __isl_null isl_local_space *isl_local_space_free(
1832 __isl_take isl_local_space *ls);
1834 Note that C<isl_local_space_get_div> can only be used on local spaces
1837 Two local spaces can be compared using
1839 isl_bool isl_local_space_is_equal(
1840 __isl_keep isl_local_space *ls1,
1841 __isl_keep isl_local_space *ls2);
1843 Local spaces can be created from other local spaces
1844 using the functions described in L</"Unary Operations">
1845 and L</"Binary Operations">.
1847 =head2 Creating New Sets and Relations
1849 C<isl> has functions for creating some standard sets and relations.
1853 =item * Empty sets and relations
1855 __isl_give isl_basic_set *isl_basic_set_empty(
1856 __isl_take isl_space *space);
1857 __isl_give isl_basic_map *isl_basic_map_empty(
1858 __isl_take isl_space *space);
1859 __isl_give isl_set *isl_set_empty(
1860 __isl_take isl_space *space);
1861 __isl_give isl_map *isl_map_empty(
1862 __isl_take isl_space *space);
1863 __isl_give isl_union_set *isl_union_set_empty(
1864 __isl_take isl_space *space);
1865 __isl_give isl_union_map *isl_union_map_empty(
1866 __isl_take isl_space *space);
1868 For C<isl_union_set>s and C<isl_union_map>s, the space
1869 is only used to specify the parameters.
1871 =item * Universe sets and relations
1873 __isl_give isl_basic_set *isl_basic_set_universe(
1874 __isl_take isl_space *space);
1875 __isl_give isl_basic_map *isl_basic_map_universe(
1876 __isl_take isl_space *space);
1877 __isl_give isl_set *isl_set_universe(
1878 __isl_take isl_space *space);
1879 __isl_give isl_map *isl_map_universe(
1880 __isl_take isl_space *space);
1881 __isl_give isl_union_set *isl_union_set_universe(
1882 __isl_take isl_union_set *uset);
1883 __isl_give isl_union_map *isl_union_map_universe(
1884 __isl_take isl_union_map *umap);
1886 The sets and relations constructed by the functions above
1887 contain all integer values, while those constructed by the
1888 functions below only contain non-negative values.
1890 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1891 __isl_take isl_space *space);
1892 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1893 __isl_take isl_space *space);
1894 __isl_give isl_set *isl_set_nat_universe(
1895 __isl_take isl_space *space);
1896 __isl_give isl_map *isl_map_nat_universe(
1897 __isl_take isl_space *space);
1899 =item * Identity relations
1901 __isl_give isl_basic_map *isl_basic_map_identity(
1902 __isl_take isl_space *space);
1903 __isl_give isl_map *isl_map_identity(
1904 __isl_take isl_space *space);
1906 The number of input and output dimensions in C<space> needs
1909 =item * Lexicographic order
1911 __isl_give isl_map *isl_map_lex_lt(
1912 __isl_take isl_space *set_space);
1913 __isl_give isl_map *isl_map_lex_le(
1914 __isl_take isl_space *set_space);
1915 __isl_give isl_map *isl_map_lex_gt(
1916 __isl_take isl_space *set_space);
1917 __isl_give isl_map *isl_map_lex_ge(
1918 __isl_take isl_space *set_space);
1919 __isl_give isl_map *isl_map_lex_lt_first(
1920 __isl_take isl_space *space, unsigned n);
1921 __isl_give isl_map *isl_map_lex_le_first(
1922 __isl_take isl_space *space, unsigned n);
1923 __isl_give isl_map *isl_map_lex_gt_first(
1924 __isl_take isl_space *space, unsigned n);
1925 __isl_give isl_map *isl_map_lex_ge_first(
1926 __isl_take isl_space *space, unsigned n);
1928 The first four functions take a space for a B<set>
1929 and return relations that express that the elements in the domain
1930 are lexicographically less
1931 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1932 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1933 than the elements in the range.
1934 The last four functions take a space for a map
1935 and return relations that express that the first C<n> dimensions
1936 in the domain are lexicographically less
1937 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1938 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1939 than the first C<n> dimensions in the range.
1943 A basic set or relation can be converted to a set or relation
1944 using the following functions.
1946 __isl_give isl_set *isl_set_from_basic_set(
1947 __isl_take isl_basic_set *bset);
1948 __isl_give isl_map *isl_map_from_basic_map(
1949 __isl_take isl_basic_map *bmap);
1951 Sets and relations can be converted to union sets and relations
1952 using the following functions.
1954 __isl_give isl_union_set *isl_union_set_from_basic_set(
1955 __isl_take isl_basic_set *bset);
1956 __isl_give isl_union_map *isl_union_map_from_basic_map(
1957 __isl_take isl_basic_map *bmap);
1958 __isl_give isl_union_set *isl_union_set_from_set(
1959 __isl_take isl_set *set);
1960 __isl_give isl_union_map *isl_union_map_from_map(
1961 __isl_take isl_map *map);
1963 The inverse conversions below can only be used if the input
1964 union set or relation is known to contain elements in exactly one
1967 __isl_give isl_set *isl_set_from_union_set(
1968 __isl_take isl_union_set *uset);
1969 __isl_give isl_map *isl_map_from_union_map(
1970 __isl_take isl_union_map *umap);
1972 Sets and relations can be copied and freed again using the following
1975 __isl_give isl_basic_set *isl_basic_set_copy(
1976 __isl_keep isl_basic_set *bset);
1977 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1978 __isl_give isl_union_set *isl_union_set_copy(
1979 __isl_keep isl_union_set *uset);
1980 __isl_give isl_basic_map *isl_basic_map_copy(
1981 __isl_keep isl_basic_map *bmap);
1982 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1983 __isl_give isl_union_map *isl_union_map_copy(
1984 __isl_keep isl_union_map *umap);
1985 __isl_null isl_basic_set *isl_basic_set_free(
1986 __isl_take isl_basic_set *bset);
1987 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1988 __isl_null isl_union_set *isl_union_set_free(
1989 __isl_take isl_union_set *uset);
1990 __isl_null isl_basic_map *isl_basic_map_free(
1991 __isl_take isl_basic_map *bmap);
1992 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1993 __isl_null isl_union_map *isl_union_map_free(
1994 __isl_take isl_union_map *umap);
1996 Other sets and relations can be constructed by starting
1997 from a universe set or relation, adding equality and/or
1998 inequality constraints and then projecting out the
1999 existentially quantified variables, if any.
2000 Constraints can be constructed, manipulated and
2001 added to (or removed from) (basic) sets and relations
2002 using the following functions.
2004 #include <isl/constraint.h>
2005 __isl_give isl_constraint *isl_constraint_alloc_equality(
2006 __isl_take isl_local_space *ls);
2007 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2008 __isl_take isl_local_space *ls);
2009 __isl_give isl_constraint *isl_constraint_set_constant_si(
2010 __isl_take isl_constraint *constraint, int v);
2011 __isl_give isl_constraint *isl_constraint_set_constant_val(
2012 __isl_take isl_constraint *constraint,
2013 __isl_take isl_val *v);
2014 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2015 __isl_take isl_constraint *constraint,
2016 enum isl_dim_type type, int pos, int v);
2017 __isl_give isl_constraint *
2018 isl_constraint_set_coefficient_val(
2019 __isl_take isl_constraint *constraint,
2020 enum isl_dim_type type, int pos,
2021 __isl_take isl_val *v);
2022 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2023 __isl_take isl_basic_map *bmap,
2024 __isl_take isl_constraint *constraint);
2025 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2026 __isl_take isl_basic_set *bset,
2027 __isl_take isl_constraint *constraint);
2028 __isl_give isl_map *isl_map_add_constraint(
2029 __isl_take isl_map *map,
2030 __isl_take isl_constraint *constraint);
2031 __isl_give isl_set *isl_set_add_constraint(
2032 __isl_take isl_set *set,
2033 __isl_take isl_constraint *constraint);
2035 For example, to create a set containing the even integers
2036 between 10 and 42, you would use the following code.
2039 isl_local_space *ls;
2041 isl_basic_set *bset;
2043 space = isl_space_set_alloc(ctx, 0, 2);
2044 bset = isl_basic_set_universe(isl_space_copy(space));
2045 ls = isl_local_space_from_space(space);
2047 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2048 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2049 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2050 bset = isl_basic_set_add_constraint(bset, c);
2052 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2053 c = isl_constraint_set_constant_si(c, -10);
2054 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2055 bset = isl_basic_set_add_constraint(bset, c);
2057 c = isl_constraint_alloc_inequality(ls);
2058 c = isl_constraint_set_constant_si(c, 42);
2059 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2060 bset = isl_basic_set_add_constraint(bset, c);
2062 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2066 isl_basic_set *bset;
2067 bset = isl_basic_set_read_from_str(ctx,
2068 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2070 A basic set or relation can also be constructed from two matrices
2071 describing the equalities and the inequalities.
2073 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2074 __isl_take isl_space *space,
2075 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2076 enum isl_dim_type c1,
2077 enum isl_dim_type c2, enum isl_dim_type c3,
2078 enum isl_dim_type c4);
2079 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2080 __isl_take isl_space *space,
2081 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2082 enum isl_dim_type c1,
2083 enum isl_dim_type c2, enum isl_dim_type c3,
2084 enum isl_dim_type c4, enum isl_dim_type c5);
2086 The C<isl_dim_type> arguments indicate the order in which
2087 different kinds of variables appear in the input matrices
2088 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2089 C<isl_dim_set> and C<isl_dim_div> for sets and
2090 of C<isl_dim_cst>, C<isl_dim_param>,
2091 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2093 A (basic or union) set or relation can also be constructed from a
2094 (union) (piecewise) (multiple) affine expression
2095 or a list of affine expressions
2096 (See L</"Functions">), provided these affine expressions do not
2099 #include <isl/set.h>
2100 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2101 __isl_take isl_multi_aff *ma);
2103 #include <isl/map.h>
2104 __isl_give isl_basic_map *isl_basic_map_from_aff(
2105 __isl_take isl_aff *aff);
2106 __isl_give isl_map *isl_map_from_aff(
2107 __isl_take isl_aff *aff);
2108 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2109 __isl_take isl_space *domain_space,
2110 __isl_take isl_aff_list *list);
2111 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2112 __isl_take isl_multi_aff *maff)
2113 __isl_give isl_map *isl_map_from_multi_aff(
2114 __isl_take isl_multi_aff *maff)
2116 #include <isl/aff.h>
2117 __isl_give isl_set *isl_set_from_pw_aff(
2118 __isl_take isl_pw_aff *pwaff);
2119 __isl_give isl_map *isl_map_from_pw_aff(
2120 __isl_take isl_pw_aff *pwaff);
2121 __isl_give isl_set *isl_set_from_pw_multi_aff(
2122 __isl_take isl_pw_multi_aff *pma);
2123 __isl_give isl_map *isl_map_from_pw_multi_aff(
2124 __isl_take isl_pw_multi_aff *pma);
2125 __isl_give isl_set *isl_set_from_multi_pw_aff(
2126 __isl_take isl_multi_pw_aff *mpa);
2127 __isl_give isl_map *isl_map_from_multi_pw_aff(
2128 __isl_take isl_multi_pw_aff *mpa);
2129 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2130 __isl_take isl_union_pw_aff *upa);
2131 __isl_give isl_union_map *
2132 isl_union_map_from_union_pw_multi_aff(
2133 __isl_take isl_union_pw_multi_aff *upma);
2134 __isl_give isl_union_map *
2135 isl_union_map_from_multi_union_pw_aff(
2136 __isl_take isl_multi_union_pw_aff *mupa);
2138 The C<domain_space> argument describes the domain of the resulting
2139 basic relation. It is required because the C<list> may consist
2140 of zero affine expressions.
2141 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2142 is not allowed to be zero-dimensional. The domain of the result
2143 is the shared domain of the union piecewise affine elements.
2145 =head2 Inspecting Sets and Relations
2147 Usually, the user should not have to care about the actual constraints
2148 of the sets and maps, but should instead apply the abstract operations
2149 explained in the following sections.
2150 Occasionally, however, it may be required to inspect the individual
2151 coefficients of the constraints. This section explains how to do so.
2152 In these cases, it may also be useful to have C<isl> compute
2153 an explicit representation of the existentially quantified variables.
2155 __isl_give isl_set *isl_set_compute_divs(
2156 __isl_take isl_set *set);
2157 __isl_give isl_map *isl_map_compute_divs(
2158 __isl_take isl_map *map);
2159 __isl_give isl_union_set *isl_union_set_compute_divs(
2160 __isl_take isl_union_set *uset);
2161 __isl_give isl_union_map *isl_union_map_compute_divs(
2162 __isl_take isl_union_map *umap);
2164 This explicit representation defines the existentially quantified
2165 variables as integer divisions of the other variables, possibly
2166 including earlier existentially quantified variables.
2167 An explicitly represented existentially quantified variable therefore
2168 has a unique value when the values of the other variables are known.
2170 Alternatively, the existentially quantified variables can be removed
2171 using the following functions, which compute an overapproximation.
2173 #include <isl/set.h>
2174 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2175 __isl_take isl_basic_set *bset);
2176 __isl_give isl_set *isl_set_remove_divs(
2177 __isl_take isl_set *set);
2179 #include <isl/map.h>
2180 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2181 __isl_take isl_basic_map *bmap);
2182 __isl_give isl_map *isl_map_remove_divs(
2183 __isl_take isl_map *map);
2185 #include <isl/union_set.h>
2186 __isl_give isl_union_set *isl_union_set_remove_divs(
2187 __isl_take isl_union_set *bset);
2189 #include <isl/union_map.h>
2190 __isl_give isl_union_map *isl_union_map_remove_divs(
2191 __isl_take isl_union_map *bmap);
2193 It is also possible to only remove those divs that are defined
2194 in terms of a given range of dimensions or only those for which
2195 no explicit representation is known.
2197 __isl_give isl_basic_set *
2198 isl_basic_set_remove_divs_involving_dims(
2199 __isl_take isl_basic_set *bset,
2200 enum isl_dim_type type,
2201 unsigned first, unsigned n);
2202 __isl_give isl_basic_map *
2203 isl_basic_map_remove_divs_involving_dims(
2204 __isl_take isl_basic_map *bmap,
2205 enum isl_dim_type type,
2206 unsigned first, unsigned n);
2207 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2208 __isl_take isl_set *set, enum isl_dim_type type,
2209 unsigned first, unsigned n);
2210 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2211 __isl_take isl_map *map, enum isl_dim_type type,
2212 unsigned first, unsigned n);
2214 __isl_give isl_basic_set *
2215 isl_basic_set_remove_unknown_divs(
2216 __isl_take isl_basic_set *bset);
2217 __isl_give isl_set *isl_set_remove_unknown_divs(
2218 __isl_take isl_set *set);
2219 __isl_give isl_map *isl_map_remove_unknown_divs(
2220 __isl_take isl_map *map);
2222 To iterate over all the sets or maps in a union set or map, use
2224 #include <isl/union_set.h>
2225 isl_stat isl_union_set_foreach_set(
2226 __isl_keep isl_union_set *uset,
2227 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2230 #include <isl/union_map.h>
2231 isl_stat isl_union_map_foreach_map(
2232 __isl_keep isl_union_map *umap,
2233 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2235 isl_bool isl_union_map_every_map(
2236 __isl_keep isl_union_map *umap,
2237 isl_bool (*test)(__isl_keep isl_map *map,
2241 These functions call the callback function once for each
2242 (pair of) space(s) for which there are elements in the input.
2243 The argument to the callback contains all elements in the input
2244 with that (pair of) space(s).
2245 The C<isl_union_map_every_map> variant check whether each
2246 call to the callback returns true and stops checking as soon as one
2247 of these calls returns false.
2249 The number of sets or maps in a union set or map can be obtained
2252 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2253 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2255 To extract the set or map in a given space from a union, use
2257 __isl_give isl_set *isl_union_set_extract_set(
2258 __isl_keep isl_union_set *uset,
2259 __isl_take isl_space *space);
2260 __isl_give isl_map *isl_union_map_extract_map(
2261 __isl_keep isl_union_map *umap,
2262 __isl_take isl_space *space);
2264 To iterate over all the basic sets or maps in a set or map, use
2266 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2267 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2270 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2271 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2275 The callback function C<fn> should return C<isl_stat_ok> if successful and
2276 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2277 occurs, the above functions will return C<isl_stat_error>.
2279 It should be noted that C<isl> does not guarantee that
2280 the basic sets or maps passed to C<fn> are disjoint.
2281 If this is required, then the user should call one of
2282 the following functions first.
2284 __isl_give isl_set *isl_set_make_disjoint(
2285 __isl_take isl_set *set);
2286 __isl_give isl_map *isl_map_make_disjoint(
2287 __isl_take isl_map *map);
2289 The number of basic sets in a set can be obtained
2290 or the number of basic maps in a map can be obtained
2293 #include <isl/set.h>
2294 int isl_set_n_basic_set(__isl_keep isl_set *set);
2296 #include <isl/map.h>
2297 int isl_map_n_basic_map(__isl_keep isl_map *map);
2299 It is also possible to obtain a list of (basic) sets from a set
2300 or union set, a list of basic maps from a map and a list of maps from a union
2303 #include <isl/set.h>
2304 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2305 __isl_keep isl_set *set);
2307 #include <isl/union_set.h>
2308 __isl_give isl_basic_set_list *
2309 isl_union_set_get_basic_set_list(
2310 __isl_keep isl_union_set *uset);
2311 __isl_give isl_set_list *isl_union_set_get_set_list(
2312 __isl_keep isl_union_set *uset);
2314 #include <isl/map.h>
2315 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2316 __isl_keep isl_map *map);
2318 #include <isl/union_map.h>
2319 __isl_give isl_map_list *isl_union_map_get_map_list(
2320 __isl_keep isl_union_map *umap);
2322 The returned list can be manipulated using the functions in L<"Lists">.
2324 To iterate over the constraints of a basic set or map, use
2326 #include <isl/constraint.h>
2328 int isl_basic_set_n_constraint(
2329 __isl_keep isl_basic_set *bset);
2330 isl_stat isl_basic_set_foreach_constraint(
2331 __isl_keep isl_basic_set *bset,
2332 isl_stat (*fn)(__isl_take isl_constraint *c,
2335 int isl_basic_map_n_constraint(
2336 __isl_keep isl_basic_map *bmap);
2337 isl_stat isl_basic_map_foreach_constraint(
2338 __isl_keep isl_basic_map *bmap,
2339 isl_stat (*fn)(__isl_take isl_constraint *c,
2342 __isl_null isl_constraint *isl_constraint_free(
2343 __isl_take isl_constraint *c);
2345 Again, the callback function C<fn> should return C<isl_stat_ok>
2347 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2348 occurs, the above functions will return C<isl_stat_error>.
2349 The constraint C<c> represents either an equality or an inequality.
2350 Use the following function to find out whether a constraint
2351 represents an equality. If not, it represents an inequality.
2353 isl_bool isl_constraint_is_equality(
2354 __isl_keep isl_constraint *constraint);
2356 It is also possible to obtain a list of constraints from a basic
2359 #include <isl/constraint.h>
2360 __isl_give isl_constraint_list *
2361 isl_basic_map_get_constraint_list(
2362 __isl_keep isl_basic_map *bmap);
2363 __isl_give isl_constraint_list *
2364 isl_basic_set_get_constraint_list(
2365 __isl_keep isl_basic_set *bset);
2367 These functions require that all existentially quantified variables
2368 have an explicit representation.
2369 The returned list can be manipulated using the functions in L<"Lists">.
2371 The coefficients of the constraints can be inspected using
2372 the following functions.
2374 isl_bool isl_constraint_is_lower_bound(
2375 __isl_keep isl_constraint *constraint,
2376 enum isl_dim_type type, unsigned pos);
2377 isl_bool isl_constraint_is_upper_bound(
2378 __isl_keep isl_constraint *constraint,
2379 enum isl_dim_type type, unsigned pos);
2380 __isl_give isl_val *isl_constraint_get_constant_val(
2381 __isl_keep isl_constraint *constraint);
2382 __isl_give isl_val *isl_constraint_get_coefficient_val(
2383 __isl_keep isl_constraint *constraint,
2384 enum isl_dim_type type, int pos);
2386 The explicit representations of the existentially quantified
2387 variables can be inspected using the following function.
2388 Note that the user is only allowed to use this function
2389 if the inspected set or map is the result of a call
2390 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2391 The existentially quantified variable is equal to the floor
2392 of the returned affine expression. The affine expression
2393 itself can be inspected using the functions in
2396 __isl_give isl_aff *isl_constraint_get_div(
2397 __isl_keep isl_constraint *constraint, int pos);
2399 To obtain the constraints of a basic set or map in matrix
2400 form, use the following functions.
2402 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2403 __isl_keep isl_basic_set *bset,
2404 enum isl_dim_type c1, enum isl_dim_type c2,
2405 enum isl_dim_type c3, enum isl_dim_type c4);
2406 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2407 __isl_keep isl_basic_set *bset,
2408 enum isl_dim_type c1, enum isl_dim_type c2,
2409 enum isl_dim_type c3, enum isl_dim_type c4);
2410 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2411 __isl_keep isl_basic_map *bmap,
2412 enum isl_dim_type c1,
2413 enum isl_dim_type c2, enum isl_dim_type c3,
2414 enum isl_dim_type c4, enum isl_dim_type c5);
2415 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2416 __isl_keep isl_basic_map *bmap,
2417 enum isl_dim_type c1,
2418 enum isl_dim_type c2, enum isl_dim_type c3,
2419 enum isl_dim_type c4, enum isl_dim_type c5);
2421 The C<isl_dim_type> arguments dictate the order in which
2422 different kinds of variables appear in the resulting matrix.
2423 For set inputs, they should be a permutation of
2424 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2425 For map inputs, they should be a permutation of
2426 C<isl_dim_cst>, C<isl_dim_param>,
2427 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2431 Points are elements of a set. They can be used to construct
2432 simple sets (boxes) or they can be used to represent the
2433 individual elements of a set.
2434 The zero point (the origin) can be created using
2436 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2438 The coordinates of a point can be inspected, set and changed
2441 __isl_give isl_val *isl_point_get_coordinate_val(
2442 __isl_keep isl_point *pnt,
2443 enum isl_dim_type type, int pos);
2444 __isl_give isl_point *isl_point_set_coordinate_val(
2445 __isl_take isl_point *pnt,
2446 enum isl_dim_type type, int pos,
2447 __isl_take isl_val *v);
2449 __isl_give isl_point *isl_point_add_ui(
2450 __isl_take isl_point *pnt,
2451 enum isl_dim_type type, int pos, unsigned val);
2452 __isl_give isl_point *isl_point_sub_ui(
2453 __isl_take isl_point *pnt,
2454 enum isl_dim_type type, int pos, unsigned val);
2456 Points can be copied or freed using
2458 __isl_give isl_point *isl_point_copy(
2459 __isl_keep isl_point *pnt);
2460 __isl_null isl_point *isl_point_free(
2461 __isl_take isl_point *pnt);
2463 A singleton set can be created from a point using
2465 __isl_give isl_basic_set *isl_basic_set_from_point(
2466 __isl_take isl_point *pnt);
2467 __isl_give isl_set *isl_set_from_point(
2468 __isl_take isl_point *pnt);
2469 __isl_give isl_union_set *isl_union_set_from_point(
2470 __isl_take isl_point *pnt);
2472 and a box can be created from two opposite extremal points using
2474 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2475 __isl_take isl_point *pnt1,
2476 __isl_take isl_point *pnt2);
2477 __isl_give isl_set *isl_set_box_from_points(
2478 __isl_take isl_point *pnt1,
2479 __isl_take isl_point *pnt2);
2481 All elements of a B<bounded> (union) set can be enumerated using
2482 the following functions.
2484 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2485 isl_stat (*fn)(__isl_take isl_point *pnt,
2488 isl_stat isl_union_set_foreach_point(
2489 __isl_keep isl_union_set *uset,
2490 isl_stat (*fn)(__isl_take isl_point *pnt,
2494 The function C<fn> is called for each integer point in
2495 C<set> with as second argument the last argument of
2496 the C<isl_set_foreach_point> call. The function C<fn>
2497 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2498 In the latter case, C<isl_set_foreach_point> will stop
2499 enumerating and return C<isl_stat_error> as well.
2500 If the enumeration is performed successfully and to completion,
2501 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2503 To obtain a single point of a (basic or union) set, use
2505 __isl_give isl_point *isl_basic_set_sample_point(
2506 __isl_take isl_basic_set *bset);
2507 __isl_give isl_point *isl_set_sample_point(
2508 __isl_take isl_set *set);
2509 __isl_give isl_point *isl_union_set_sample_point(
2510 __isl_take isl_union_set *uset);
2512 If C<set> does not contain any (integer) points, then the
2513 resulting point will be ``void'', a property that can be
2516 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2520 Besides sets and relation, C<isl> also supports various types of functions.
2521 Each of these types is derived from the value type (see L</"Values">)
2522 or from one of two primitive function types
2523 through the application of zero or more type constructors.
2524 We first describe the primitive type and then we describe
2525 the types derived from these primitive types.
2527 =head3 Primitive Functions
2529 C<isl> support two primitive function types, quasi-affine
2530 expressions and quasipolynomials.
2531 A quasi-affine expression is defined either over a parameter
2532 space or over a set and is composed of integer constants,
2533 parameters and set variables, addition, subtraction and
2534 integer division by an integer constant.
2535 For example, the quasi-affine expression
2537 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2539 maps C<x> to C<2*floor((4 n + x)/9>.
2540 A quasipolynomial is a polynomial expression in quasi-affine
2541 expression. That is, it additionally allows for multiplication.
2542 Note, though, that it is not allowed to construct an integer
2543 division of an expression involving multiplications.
2544 Here is an example of a quasipolynomial that is not
2545 quasi-affine expression
2547 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2549 Note that the external representations of quasi-affine expressions
2550 and quasipolynomials are different. Quasi-affine expressions
2551 use a notation with square brackets just like binary relations,
2552 while quasipolynomials do not. This might change at some point.
2554 If a primitive function is defined over a parameter space,
2555 then the space of the function itself is that of a set.
2556 If it is defined over a set, then the space of the function
2557 is that of a relation. In both cases, the set space (or
2558 the output space) is single-dimensional, anonymous and unstructured.
2559 To create functions with multiple dimensions or with other kinds
2560 of set or output spaces, use multiple expressions
2561 (see L</"Multiple Expressions">).
2565 =item * Quasi-affine Expressions
2567 Besides the expressions described above, a quasi-affine
2568 expression can also be set to NaN. Such expressions
2569 typically represent a failure to represent a result
2570 as a quasi-affine expression.
2572 The zero quasi affine expression or the quasi affine expression
2573 that is equal to a given value, parameter or
2574 a specified dimension on a given domain can be created using
2576 #include <isl/aff.h>
2577 __isl_give isl_aff *isl_aff_zero_on_domain(
2578 __isl_take isl_local_space *ls);
2579 __isl_give isl_aff *isl_aff_val_on_domain(
2580 __isl_take isl_local_space *ls,
2581 __isl_take isl_val *val);
2582 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2583 __isl_take isl_space *space,
2584 __isl_take isl_id *id);
2585 __isl_give isl_aff *isl_aff_var_on_domain(
2586 __isl_take isl_local_space *ls,
2587 enum isl_dim_type type, unsigned pos);
2588 __isl_give isl_aff *isl_aff_nan_on_domain(
2589 __isl_take isl_local_space *ls);
2591 The space passed to C<isl_aff_param_on_domain_space_id>
2592 is required to have a parameter with the given identifier.
2594 Quasi affine expressions can be copied and freed using
2596 #include <isl/aff.h>
2597 __isl_give isl_aff *isl_aff_copy(
2598 __isl_keep isl_aff *aff);
2599 __isl_null isl_aff *isl_aff_free(
2600 __isl_take isl_aff *aff);
2602 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2603 using the following function. The constraint is required to have
2604 a non-zero coefficient for the specified dimension.
2606 #include <isl/constraint.h>
2607 __isl_give isl_aff *isl_constraint_get_bound(
2608 __isl_keep isl_constraint *constraint,
2609 enum isl_dim_type type, int pos);
2611 The entire affine expression of the constraint can also be extracted
2612 using the following function.
2614 #include <isl/constraint.h>
2615 __isl_give isl_aff *isl_constraint_get_aff(
2616 __isl_keep isl_constraint *constraint);
2618 Conversely, an equality constraint equating
2619 the affine expression to zero or an inequality constraint enforcing
2620 the affine expression to be non-negative, can be constructed using
2622 __isl_give isl_constraint *isl_equality_from_aff(
2623 __isl_take isl_aff *aff);
2624 __isl_give isl_constraint *isl_inequality_from_aff(
2625 __isl_take isl_aff *aff);
2627 The coefficients and the integer divisions of an affine expression
2628 can be inspected using the following functions.
2630 #include <isl/aff.h>
2631 __isl_give isl_val *isl_aff_get_constant_val(
2632 __isl_keep isl_aff *aff);
2633 __isl_give isl_val *isl_aff_get_coefficient_val(
2634 __isl_keep isl_aff *aff,
2635 enum isl_dim_type type, int pos);
2636 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2637 enum isl_dim_type type, int pos);
2638 __isl_give isl_val *isl_aff_get_denominator_val(
2639 __isl_keep isl_aff *aff);
2640 __isl_give isl_aff *isl_aff_get_div(
2641 __isl_keep isl_aff *aff, int pos);
2643 They can be modified using the following functions.
2645 #include <isl/aff.h>
2646 __isl_give isl_aff *isl_aff_set_constant_si(
2647 __isl_take isl_aff *aff, int v);
2648 __isl_give isl_aff *isl_aff_set_constant_val(
2649 __isl_take isl_aff *aff, __isl_take isl_val *v);
2650 __isl_give isl_aff *isl_aff_set_coefficient_si(
2651 __isl_take isl_aff *aff,
2652 enum isl_dim_type type, int pos, int v);
2653 __isl_give isl_aff *isl_aff_set_coefficient_val(
2654 __isl_take isl_aff *aff,
2655 enum isl_dim_type type, int pos,
2656 __isl_take isl_val *v);
2658 __isl_give isl_aff *isl_aff_add_constant_si(
2659 __isl_take isl_aff *aff, int v);
2660 __isl_give isl_aff *isl_aff_add_constant_val(
2661 __isl_take isl_aff *aff, __isl_take isl_val *v);
2662 __isl_give isl_aff *isl_aff_add_constant_num_si(
2663 __isl_take isl_aff *aff, int v);
2664 __isl_give isl_aff *isl_aff_add_coefficient_si(
2665 __isl_take isl_aff *aff,
2666 enum isl_dim_type type, int pos, int v);
2667 __isl_give isl_aff *isl_aff_add_coefficient_val(
2668 __isl_take isl_aff *aff,
2669 enum isl_dim_type type, int pos,
2670 __isl_take isl_val *v);
2672 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2673 set the I<numerator> of the constant or coefficient, while
2674 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2675 the constant or coefficient as a whole.
2676 The C<add_constant> and C<add_coefficient> functions add an integer
2677 or rational value to
2678 the possibly rational constant or coefficient.
2679 The C<add_constant_num> functions add an integer value to
2682 =item * Quasipolynomials
2684 Some simple quasipolynomials can be created using the following functions.
2686 #include <isl/polynomial.h>
2687 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2688 __isl_take isl_space *domain);
2689 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2690 __isl_take isl_space *domain);
2691 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2692 __isl_take isl_space *domain);
2693 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2694 __isl_take isl_space *domain);
2695 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2696 __isl_take isl_space *domain);
2697 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2698 __isl_take isl_space *domain,
2699 __isl_take isl_val *val);
2700 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2701 __isl_take isl_space *domain,
2702 enum isl_dim_type type, unsigned pos);
2703 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2704 __isl_take isl_aff *aff);
2706 Recall that the space in which a quasipolynomial lives is a map space
2707 with a one-dimensional range. The C<domain> argument in some of
2708 the functions above corresponds to the domain of this map space.
2710 Quasipolynomials can be copied and freed again using the following
2713 #include <isl/polynomial.h>
2714 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2715 __isl_keep isl_qpolynomial *qp);
2716 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2717 __isl_take isl_qpolynomial *qp);
2719 The constant term of a quasipolynomial can be extracted using
2721 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2722 __isl_keep isl_qpolynomial *qp);
2724 To iterate over all terms in a quasipolynomial,
2727 isl_stat isl_qpolynomial_foreach_term(
2728 __isl_keep isl_qpolynomial *qp,
2729 isl_stat (*fn)(__isl_take isl_term *term,
2730 void *user), void *user);
2732 The terms themselves can be inspected and freed using
2735 unsigned isl_term_dim(__isl_keep isl_term *term,
2736 enum isl_dim_type type);
2737 __isl_give isl_val *isl_term_get_coefficient_val(
2738 __isl_keep isl_term *term);
2739 int isl_term_get_exp(__isl_keep isl_term *term,
2740 enum isl_dim_type type, unsigned pos);
2741 __isl_give isl_aff *isl_term_get_div(
2742 __isl_keep isl_term *term, unsigned pos);
2743 void isl_term_free(__isl_take isl_term *term);
2745 Each term is a product of parameters, set variables and
2746 integer divisions. The function C<isl_term_get_exp>
2747 returns the exponent of a given dimensions in the given term.
2753 A reduction represents a maximum or a minimum of its
2755 The only reduction type defined by C<isl> is
2756 C<isl_qpolynomial_fold>.
2758 There are currently no functions to directly create such
2759 objects, but they do appear in the piecewise quasipolynomial
2760 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2762 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2764 Reductions can be copied and freed using
2765 the following functions.
2767 #include <isl/polynomial.h>
2768 __isl_give isl_qpolynomial_fold *
2769 isl_qpolynomial_fold_copy(
2770 __isl_keep isl_qpolynomial_fold *fold);
2771 void isl_qpolynomial_fold_free(
2772 __isl_take isl_qpolynomial_fold *fold);
2774 To iterate over all quasipolynomials in a reduction, use
2776 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2777 __isl_keep isl_qpolynomial_fold *fold,
2778 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2779 void *user), void *user);
2781 =head3 Multiple Expressions
2783 A multiple expression represents a sequence of zero or
2784 more base expressions, all defined on the same domain space.
2785 The domain space of the multiple expression is the same
2786 as that of the base expressions, but the range space
2787 can be any space. In case the base expressions have
2788 a set space, the corresponding multiple expression
2789 also has a set space.
2790 Objects of the value type do not have an associated space.
2791 The space of a multiple value is therefore always a set space.
2792 Similarly, the space of a multiple union piecewise
2793 affine expression is always a set space.
2794 If the base expressions are not total, then
2795 a corresponding zero-dimensional multiple expression may
2796 have an explicit domain that keeps track of the domain
2797 outside of any base expressions.
2799 The multiple expression types defined by C<isl>
2800 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2801 C<isl_multi_union_pw_aff>.
2803 A multiple expression with the value zero for
2804 each output (or set) dimension can be created
2805 using the following functions.
2807 #include <isl/val.h>
2808 __isl_give isl_multi_val *isl_multi_val_zero(
2809 __isl_take isl_space *space);
2811 #include <isl/aff.h>
2812 __isl_give isl_multi_aff *isl_multi_aff_zero(
2813 __isl_take isl_space *space);
2814 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2815 __isl_take isl_space *space);
2816 __isl_give isl_multi_union_pw_aff *
2817 isl_multi_union_pw_aff_zero(
2818 __isl_take isl_space *space);
2820 Since there is no canonical way of representing a zero
2821 value of type C<isl_union_pw_aff>, the space passed
2822 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2824 An identity function can be created using the following
2825 functions. The space needs to be that of a relation
2826 with the same number of input and output dimensions.
2828 #include <isl/aff.h>
2829 __isl_give isl_multi_aff *isl_multi_aff_identity(
2830 __isl_take isl_space *space);
2831 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2832 __isl_take isl_space *space);
2834 A function that performs a projection on a universe
2835 relation or set can be created using the following functions.
2836 See also the corresponding
2837 projection operations in L</"Unary Operations">.
2839 #include <isl/aff.h>
2840 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2841 __isl_take isl_space *space);
2842 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2843 __isl_take isl_space *space);
2844 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2845 __isl_take isl_space *space,
2846 enum isl_dim_type type,
2847 unsigned first, unsigned n);
2849 A multiple expression can be created from a single
2850 base expression using the following functions.
2851 The space of the created multiple expression is the same
2852 as that of the base expression, except for
2853 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2854 lives in a parameter space and the output lives
2855 in a single-dimensional set space.
2857 #include <isl/aff.h>
2858 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2859 __isl_take isl_aff *aff);
2860 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2861 __isl_take isl_pw_aff *pa);
2862 __isl_give isl_multi_union_pw_aff *
2863 isl_multi_union_pw_aff_from_union_pw_aff(
2864 __isl_take isl_union_pw_aff *upa);
2866 A multiple expression can be created from a list
2867 of base expression in a specified space.
2868 The domain of this space needs to be the same
2869 as the domains of the base expressions in the list.
2870 If the base expressions have a set space (or no associated space),
2871 then this space also needs to be a set space.
2873 #include <isl/val.h>
2874 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2875 __isl_take isl_space *space,
2876 __isl_take isl_val_list *list);
2878 #include <isl/aff.h>
2879 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2880 __isl_take isl_space *space,
2881 __isl_take isl_aff_list *list);
2882 __isl_give isl_multi_pw_aff *
2883 isl_multi_pw_aff_from_pw_aff_list(
2884 __isl_take isl_space *space,
2885 __isl_take isl_pw_aff_list *list);
2886 __isl_give isl_multi_union_pw_aff *
2887 isl_multi_union_pw_aff_from_union_pw_aff_list(
2888 __isl_take isl_space *space,
2889 __isl_take isl_union_pw_aff_list *list);
2891 As a convenience, a multiple piecewise expression can
2892 also be created from a multiple expression.
2893 Each piecewise expression in the result has a single
2896 #include <isl/aff.h>
2897 __isl_give isl_multi_pw_aff *
2898 isl_multi_pw_aff_from_multi_aff(
2899 __isl_take isl_multi_aff *ma);
2901 Similarly, a multiple union expression can be
2902 created from a multiple expression.
2904 #include <isl/aff.h>
2905 __isl_give isl_multi_union_pw_aff *
2906 isl_multi_union_pw_aff_from_multi_aff(
2907 __isl_take isl_multi_aff *ma);
2908 __isl_give isl_multi_union_pw_aff *
2909 isl_multi_union_pw_aff_from_multi_pw_aff(
2910 __isl_take isl_multi_pw_aff *mpa);
2912 A multiple quasi-affine expression can be created from
2913 a multiple value with a given domain space using the following
2916 #include <isl/aff.h>
2917 __isl_give isl_multi_aff *
2918 isl_multi_aff_multi_val_on_space(
2919 __isl_take isl_space *space,
2920 __isl_take isl_multi_val *mv);
2923 a multiple union piecewise affine expression can be created from
2924 a multiple value with a given domain or
2925 a (piecewise) multiple affine expression with a given domain
2926 using the following functions.
2928 #include <isl/aff.h>
2929 __isl_give isl_multi_union_pw_aff *
2930 isl_multi_union_pw_aff_multi_val_on_domain(
2931 __isl_take isl_union_set *domain,
2932 __isl_take isl_multi_val *mv);
2933 __isl_give isl_multi_union_pw_aff *
2934 isl_multi_union_pw_aff_multi_aff_on_domain(
2935 __isl_take isl_union_set *domain,
2936 __isl_take isl_multi_aff *ma);
2937 __isl_give isl_multi_union_pw_aff *
2938 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2939 __isl_take isl_union_set *domain,
2940 __isl_take isl_pw_multi_aff *pma);
2942 Multiple expressions can be copied and freed using
2943 the following functions.
2945 #include <isl/val.h>
2946 __isl_give isl_multi_val *isl_multi_val_copy(
2947 __isl_keep isl_multi_val *mv);
2948 __isl_null isl_multi_val *isl_multi_val_free(
2949 __isl_take isl_multi_val *mv);
2951 #include <isl/aff.h>
2952 __isl_give isl_multi_aff *isl_multi_aff_copy(
2953 __isl_keep isl_multi_aff *maff);
2954 __isl_null isl_multi_aff *isl_multi_aff_free(
2955 __isl_take isl_multi_aff *maff);
2956 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2957 __isl_keep isl_multi_pw_aff *mpa);
2958 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2959 __isl_take isl_multi_pw_aff *mpa);
2960 __isl_give isl_multi_union_pw_aff *
2961 isl_multi_union_pw_aff_copy(
2962 __isl_keep isl_multi_union_pw_aff *mupa);
2963 __isl_null isl_multi_union_pw_aff *
2964 isl_multi_union_pw_aff_free(
2965 __isl_take isl_multi_union_pw_aff *mupa);
2967 The base expression at a given position of a multiple
2968 expression can be extracted using the following functions.
2970 #include <isl/val.h>
2971 __isl_give isl_val *isl_multi_val_get_val(
2972 __isl_keep isl_multi_val *mv, int pos);
2974 #include <isl/aff.h>
2975 __isl_give isl_aff *isl_multi_aff_get_aff(
2976 __isl_keep isl_multi_aff *multi, int pos);
2977 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2978 __isl_keep isl_multi_pw_aff *mpa, int pos);
2979 __isl_give isl_union_pw_aff *
2980 isl_multi_union_pw_aff_get_union_pw_aff(
2981 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2983 It can be replaced using the following functions.
2985 #include <isl/val.h>
2986 __isl_give isl_multi_val *isl_multi_val_set_val(
2987 __isl_take isl_multi_val *mv, int pos,
2988 __isl_take isl_val *val);
2990 #include <isl/aff.h>
2991 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2992 __isl_take isl_multi_aff *multi, int pos,
2993 __isl_take isl_aff *aff);
2994 __isl_give isl_multi_union_pw_aff *
2995 isl_multi_union_pw_aff_set_union_pw_aff(
2996 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2997 __isl_take isl_union_pw_aff *upa);
2999 As a convenience, a sequence of base expressions that have
3000 their domains in a given space can be extracted from a sequence
3001 of union expressions using the following function.
3003 #include <isl/aff.h>
3004 __isl_give isl_multi_pw_aff *
3005 isl_multi_union_pw_aff_extract_multi_pw_aff(
3006 __isl_keep isl_multi_union_pw_aff *mupa,
3007 __isl_take isl_space *space);
3009 Note that there is a difference between C<isl_multi_union_pw_aff>
3010 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3011 of unions of piecewise expressions, while the second is a union
3012 of piecewise sequences. In particular, multiple affine expressions
3013 in an C<isl_union_pw_multi_aff> may live in different spaces,
3014 while there is only a single multiple expression in
3015 an C<isl_multi_union_pw_aff>, which can therefore only live
3016 in a single space. This means that not every
3017 C<isl_union_pw_multi_aff> can be converted to
3018 an C<isl_multi_union_pw_aff>. Conversely, the elements
3019 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3020 while each multiple expression inside an C<isl_union_pw_multi_aff>
3021 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3022 of dimension greater than one may therefore not be exact.
3023 The following functions can
3024 be used to perform these conversions when they are possible.
3026 #include <isl/aff.h>
3027 __isl_give isl_multi_union_pw_aff *
3028 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3029 __isl_take isl_union_pw_multi_aff *upma);
3030 __isl_give isl_union_pw_multi_aff *
3031 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3032 __isl_take isl_multi_union_pw_aff *mupa);
3034 =head3 Piecewise Expressions
3036 A piecewise expression is an expression that is described
3037 using zero or more base expression defined over the same
3038 number of cells in the domain space of the base expressions.
3039 All base expressions are defined over the same
3040 domain space and the cells are disjoint.
3041 The space of a piecewise expression is the same as
3042 that of the base expressions.
3043 If the union of the cells is a strict subset of the domain
3044 space, then the value of the piecewise expression outside
3045 this union is different for types derived from quasi-affine
3046 expressions and those derived from quasipolynomials.
3047 Piecewise expressions derived from quasi-affine expressions
3048 are considered to be undefined outside the union of their cells.
3049 Piecewise expressions derived from quasipolynomials
3050 are considered to be zero outside the union of their cells.
3052 Piecewise quasipolynomials are mainly used by the C<barvinok>
3053 library for representing the number of elements in a parametric set or map.
3054 For example, the piecewise quasipolynomial
3056 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3058 represents the number of points in the map
3060 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3062 The piecewise expression types defined by C<isl>
3063 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3064 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3066 A piecewise expression with no cells can be created using
3067 the following functions.
3069 #include <isl/aff.h>
3070 __isl_give isl_pw_aff *isl_pw_aff_empty(
3071 __isl_take isl_space *space);
3072 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3073 __isl_take isl_space *space);
3075 A piecewise expression with a single universe cell can be
3076 created using the following functions.
3078 #include <isl/aff.h>
3079 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3080 __isl_take isl_aff *aff);
3081 __isl_give isl_pw_multi_aff *
3082 isl_pw_multi_aff_from_multi_aff(
3083 __isl_take isl_multi_aff *ma);
3085 #include <isl/polynomial.h>
3086 __isl_give isl_pw_qpolynomial *
3087 isl_pw_qpolynomial_from_qpolynomial(
3088 __isl_take isl_qpolynomial *qp);
3090 A piecewise expression with a single specified cell can be
3091 created using the following functions.
3093 #include <isl/aff.h>
3094 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3095 __isl_take isl_set *set, __isl_take isl_aff *aff);
3096 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3097 __isl_take isl_set *set,
3098 __isl_take isl_multi_aff *maff);
3100 #include <isl/polynomial.h>
3101 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3102 __isl_take isl_set *set,
3103 __isl_take isl_qpolynomial *qp);
3105 The following convenience functions first create a base expression and
3106 then create a piecewise expression over a universe domain.
3108 #include <isl/aff.h>
3109 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3110 __isl_take isl_local_space *ls);
3111 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3112 __isl_take isl_local_space *ls,
3113 enum isl_dim_type type, unsigned pos);
3114 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3115 __isl_take isl_local_space *ls);
3116 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3117 __isl_take isl_space *space);
3118 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3119 __isl_take isl_space *space);
3120 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3121 __isl_take isl_space *space);
3122 __isl_give isl_pw_multi_aff *
3123 isl_pw_multi_aff_project_out_map(
3124 __isl_take isl_space *space,
3125 enum isl_dim_type type,
3126 unsigned first, unsigned n);
3128 #include <isl/polynomial.h>
3129 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3130 __isl_take isl_space *space);
3132 The following convenience functions first create a base expression and
3133 then create a piecewise expression over a given domain.
3135 #include <isl/aff.h>
3136 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3137 __isl_take isl_set *domain,
3138 __isl_take isl_val *v);
3139 __isl_give isl_pw_multi_aff *
3140 isl_pw_multi_aff_multi_val_on_domain(
3141 __isl_take isl_set *domain,
3142 __isl_take isl_multi_val *mv);
3144 As a convenience, a piecewise multiple expression can
3145 also be created from a piecewise expression.
3146 Each multiple expression in the result is derived
3147 from the corresponding base expression.
3149 #include <isl/aff.h>
3150 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3151 __isl_take isl_pw_aff *pa);
3153 Similarly, a piecewise quasipolynomial can be
3154 created from a piecewise quasi-affine expression using
3155 the following function.
3157 #include <isl/polynomial.h>
3158 __isl_give isl_pw_qpolynomial *
3159 isl_pw_qpolynomial_from_pw_aff(
3160 __isl_take isl_pw_aff *pwaff);
3162 Piecewise expressions can be copied and freed using the following functions.
3164 #include <isl/aff.h>
3165 __isl_give isl_pw_aff *isl_pw_aff_copy(
3166 __isl_keep isl_pw_aff *pwaff);
3167 __isl_null isl_pw_aff *isl_pw_aff_free(
3168 __isl_take isl_pw_aff *pwaff);
3169 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3170 __isl_keep isl_pw_multi_aff *pma);
3171 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3172 __isl_take isl_pw_multi_aff *pma);
3174 #include <isl/polynomial.h>
3175 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3176 __isl_keep isl_pw_qpolynomial *pwqp);
3177 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3178 __isl_take isl_pw_qpolynomial *pwqp);
3179 __isl_give isl_pw_qpolynomial_fold *
3180 isl_pw_qpolynomial_fold_copy(
3181 __isl_keep isl_pw_qpolynomial_fold *pwf);
3182 __isl_null isl_pw_qpolynomial_fold *
3183 isl_pw_qpolynomial_fold_free(
3184 __isl_take isl_pw_qpolynomial_fold *pwf);
3186 To iterate over the different cells of a piecewise expression,
3187 use the following functions.
3189 #include <isl/aff.h>
3190 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3191 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3192 isl_stat isl_pw_aff_foreach_piece(
3193 __isl_keep isl_pw_aff *pwaff,
3194 isl_stat (*fn)(__isl_take isl_set *set,
3195 __isl_take isl_aff *aff,
3196 void *user), void *user);
3197 int isl_pw_multi_aff_n_piece(
3198 __isl_keep isl_pw_multi_aff *pma);
3199 isl_stat isl_pw_multi_aff_foreach_piece(
3200 __isl_keep isl_pw_multi_aff *pma,
3201 isl_stat (*fn)(__isl_take isl_set *set,
3202 __isl_take isl_multi_aff *maff,
3203 void *user), void *user);
3205 #include <isl/polynomial.h>
3206 int isl_pw_qpolynomial_n_piece(
3207 __isl_keep isl_pw_qpolynomial *pwqp);
3208 isl_stat isl_pw_qpolynomial_foreach_piece(
3209 __isl_keep isl_pw_qpolynomial *pwqp,
3210 isl_stat (*fn)(__isl_take isl_set *set,
3211 __isl_take isl_qpolynomial *qp,
3212 void *user), void *user);
3213 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3214 __isl_keep isl_pw_qpolynomial *pwqp,
3215 isl_stat (*fn)(__isl_take isl_set *set,
3216 __isl_take isl_qpolynomial *qp,
3217 void *user), void *user);
3218 int isl_pw_qpolynomial_fold_n_piece(
3219 __isl_keep isl_pw_qpolynomial_fold *pwf);
3220 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3221 __isl_keep isl_pw_qpolynomial_fold *pwf,
3222 isl_stat (*fn)(__isl_take isl_set *set,
3223 __isl_take isl_qpolynomial_fold *fold,
3224 void *user), void *user);
3225 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3226 __isl_keep isl_pw_qpolynomial_fold *pwf,
3227 isl_stat (*fn)(__isl_take isl_set *set,
3228 __isl_take isl_qpolynomial_fold *fold,
3229 void *user), void *user);
3231 As usual, the function C<fn> should return C<isl_stat_ok> on success
3232 and C<isl_stat_error> on failure. The difference between
3233 C<isl_pw_qpolynomial_foreach_piece> and
3234 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3235 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3236 compute unique representations for all existentially quantified
3237 variables and then turn these existentially quantified variables
3238 into extra set variables, adapting the associated quasipolynomial
3239 accordingly. This means that the C<set> passed to C<fn>
3240 will not have any existentially quantified variables, but that
3241 the dimensions of the sets may be different for different
3242 invocations of C<fn>.
3243 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3244 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3246 A piecewise expression consisting of the expressions at a given
3247 position of a piecewise multiple expression can be extracted
3248 using the following function.
3250 #include <isl/aff.h>
3251 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3252 __isl_keep isl_pw_multi_aff *pma, int pos);
3254 These expressions can be replaced using the following function.
3256 #include <isl/aff.h>
3257 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3258 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3259 __isl_take isl_pw_aff *pa);
3261 Note that there is a difference between C<isl_multi_pw_aff> and
3262 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3263 affine expressions, while the second is a piecewise sequence
3264 of affine expressions. In particular, each of the piecewise
3265 affine expressions in an C<isl_multi_pw_aff> may have a different
3266 domain, while all multiple expressions associated to a cell
3267 in an C<isl_pw_multi_aff> have the same domain.
3268 It is possible to convert between the two, but when converting
3269 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3270 of the result is the intersection of the domains of the input.
3271 The reverse conversion is exact.
3273 #include <isl/aff.h>
3274 __isl_give isl_pw_multi_aff *
3275 isl_pw_multi_aff_from_multi_pw_aff(
3276 __isl_take isl_multi_pw_aff *mpa);
3277 __isl_give isl_multi_pw_aff *
3278 isl_multi_pw_aff_from_pw_multi_aff(
3279 __isl_take isl_pw_multi_aff *pma);
3281 =head3 Union Expressions
3283 A union expression collects base expressions defined
3284 over different domains. The space of a union expression
3285 is that of the shared parameter space.
3287 The union expression types defined by C<isl>
3288 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3289 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3291 C<isl_union_pw_aff>,
3292 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3293 there can be at most one base expression for a given domain space.
3295 C<isl_union_pw_multi_aff>,
3296 there can be multiple such expressions for a given domain space,
3297 but the domains of these expressions need to be disjoint.
3299 An empty union expression can be created using the following functions.
3301 #include <isl/aff.h>
3302 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3303 __isl_take isl_space *space);
3304 __isl_give isl_union_pw_multi_aff *
3305 isl_union_pw_multi_aff_empty(
3306 __isl_take isl_space *space);
3308 #include <isl/polynomial.h>
3309 __isl_give isl_union_pw_qpolynomial *
3310 isl_union_pw_qpolynomial_zero(
3311 __isl_take isl_space *space);
3313 A union expression containing a single base expression
3314 can be created using the following functions.
3316 #include <isl/aff.h>
3317 __isl_give isl_union_pw_aff *
3318 isl_union_pw_aff_from_pw_aff(
3319 __isl_take isl_pw_aff *pa);
3320 __isl_give isl_union_pw_multi_aff *
3321 isl_union_pw_multi_aff_from_aff(
3322 __isl_take isl_aff *aff);
3323 __isl_give isl_union_pw_multi_aff *
3324 isl_union_pw_multi_aff_from_pw_multi_aff(
3325 __isl_take isl_pw_multi_aff *pma);
3327 #include <isl/polynomial.h>
3328 __isl_give isl_union_pw_qpolynomial *
3329 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3330 __isl_take isl_pw_qpolynomial *pwqp);
3332 The following functions create a base expression on each
3333 of the sets in the union set and collect the results.
3335 #include <isl/aff.h>
3336 __isl_give isl_union_pw_multi_aff *
3337 isl_union_pw_multi_aff_from_union_pw_aff(
3338 __isl_take isl_union_pw_aff *upa);
3339 __isl_give isl_union_pw_aff *
3340 isl_union_pw_multi_aff_get_union_pw_aff(
3341 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3342 __isl_give isl_union_pw_aff *
3343 isl_union_pw_aff_val_on_domain(
3344 __isl_take isl_union_set *domain,
3345 __isl_take isl_val *v);
3346 __isl_give isl_union_pw_multi_aff *
3347 isl_union_pw_multi_aff_multi_val_on_domain(
3348 __isl_take isl_union_set *domain,
3349 __isl_take isl_multi_val *mv);
3350 __isl_give isl_union_pw_aff *
3351 isl_union_pw_aff_param_on_domain_id(
3352 __isl_take isl_union_set *domain,
3353 __isl_take isl_id *id);
3355 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3356 is the identifier of a parameter that may or may not already
3357 be present in C<domain>.
3359 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3361 expression on a given domain can be created using the following
3364 #include <isl/aff.h>
3365 __isl_give isl_union_pw_aff *
3366 isl_union_pw_aff_aff_on_domain(
3367 __isl_take isl_union_set *domain,
3368 __isl_take isl_aff *aff);
3369 __isl_give isl_union_pw_aff *
3370 isl_union_pw_aff_pw_aff_on_domain(
3371 __isl_take isl_union_set *domain,
3372 __isl_take isl_pw_aff *pa);
3374 A base expression can be added to a union expression using
3375 the following functions.
3377 #include <isl/aff.h>
3378 __isl_give isl_union_pw_aff *
3379 isl_union_pw_aff_add_pw_aff(
3380 __isl_take isl_union_pw_aff *upa,
3381 __isl_take isl_pw_aff *pa);
3382 __isl_give isl_union_pw_multi_aff *
3383 isl_union_pw_multi_aff_add_pw_multi_aff(
3384 __isl_take isl_union_pw_multi_aff *upma,
3385 __isl_take isl_pw_multi_aff *pma);
3387 #include <isl/polynomial.h>
3388 __isl_give isl_union_pw_qpolynomial *
3389 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3390 __isl_take isl_union_pw_qpolynomial *upwqp,
3391 __isl_take isl_pw_qpolynomial *pwqp);
3393 Union expressions can be copied and freed using
3394 the following functions.
3396 #include <isl/aff.h>
3397 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3398 __isl_keep isl_union_pw_aff *upa);
3399 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3400 __isl_take isl_union_pw_aff *upa);
3401 __isl_give isl_union_pw_multi_aff *
3402 isl_union_pw_multi_aff_copy(
3403 __isl_keep isl_union_pw_multi_aff *upma);
3404 __isl_null isl_union_pw_multi_aff *
3405 isl_union_pw_multi_aff_free(
3406 __isl_take isl_union_pw_multi_aff *upma);
3408 #include <isl/polynomial.h>
3409 __isl_give isl_union_pw_qpolynomial *
3410 isl_union_pw_qpolynomial_copy(
3411 __isl_keep isl_union_pw_qpolynomial *upwqp);
3412 __isl_null isl_union_pw_qpolynomial *
3413 isl_union_pw_qpolynomial_free(
3414 __isl_take isl_union_pw_qpolynomial *upwqp);
3415 __isl_give isl_union_pw_qpolynomial_fold *
3416 isl_union_pw_qpolynomial_fold_copy(
3417 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3418 __isl_null isl_union_pw_qpolynomial_fold *
3419 isl_union_pw_qpolynomial_fold_free(
3420 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3422 To iterate over the base expressions in a union expression,
3423 use the following functions.
3425 #include <isl/aff.h>
3426 int isl_union_pw_aff_n_pw_aff(
3427 __isl_keep isl_union_pw_aff *upa);
3428 isl_stat isl_union_pw_aff_foreach_pw_aff(
3429 __isl_keep isl_union_pw_aff *upa,
3430 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3431 void *user), void *user);
3432 int isl_union_pw_multi_aff_n_pw_multi_aff(
3433 __isl_keep isl_union_pw_multi_aff *upma);
3434 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3435 __isl_keep isl_union_pw_multi_aff *upma,
3436 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3437 void *user), void *user);
3439 #include <isl/polynomial.h>
3440 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3441 __isl_keep isl_union_pw_qpolynomial *upwqp);
3442 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3443 __isl_keep isl_union_pw_qpolynomial *upwqp,
3444 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3445 void *user), void *user);
3446 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3447 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3448 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3449 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3450 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3451 void *user), void *user);
3453 To extract the base expression in a given space from a union, use
3454 the following functions.
3456 #include <isl/aff.h>
3457 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3458 __isl_keep isl_union_pw_aff *upa,
3459 __isl_take isl_space *space);
3460 __isl_give isl_pw_multi_aff *
3461 isl_union_pw_multi_aff_extract_pw_multi_aff(
3462 __isl_keep isl_union_pw_multi_aff *upma,
3463 __isl_take isl_space *space);
3465 #include <isl/polynomial.h>
3466 __isl_give isl_pw_qpolynomial *
3467 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3468 __isl_keep isl_union_pw_qpolynomial *upwqp,
3469 __isl_take isl_space *space);
3471 It is also possible to obtain a list of the base expressions using
3472 the following functions.
3474 #include <isl/aff.h>
3475 __isl_give isl_pw_aff_list *
3476 isl_union_pw_aff_get_pw_aff_list(
3477 __isl_keep isl_union_pw_aff *upa);
3478 __isl_give isl_pw_multi_aff_list *
3479 isl_union_pw_multi_aff_get_pw_multi_aff_list(
3480 __isl_keep isl_union_pw_multi_aff *upma);
3482 #include <isl/polynomial.h>
3483 __isl_give isl_pw_qpolynomial_list *
3484 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
3485 __isl_keep isl_union_pw_qpolynomial *upwqp);
3486 __isl_give isl_pw_qpolynomial_fold_list *
3487 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
3488 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3490 The returned list can be manipulated using the functions in L<"Lists">.
3492 =head2 Input and Output
3494 For set and relation,
3495 C<isl> supports its own input/output format, which is similar
3496 to the C<Omega> format, but also supports the C<PolyLib> format
3498 For other object types, typically only an C<isl> format is supported.
3500 =head3 C<isl> format
3502 The C<isl> format is similar to that of C<Omega>, but has a different
3503 syntax for describing the parameters and allows for the definition
3504 of an existentially quantified variable as the integer division
3505 of an affine expression.
3506 For example, the set of integers C<i> between C<0> and C<n>
3507 such that C<i % 10 <= 6> can be described as
3509 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3512 A set or relation can have several disjuncts, separated
3513 by the keyword C<or>. Each disjunct is either a conjunction
3514 of constraints or a projection (C<exists>) of a conjunction
3515 of constraints. The constraints are separated by the keyword
3518 =head3 C<PolyLib> format
3520 If the represented set is a union, then the first line
3521 contains a single number representing the number of disjuncts.
3522 Otherwise, a line containing the number C<1> is optional.
3524 Each disjunct is represented by a matrix of constraints.
3525 The first line contains two numbers representing
3526 the number of rows and columns,
3527 where the number of rows is equal to the number of constraints
3528 and the number of columns is equal to two plus the number of variables.
3529 The following lines contain the actual rows of the constraint matrix.
3530 In each row, the first column indicates whether the constraint
3531 is an equality (C<0>) or inequality (C<1>). The final column
3532 corresponds to the constant term.
3534 If the set is parametric, then the coefficients of the parameters
3535 appear in the last columns before the constant column.
3536 The coefficients of any existentially quantified variables appear
3537 between those of the set variables and those of the parameters.
3539 =head3 Extended C<PolyLib> format
3541 The extended C<PolyLib> format is nearly identical to the
3542 C<PolyLib> format. The only difference is that the line
3543 containing the number of rows and columns of a constraint matrix
3544 also contains four additional numbers:
3545 the number of output dimensions, the number of input dimensions,
3546 the number of local dimensions (i.e., the number of existentially
3547 quantified variables) and the number of parameters.
3548 For sets, the number of ``output'' dimensions is equal
3549 to the number of set dimensions, while the number of ``input''
3554 Objects can be read from input using the following functions.
3556 #include <isl/val.h>
3557 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3559 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3560 isl_ctx *ctx, const char *str);
3562 #include <isl/set.h>
3563 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3564 isl_ctx *ctx, FILE *input);
3565 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3566 isl_ctx *ctx, const char *str);
3567 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3569 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3572 #include <isl/map.h>
3573 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3574 isl_ctx *ctx, FILE *input);
3575 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3576 isl_ctx *ctx, const char *str);
3577 __isl_give isl_map *isl_map_read_from_file(
3578 isl_ctx *ctx, FILE *input);
3579 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3582 #include <isl/union_set.h>
3583 __isl_give isl_union_set *isl_union_set_read_from_file(
3584 isl_ctx *ctx, FILE *input);
3585 __isl_give isl_union_set *isl_union_set_read_from_str(
3586 isl_ctx *ctx, const char *str);
3588 #include <isl/union_map.h>
3589 __isl_give isl_union_map *isl_union_map_read_from_file(
3590 isl_ctx *ctx, FILE *input);
3591 __isl_give isl_union_map *isl_union_map_read_from_str(
3592 isl_ctx *ctx, const char *str);
3594 #include <isl/aff.h>
3595 __isl_give isl_aff *isl_aff_read_from_str(
3596 isl_ctx *ctx, const char *str);
3597 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3598 isl_ctx *ctx, const char *str);
3599 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3600 isl_ctx *ctx, const char *str);
3601 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3602 isl_ctx *ctx, const char *str);
3603 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3604 isl_ctx *ctx, const char *str);
3605 __isl_give isl_union_pw_aff *
3606 isl_union_pw_aff_read_from_str(
3607 isl_ctx *ctx, const char *str);
3608 __isl_give isl_union_pw_multi_aff *
3609 isl_union_pw_multi_aff_read_from_str(
3610 isl_ctx *ctx, const char *str);
3611 __isl_give isl_multi_union_pw_aff *
3612 isl_multi_union_pw_aff_read_from_str(
3613 isl_ctx *ctx, const char *str);
3615 #include <isl/polynomial.h>
3616 __isl_give isl_union_pw_qpolynomial *
3617 isl_union_pw_qpolynomial_read_from_str(
3618 isl_ctx *ctx, const char *str);
3620 For sets and relations,
3621 the input format is autodetected and may be either the C<PolyLib> format
3622 or the C<isl> format.
3626 Before anything can be printed, an C<isl_printer> needs to
3629 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3631 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3632 __isl_null isl_printer *isl_printer_free(
3633 __isl_take isl_printer *printer);
3635 C<isl_printer_to_file> prints to the given file, while
3636 C<isl_printer_to_str> prints to a string that can be extracted
3637 using the following function.
3639 #include <isl/printer.h>
3640 __isl_give char *isl_printer_get_str(
3641 __isl_keep isl_printer *printer);
3643 The printer can be inspected using the following functions.
3645 FILE *isl_printer_get_file(
3646 __isl_keep isl_printer *printer);
3647 int isl_printer_get_output_format(
3648 __isl_keep isl_printer *p);
3649 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3651 The behavior of the printer can be modified in various ways
3653 __isl_give isl_printer *isl_printer_set_output_format(
3654 __isl_take isl_printer *p, int output_format);
3655 __isl_give isl_printer *isl_printer_set_indent(
3656 __isl_take isl_printer *p, int indent);
3657 __isl_give isl_printer *isl_printer_set_indent_prefix(
3658 __isl_take isl_printer *p, const char *prefix);
3659 __isl_give isl_printer *isl_printer_indent(
3660 __isl_take isl_printer *p, int indent);
3661 __isl_give isl_printer *isl_printer_set_prefix(
3662 __isl_take isl_printer *p, const char *prefix);
3663 __isl_give isl_printer *isl_printer_set_suffix(
3664 __isl_take isl_printer *p, const char *suffix);
3665 __isl_give isl_printer *isl_printer_set_yaml_style(
3666 __isl_take isl_printer *p, int yaml_style);
3668 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3669 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3670 and defaults to C<ISL_FORMAT_ISL>.
3671 Each line in the output is prefixed by C<indent_prefix>,
3672 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3673 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3674 In the C<PolyLib> format output,
3675 the coefficients of the existentially quantified variables
3676 appear between those of the set variables and those
3678 The function C<isl_printer_indent> increases the indentation
3679 by the specified amount (which may be negative).
3680 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3681 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3684 To actually print something, use
3686 #include <isl/printer.h>
3687 __isl_give isl_printer *isl_printer_print_double(
3688 __isl_take isl_printer *p, double d);
3690 #include <isl/val.h>
3691 __isl_give isl_printer *isl_printer_print_val(
3692 __isl_take isl_printer *p, __isl_keep isl_val *v);
3694 #include <isl/set.h>
3695 __isl_give isl_printer *isl_printer_print_basic_set(
3696 __isl_take isl_printer *printer,
3697 __isl_keep isl_basic_set *bset);
3698 __isl_give isl_printer *isl_printer_print_set(
3699 __isl_take isl_printer *printer,
3700 __isl_keep isl_set *set);
3702 #include <isl/map.h>
3703 __isl_give isl_printer *isl_printer_print_basic_map(
3704 __isl_take isl_printer *printer,
3705 __isl_keep isl_basic_map *bmap);
3706 __isl_give isl_printer *isl_printer_print_map(
3707 __isl_take isl_printer *printer,
3708 __isl_keep isl_map *map);
3710 #include <isl/union_set.h>
3711 __isl_give isl_printer *isl_printer_print_union_set(
3712 __isl_take isl_printer *p,
3713 __isl_keep isl_union_set *uset);
3715 #include <isl/union_map.h>
3716 __isl_give isl_printer *isl_printer_print_union_map(
3717 __isl_take isl_printer *p,
3718 __isl_keep isl_union_map *umap);
3720 #include <isl/val.h>
3721 __isl_give isl_printer *isl_printer_print_multi_val(
3722 __isl_take isl_printer *p,
3723 __isl_keep isl_multi_val *mv);
3725 #include <isl/aff.h>
3726 __isl_give isl_printer *isl_printer_print_aff(
3727 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3728 __isl_give isl_printer *isl_printer_print_multi_aff(
3729 __isl_take isl_printer *p,
3730 __isl_keep isl_multi_aff *maff);
3731 __isl_give isl_printer *isl_printer_print_pw_aff(
3732 __isl_take isl_printer *p,
3733 __isl_keep isl_pw_aff *pwaff);
3734 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3735 __isl_take isl_printer *p,
3736 __isl_keep isl_pw_multi_aff *pma);
3737 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3738 __isl_take isl_printer *p,
3739 __isl_keep isl_multi_pw_aff *mpa);
3740 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3741 __isl_take isl_printer *p,
3742 __isl_keep isl_union_pw_aff *upa);
3743 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3744 __isl_take isl_printer *p,
3745 __isl_keep isl_union_pw_multi_aff *upma);
3746 __isl_give isl_printer *
3747 isl_printer_print_multi_union_pw_aff(
3748 __isl_take isl_printer *p,
3749 __isl_keep isl_multi_union_pw_aff *mupa);
3751 #include <isl/polynomial.h>
3752 __isl_give isl_printer *isl_printer_print_qpolynomial(
3753 __isl_take isl_printer *p,
3754 __isl_keep isl_qpolynomial *qp);
3755 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3756 __isl_take isl_printer *p,
3757 __isl_keep isl_pw_qpolynomial *pwqp);
3758 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3759 __isl_take isl_printer *p,
3760 __isl_keep isl_union_pw_qpolynomial *upwqp);
3762 __isl_give isl_printer *
3763 isl_printer_print_pw_qpolynomial_fold(
3764 __isl_take isl_printer *p,
3765 __isl_keep isl_pw_qpolynomial_fold *pwf);
3766 __isl_give isl_printer *
3767 isl_printer_print_union_pw_qpolynomial_fold(
3768 __isl_take isl_printer *p,
3769 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3771 For C<isl_printer_print_qpolynomial>,
3772 C<isl_printer_print_pw_qpolynomial> and
3773 C<isl_printer_print_pw_qpolynomial_fold>,
3774 the output format of the printer
3775 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3776 For C<isl_printer_print_union_pw_qpolynomial> and
3777 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3779 In case of printing in C<ISL_FORMAT_C>, the user may want
3780 to set the names of all dimensions first.
3782 C<isl> also provides limited support for printing YAML documents,
3783 just enough for the internal use for printing such documents.
3785 #include <isl/printer.h>
3786 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3787 __isl_take isl_printer *p);
3788 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3789 __isl_take isl_printer *p);
3790 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3791 __isl_take isl_printer *p);
3792 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3793 __isl_take isl_printer *p);
3794 __isl_give isl_printer *isl_printer_yaml_next(
3795 __isl_take isl_printer *p);
3797 A document is started by a call to either
3798 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3799 Anything printed to the printer after such a call belong to the
3800 first key of the mapping or the first element in the sequence.
3801 The function C<isl_printer_yaml_next> moves to the value if
3802 we are currently printing a mapping key, the next key if we
3803 are printing a value or the next element if we are printing
3804 an element in a sequence.
3805 Nested mappings and sequences are initiated by the same
3806 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3807 Each call to these functions needs to have a corresponding call to
3808 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3810 When called on a file printer, the following function flushes
3811 the file. When called on a string printer, the buffer is cleared.
3813 __isl_give isl_printer *isl_printer_flush(
3814 __isl_take isl_printer *p);
3816 The following functions allow the user to attach
3817 notes to a printer in order to keep track of additional state.
3819 #include <isl/printer.h>
3820 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3821 __isl_keep isl_id *id);
3822 __isl_give isl_id *isl_printer_get_note(
3823 __isl_keep isl_printer *p, __isl_take isl_id *id);
3824 __isl_give isl_printer *isl_printer_set_note(
3825 __isl_take isl_printer *p,
3826 __isl_take isl_id *id, __isl_take isl_id *note);
3828 C<isl_printer_set_note> associates the given note to the given
3829 identifier in the printer.
3830 C<isl_printer_get_note> retrieves a note associated to an
3832 C<isl_printer_has_note> checks if there is such a note.
3833 C<isl_printer_get_note> fails if the requested note does not exist.
3835 Alternatively, a string representation can be obtained
3836 directly using the following functions, which always print
3840 __isl_give char *isl_id_to_str(
3841 __isl_keep isl_id *id);
3843 #include <isl/space.h>
3844 __isl_give char *isl_space_to_str(
3845 __isl_keep isl_space *space);
3847 #include <isl/val.h>
3848 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3849 __isl_give char *isl_multi_val_to_str(
3850 __isl_keep isl_multi_val *mv);
3852 #include <isl/set.h>
3853 __isl_give char *isl_basic_set_to_str(
3854 __isl_keep isl_basic_set *bset);
3855 __isl_give char *isl_set_to_str(
3856 __isl_keep isl_set *set);
3858 #include <isl/union_set.h>
3859 __isl_give char *isl_union_set_to_str(
3860 __isl_keep isl_union_set *uset);
3862 #include <isl/map.h>
3863 __isl_give char *isl_basic_map_to_str(
3864 __isl_keep isl_basic_map *bmap);
3865 __isl_give char *isl_map_to_str(
3866 __isl_keep isl_map *map);
3868 #include <isl/union_map.h>
3869 __isl_give char *isl_union_map_to_str(
3870 __isl_keep isl_union_map *umap);
3872 #include <isl/aff.h>
3873 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3874 __isl_give char *isl_pw_aff_to_str(
3875 __isl_keep isl_pw_aff *pa);
3876 __isl_give char *isl_multi_aff_to_str(
3877 __isl_keep isl_multi_aff *ma);
3878 __isl_give char *isl_pw_multi_aff_to_str(
3879 __isl_keep isl_pw_multi_aff *pma);
3880 __isl_give char *isl_multi_pw_aff_to_str(
3881 __isl_keep isl_multi_pw_aff *mpa);
3882 __isl_give char *isl_union_pw_aff_to_str(
3883 __isl_keep isl_union_pw_aff *upa);
3884 __isl_give char *isl_union_pw_multi_aff_to_str(
3885 __isl_keep isl_union_pw_multi_aff *upma);
3886 __isl_give char *isl_multi_union_pw_aff_to_str(
3887 __isl_keep isl_multi_union_pw_aff *mupa);
3889 #include <isl/point.h>
3890 __isl_give char *isl_point_to_str(
3891 __isl_keep isl_point *pnt);
3893 #include <isl/polynomial.h>
3894 __isl_give char *isl_pw_qpolynomial_to_str(
3895 __isl_keep isl_pw_qpolynomial *pwqp);
3896 __isl_give char *isl_union_pw_qpolynomial_to_str(
3897 __isl_keep isl_union_pw_qpolynomial *upwqp);
3901 =head3 Unary Properties
3907 The following functions test whether the given set or relation
3908 contains any integer points. The ``plain'' variants do not perform
3909 any computations, but simply check if the given set or relation
3910 is already known to be empty.
3912 #include <isl/set.h>
3913 isl_bool isl_basic_set_plain_is_empty(
3914 __isl_keep isl_basic_set *bset);
3915 isl_bool isl_basic_set_is_empty(
3916 __isl_keep isl_basic_set *bset);
3917 isl_bool isl_set_plain_is_empty(
3918 __isl_keep isl_set *set);
3919 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3921 #include <isl/union_set.h>
3922 isl_bool isl_union_set_is_empty(
3923 __isl_keep isl_union_set *uset);
3925 #include <isl/map.h>
3926 isl_bool isl_basic_map_plain_is_empty(
3927 __isl_keep isl_basic_map *bmap);
3928 isl_bool isl_basic_map_is_empty(
3929 __isl_keep isl_basic_map *bmap);
3930 isl_bool isl_map_plain_is_empty(
3931 __isl_keep isl_map *map);
3932 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3934 #include <isl/union_map.h>
3935 isl_bool isl_union_map_plain_is_empty(
3936 __isl_keep isl_union_map *umap);
3937 isl_bool isl_union_map_is_empty(
3938 __isl_keep isl_union_map *umap);
3940 =item * Universality
3942 isl_bool isl_basic_set_plain_is_universe(
3943 __isl_keep isl_basic_set *bset);
3944 isl_bool isl_basic_set_is_universe(
3945 __isl_keep isl_basic_set *bset);
3946 isl_bool isl_basic_map_plain_is_universe(
3947 __isl_keep isl_basic_map *bmap);
3948 isl_bool isl_basic_map_is_universe(
3949 __isl_keep isl_basic_map *bmap);
3950 isl_bool isl_set_plain_is_universe(
3951 __isl_keep isl_set *set);
3952 isl_bool isl_map_plain_is_universe(
3953 __isl_keep isl_map *map);
3955 =item * Single-valuedness
3957 #include <isl/set.h>
3958 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3960 #include <isl/map.h>
3961 isl_bool isl_basic_map_is_single_valued(
3962 __isl_keep isl_basic_map *bmap);
3963 isl_bool isl_map_plain_is_single_valued(
3964 __isl_keep isl_map *map);
3965 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3967 #include <isl/union_map.h>
3968 isl_bool isl_union_map_is_single_valued(
3969 __isl_keep isl_union_map *umap);
3973 isl_bool isl_map_plain_is_injective(
3974 __isl_keep isl_map *map);
3975 isl_bool isl_map_is_injective(
3976 __isl_keep isl_map *map);
3977 isl_bool isl_union_map_plain_is_injective(
3978 __isl_keep isl_union_map *umap);
3979 isl_bool isl_union_map_is_injective(
3980 __isl_keep isl_union_map *umap);
3984 isl_bool isl_map_is_bijective(
3985 __isl_keep isl_map *map);
3986 isl_bool isl_union_map_is_bijective(
3987 __isl_keep isl_union_map *umap);
3991 The following functions test whether the given relation
3992 only maps elements to themselves.
3994 #include <isl/map.h>
3995 isl_bool isl_map_is_identity(
3996 __isl_keep isl_map *map);
3998 #include <isl/union_map.h>
3999 isl_bool isl_union_map_is_identity(
4000 __isl_keep isl_union_map *umap);
4004 __isl_give isl_val *
4005 isl_basic_map_plain_get_val_if_fixed(
4006 __isl_keep isl_basic_map *bmap,
4007 enum isl_dim_type type, unsigned pos);
4008 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4009 __isl_keep isl_set *set,
4010 enum isl_dim_type type, unsigned pos);
4011 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4012 __isl_keep isl_map *map,
4013 enum isl_dim_type type, unsigned pos);
4015 If the set or relation obviously lies on a hyperplane where the given dimension
4016 has a fixed value, then return that value.
4017 Otherwise return NaN.
4021 isl_stat isl_set_dim_residue_class_val(
4022 __isl_keep isl_set *set,
4023 int pos, __isl_give isl_val **modulo,
4024 __isl_give isl_val **residue);
4026 Check if the values of the given set dimension are equal to a fixed
4027 value modulo some integer value. If so, assign the modulo to C<*modulo>
4028 and the fixed value to C<*residue>. If the given dimension attains only
4029 a single value, then assign C<0> to C<*modulo> and the fixed value to
4031 If the dimension does not attain only a single value and if no modulo
4032 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4034 #include <isl/set.h>
4035 __isl_give isl_stride_info *isl_set_get_stride_info(
4036 __isl_keep isl_set *set, int pos);
4037 __isl_give isl_val *isl_set_get_stride(
4038 __isl_keep isl_set *set, int pos);
4040 #include <isl/map.h>
4041 __isl_give isl_stride_info *
4042 isl_map_get_range_stride_info(
4043 __isl_keep isl_map *map, int pos);
4045 Check if the values of the given set dimension are equal to
4046 some affine expression of the other dimensions (the offset)
4047 modulo some integer stride or
4048 check if the values of the given output dimensions are equal to
4049 some affine expression of the input dimensions (the offset)
4050 modulo some integer stride.
4051 If no more specific information can be found, then the stride
4052 is taken to be one and the offset is taken to be the zero expression.
4053 The function C<isl_set_get_stride> performs the same
4054 computation as C<isl_set_get_stride_info> but only returns the stride.
4055 For the other functions,
4056 the stride and offset can be extracted from the returned object
4057 using the following functions.
4059 #include <isl/stride_info.h>
4060 __isl_give isl_val *isl_stride_info_get_stride(
4061 __isl_keep isl_stride_info *si);
4062 __isl_give isl_aff *isl_stride_info_get_offset(
4063 __isl_keep isl_stride_info *si);
4065 The stride info object can be copied and released using the following
4068 #include <isl/stride_info.h>
4069 __isl_give isl_stride_info *isl_stride_info_copy(
4070 __isl_keep isl_stride_info *si);
4071 __isl_null isl_stride_info *isl_stride_info_free(
4072 __isl_take isl_stride_info *si);
4076 To check whether the description of a set, relation or function depends
4077 on one or more given dimensions,
4078 the following functions can be used.
4080 #include <isl/constraint.h>
4081 isl_bool isl_constraint_involves_dims(
4082 __isl_keep isl_constraint *constraint,
4083 enum isl_dim_type type, unsigned first, unsigned n);
4085 #include <isl/set.h>
4086 isl_bool isl_basic_set_involves_dims(
4087 __isl_keep isl_basic_set *bset,
4088 enum isl_dim_type type, unsigned first, unsigned n);
4089 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4090 enum isl_dim_type type, unsigned first, unsigned n);
4092 #include <isl/map.h>
4093 isl_bool isl_basic_map_involves_dims(
4094 __isl_keep isl_basic_map *bmap,
4095 enum isl_dim_type type, unsigned first, unsigned n);
4096 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4097 enum isl_dim_type type, unsigned first, unsigned n);
4099 #include <isl/union_map.h>
4100 isl_bool isl_union_map_involves_dims(
4101 __isl_keep isl_union_map *umap,
4102 enum isl_dim_type type, unsigned first, unsigned n);
4104 #include <isl/aff.h>
4105 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4106 enum isl_dim_type type, unsigned first, unsigned n);
4107 isl_bool isl_pw_aff_involves_dims(
4108 __isl_keep isl_pw_aff *pwaff,
4109 enum isl_dim_type type, unsigned first, unsigned n);
4110 isl_bool isl_multi_aff_involves_dims(
4111 __isl_keep isl_multi_aff *ma,
4112 enum isl_dim_type type, unsigned first, unsigned n);
4113 isl_bool isl_pw_multi_aff_involves_dims(
4114 __isl_keep isl_pw_multi_aff *pma,
4115 enum isl_dim_type type, unsigned first, unsigned n);
4116 isl_bool isl_multi_pw_aff_involves_dims(
4117 __isl_keep isl_multi_pw_aff *mpa,
4118 enum isl_dim_type type, unsigned first, unsigned n);
4120 #include <isl/polynomial.h>
4121 isl_bool isl_qpolynomial_involves_dims(
4122 __isl_keep isl_qpolynomial *qp,
4123 enum isl_dim_type type, unsigned first, unsigned n);
4125 Similarly, the following functions can be used to check whether
4126 a given dimension is involved in any lower or upper bound.
4128 #include <isl/set.h>
4129 isl_bool isl_set_dim_has_any_lower_bound(
4130 __isl_keep isl_set *set,
4131 enum isl_dim_type type, unsigned pos);
4132 isl_bool isl_set_dim_has_any_upper_bound(
4133 __isl_keep isl_set *set,
4134 enum isl_dim_type type, unsigned pos);
4136 Note that these functions return true even if there is a bound on
4137 the dimension on only some of the basic sets of C<set>.
4138 To check if they have a bound for all of the basic sets in C<set>,
4139 use the following functions instead.
4141 #include <isl/set.h>
4142 isl_bool isl_set_dim_has_lower_bound(
4143 __isl_keep isl_set *set,
4144 enum isl_dim_type type, unsigned pos);
4145 isl_bool isl_set_dim_has_upper_bound(
4146 __isl_keep isl_set *set,
4147 enum isl_dim_type type, unsigned pos);
4151 To check whether a set is a parameter domain, use this function:
4153 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4154 isl_bool isl_union_set_is_params(
4155 __isl_keep isl_union_set *uset);
4159 The following functions check whether the space of the given
4160 (basic) set or relation domain and/or range is a wrapped relation.
4162 #include <isl/space.h>
4163 isl_bool isl_space_is_wrapping(
4164 __isl_keep isl_space *space);
4165 isl_bool isl_space_domain_is_wrapping(
4166 __isl_keep isl_space *space);
4167 isl_bool isl_space_range_is_wrapping(
4168 __isl_keep isl_space *space);
4169 isl_bool isl_space_is_product(
4170 __isl_keep isl_space *space);
4172 #include <isl/set.h>
4173 isl_bool isl_basic_set_is_wrapping(
4174 __isl_keep isl_basic_set *bset);
4175 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4177 #include <isl/map.h>
4178 isl_bool isl_map_domain_is_wrapping(
4179 __isl_keep isl_map *map);
4180 isl_bool isl_map_range_is_wrapping(
4181 __isl_keep isl_map *map);
4182 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4184 #include <isl/val.h>
4185 isl_bool isl_multi_val_range_is_wrapping(
4186 __isl_keep isl_multi_val *mv);
4188 #include <isl/aff.h>
4189 isl_bool isl_multi_aff_range_is_wrapping(
4190 __isl_keep isl_multi_aff *ma);
4191 isl_bool isl_multi_pw_aff_range_is_wrapping(
4192 __isl_keep isl_multi_pw_aff *mpa);
4193 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4194 __isl_keep isl_multi_union_pw_aff *mupa);
4196 The input to C<isl_space_is_wrapping> should
4197 be the space of a set, while that of
4198 C<isl_space_domain_is_wrapping> and
4199 C<isl_space_range_is_wrapping> should be the space of a relation.
4200 The input to C<isl_space_is_product> can be either the space
4201 of a set or that of a binary relation.
4202 In case the input is the space of a binary relation, it checks
4203 whether both domain and range are wrapping.
4205 =item * Internal Product
4207 isl_bool isl_basic_map_can_zip(
4208 __isl_keep isl_basic_map *bmap);
4209 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4211 Check whether the product of domain and range of the given relation
4213 i.e., whether both domain and range are nested relations.
4217 #include <isl/space.h>
4218 isl_bool isl_space_can_curry(
4219 __isl_keep isl_space *space);
4221 #include <isl/map.h>
4222 isl_bool isl_basic_map_can_curry(
4223 __isl_keep isl_basic_map *bmap);
4224 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4226 Check whether the domain of the (basic) relation is a wrapped relation.
4228 #include <isl/space.h>
4229 __isl_give isl_space *isl_space_uncurry(
4230 __isl_take isl_space *space);
4232 #include <isl/map.h>
4233 isl_bool isl_basic_map_can_uncurry(
4234 __isl_keep isl_basic_map *bmap);
4235 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4237 Check whether the range of the (basic) relation is a wrapped relation.
4239 #include <isl/space.h>
4240 isl_bool isl_space_can_range_curry(
4241 __isl_keep isl_space *space);
4243 #include <isl/map.h>
4244 isl_bool isl_map_can_range_curry(
4245 __isl_keep isl_map *map);
4247 Check whether the domain of the relation wrapped in the range of
4248 the input is itself a wrapped relation.
4250 =item * Special Values
4252 #include <isl/aff.h>
4253 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4254 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4255 isl_bool isl_multi_pw_aff_is_cst(
4256 __isl_keep isl_multi_pw_aff *mpa);
4258 Check whether the given expression is a constant.
4260 #include <isl/val.h>
4261 isl_bool isl_multi_val_involves_nan(
4262 __isl_keep isl_multi_val *mv);
4264 #include <isl/aff.h>
4265 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4266 isl_bool isl_multi_aff_involves_nan(
4267 __isl_keep isl_multi_aff *ma);
4268 isl_bool isl_pw_aff_involves_nan(
4269 __isl_keep isl_pw_aff *pa);
4270 isl_bool isl_pw_multi_aff_involves_nan(
4271 __isl_keep isl_pw_multi_aff *pma);
4272 isl_bool isl_multi_pw_aff_involves_nan(
4273 __isl_keep isl_multi_pw_aff *mpa);
4274 isl_bool isl_union_pw_aff_involves_nan(
4275 __isl_keep isl_union_pw_aff *upa);
4276 isl_bool isl_union_pw_multi_aff_involves_nan(
4277 __isl_keep isl_union_pw_multi_aff *upma);
4278 isl_bool isl_multi_union_pw_aff_involves_nan(
4279 __isl_keep isl_multi_union_pw_aff *mupa);
4281 #include <isl/polynomial.h>
4282 isl_bool isl_qpolynomial_is_nan(
4283 __isl_keep isl_qpolynomial *qp);
4284 isl_bool isl_qpolynomial_fold_is_nan(
4285 __isl_keep isl_qpolynomial_fold *fold);
4286 isl_bool isl_pw_qpolynomial_involves_nan(
4287 __isl_keep isl_pw_qpolynomial *pwqp);
4288 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4289 __isl_keep isl_pw_qpolynomial_fold *pwf);
4290 isl_bool isl_union_pw_qpolynomial_involves_nan(
4291 __isl_keep isl_union_pw_qpolynomial *upwqp);
4292 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4293 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4295 Check whether the given expression is equal to or involves NaN.
4297 #include <isl/aff.h>
4298 isl_bool isl_aff_plain_is_zero(
4299 __isl_keep isl_aff *aff);
4301 Check whether the affine expression is obviously zero.
4305 =head3 Binary Properties
4311 The following functions check whether two objects
4312 represent the same set, relation or function.
4313 The C<plain> variants only return true if the objects
4314 are obviously the same. That is, they may return false
4315 even if the objects are the same, but they will never
4316 return true if the objects are not the same.
4318 #include <isl/set.h>
4319 isl_bool isl_basic_set_plain_is_equal(
4320 __isl_keep isl_basic_set *bset1,
4321 __isl_keep isl_basic_set *bset2);
4322 isl_bool isl_basic_set_is_equal(
4323 __isl_keep isl_basic_set *bset1,
4324 __isl_keep isl_basic_set *bset2);
4325 isl_bool isl_set_plain_is_equal(
4326 __isl_keep isl_set *set1,
4327 __isl_keep isl_set *set2);
4328 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4329 __isl_keep isl_set *set2);
4331 #include <isl/map.h>
4332 isl_bool isl_basic_map_is_equal(
4333 __isl_keep isl_basic_map *bmap1,
4334 __isl_keep isl_basic_map *bmap2);
4335 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4336 __isl_keep isl_map *map2);
4337 isl_bool isl_map_plain_is_equal(
4338 __isl_keep isl_map *map1,
4339 __isl_keep isl_map *map2);
4341 #include <isl/union_set.h>
4342 isl_bool isl_union_set_is_equal(
4343 __isl_keep isl_union_set *uset1,
4344 __isl_keep isl_union_set *uset2);
4346 #include <isl/union_map.h>
4347 isl_bool isl_union_map_is_equal(
4348 __isl_keep isl_union_map *umap1,
4349 __isl_keep isl_union_map *umap2);
4351 #include <isl/val.h>
4352 isl_bool isl_multi_val_plain_is_equal(
4353 __isl_keep isl_multi_val *mv1,
4354 __isl_keep isl_multi_val *mv2);
4356 #include <isl/aff.h>
4357 isl_bool isl_aff_plain_is_equal(
4358 __isl_keep isl_aff *aff1,
4359 __isl_keep isl_aff *aff2);
4360 isl_bool isl_multi_aff_plain_is_equal(
4361 __isl_keep isl_multi_aff *maff1,
4362 __isl_keep isl_multi_aff *maff2);
4363 isl_bool isl_pw_aff_plain_is_equal(
4364 __isl_keep isl_pw_aff *pwaff1,
4365 __isl_keep isl_pw_aff *pwaff2);
4366 isl_bool isl_pw_aff_is_equal(
4367 __isl_keep isl_pw_aff *pa1,
4368 __isl_keep isl_pw_aff *pa2);
4369 isl_bool isl_pw_multi_aff_plain_is_equal(
4370 __isl_keep isl_pw_multi_aff *pma1,
4371 __isl_keep isl_pw_multi_aff *pma2);
4372 isl_bool isl_pw_multi_aff_is_equal(
4373 __isl_keep isl_pw_multi_aff *pma1,
4374 __isl_keep isl_pw_multi_aff *pma2);
4375 isl_bool isl_multi_pw_aff_plain_is_equal(
4376 __isl_keep isl_multi_pw_aff *mpa1,
4377 __isl_keep isl_multi_pw_aff *mpa2);
4378 isl_bool isl_multi_pw_aff_is_equal(
4379 __isl_keep isl_multi_pw_aff *mpa1,
4380 __isl_keep isl_multi_pw_aff *mpa2);
4381 isl_bool isl_union_pw_aff_plain_is_equal(
4382 __isl_keep isl_union_pw_aff *upa1,
4383 __isl_keep isl_union_pw_aff *upa2);
4384 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4385 __isl_keep isl_union_pw_multi_aff *upma1,
4386 __isl_keep isl_union_pw_multi_aff *upma2);
4387 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4388 __isl_keep isl_multi_union_pw_aff *mupa1,
4389 __isl_keep isl_multi_union_pw_aff *mupa2);
4391 #include <isl/polynomial.h>
4392 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4393 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4394 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4395 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4396 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4397 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4399 =item * Disjointness
4401 #include <isl/set.h>
4402 isl_bool isl_basic_set_is_disjoint(
4403 __isl_keep isl_basic_set *bset1,
4404 __isl_keep isl_basic_set *bset2);
4405 isl_bool isl_set_plain_is_disjoint(
4406 __isl_keep isl_set *set1,
4407 __isl_keep isl_set *set2);
4408 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4409 __isl_keep isl_set *set2);
4411 #include <isl/map.h>
4412 isl_bool isl_basic_map_is_disjoint(
4413 __isl_keep isl_basic_map *bmap1,
4414 __isl_keep isl_basic_map *bmap2);
4415 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4416 __isl_keep isl_map *map2);
4418 #include <isl/union_set.h>
4419 isl_bool isl_union_set_is_disjoint(
4420 __isl_keep isl_union_set *uset1,
4421 __isl_keep isl_union_set *uset2);
4423 #include <isl/union_map.h>
4424 isl_bool isl_union_map_is_disjoint(
4425 __isl_keep isl_union_map *umap1,
4426 __isl_keep isl_union_map *umap2);
4430 isl_bool isl_basic_set_is_subset(
4431 __isl_keep isl_basic_set *bset1,
4432 __isl_keep isl_basic_set *bset2);
4433 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4434 __isl_keep isl_set *set2);
4435 isl_bool isl_set_is_strict_subset(
4436 __isl_keep isl_set *set1,
4437 __isl_keep isl_set *set2);
4438 isl_bool isl_union_set_is_subset(
4439 __isl_keep isl_union_set *uset1,
4440 __isl_keep isl_union_set *uset2);
4441 isl_bool isl_union_set_is_strict_subset(
4442 __isl_keep isl_union_set *uset1,
4443 __isl_keep isl_union_set *uset2);
4444 isl_bool isl_basic_map_is_subset(
4445 __isl_keep isl_basic_map *bmap1,
4446 __isl_keep isl_basic_map *bmap2);
4447 isl_bool isl_basic_map_is_strict_subset(
4448 __isl_keep isl_basic_map *bmap1,
4449 __isl_keep isl_basic_map *bmap2);
4450 isl_bool isl_map_is_subset(
4451 __isl_keep isl_map *map1,
4452 __isl_keep isl_map *map2);
4453 isl_bool isl_map_is_strict_subset(
4454 __isl_keep isl_map *map1,
4455 __isl_keep isl_map *map2);
4456 isl_bool isl_union_map_is_subset(
4457 __isl_keep isl_union_map *umap1,
4458 __isl_keep isl_union_map *umap2);
4459 isl_bool isl_union_map_is_strict_subset(
4460 __isl_keep isl_union_map *umap1,
4461 __isl_keep isl_union_map *umap2);
4463 Check whether the first argument is a (strict) subset of the
4468 Every comparison function returns a negative value if the first
4469 argument is considered smaller than the second, a positive value
4470 if the first argument is considered greater and zero if the two
4471 constraints are considered the same by the comparison criterion.
4473 #include <isl/constraint.h>
4474 int isl_constraint_plain_cmp(
4475 __isl_keep isl_constraint *c1,
4476 __isl_keep isl_constraint *c2);
4478 This function is useful for sorting C<isl_constraint>s.
4479 The order depends on the internal representation of the inputs.
4480 The order is fixed over different calls to the function (assuming
4481 the internal representation of the inputs has not changed), but may
4482 change over different versions of C<isl>.
4484 #include <isl/constraint.h>
4485 int isl_constraint_cmp_last_non_zero(
4486 __isl_keep isl_constraint *c1,
4487 __isl_keep isl_constraint *c2);
4489 This function can be used to sort constraints that live in the same
4490 local space. Constraints that involve ``earlier'' dimensions or
4491 that have a smaller coefficient for the shared latest dimension
4492 are considered smaller than other constraints.
4493 This function only defines a B<partial> order.
4495 #include <isl/set.h>
4496 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4497 __isl_keep isl_set *set2);
4499 This function is useful for sorting C<isl_set>s.
4500 The order depends on the internal representation of the inputs.
4501 The order is fixed over different calls to the function (assuming
4502 the internal representation of the inputs has not changed), but may
4503 change over different versions of C<isl>.
4505 #include <isl/aff.h>
4506 int isl_multi_aff_plain_cmp(
4507 __isl_keep isl_multi_aff *ma1,
4508 __isl_keep isl_multi_aff *ma2);
4509 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4510 __isl_keep isl_pw_aff *pa2);
4512 The functions C<isl_multi_aff_plain_cmp> and
4513 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4514 C<isl_pw_aff>s. The order is not strictly defined.
4515 The current order sorts expressions that only involve
4516 earlier dimensions before those that involve later dimensions.
4520 =head2 Unary Operations
4526 __isl_give isl_set *isl_set_complement(
4527 __isl_take isl_set *set);
4528 __isl_give isl_map *isl_map_complement(
4529 __isl_take isl_map *map);
4533 #include <isl/space.h>
4534 __isl_give isl_space *isl_space_reverse(
4535 __isl_take isl_space *space);
4537 #include <isl/map.h>
4538 __isl_give isl_basic_map *isl_basic_map_reverse(
4539 __isl_take isl_basic_map *bmap);
4540 __isl_give isl_map *isl_map_reverse(
4541 __isl_take isl_map *map);
4543 #include <isl/union_map.h>
4544 __isl_give isl_union_map *isl_union_map_reverse(
4545 __isl_take isl_union_map *umap);
4549 #include <isl/space.h>
4550 __isl_give isl_space *isl_space_domain(
4551 __isl_take isl_space *space);
4552 __isl_give isl_space *isl_space_range(
4553 __isl_take isl_space *space);
4554 __isl_give isl_space *isl_space_params(
4555 __isl_take isl_space *space);
4557 #include <isl/local_space.h>
4558 __isl_give isl_local_space *isl_local_space_domain(
4559 __isl_take isl_local_space *ls);
4560 __isl_give isl_local_space *isl_local_space_range(
4561 __isl_take isl_local_space *ls);
4563 #include <isl/set.h>
4564 __isl_give isl_basic_set *isl_basic_set_project_out(
4565 __isl_take isl_basic_set *bset,
4566 enum isl_dim_type type, unsigned first, unsigned n);
4567 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4568 enum isl_dim_type type, unsigned first, unsigned n);
4569 __isl_give isl_map *isl_set_project_onto_map(
4570 __isl_take isl_set *set,
4571 enum isl_dim_type type, unsigned first,
4573 __isl_give isl_basic_set *isl_basic_set_params(
4574 __isl_take isl_basic_set *bset);
4575 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4577 The function C<isl_set_project_onto_map> returns a relation
4578 that projects the input set onto the given set dimensions.
4580 #include <isl/map.h>
4581 __isl_give isl_basic_map *isl_basic_map_project_out(
4582 __isl_take isl_basic_map *bmap,
4583 enum isl_dim_type type, unsigned first, unsigned n);
4584 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4585 enum isl_dim_type type, unsigned first, unsigned n);
4586 __isl_give isl_basic_set *isl_basic_map_domain(
4587 __isl_take isl_basic_map *bmap);
4588 __isl_give isl_basic_set *isl_basic_map_range(
4589 __isl_take isl_basic_map *bmap);
4590 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4591 __isl_give isl_set *isl_map_domain(
4592 __isl_take isl_map *bmap);
4593 __isl_give isl_set *isl_map_range(
4594 __isl_take isl_map *map);
4596 #include <isl/union_set.h>
4597 __isl_give isl_union_set *isl_union_set_project_out(
4598 __isl_take isl_union_set *uset,
4599 enum isl_dim_type type,
4600 unsigned first, unsigned n);
4601 __isl_give isl_set *isl_union_set_params(
4602 __isl_take isl_union_set *uset);
4604 The function C<isl_union_set_project_out> can only project out
4607 #include <isl/union_map.h>
4608 __isl_give isl_union_map *isl_union_map_project_out(
4609 __isl_take isl_union_map *umap,
4610 enum isl_dim_type type, unsigned first, unsigned n);
4611 __isl_give isl_union_map *
4612 isl_union_map_project_out_all_params(
4613 __isl_take isl_union_map *umap);
4614 __isl_give isl_set *isl_union_map_params(
4615 __isl_take isl_union_map *umap);
4616 __isl_give isl_union_set *isl_union_map_domain(
4617 __isl_take isl_union_map *umap);
4618 __isl_give isl_union_set *isl_union_map_range(
4619 __isl_take isl_union_map *umap);
4621 The function C<isl_union_map_project_out> can only project out
4624 #include <isl/aff.h>
4625 __isl_give isl_aff *isl_aff_project_domain_on_params(
4626 __isl_take isl_aff *aff);
4627 __isl_give isl_multi_aff *
4628 isl_multi_aff_project_domain_on_params(
4629 __isl_take isl_multi_aff *ma);
4630 __isl_give isl_pw_aff *
4631 isl_pw_aff_project_domain_on_params(
4632 __isl_take isl_pw_aff *pa);
4633 __isl_give isl_multi_pw_aff *
4634 isl_multi_pw_aff_project_domain_on_params(
4635 __isl_take isl_multi_pw_aff *mpa);
4636 __isl_give isl_pw_multi_aff *
4637 isl_pw_multi_aff_project_domain_on_params(
4638 __isl_take isl_pw_multi_aff *pma);
4639 __isl_give isl_set *isl_pw_aff_domain(
4640 __isl_take isl_pw_aff *pwaff);
4641 __isl_give isl_set *isl_pw_multi_aff_domain(
4642 __isl_take isl_pw_multi_aff *pma);
4643 __isl_give isl_set *isl_multi_pw_aff_domain(
4644 __isl_take isl_multi_pw_aff *mpa);
4645 __isl_give isl_union_set *isl_union_pw_aff_domain(
4646 __isl_take isl_union_pw_aff *upa);
4647 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4648 __isl_take isl_union_pw_multi_aff *upma);
4649 __isl_give isl_union_set *
4650 isl_multi_union_pw_aff_domain(
4651 __isl_take isl_multi_union_pw_aff *mupa);
4652 __isl_give isl_set *isl_pw_aff_params(
4653 __isl_take isl_pw_aff *pwa);
4655 If no explicit domain was set on a zero-dimensional input to
4656 C<isl_multi_union_pw_aff_domain>, then this function will
4657 return a parameter set.
4659 #include <isl/polynomial.h>
4660 __isl_give isl_qpolynomial *
4661 isl_qpolynomial_project_domain_on_params(
4662 __isl_take isl_qpolynomial *qp);
4663 __isl_give isl_pw_qpolynomial *
4664 isl_pw_qpolynomial_project_domain_on_params(
4665 __isl_take isl_pw_qpolynomial *pwqp);
4666 __isl_give isl_pw_qpolynomial_fold *
4667 isl_pw_qpolynomial_fold_project_domain_on_params(
4668 __isl_take isl_pw_qpolynomial_fold *pwf);
4669 __isl_give isl_set *isl_pw_qpolynomial_domain(
4670 __isl_take isl_pw_qpolynomial *pwqp);
4671 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4672 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4673 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4674 __isl_take isl_union_pw_qpolynomial *upwqp);
4676 #include <isl/space.h>
4677 __isl_give isl_space *isl_space_domain_map(
4678 __isl_take isl_space *space);
4679 __isl_give isl_space *isl_space_range_map(
4680 __isl_take isl_space *space);
4682 #include <isl/map.h>
4683 __isl_give isl_map *isl_set_wrapped_domain_map(
4684 __isl_take isl_set *set);
4685 __isl_give isl_basic_map *isl_basic_map_domain_map(
4686 __isl_take isl_basic_map *bmap);
4687 __isl_give isl_basic_map *isl_basic_map_range_map(
4688 __isl_take isl_basic_map *bmap);
4689 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4690 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4692 #include <isl/union_map.h>
4693 __isl_give isl_union_map *isl_union_map_domain_map(
4694 __isl_take isl_union_map *umap);
4695 __isl_give isl_union_pw_multi_aff *
4696 isl_union_map_domain_map_union_pw_multi_aff(
4697 __isl_take isl_union_map *umap);
4698 __isl_give isl_union_map *isl_union_map_range_map(
4699 __isl_take isl_union_map *umap);
4700 __isl_give isl_union_map *
4701 isl_union_set_wrapped_domain_map(
4702 __isl_take isl_union_set *uset);
4704 The functions above construct a (basic, regular or union) relation
4705 that maps (a wrapped version of) the input relation to its domain or range.
4706 C<isl_set_wrapped_domain_map> maps the input set to the domain
4707 of its wrapped relation.
4711 __isl_give isl_basic_set *isl_basic_set_eliminate(
4712 __isl_take isl_basic_set *bset,
4713 enum isl_dim_type type,
4714 unsigned first, unsigned n);
4715 __isl_give isl_set *isl_set_eliminate(
4716 __isl_take isl_set *set, enum isl_dim_type type,
4717 unsigned first, unsigned n);
4718 __isl_give isl_basic_map *isl_basic_map_eliminate(
4719 __isl_take isl_basic_map *bmap,
4720 enum isl_dim_type type,
4721 unsigned first, unsigned n);
4722 __isl_give isl_map *isl_map_eliminate(
4723 __isl_take isl_map *map, enum isl_dim_type type,
4724 unsigned first, unsigned n);
4726 Eliminate the coefficients for the given dimensions from the constraints,
4727 without removing the dimensions.
4729 =item * Constructing a set from a parameter domain
4731 A zero-dimensional (local) space or (basic) set can be constructed
4732 on a given parameter domain using the following functions.
4734 #include <isl/space.h>
4735 __isl_give isl_space *isl_space_set_from_params(
4736 __isl_take isl_space *space);
4738 #include <isl/local_space.h>
4739 __isl_give isl_local_space *
4740 isl_local_space_set_from_params(
4741 __isl_take isl_local_space *ls);
4743 #include <isl/set.h>
4744 __isl_give isl_basic_set *isl_basic_set_from_params(
4745 __isl_take isl_basic_set *bset);
4746 __isl_give isl_set *isl_set_from_params(
4747 __isl_take isl_set *set);
4749 =item * Constructing a relation from one or two sets
4751 Create a relation with the given set(s) as domain and/or range.
4752 If only the domain or the range is specified, then
4753 the range or domain of the created relation is a zero-dimensional
4754 flat anonymous space.
4756 #include <isl/space.h>
4757 __isl_give isl_space *isl_space_from_domain(
4758 __isl_take isl_space *space);
4759 __isl_give isl_space *isl_space_from_range(
4760 __isl_take isl_space *space);
4761 __isl_give isl_space *isl_space_map_from_set(
4762 __isl_take isl_space *space);
4763 __isl_give isl_space *isl_space_map_from_domain_and_range(
4764 __isl_take isl_space *domain,
4765 __isl_take isl_space *range);
4767 #include <isl/local_space.h>
4768 __isl_give isl_local_space *isl_local_space_from_domain(
4769 __isl_take isl_local_space *ls);
4771 #include <isl/map.h>
4772 __isl_give isl_map *isl_map_from_domain(
4773 __isl_take isl_set *set);
4774 __isl_give isl_map *isl_map_from_range(
4775 __isl_take isl_set *set);
4777 #include <isl/union_map.h>
4778 __isl_give isl_union_map *isl_union_map_from_domain(
4779 __isl_take isl_union_set *uset);
4780 __isl_give isl_union_map *isl_union_map_from_range(
4781 __isl_take isl_union_set *uset);
4782 __isl_give isl_union_map *
4783 isl_union_map_from_domain_and_range(
4784 __isl_take isl_union_set *domain,
4785 __isl_take isl_union_set *range);
4787 #include <isl/val.h>
4788 __isl_give isl_multi_val *isl_multi_val_from_range(
4789 __isl_take isl_multi_val *mv);
4791 #include <isl/aff.h>
4792 __isl_give isl_aff *isl_aff_from_range(
4793 __isl_take isl_aff *aff);
4794 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4795 __isl_take isl_multi_aff *ma);
4796 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4797 __isl_take isl_pw_aff *pwa);
4798 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4799 __isl_take isl_multi_pw_aff *mpa);
4800 __isl_give isl_multi_union_pw_aff *
4801 isl_multi_union_pw_aff_from_range(
4802 __isl_take isl_multi_union_pw_aff *mupa);
4803 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4804 __isl_take isl_set *set);
4805 __isl_give isl_union_pw_multi_aff *
4806 isl_union_pw_multi_aff_from_domain(
4807 __isl_take isl_union_set *uset);
4809 #include <isl/polynomial.h>
4810 __isl_give isl_pw_qpolynomial *
4811 isl_pw_qpolynomial_from_range(
4812 __isl_take isl_pw_qpolynomial *pwqp);
4813 __isl_give isl_pw_qpolynomial_fold *
4814 isl_pw_qpolynomial_fold_from_range(
4815 __isl_take isl_pw_qpolynomial_fold *pwf);
4819 #include <isl/set.h>
4820 __isl_give isl_basic_set *isl_basic_set_fix_si(
4821 __isl_take isl_basic_set *bset,
4822 enum isl_dim_type type, unsigned pos, int value);
4823 __isl_give isl_basic_set *isl_basic_set_fix_val(
4824 __isl_take isl_basic_set *bset,
4825 enum isl_dim_type type, unsigned pos,
4826 __isl_take isl_val *v);
4827 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4828 enum isl_dim_type type, unsigned pos, int value);
4829 __isl_give isl_set *isl_set_fix_val(
4830 __isl_take isl_set *set,
4831 enum isl_dim_type type, unsigned pos,
4832 __isl_take isl_val *v);
4834 #include <isl/map.h>
4835 __isl_give isl_basic_map *isl_basic_map_fix_si(
4836 __isl_take isl_basic_map *bmap,
4837 enum isl_dim_type type, unsigned pos, int value);
4838 __isl_give isl_basic_map *isl_basic_map_fix_val(
4839 __isl_take isl_basic_map *bmap,
4840 enum isl_dim_type type, unsigned pos,
4841 __isl_take isl_val *v);
4842 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4843 enum isl_dim_type type, unsigned pos, int value);
4844 __isl_give isl_map *isl_map_fix_val(
4845 __isl_take isl_map *map,
4846 enum isl_dim_type type, unsigned pos,
4847 __isl_take isl_val *v);
4849 #include <isl/aff.h>
4850 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4851 __isl_take isl_pw_multi_aff *pma,
4852 enum isl_dim_type type, unsigned pos, int value);
4854 #include <isl/polynomial.h>
4855 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4856 __isl_take isl_pw_qpolynomial *pwqp,
4857 enum isl_dim_type type, unsigned n,
4858 __isl_take isl_val *v);
4859 __isl_give isl_pw_qpolynomial_fold *
4860 isl_pw_qpolynomial_fold_fix_val(
4861 __isl_take isl_pw_qpolynomial_fold *pwf,
4862 enum isl_dim_type type, unsigned n,
4863 __isl_take isl_val *v);
4865 Intersect the set, relation or function domain
4866 with the hyperplane where the given
4867 dimension has the fixed given value.
4869 #include <isl/set.h>
4870 __isl_give isl_basic_set *
4871 isl_basic_set_lower_bound_val(
4872 __isl_take isl_basic_set *bset,
4873 enum isl_dim_type type, unsigned pos,
4874 __isl_take isl_val *value);
4875 __isl_give isl_basic_set *
4876 isl_basic_set_upper_bound_val(
4877 __isl_take isl_basic_set *bset,
4878 enum isl_dim_type type, unsigned pos,
4879 __isl_take isl_val *value);
4880 __isl_give isl_set *isl_set_lower_bound_si(
4881 __isl_take isl_set *set,
4882 enum isl_dim_type type, unsigned pos, int value);
4883 __isl_give isl_set *isl_set_lower_bound_val(
4884 __isl_take isl_set *set,
4885 enum isl_dim_type type, unsigned pos,
4886 __isl_take isl_val *value);
4887 __isl_give isl_set *isl_set_upper_bound_si(
4888 __isl_take isl_set *set,
4889 enum isl_dim_type type, unsigned pos, int value);
4890 __isl_give isl_set *isl_set_upper_bound_val(
4891 __isl_take isl_set *set,
4892 enum isl_dim_type type, unsigned pos,
4893 __isl_take isl_val *value);
4895 #include <isl/map.h>
4896 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4897 __isl_take isl_basic_map *bmap,
4898 enum isl_dim_type type, unsigned pos, int value);
4899 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4900 __isl_take isl_basic_map *bmap,
4901 enum isl_dim_type type, unsigned pos, int value);
4902 __isl_give isl_map *isl_map_lower_bound_si(
4903 __isl_take isl_map *map,
4904 enum isl_dim_type type, unsigned pos, int value);
4905 __isl_give isl_map *isl_map_upper_bound_si(
4906 __isl_take isl_map *map,
4907 enum isl_dim_type type, unsigned pos, int value);
4909 Intersect the set or relation with the half-space where the given
4910 dimension has a value bounded by the fixed given integer value.
4912 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4913 enum isl_dim_type type1, int pos1,
4914 enum isl_dim_type type2, int pos2);
4915 __isl_give isl_basic_map *isl_basic_map_equate(
4916 __isl_take isl_basic_map *bmap,
4917 enum isl_dim_type type1, int pos1,
4918 enum isl_dim_type type2, int pos2);
4919 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4920 enum isl_dim_type type1, int pos1,
4921 enum isl_dim_type type2, int pos2);
4923 Intersect the set or relation with the hyperplane where the given
4924 dimensions are equal to each other.
4926 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4927 enum isl_dim_type type1, int pos1,
4928 enum isl_dim_type type2, int pos2);
4930 Intersect the relation with the hyperplane where the given
4931 dimensions have opposite values.
4933 __isl_give isl_map *isl_map_order_le(
4934 __isl_take isl_map *map,
4935 enum isl_dim_type type1, int pos1,
4936 enum isl_dim_type type2, int pos2);
4937 __isl_give isl_basic_map *isl_basic_map_order_ge(
4938 __isl_take isl_basic_map *bmap,
4939 enum isl_dim_type type1, int pos1,
4940 enum isl_dim_type type2, int pos2);
4941 __isl_give isl_map *isl_map_order_ge(
4942 __isl_take isl_map *map,
4943 enum isl_dim_type type1, int pos1,
4944 enum isl_dim_type type2, int pos2);
4945 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4946 enum isl_dim_type type1, int pos1,
4947 enum isl_dim_type type2, int pos2);
4948 __isl_give isl_basic_map *isl_basic_map_order_gt(
4949 __isl_take isl_basic_map *bmap,
4950 enum isl_dim_type type1, int pos1,
4951 enum isl_dim_type type2, int pos2);
4952 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4953 enum isl_dim_type type1, int pos1,
4954 enum isl_dim_type type2, int pos2);
4956 Intersect the relation with the half-space where the given
4957 dimensions satisfy the given ordering.
4959 #include <isl/union_set.h>
4960 __isl_give isl_union_map *isl_union_map_remove_map_if(
4961 __isl_take isl_union_map *umap,
4962 isl_bool (*fn)(__isl_keep isl_map *map,
4963 void *user), void *user);
4965 This function calls the callback function once for each
4966 pair of spaces for which there are elements in the input.
4967 If the callback returns C<isl_bool_true>, then all those elements
4968 are removed from the result. The only remaining elements in the output
4969 are then those for which the callback returns C<isl_bool_false>.
4973 #include <isl/aff.h>
4974 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4975 __isl_take isl_aff *aff);
4976 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4977 __isl_take isl_aff *aff);
4978 __isl_give isl_set *isl_pw_aff_pos_set(
4979 __isl_take isl_pw_aff *pa);
4980 __isl_give isl_set *isl_pw_aff_nonneg_set(
4981 __isl_take isl_pw_aff *pwaff);
4982 __isl_give isl_set *isl_pw_aff_zero_set(
4983 __isl_take isl_pw_aff *pwaff);
4984 __isl_give isl_set *isl_pw_aff_non_zero_set(
4985 __isl_take isl_pw_aff *pwaff);
4986 __isl_give isl_union_set *
4987 isl_union_pw_aff_zero_union_set(
4988 __isl_take isl_union_pw_aff *upa);
4989 __isl_give isl_union_set *
4990 isl_multi_union_pw_aff_zero_union_set(
4991 __isl_take isl_multi_union_pw_aff *mupa);
4993 The function C<isl_aff_neg_basic_set> returns a basic set
4994 containing those elements in the domain space
4995 of C<aff> where C<aff> is negative.
4996 The function C<isl_pw_aff_nonneg_set> returns a set
4997 containing those elements in the domain
4998 of C<pwaff> where C<pwaff> is non-negative.
4999 The function C<isl_multi_union_pw_aff_zero_union_set>
5000 returns a union set containing those elements
5001 in the domains of its elements where they are all zero.
5005 __isl_give isl_map *isl_set_identity(
5006 __isl_take isl_set *set);
5007 __isl_give isl_union_map *isl_union_set_identity(
5008 __isl_take isl_union_set *uset);
5009 __isl_give isl_union_pw_multi_aff *
5010 isl_union_set_identity_union_pw_multi_aff(
5011 __isl_take isl_union_set *uset);
5013 Construct an identity relation on the given (union) set.
5015 =item * Function Extraction
5017 A piecewise quasi affine expression that is equal to 1 on a set
5018 and 0 outside the set can be created using the following function.
5020 #include <isl/aff.h>
5021 __isl_give isl_pw_aff *isl_set_indicator_function(
5022 __isl_take isl_set *set);
5024 A piecewise multiple quasi affine expression can be extracted
5025 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
5026 and the C<isl_map> is single-valued.
5027 In case of a conversion from an C<isl_union_map>
5028 to an C<isl_union_pw_multi_aff>, these properties need to hold
5029 in each domain space.
5030 A conversion to a C<isl_multi_union_pw_aff> additionally
5031 requires that the input is non-empty and involves only a single
5034 #include <isl/aff.h>
5035 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
5036 __isl_take isl_set *set);
5037 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
5038 __isl_take isl_map *map);
5040 __isl_give isl_union_pw_multi_aff *
5041 isl_union_pw_multi_aff_from_union_set(
5042 __isl_take isl_union_set *uset);
5043 __isl_give isl_union_pw_multi_aff *
5044 isl_union_pw_multi_aff_from_union_map(
5045 __isl_take isl_union_map *umap);
5047 __isl_give isl_multi_union_pw_aff *
5048 isl_multi_union_pw_aff_from_union_map(
5049 __isl_take isl_union_map *umap);
5053 __isl_give isl_basic_set *isl_basic_map_deltas(
5054 __isl_take isl_basic_map *bmap);
5055 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
5056 __isl_give isl_union_set *isl_union_map_deltas(
5057 __isl_take isl_union_map *umap);
5059 These functions return a (basic) set containing the differences
5060 between image elements and corresponding domain elements in the input.
5062 __isl_give isl_basic_map *isl_basic_map_deltas_map(
5063 __isl_take isl_basic_map *bmap);
5064 __isl_give isl_map *isl_map_deltas_map(
5065 __isl_take isl_map *map);
5066 __isl_give isl_union_map *isl_union_map_deltas_map(
5067 __isl_take isl_union_map *umap);
5069 The functions above construct a (basic, regular or union) relation
5070 that maps (a wrapped version of) the input relation to its delta set.
5074 Simplify the representation of a set, relation or functions by trying
5075 to combine pairs of basic sets or relations into a single
5076 basic set or relation.
5078 #include <isl/set.h>
5079 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
5081 #include <isl/map.h>
5082 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5084 #include <isl/union_set.h>
5085 __isl_give isl_union_set *isl_union_set_coalesce(
5086 __isl_take isl_union_set *uset);
5088 #include <isl/union_map.h>
5089 __isl_give isl_union_map *isl_union_map_coalesce(
5090 __isl_take isl_union_map *umap);
5092 #include <isl/aff.h>
5093 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5094 __isl_take isl_pw_aff *pwqp);
5095 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5096 __isl_take isl_pw_multi_aff *pma);
5097 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5098 __isl_take isl_multi_pw_aff *mpa);
5099 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5100 __isl_take isl_union_pw_aff *upa);
5101 __isl_give isl_union_pw_multi_aff *
5102 isl_union_pw_multi_aff_coalesce(
5103 __isl_take isl_union_pw_multi_aff *upma);
5104 __isl_give isl_multi_union_pw_aff *
5105 isl_multi_union_pw_aff_coalesce(
5106 __isl_take isl_multi_union_pw_aff *aff);
5108 #include <isl/polynomial.h>
5109 __isl_give isl_pw_qpolynomial_fold *
5110 isl_pw_qpolynomial_fold_coalesce(
5111 __isl_take isl_pw_qpolynomial_fold *pwf);
5112 __isl_give isl_union_pw_qpolynomial *
5113 isl_union_pw_qpolynomial_coalesce(
5114 __isl_take isl_union_pw_qpolynomial *upwqp);
5115 __isl_give isl_union_pw_qpolynomial_fold *
5116 isl_union_pw_qpolynomial_fold_coalesce(
5117 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5119 One of the methods for combining pairs of basic sets or relations
5120 can result in coefficients that are much larger than those that appear
5121 in the constraints of the input. By default, the coefficients are
5122 not allowed to grow larger, but this can be changed by unsetting
5123 the following option.
5125 isl_stat isl_options_set_coalesce_bounded_wrapping(
5126 isl_ctx *ctx, int val);
5127 int isl_options_get_coalesce_bounded_wrapping(
5130 =item * Detecting equalities
5132 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5133 __isl_take isl_basic_set *bset);
5134 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5135 __isl_take isl_basic_map *bmap);
5136 __isl_give isl_set *isl_set_detect_equalities(
5137 __isl_take isl_set *set);
5138 __isl_give isl_map *isl_map_detect_equalities(
5139 __isl_take isl_map *map);
5140 __isl_give isl_union_set *isl_union_set_detect_equalities(
5141 __isl_take isl_union_set *uset);
5142 __isl_give isl_union_map *isl_union_map_detect_equalities(
5143 __isl_take isl_union_map *umap);
5145 Simplify the representation of a set or relation by detecting implicit
5148 =item * Removing redundant constraints
5150 #include <isl/set.h>
5151 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5152 __isl_take isl_basic_set *bset);
5153 __isl_give isl_set *isl_set_remove_redundancies(
5154 __isl_take isl_set *set);
5156 #include <isl/union_set.h>
5157 __isl_give isl_union_set *
5158 isl_union_set_remove_redundancies(
5159 __isl_take isl_union_set *uset);
5161 #include <isl/map.h>
5162 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5163 __isl_take isl_basic_map *bmap);
5164 __isl_give isl_map *isl_map_remove_redundancies(
5165 __isl_take isl_map *map);
5167 #include <isl/union_map.h>
5168 __isl_give isl_union_map *
5169 isl_union_map_remove_redundancies(
5170 __isl_take isl_union_map *umap);
5174 __isl_give isl_basic_set *isl_set_convex_hull(
5175 __isl_take isl_set *set);
5176 __isl_give isl_basic_map *isl_map_convex_hull(
5177 __isl_take isl_map *map);
5179 If the input set or relation has any existentially quantified
5180 variables, then the result of these operations is currently undefined.
5184 #include <isl/set.h>
5185 __isl_give isl_basic_set *
5186 isl_set_unshifted_simple_hull(
5187 __isl_take isl_set *set);
5188 __isl_give isl_basic_set *isl_set_simple_hull(
5189 __isl_take isl_set *set);
5190 __isl_give isl_basic_set *
5191 isl_set_plain_unshifted_simple_hull(
5192 __isl_take isl_set *set);
5193 __isl_give isl_basic_set *
5194 isl_set_unshifted_simple_hull_from_set_list(
5195 __isl_take isl_set *set,
5196 __isl_take isl_set_list *list);
5198 #include <isl/map.h>
5199 __isl_give isl_basic_map *
5200 isl_map_unshifted_simple_hull(
5201 __isl_take isl_map *map);
5202 __isl_give isl_basic_map *isl_map_simple_hull(
5203 __isl_take isl_map *map);
5204 __isl_give isl_basic_map *
5205 isl_map_plain_unshifted_simple_hull(
5206 __isl_take isl_map *map);
5207 __isl_give isl_basic_map *
5208 isl_map_unshifted_simple_hull_from_map_list(
5209 __isl_take isl_map *map,
5210 __isl_take isl_map_list *list);
5212 #include <isl/union_map.h>
5213 __isl_give isl_union_map *isl_union_map_simple_hull(
5214 __isl_take isl_union_map *umap);
5216 These functions compute a single basic set or relation
5217 that contains the whole input set or relation.
5218 In particular, the output is described by translates
5219 of the constraints describing the basic sets or relations in the input.
5220 In case of C<isl_set_unshifted_simple_hull>, only the original
5221 constraints are used, without any translation.
5222 In case of C<isl_set_plain_unshifted_simple_hull> and
5223 C<isl_map_plain_unshifted_simple_hull>, the result is described
5224 by original constraints that are obviously satisfied
5225 by the entire input set or relation.
5226 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5227 C<isl_map_unshifted_simple_hull_from_map_list>, the
5228 constraints are taken from the elements of the second argument.
5232 (See \autoref{s:simple hull}.)
5238 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5239 __isl_take isl_basic_set *bset);
5240 __isl_give isl_basic_set *isl_set_affine_hull(
5241 __isl_take isl_set *set);
5242 __isl_give isl_union_set *isl_union_set_affine_hull(
5243 __isl_take isl_union_set *uset);
5244 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5245 __isl_take isl_basic_map *bmap);
5246 __isl_give isl_basic_map *isl_map_affine_hull(
5247 __isl_take isl_map *map);
5248 __isl_give isl_union_map *isl_union_map_affine_hull(
5249 __isl_take isl_union_map *umap);
5251 In case of union sets and relations, the affine hull is computed
5254 =item * Polyhedral hull
5256 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5257 __isl_take isl_set *set);
5258 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5259 __isl_take isl_map *map);
5260 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5261 __isl_take isl_union_set *uset);
5262 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5263 __isl_take isl_union_map *umap);
5265 These functions compute a single basic set or relation
5266 not involving any existentially quantified variables
5267 that contains the whole input set or relation.
5268 In case of union sets and relations, the polyhedral hull is computed
5273 #include <isl/map.h>
5274 __isl_give isl_fixed_box *
5275 isl_map_get_range_simple_fixed_box_hull(
5276 __isl_keep isl_map *map);
5278 This function tries to approximate the range of the map by a box of fixed size.
5279 The box is described in terms of an offset living in the same space as
5280 the input map and a size living in the range space. For any element
5281 in the input map, the range value is greater than or equal to
5282 the offset applied to the domain value and the difference with
5283 this offset is strictly smaller than the size.
5284 If no fixed-size approximation of the range can be found,
5285 an I<invalid> box is returned, i.e., one for which
5286 C<isl_fixed_box_is_valid> below returns false.
5288 The validity, the offset and the size of the box can be obtained using
5289 the following functions.
5291 #include <isl/fixed_box.h>
5292 isl_bool isl_fixed_box_is_valid(
5293 __isl_keep isl_fixed_box *box);
5294 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
5295 __isl_keep isl_fixed_box *box);
5296 __isl_give isl_multi_val *isl_fixed_box_get_size(
5297 __isl_keep isl_fixed_box *box);
5299 The box can be copied and freed using the following functions.
5301 #include <isl/fixed_box.h>
5302 __isl_give isl_fixed_box *isl_fixed_box_copy(
5303 __isl_keep isl_fixed_box *box);
5304 __isl_null isl_fixed_box *isl_fixed_box_free(
5305 __isl_take isl_fixed_box *box);
5307 =item * Other approximations
5309 #include <isl/set.h>
5310 __isl_give isl_basic_set *
5311 isl_basic_set_drop_constraints_involving_dims(
5312 __isl_take isl_basic_set *bset,
5313 enum isl_dim_type type,
5314 unsigned first, unsigned n);
5315 __isl_give isl_basic_set *
5316 isl_basic_set_drop_constraints_not_involving_dims(
5317 __isl_take isl_basic_set *bset,
5318 enum isl_dim_type type,
5319 unsigned first, unsigned n);
5320 __isl_give isl_set *
5321 isl_set_drop_constraints_involving_dims(
5322 __isl_take isl_set *set,
5323 enum isl_dim_type type,
5324 unsigned first, unsigned n);
5325 __isl_give isl_set *
5326 isl_set_drop_constraints_not_involving_dims(
5327 __isl_take isl_set *set,
5328 enum isl_dim_type type,
5329 unsigned first, unsigned n);
5331 #include <isl/map.h>
5332 __isl_give isl_basic_map *
5333 isl_basic_map_drop_constraints_involving_dims(
5334 __isl_take isl_basic_map *bmap,
5335 enum isl_dim_type type,
5336 unsigned first, unsigned n);
5337 __isl_give isl_basic_map *
5338 isl_basic_map_drop_constraints_not_involving_dims(
5339 __isl_take isl_basic_map *bmap,
5340 enum isl_dim_type type,
5341 unsigned first, unsigned n);
5342 __isl_give isl_map *
5343 isl_map_drop_constraints_involving_dims(
5344 __isl_take isl_map *map,
5345 enum isl_dim_type type,
5346 unsigned first, unsigned n);
5347 __isl_give isl_map *
5348 isl_map_drop_constraints_not_involving_dims(
5349 __isl_take isl_map *map,
5350 enum isl_dim_type type,
5351 unsigned first, unsigned n);
5353 These functions drop any constraints (not) involving the specified dimensions.
5354 Note that the result depends on the representation of the input.
5356 #include <isl/polynomial.h>
5357 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5358 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5359 __isl_give isl_union_pw_qpolynomial *
5360 isl_union_pw_qpolynomial_to_polynomial(
5361 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5363 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5364 the polynomial will be an overapproximation. If C<sign> is negative,
5365 it will be an underapproximation. If C<sign> is zero, the approximation
5366 will lie somewhere in between.
5370 __isl_give isl_basic_set *isl_basic_set_sample(
5371 __isl_take isl_basic_set *bset);
5372 __isl_give isl_basic_set *isl_set_sample(
5373 __isl_take isl_set *set);
5374 __isl_give isl_basic_map *isl_basic_map_sample(
5375 __isl_take isl_basic_map *bmap);
5376 __isl_give isl_basic_map *isl_map_sample(
5377 __isl_take isl_map *map);
5379 If the input (basic) set or relation is non-empty, then return
5380 a singleton subset of the input. Otherwise, return an empty set.
5382 =item * Optimization
5384 #include <isl/ilp.h>
5385 __isl_give isl_val *isl_basic_set_max_val(
5386 __isl_keep isl_basic_set *bset,
5387 __isl_keep isl_aff *obj);
5388 __isl_give isl_val *isl_set_min_val(
5389 __isl_keep isl_set *set,
5390 __isl_keep isl_aff *obj);
5391 __isl_give isl_val *isl_set_max_val(
5392 __isl_keep isl_set *set,
5393 __isl_keep isl_aff *obj);
5394 __isl_give isl_multi_val *
5395 isl_union_set_min_multi_union_pw_aff(
5396 __isl_keep isl_union_set *set,
5397 __isl_keep isl_multi_union_pw_aff *obj);
5399 Compute the minimum or maximum of the integer affine expression C<obj>
5400 over the points in C<set>, returning the result in C<opt>.
5401 The result is C<NULL> in case of an error, the optimal value in case
5402 there is one, negative infinity or infinity if the problem is unbounded and
5403 NaN if the problem is empty.
5405 #include <isl/ilp.h>
5406 __isl_give isl_val *isl_basic_set_dim_max_val(
5407 __isl_take isl_basic_set *bset, int pos);
5409 Return the maximal value attained by the given set dimension,
5410 independently of the parameter values and of any other dimensions.
5411 The result is C<NULL> in case of an error, the optimal value in case
5412 there is one, infinity if the problem is unbounded and
5413 NaN if the input is empty.
5415 =item * Parametric optimization
5417 __isl_give isl_pw_aff *isl_set_dim_min(
5418 __isl_take isl_set *set, int pos);
5419 __isl_give isl_pw_aff *isl_set_dim_max(
5420 __isl_take isl_set *set, int pos);
5421 __isl_give isl_pw_aff *isl_map_dim_min(
5422 __isl_take isl_map *map, int pos);
5423 __isl_give isl_pw_aff *isl_map_dim_max(
5424 __isl_take isl_map *map, int pos);
5426 Compute the minimum or maximum of the given set or output dimension
5427 as a function of the parameters (and input dimensions), but independently
5428 of the other set or output dimensions.
5429 For lexicographic optimization, see L<"Lexicographic Optimization">.
5433 The following functions compute either the set of (rational) coefficient
5434 values of valid constraints for the given set or the set of (rational)
5435 values satisfying the constraints with coefficients from the given set.
5436 Internally, these two sets of functions perform essentially the
5437 same operations, except that the set of coefficients is assumed to
5438 be a cone, while the set of values may be any polyhedron.
5439 The current implementation is based on the Farkas lemma and
5440 Fourier-Motzkin elimination, but this may change or be made optional
5441 in future. In particular, future implementations may use different
5442 dualization algorithms or skip the elimination step.
5444 #include <isl/set.h>
5445 __isl_give isl_basic_set *isl_basic_set_coefficients(
5446 __isl_take isl_basic_set *bset);
5447 __isl_give isl_basic_set_list *
5448 isl_basic_set_list_coefficients(
5449 __isl_take isl_basic_set_list *list);
5450 __isl_give isl_basic_set *isl_set_coefficients(
5451 __isl_take isl_set *set);
5452 __isl_give isl_union_set *isl_union_set_coefficients(
5453 __isl_take isl_union_set *bset);
5454 __isl_give isl_basic_set *isl_basic_set_solutions(
5455 __isl_take isl_basic_set *bset);
5456 __isl_give isl_basic_set *isl_set_solutions(
5457 __isl_take isl_set *set);
5458 __isl_give isl_union_set *isl_union_set_solutions(
5459 __isl_take isl_union_set *bset);
5463 __isl_give isl_map *isl_map_fixed_power_val(
5464 __isl_take isl_map *map,
5465 __isl_take isl_val *exp);
5466 __isl_give isl_union_map *
5467 isl_union_map_fixed_power_val(
5468 __isl_take isl_union_map *umap,
5469 __isl_take isl_val *exp);
5471 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5472 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5473 of C<map> is computed.
5475 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5477 __isl_give isl_union_map *isl_union_map_power(
5478 __isl_take isl_union_map *umap, int *exact);
5480 Compute a parametric representation for all positive powers I<k> of C<map>.
5481 The result maps I<k> to a nested relation corresponding to the
5482 I<k>th power of C<map>.
5483 The result may be an overapproximation. If the result is known to be exact,
5484 then C<*exact> is set to C<1>.
5486 =item * Transitive closure
5488 __isl_give isl_map *isl_map_transitive_closure(
5489 __isl_take isl_map *map, int *exact);
5490 __isl_give isl_union_map *isl_union_map_transitive_closure(
5491 __isl_take isl_union_map *umap, int *exact);
5493 Compute the transitive closure of C<map>.
5494 The result may be an overapproximation. If the result is known to be exact,
5495 then C<*exact> is set to C<1>.
5497 =item * Reaching path lengths
5499 __isl_give isl_map *isl_map_reaching_path_lengths(
5500 __isl_take isl_map *map, int *exact);
5502 Compute a relation that maps each element in the range of C<map>
5503 to the lengths of all paths composed of edges in C<map> that
5504 end up in the given element.
5505 The result may be an overapproximation. If the result is known to be exact,
5506 then C<*exact> is set to C<1>.
5507 To compute the I<maximal> path length, the resulting relation
5508 should be postprocessed by C<isl_map_lexmax>.
5509 In particular, if the input relation is a dependence relation
5510 (mapping sources to sinks), then the maximal path length corresponds
5511 to the free schedule.
5512 Note, however, that C<isl_map_lexmax> expects the maximum to be
5513 finite, so if the path lengths are unbounded (possibly due to
5514 the overapproximation), then you will get an error message.
5518 #include <isl/space.h>
5519 __isl_give isl_space *isl_space_wrap(
5520 __isl_take isl_space *space);
5521 __isl_give isl_space *isl_space_unwrap(
5522 __isl_take isl_space *space);
5524 #include <isl/local_space.h>
5525 __isl_give isl_local_space *isl_local_space_wrap(
5526 __isl_take isl_local_space *ls);
5528 #include <isl/set.h>
5529 __isl_give isl_basic_map *isl_basic_set_unwrap(
5530 __isl_take isl_basic_set *bset);
5531 __isl_give isl_map *isl_set_unwrap(
5532 __isl_take isl_set *set);
5534 #include <isl/map.h>
5535 __isl_give isl_basic_set *isl_basic_map_wrap(
5536 __isl_take isl_basic_map *bmap);
5537 __isl_give isl_set *isl_map_wrap(
5538 __isl_take isl_map *map);
5540 #include <isl/union_set.h>
5541 __isl_give isl_union_map *isl_union_set_unwrap(
5542 __isl_take isl_union_set *uset);
5544 #include <isl/union_map.h>
5545 __isl_give isl_union_set *isl_union_map_wrap(
5546 __isl_take isl_union_map *umap);
5548 The input to C<isl_space_unwrap> should
5549 be the space of a set, while that of
5550 C<isl_space_wrap> should be the space of a relation.
5551 Conversely, the output of C<isl_space_unwrap> is the space
5552 of a relation, while that of C<isl_space_wrap> is the space of a set.
5556 Remove any internal structure of domain (and range) of the given
5557 set or relation. If there is any such internal structure in the input,
5558 then the name of the space is also removed.
5560 #include <isl/space.h>
5561 __isl_give isl_space *isl_space_flatten_domain(
5562 __isl_take isl_space *space);
5563 __isl_give isl_space *isl_space_flatten_range(
5564 __isl_take isl_space *space);
5566 #include <isl/local_space.h>
5567 __isl_give isl_local_space *
5568 isl_local_space_flatten_domain(
5569 __isl_take isl_local_space *ls);
5570 __isl_give isl_local_space *
5571 isl_local_space_flatten_range(
5572 __isl_take isl_local_space *ls);
5574 #include <isl/set.h>
5575 __isl_give isl_basic_set *isl_basic_set_flatten(
5576 __isl_take isl_basic_set *bset);
5577 __isl_give isl_set *isl_set_flatten(
5578 __isl_take isl_set *set);
5580 #include <isl/map.h>
5581 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5582 __isl_take isl_basic_map *bmap);
5583 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5584 __isl_take isl_basic_map *bmap);
5585 __isl_give isl_map *isl_map_flatten_range(
5586 __isl_take isl_map *map);
5587 __isl_give isl_map *isl_map_flatten_domain(
5588 __isl_take isl_map *map);
5589 __isl_give isl_basic_map *isl_basic_map_flatten(
5590 __isl_take isl_basic_map *bmap);
5591 __isl_give isl_map *isl_map_flatten(
5592 __isl_take isl_map *map);
5594 #include <isl/val.h>
5595 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5596 __isl_take isl_multi_val *mv);
5598 #include <isl/aff.h>
5599 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5600 __isl_take isl_multi_aff *ma);
5601 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5602 __isl_take isl_multi_aff *ma);
5603 __isl_give isl_multi_pw_aff *
5604 isl_multi_pw_aff_flatten_range(
5605 __isl_take isl_multi_pw_aff *mpa);
5606 __isl_give isl_multi_union_pw_aff *
5607 isl_multi_union_pw_aff_flatten_range(
5608 __isl_take isl_multi_union_pw_aff *mupa);
5610 #include <isl/map.h>
5611 __isl_give isl_map *isl_set_flatten_map(
5612 __isl_take isl_set *set);
5614 The function above constructs a relation
5615 that maps the input set to a flattened version of the set.
5619 Lift the input set to a space with extra dimensions corresponding
5620 to the existentially quantified variables in the input.
5621 In particular, the result lives in a wrapped map where the domain
5622 is the original space and the range corresponds to the original
5623 existentially quantified variables.
5625 #include <isl/set.h>
5626 __isl_give isl_basic_set *isl_basic_set_lift(
5627 __isl_take isl_basic_set *bset);
5628 __isl_give isl_set *isl_set_lift(
5629 __isl_take isl_set *set);
5630 __isl_give isl_union_set *isl_union_set_lift(
5631 __isl_take isl_union_set *uset);
5633 Given a local space that contains the existentially quantified
5634 variables of a set, a basic relation that, when applied to
5635 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5636 can be constructed using the following function.
5638 #include <isl/local_space.h>
5639 __isl_give isl_basic_map *isl_local_space_lifting(
5640 __isl_take isl_local_space *ls);
5642 #include <isl/aff.h>
5643 __isl_give isl_multi_aff *isl_multi_aff_lift(
5644 __isl_take isl_multi_aff *maff,
5645 __isl_give isl_local_space **ls);
5647 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5648 then it is assigned the local space that lies at the basis of
5649 the lifting applied.
5651 =item * Internal Product
5653 #include <isl/space.h>
5654 __isl_give isl_space *isl_space_zip(
5655 __isl_take isl_space *space);
5657 #include <isl/map.h>
5658 __isl_give isl_basic_map *isl_basic_map_zip(
5659 __isl_take isl_basic_map *bmap);
5660 __isl_give isl_map *isl_map_zip(
5661 __isl_take isl_map *map);
5663 #include <isl/union_map.h>
5664 __isl_give isl_union_map *isl_union_map_zip(
5665 __isl_take isl_union_map *umap);
5667 Given a relation with nested relations for domain and range,
5668 interchange the range of the domain with the domain of the range.
5672 #include <isl/space.h>
5673 __isl_give isl_space *isl_space_curry(
5674 __isl_take isl_space *space);
5675 __isl_give isl_space *isl_space_uncurry(
5676 __isl_take isl_space *space);
5678 #include <isl/map.h>
5679 __isl_give isl_basic_map *isl_basic_map_curry(
5680 __isl_take isl_basic_map *bmap);
5681 __isl_give isl_basic_map *isl_basic_map_uncurry(
5682 __isl_take isl_basic_map *bmap);
5683 __isl_give isl_map *isl_map_curry(
5684 __isl_take isl_map *map);
5685 __isl_give isl_map *isl_map_uncurry(
5686 __isl_take isl_map *map);
5688 #include <isl/union_map.h>
5689 __isl_give isl_union_map *isl_union_map_curry(
5690 __isl_take isl_union_map *umap);
5691 __isl_give isl_union_map *isl_union_map_uncurry(
5692 __isl_take isl_union_map *umap);
5694 Given a relation with a nested relation for domain,
5695 the C<curry> functions
5696 move the range of the nested relation out of the domain
5697 and use it as the domain of a nested relation in the range,
5698 with the original range as range of this nested relation.
5699 The C<uncurry> functions perform the inverse operation.
5701 #include <isl/space.h>
5702 __isl_give isl_space *isl_space_range_curry(
5703 __isl_take isl_space *space);
5705 #include <isl/map.h>
5706 __isl_give isl_map *isl_map_range_curry(
5707 __isl_take isl_map *map);
5709 #include <isl/union_map.h>
5710 __isl_give isl_union_map *isl_union_map_range_curry(
5711 __isl_take isl_union_map *umap);
5713 These functions apply the currying to the relation that
5714 is nested inside the range of the input.
5716 =item * Aligning parameters
5718 Change the order of the parameters of the given set, relation
5720 such that the first parameters match those of C<model>.
5721 This may involve the introduction of extra parameters.
5722 All parameters need to be named.
5724 #include <isl/space.h>
5725 __isl_give isl_space *isl_space_align_params(
5726 __isl_take isl_space *space1,
5727 __isl_take isl_space *space2)
5729 #include <isl/set.h>
5730 __isl_give isl_basic_set *isl_basic_set_align_params(
5731 __isl_take isl_basic_set *bset,
5732 __isl_take isl_space *model);
5733 __isl_give isl_set *isl_set_align_params(
5734 __isl_take isl_set *set,
5735 __isl_take isl_space *model);
5737 #include <isl/map.h>
5738 __isl_give isl_basic_map *isl_basic_map_align_params(
5739 __isl_take isl_basic_map *bmap,
5740 __isl_take isl_space *model);
5741 __isl_give isl_map *isl_map_align_params(
5742 __isl_take isl_map *map,
5743 __isl_take isl_space *model);
5745 #include <isl/val.h>
5746 __isl_give isl_multi_val *isl_multi_val_align_params(
5747 __isl_take isl_multi_val *mv,
5748 __isl_take isl_space *model);
5750 #include <isl/aff.h>
5751 __isl_give isl_aff *isl_aff_align_params(
5752 __isl_take isl_aff *aff,
5753 __isl_take isl_space *model);
5754 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5755 __isl_take isl_multi_aff *multi,
5756 __isl_take isl_space *model);
5757 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5758 __isl_take isl_pw_aff *pwaff,
5759 __isl_take isl_space *model);
5760 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5761 __isl_take isl_pw_multi_aff *pma,
5762 __isl_take isl_space *model);
5763 __isl_give isl_union_pw_aff *
5764 isl_union_pw_aff_align_params(
5765 __isl_take isl_union_pw_aff *upa,
5766 __isl_take isl_space *model);
5767 __isl_give isl_union_pw_multi_aff *
5768 isl_union_pw_multi_aff_align_params(
5769 __isl_take isl_union_pw_multi_aff *upma,
5770 __isl_take isl_space *model);
5771 __isl_give isl_multi_union_pw_aff *
5772 isl_multi_union_pw_aff_align_params(
5773 __isl_take isl_multi_union_pw_aff *mupa,
5774 __isl_take isl_space *model);
5776 #include <isl/polynomial.h>
5777 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5778 __isl_take isl_qpolynomial *qp,
5779 __isl_take isl_space *model);
5781 =item * Drop unused parameters
5783 Drop parameters that are not referenced by the isl object.
5784 All parameters need to be named.
5786 #include <isl/set.h>
5787 __isl_give isl_basic_set *
5788 isl_basic_set_drop_unused_params(
5789 __isl_take isl_basic_set *bset);
5790 __isl_give isl_set *isl_set_drop_unused_params(
5791 __isl_take isl_set *set);
5793 #include <isl/map.h>
5794 __isl_give isl_basic_map *
5795 isl_basic_map_drop_unused_params(
5796 __isl_take isl_basic_map *bmap);
5797 __isl_give isl_map *isl_map_drop_unused_params(
5798 __isl_take isl_map *map);
5800 #include <isl/aff.h>
5801 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
5802 __isl_take isl_pw_aff *pa);
5803 __isl_give isl_pw_multi_aff *
5804 isl_pw_multi_aff_drop_unused_params(
5805 __isl_take isl_pw_multi_aff *pma);
5807 #include <isl/polynomial.h>
5808 __isl_give isl_pw_qpolynomial *
5809 isl_pw_qpolynomial_drop_unused_params(
5810 __isl_take isl_pw_qpolynomial *pwqp);
5811 __isl_give isl_pw_qpolynomial_fold *
5812 isl_pw_qpolynomial_fold_drop_unused_params(
5813 __isl_take isl_pw_qpolynomial_fold *pwf);
5815 =item * Unary Arithmetic Operations
5817 #include <isl/set.h>
5818 __isl_give isl_set *isl_set_neg(
5819 __isl_take isl_set *set);
5820 #include <isl/map.h>
5821 __isl_give isl_map *isl_map_neg(
5822 __isl_take isl_map *map);
5824 C<isl_set_neg> constructs a set containing the opposites of
5825 the elements in its argument.
5826 The domain of the result of C<isl_map_neg> is the same
5827 as the domain of its argument. The corresponding range
5828 elements are the opposites of the corresponding range
5829 elements in the argument.
5831 #include <isl/val.h>
5832 __isl_give isl_multi_val *isl_multi_val_neg(
5833 __isl_take isl_multi_val *mv);
5835 #include <isl/aff.h>
5836 __isl_give isl_aff *isl_aff_neg(
5837 __isl_take isl_aff *aff);
5838 __isl_give isl_multi_aff *isl_multi_aff_neg(
5839 __isl_take isl_multi_aff *ma);
5840 __isl_give isl_pw_aff *isl_pw_aff_neg(
5841 __isl_take isl_pw_aff *pwaff);
5842 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5843 __isl_take isl_pw_multi_aff *pma);
5844 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5845 __isl_take isl_multi_pw_aff *mpa);
5846 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5847 __isl_take isl_union_pw_aff *upa);
5848 __isl_give isl_union_pw_multi_aff *
5849 isl_union_pw_multi_aff_neg(
5850 __isl_take isl_union_pw_multi_aff *upma);
5851 __isl_give isl_multi_union_pw_aff *
5852 isl_multi_union_pw_aff_neg(
5853 __isl_take isl_multi_union_pw_aff *mupa);
5854 __isl_give isl_aff *isl_aff_ceil(
5855 __isl_take isl_aff *aff);
5856 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5857 __isl_take isl_pw_aff *pwaff);
5858 __isl_give isl_aff *isl_aff_floor(
5859 __isl_take isl_aff *aff);
5860 __isl_give isl_multi_aff *isl_multi_aff_floor(
5861 __isl_take isl_multi_aff *ma);
5862 __isl_give isl_pw_aff *isl_pw_aff_floor(
5863 __isl_take isl_pw_aff *pwaff);
5864 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5865 __isl_take isl_union_pw_aff *upa);
5866 __isl_give isl_multi_union_pw_aff *
5867 isl_multi_union_pw_aff_floor(
5868 __isl_take isl_multi_union_pw_aff *mupa);
5870 #include <isl/aff.h>
5871 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5872 __isl_take isl_pw_aff_list *list);
5873 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5874 __isl_take isl_pw_aff_list *list);
5876 #include <isl/polynomial.h>
5877 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5878 __isl_take isl_qpolynomial *qp);
5879 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5880 __isl_take isl_pw_qpolynomial *pwqp);
5881 __isl_give isl_union_pw_qpolynomial *
5882 isl_union_pw_qpolynomial_neg(
5883 __isl_take isl_union_pw_qpolynomial *upwqp);
5884 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5885 __isl_take isl_qpolynomial *qp,
5887 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5888 __isl_take isl_pw_qpolynomial *pwqp,
5893 The following functions evaluate a function in a point.
5895 #include <isl/aff.h>
5896 __isl_give isl_val *isl_aff_eval(
5897 __isl_take isl_aff *aff,
5898 __isl_take isl_point *pnt);
5899 __isl_give isl_val *isl_pw_aff_eval(
5900 __isl_take isl_pw_aff *pa,
5901 __isl_take isl_point *pnt);
5903 #include <isl/polynomial.h>
5904 __isl_give isl_val *isl_pw_qpolynomial_eval(
5905 __isl_take isl_pw_qpolynomial *pwqp,
5906 __isl_take isl_point *pnt);
5907 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5908 __isl_take isl_pw_qpolynomial_fold *pwf,
5909 __isl_take isl_point *pnt);
5910 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5911 __isl_take isl_union_pw_qpolynomial *upwqp,
5912 __isl_take isl_point *pnt);
5913 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5914 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5915 __isl_take isl_point *pnt);
5917 These functions return NaN when evaluated at a void point.
5918 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
5919 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
5920 when the function is evaluated outside its explicit domain.
5922 =item * Dimension manipulation
5924 It is usually not advisable to directly change the (input or output)
5925 space of a set or a relation as this removes the name and the internal
5926 structure of the space. However, the functions below can be useful
5927 to add new parameters, assuming
5928 C<isl_set_align_params> and C<isl_map_align_params>
5931 #include <isl/space.h>
5932 __isl_give isl_space *isl_space_add_dims(
5933 __isl_take isl_space *space,
5934 enum isl_dim_type type, unsigned n);
5935 __isl_give isl_space *isl_space_insert_dims(
5936 __isl_take isl_space *space,
5937 enum isl_dim_type type, unsigned pos, unsigned n);
5938 __isl_give isl_space *isl_space_drop_dims(
5939 __isl_take isl_space *space,
5940 enum isl_dim_type type, unsigned first, unsigned n);
5941 __isl_give isl_space *isl_space_move_dims(
5942 __isl_take isl_space *space,
5943 enum isl_dim_type dst_type, unsigned dst_pos,
5944 enum isl_dim_type src_type, unsigned src_pos,
5947 #include <isl/local_space.h>
5948 __isl_give isl_local_space *isl_local_space_add_dims(
5949 __isl_take isl_local_space *ls,
5950 enum isl_dim_type type, unsigned n);
5951 __isl_give isl_local_space *isl_local_space_insert_dims(
5952 __isl_take isl_local_space *ls,
5953 enum isl_dim_type type, unsigned first, unsigned n);
5954 __isl_give isl_local_space *isl_local_space_drop_dims(
5955 __isl_take isl_local_space *ls,
5956 enum isl_dim_type type, unsigned first, unsigned n);
5958 #include <isl/set.h>
5959 __isl_give isl_basic_set *isl_basic_set_add_dims(
5960 __isl_take isl_basic_set *bset,
5961 enum isl_dim_type type, unsigned n);
5962 __isl_give isl_set *isl_set_add_dims(
5963 __isl_take isl_set *set,
5964 enum isl_dim_type type, unsigned n);
5965 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5966 __isl_take isl_basic_set *bset,
5967 enum isl_dim_type type, unsigned pos,
5969 __isl_give isl_set *isl_set_insert_dims(
5970 __isl_take isl_set *set,
5971 enum isl_dim_type type, unsigned pos, unsigned n);
5972 __isl_give isl_basic_set *isl_basic_set_move_dims(
5973 __isl_take isl_basic_set *bset,
5974 enum isl_dim_type dst_type, unsigned dst_pos,
5975 enum isl_dim_type src_type, unsigned src_pos,
5977 __isl_give isl_set *isl_set_move_dims(
5978 __isl_take isl_set *set,
5979 enum isl_dim_type dst_type, unsigned dst_pos,
5980 enum isl_dim_type src_type, unsigned src_pos,
5983 #include <isl/map.h>
5984 __isl_give isl_basic_map *isl_basic_map_add_dims(
5985 __isl_take isl_basic_map *bmap,
5986 enum isl_dim_type type, unsigned n);
5987 __isl_give isl_map *isl_map_add_dims(
5988 __isl_take isl_map *map,
5989 enum isl_dim_type type, unsigned n);
5990 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5991 __isl_take isl_basic_map *bmap,
5992 enum isl_dim_type type, unsigned pos,
5994 __isl_give isl_map *isl_map_insert_dims(
5995 __isl_take isl_map *map,
5996 enum isl_dim_type type, unsigned pos, unsigned n);
5997 __isl_give isl_basic_map *isl_basic_map_move_dims(
5998 __isl_take isl_basic_map *bmap,
5999 enum isl_dim_type dst_type, unsigned dst_pos,
6000 enum isl_dim_type src_type, unsigned src_pos,
6002 __isl_give isl_map *isl_map_move_dims(
6003 __isl_take isl_map *map,
6004 enum isl_dim_type dst_type, unsigned dst_pos,
6005 enum isl_dim_type src_type, unsigned src_pos,
6008 #include <isl/val.h>
6009 __isl_give isl_multi_val *isl_multi_val_insert_dims(
6010 __isl_take isl_multi_val *mv,
6011 enum isl_dim_type type, unsigned first, unsigned n);
6012 __isl_give isl_multi_val *isl_multi_val_add_dims(
6013 __isl_take isl_multi_val *mv,
6014 enum isl_dim_type type, unsigned n);
6015 __isl_give isl_multi_val *isl_multi_val_drop_dims(
6016 __isl_take isl_multi_val *mv,
6017 enum isl_dim_type type, unsigned first, unsigned n);
6019 #include <isl/aff.h>
6020 __isl_give isl_aff *isl_aff_insert_dims(
6021 __isl_take isl_aff *aff,
6022 enum isl_dim_type type, unsigned first, unsigned n);
6023 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
6024 __isl_take isl_multi_aff *ma,
6025 enum isl_dim_type type, unsigned first, unsigned n);
6026 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
6027 __isl_take isl_pw_aff *pwaff,
6028 enum isl_dim_type type, unsigned first, unsigned n);
6029 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
6030 __isl_take isl_multi_pw_aff *mpa,
6031 enum isl_dim_type type, unsigned first, unsigned n);
6032 __isl_give isl_aff *isl_aff_add_dims(
6033 __isl_take isl_aff *aff,
6034 enum isl_dim_type type, unsigned n);
6035 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
6036 __isl_take isl_multi_aff *ma,
6037 enum isl_dim_type type, unsigned n);
6038 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
6039 __isl_take isl_pw_aff *pwaff,
6040 enum isl_dim_type type, unsigned n);
6041 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
6042 __isl_take isl_multi_pw_aff *mpa,
6043 enum isl_dim_type type, unsigned n);
6044 __isl_give isl_aff *isl_aff_drop_dims(
6045 __isl_take isl_aff *aff,
6046 enum isl_dim_type type, unsigned first, unsigned n);
6047 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
6048 __isl_take isl_multi_aff *maff,
6049 enum isl_dim_type type, unsigned first, unsigned n);
6050 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
6051 __isl_take isl_pw_aff *pwaff,
6052 enum isl_dim_type type, unsigned first, unsigned n);
6053 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
6054 __isl_take isl_pw_multi_aff *pma,
6055 enum isl_dim_type type, unsigned first, unsigned n);
6056 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
6057 __isl_take isl_union_pw_aff *upa,
6058 enum isl_dim_type type, unsigned first, unsigned n);
6059 __isl_give isl_union_pw_multi_aff *
6060 isl_union_pw_multi_aff_drop_dims(
6061 __isl_take isl_union_pw_multi_aff *upma,
6062 enum isl_dim_type type,
6063 unsigned first, unsigned n);
6064 __isl_give isl_multi_union_pw_aff *
6065 isl_multi_union_pw_aff_drop_dims(
6066 __isl_take isl_multi_union_pw_aff *mupa,
6067 enum isl_dim_type type, unsigned first,
6069 __isl_give isl_aff *isl_aff_move_dims(
6070 __isl_take isl_aff *aff,
6071 enum isl_dim_type dst_type, unsigned dst_pos,
6072 enum isl_dim_type src_type, unsigned src_pos,
6074 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
6075 __isl_take isl_multi_aff *ma,
6076 enum isl_dim_type dst_type, unsigned dst_pos,
6077 enum isl_dim_type src_type, unsigned src_pos,
6079 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
6080 __isl_take isl_pw_aff *pa,
6081 enum isl_dim_type dst_type, unsigned dst_pos,
6082 enum isl_dim_type src_type, unsigned src_pos,
6084 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
6085 __isl_take isl_multi_pw_aff *pma,
6086 enum isl_dim_type dst_type, unsigned dst_pos,
6087 enum isl_dim_type src_type, unsigned src_pos,
6090 #include <isl/polynomial.h>
6091 __isl_give isl_union_pw_qpolynomial *
6092 isl_union_pw_qpolynomial_drop_dims(
6093 __isl_take isl_union_pw_qpolynomial *upwqp,
6094 enum isl_dim_type type,
6095 unsigned first, unsigned n);
6096 __isl_give isl_union_pw_qpolynomial_fold *
6097 isl_union_pw_qpolynomial_fold_drop_dims(
6098 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6099 enum isl_dim_type type,
6100 unsigned first, unsigned n);
6102 The operations on union expressions can only manipulate parameters.
6106 =head2 Binary Operations
6108 The two arguments of a binary operation not only need to live
6109 in the same C<isl_ctx>, they currently also need to have
6110 the same (number of) parameters.
6112 =head3 Basic Operations
6116 =item * Intersection
6118 #include <isl/local_space.h>
6119 __isl_give isl_local_space *isl_local_space_intersect(
6120 __isl_take isl_local_space *ls1,
6121 __isl_take isl_local_space *ls2);
6123 #include <isl/set.h>
6124 __isl_give isl_basic_set *isl_basic_set_intersect_params(
6125 __isl_take isl_basic_set *bset1,
6126 __isl_take isl_basic_set *bset2);
6127 __isl_give isl_basic_set *isl_basic_set_intersect(
6128 __isl_take isl_basic_set *bset1,
6129 __isl_take isl_basic_set *bset2);
6130 __isl_give isl_basic_set *isl_basic_set_list_intersect(
6131 __isl_take struct isl_basic_set_list *list);
6132 __isl_give isl_set *isl_set_intersect_params(
6133 __isl_take isl_set *set,
6134 __isl_take isl_set *params);
6135 __isl_give isl_set *isl_set_intersect(
6136 __isl_take isl_set *set1,
6137 __isl_take isl_set *set2);
6139 #include <isl/map.h>
6140 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
6141 __isl_take isl_basic_map *bmap,
6142 __isl_take isl_basic_set *bset);
6143 __isl_give isl_basic_map *isl_basic_map_intersect_range(
6144 __isl_take isl_basic_map *bmap,
6145 __isl_take isl_basic_set *bset);
6146 __isl_give isl_basic_map *isl_basic_map_intersect(
6147 __isl_take isl_basic_map *bmap1,
6148 __isl_take isl_basic_map *bmap2);
6149 __isl_give isl_basic_map *isl_basic_map_list_intersect(
6150 __isl_take isl_basic_map_list *list);
6151 __isl_give isl_map *isl_map_intersect_params(
6152 __isl_take isl_map *map,
6153 __isl_take isl_set *params);
6154 __isl_give isl_map *isl_map_intersect_domain(
6155 __isl_take isl_map *map,
6156 __isl_take isl_set *set);
6157 __isl_give isl_map *isl_map_intersect_range(
6158 __isl_take isl_map *map,
6159 __isl_take isl_set *set);
6160 __isl_give isl_map *isl_map_intersect(
6161 __isl_take isl_map *map1,
6162 __isl_take isl_map *map2);
6163 __isl_give isl_map *
6164 isl_map_intersect_domain_factor_range(
6165 __isl_take isl_map *map,
6166 __isl_take isl_map *factor);
6167 __isl_give isl_map *
6168 isl_map_intersect_range_factor_range(
6169 __isl_take isl_map *map,
6170 __isl_take isl_map *factor);
6172 #include <isl/union_set.h>
6173 __isl_give isl_union_set *isl_union_set_intersect_params(
6174 __isl_take isl_union_set *uset,
6175 __isl_take isl_set *set);
6176 __isl_give isl_union_set *isl_union_set_intersect(
6177 __isl_take isl_union_set *uset1,
6178 __isl_take isl_union_set *uset2);
6180 #include <isl/union_map.h>
6181 __isl_give isl_union_map *isl_union_map_intersect_params(
6182 __isl_take isl_union_map *umap,
6183 __isl_take isl_set *set);
6184 __isl_give isl_union_map *isl_union_map_intersect_domain(
6185 __isl_take isl_union_map *umap,
6186 __isl_take isl_union_set *uset);
6187 __isl_give isl_union_map *isl_union_map_intersect_range(
6188 __isl_take isl_union_map *umap,
6189 __isl_take isl_union_set *uset);
6190 __isl_give isl_union_map *isl_union_map_intersect(
6191 __isl_take isl_union_map *umap1,
6192 __isl_take isl_union_map *umap2);
6193 __isl_give isl_union_map *
6194 isl_union_map_intersect_range_factor_range(
6195 __isl_take isl_union_map *umap,
6196 __isl_take isl_union_map *factor);
6198 #include <isl/aff.h>
6199 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6200 __isl_take isl_pw_aff *pa,
6201 __isl_take isl_set *set);
6202 __isl_give isl_multi_pw_aff *
6203 isl_multi_pw_aff_intersect_domain(
6204 __isl_take isl_multi_pw_aff *mpa,
6205 __isl_take isl_set *domain);
6206 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6207 __isl_take isl_pw_multi_aff *pma,
6208 __isl_take isl_set *set);
6209 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6210 __isl_take isl_union_pw_aff *upa,
6211 __isl_take isl_union_set *uset);
6212 __isl_give isl_union_pw_multi_aff *
6213 isl_union_pw_multi_aff_intersect_domain(
6214 __isl_take isl_union_pw_multi_aff *upma,
6215 __isl_take isl_union_set *uset);
6216 __isl_give isl_multi_union_pw_aff *
6217 isl_multi_union_pw_aff_intersect_domain(
6218 __isl_take isl_multi_union_pw_aff *mupa,
6219 __isl_take isl_union_set *uset);
6220 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6221 __isl_take isl_pw_aff *pa,
6222 __isl_take isl_set *set);
6223 __isl_give isl_multi_pw_aff *
6224 isl_multi_pw_aff_intersect_params(
6225 __isl_take isl_multi_pw_aff *mpa,
6226 __isl_take isl_set *set);
6227 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6228 __isl_take isl_pw_multi_aff *pma,
6229 __isl_take isl_set *set);
6230 __isl_give isl_union_pw_aff *
6231 isl_union_pw_aff_intersect_params(
6232 __isl_take isl_union_pw_aff *upa,
6233 __isl_give isl_union_pw_multi_aff *
6234 isl_union_pw_multi_aff_intersect_params(
6235 __isl_take isl_union_pw_multi_aff *upma,
6236 __isl_take isl_set *set);
6237 __isl_give isl_multi_union_pw_aff *
6238 isl_multi_union_pw_aff_intersect_params(
6239 __isl_take isl_multi_union_pw_aff *mupa,
6240 __isl_take isl_set *params);
6241 isl_multi_union_pw_aff_intersect_range(
6242 __isl_take isl_multi_union_pw_aff *mupa,
6243 __isl_take isl_set *set);
6245 #include <isl/polynomial.h>
6246 __isl_give isl_pw_qpolynomial *
6247 isl_pw_qpolynomial_intersect_domain(
6248 __isl_take isl_pw_qpolynomial *pwpq,
6249 __isl_take isl_set *set);
6250 __isl_give isl_union_pw_qpolynomial *
6251 isl_union_pw_qpolynomial_intersect_domain(
6252 __isl_take isl_union_pw_qpolynomial *upwpq,
6253 __isl_take isl_union_set *uset);
6254 __isl_give isl_union_pw_qpolynomial_fold *
6255 isl_union_pw_qpolynomial_fold_intersect_domain(
6256 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6257 __isl_take isl_union_set *uset);
6258 __isl_give isl_pw_qpolynomial *
6259 isl_pw_qpolynomial_intersect_params(
6260 __isl_take isl_pw_qpolynomial *pwpq,
6261 __isl_take isl_set *set);
6262 __isl_give isl_pw_qpolynomial_fold *
6263 isl_pw_qpolynomial_fold_intersect_params(
6264 __isl_take isl_pw_qpolynomial_fold *pwf,
6265 __isl_take isl_set *set);
6266 __isl_give isl_union_pw_qpolynomial *
6267 isl_union_pw_qpolynomial_intersect_params(
6268 __isl_take isl_union_pw_qpolynomial *upwpq,
6269 __isl_take isl_set *set);
6270 __isl_give isl_union_pw_qpolynomial_fold *
6271 isl_union_pw_qpolynomial_fold_intersect_params(
6272 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6273 __isl_take isl_set *set);
6275 The second argument to the C<_params> functions needs to be
6276 a parametric (basic) set. For the other functions, a parametric set
6277 for either argument is only allowed if the other argument is
6278 a parametric set as well.
6279 The list passed to C<isl_basic_set_list_intersect> needs to have
6280 at least one element and all elements need to live in the same space.
6281 The function C<isl_multi_union_pw_aff_intersect_range>
6282 restricts the input function to those shared domain elements
6283 that map to the specified range.
6287 #include <isl/set.h>
6288 __isl_give isl_set *isl_basic_set_union(
6289 __isl_take isl_basic_set *bset1,
6290 __isl_take isl_basic_set *bset2);
6291 __isl_give isl_set *isl_set_union(
6292 __isl_take isl_set *set1,
6293 __isl_take isl_set *set2);
6294 __isl_give isl_set *isl_set_list_union(
6295 __isl_take isl_set_list *list);
6297 #include <isl/map.h>
6298 __isl_give isl_map *isl_basic_map_union(
6299 __isl_take isl_basic_map *bmap1,
6300 __isl_take isl_basic_map *bmap2);
6301 __isl_give isl_map *isl_map_union(
6302 __isl_take isl_map *map1,
6303 __isl_take isl_map *map2);
6305 #include <isl/union_set.h>
6306 __isl_give isl_union_set *isl_union_set_union(
6307 __isl_take isl_union_set *uset1,
6308 __isl_take isl_union_set *uset2);
6309 __isl_give isl_union_set *isl_union_set_list_union(
6310 __isl_take isl_union_set_list *list);
6312 #include <isl/union_map.h>
6313 __isl_give isl_union_map *isl_union_map_union(
6314 __isl_take isl_union_map *umap1,
6315 __isl_take isl_union_map *umap2);
6317 The list passed to C<isl_set_list_union> needs to have
6318 at least one element and all elements need to live in the same space.
6320 =item * Set difference
6322 #include <isl/set.h>
6323 __isl_give isl_set *isl_set_subtract(
6324 __isl_take isl_set *set1,
6325 __isl_take isl_set *set2);
6327 #include <isl/map.h>
6328 __isl_give isl_map *isl_map_subtract(
6329 __isl_take isl_map *map1,
6330 __isl_take isl_map *map2);
6331 __isl_give isl_map *isl_map_subtract_domain(
6332 __isl_take isl_map *map,
6333 __isl_take isl_set *dom);
6334 __isl_give isl_map *isl_map_subtract_range(
6335 __isl_take isl_map *map,
6336 __isl_take isl_set *dom);
6338 #include <isl/union_set.h>
6339 __isl_give isl_union_set *isl_union_set_subtract(
6340 __isl_take isl_union_set *uset1,
6341 __isl_take isl_union_set *uset2);
6343 #include <isl/union_map.h>
6344 __isl_give isl_union_map *isl_union_map_subtract(
6345 __isl_take isl_union_map *umap1,
6346 __isl_take isl_union_map *umap2);
6347 __isl_give isl_union_map *isl_union_map_subtract_domain(
6348 __isl_take isl_union_map *umap,
6349 __isl_take isl_union_set *dom);
6350 __isl_give isl_union_map *isl_union_map_subtract_range(
6351 __isl_take isl_union_map *umap,
6352 __isl_take isl_union_set *dom);
6354 #include <isl/aff.h>
6355 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6356 __isl_take isl_pw_aff *pa,
6357 __isl_take isl_set *set);
6358 __isl_give isl_pw_multi_aff *
6359 isl_pw_multi_aff_subtract_domain(
6360 __isl_take isl_pw_multi_aff *pma,
6361 __isl_take isl_set *set);
6362 __isl_give isl_union_pw_aff *
6363 isl_union_pw_aff_subtract_domain(
6364 __isl_take isl_union_pw_aff *upa,
6365 __isl_take isl_union_set *uset);
6366 __isl_give isl_union_pw_multi_aff *
6367 isl_union_pw_multi_aff_subtract_domain(
6368 __isl_take isl_union_pw_multi_aff *upma,
6369 __isl_take isl_set *set);
6371 #include <isl/polynomial.h>
6372 __isl_give isl_pw_qpolynomial *
6373 isl_pw_qpolynomial_subtract_domain(
6374 __isl_take isl_pw_qpolynomial *pwpq,
6375 __isl_take isl_set *set);
6376 __isl_give isl_pw_qpolynomial_fold *
6377 isl_pw_qpolynomial_fold_subtract_domain(
6378 __isl_take isl_pw_qpolynomial_fold *pwf,
6379 __isl_take isl_set *set);
6380 __isl_give isl_union_pw_qpolynomial *
6381 isl_union_pw_qpolynomial_subtract_domain(
6382 __isl_take isl_union_pw_qpolynomial *upwpq,
6383 __isl_take isl_union_set *uset);
6384 __isl_give isl_union_pw_qpolynomial_fold *
6385 isl_union_pw_qpolynomial_fold_subtract_domain(
6386 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6387 __isl_take isl_union_set *uset);
6391 #include <isl/space.h>
6392 __isl_give isl_space *isl_space_join(
6393 __isl_take isl_space *left,
6394 __isl_take isl_space *right);
6396 #include <isl/map.h>
6397 __isl_give isl_basic_set *isl_basic_set_apply(
6398 __isl_take isl_basic_set *bset,
6399 __isl_take isl_basic_map *bmap);
6400 __isl_give isl_set *isl_set_apply(
6401 __isl_take isl_set *set,
6402 __isl_take isl_map *map);
6403 __isl_give isl_union_set *isl_union_set_apply(
6404 __isl_take isl_union_set *uset,
6405 __isl_take isl_union_map *umap);
6406 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6407 __isl_take isl_basic_map *bmap1,
6408 __isl_take isl_basic_map *bmap2);
6409 __isl_give isl_basic_map *isl_basic_map_apply_range(
6410 __isl_take isl_basic_map *bmap1,
6411 __isl_take isl_basic_map *bmap2);
6412 __isl_give isl_map *isl_map_apply_domain(
6413 __isl_take isl_map *map1,
6414 __isl_take isl_map *map2);
6415 __isl_give isl_map *isl_map_apply_range(
6416 __isl_take isl_map *map1,
6417 __isl_take isl_map *map2);
6419 #include <isl/union_map.h>
6420 __isl_give isl_union_map *isl_union_map_apply_domain(
6421 __isl_take isl_union_map *umap1,
6422 __isl_take isl_union_map *umap2);
6423 __isl_give isl_union_map *isl_union_map_apply_range(
6424 __isl_take isl_union_map *umap1,
6425 __isl_take isl_union_map *umap2);
6427 #include <isl/aff.h>
6428 __isl_give isl_union_pw_aff *
6429 isl_multi_union_pw_aff_apply_aff(
6430 __isl_take isl_multi_union_pw_aff *mupa,
6431 __isl_take isl_aff *aff);
6432 __isl_give isl_union_pw_aff *
6433 isl_multi_union_pw_aff_apply_pw_aff(
6434 __isl_take isl_multi_union_pw_aff *mupa,
6435 __isl_take isl_pw_aff *pa);
6436 __isl_give isl_multi_union_pw_aff *
6437 isl_multi_union_pw_aff_apply_multi_aff(
6438 __isl_take isl_multi_union_pw_aff *mupa,
6439 __isl_take isl_multi_aff *ma);
6440 __isl_give isl_multi_union_pw_aff *
6441 isl_multi_union_pw_aff_apply_pw_multi_aff(
6442 __isl_take isl_multi_union_pw_aff *mupa,
6443 __isl_take isl_pw_multi_aff *pma);
6445 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6446 over the shared domain of the elements of the input. The dimension is
6447 required to be greater than zero.
6448 The C<isl_multi_union_pw_aff> argument of
6449 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6450 but only if the range of the C<isl_multi_aff> argument
6451 is also zero-dimensional.
6452 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6454 #include <isl/polynomial.h>
6455 __isl_give isl_pw_qpolynomial_fold *
6456 isl_set_apply_pw_qpolynomial_fold(
6457 __isl_take isl_set *set,
6458 __isl_take isl_pw_qpolynomial_fold *pwf,
6460 __isl_give isl_pw_qpolynomial_fold *
6461 isl_map_apply_pw_qpolynomial_fold(
6462 __isl_take isl_map *map,
6463 __isl_take isl_pw_qpolynomial_fold *pwf,
6465 __isl_give isl_union_pw_qpolynomial_fold *
6466 isl_union_set_apply_union_pw_qpolynomial_fold(
6467 __isl_take isl_union_set *uset,
6468 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6470 __isl_give isl_union_pw_qpolynomial_fold *
6471 isl_union_map_apply_union_pw_qpolynomial_fold(
6472 __isl_take isl_union_map *umap,
6473 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6476 The functions taking a map
6477 compose the given map with the given piecewise quasipolynomial reduction.
6478 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6479 over all elements in the intersection of the range of the map
6480 and the domain of the piecewise quasipolynomial reduction
6481 as a function of an element in the domain of the map.
6482 The functions taking a set compute a bound over all elements in the
6483 intersection of the set and the domain of the
6484 piecewise quasipolynomial reduction.
6488 #include <isl/set.h>
6489 __isl_give isl_basic_set *
6490 isl_basic_set_preimage_multi_aff(
6491 __isl_take isl_basic_set *bset,
6492 __isl_take isl_multi_aff *ma);
6493 __isl_give isl_set *isl_set_preimage_multi_aff(
6494 __isl_take isl_set *set,
6495 __isl_take isl_multi_aff *ma);
6496 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6497 __isl_take isl_set *set,
6498 __isl_take isl_pw_multi_aff *pma);
6499 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6500 __isl_take isl_set *set,
6501 __isl_take isl_multi_pw_aff *mpa);
6503 #include <isl/union_set.h>
6504 __isl_give isl_union_set *
6505 isl_union_set_preimage_multi_aff(
6506 __isl_take isl_union_set *uset,
6507 __isl_take isl_multi_aff *ma);
6508 __isl_give isl_union_set *
6509 isl_union_set_preimage_pw_multi_aff(
6510 __isl_take isl_union_set *uset,
6511 __isl_take isl_pw_multi_aff *pma);
6512 __isl_give isl_union_set *
6513 isl_union_set_preimage_union_pw_multi_aff(
6514 __isl_take isl_union_set *uset,
6515 __isl_take isl_union_pw_multi_aff *upma);
6517 #include <isl/map.h>
6518 __isl_give isl_basic_map *
6519 isl_basic_map_preimage_domain_multi_aff(
6520 __isl_take isl_basic_map *bmap,
6521 __isl_take isl_multi_aff *ma);
6522 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6523 __isl_take isl_map *map,
6524 __isl_take isl_multi_aff *ma);
6525 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6526 __isl_take isl_map *map,
6527 __isl_take isl_multi_aff *ma);
6528 __isl_give isl_map *
6529 isl_map_preimage_domain_pw_multi_aff(
6530 __isl_take isl_map *map,
6531 __isl_take isl_pw_multi_aff *pma);
6532 __isl_give isl_map *
6533 isl_map_preimage_range_pw_multi_aff(
6534 __isl_take isl_map *map,
6535 __isl_take isl_pw_multi_aff *pma);
6536 __isl_give isl_map *
6537 isl_map_preimage_domain_multi_pw_aff(
6538 __isl_take isl_map *map,
6539 __isl_take isl_multi_pw_aff *mpa);
6540 __isl_give isl_basic_map *
6541 isl_basic_map_preimage_range_multi_aff(
6542 __isl_take isl_basic_map *bmap,
6543 __isl_take isl_multi_aff *ma);
6545 #include <isl/union_map.h>
6546 __isl_give isl_union_map *
6547 isl_union_map_preimage_domain_multi_aff(
6548 __isl_take isl_union_map *umap,
6549 __isl_take isl_multi_aff *ma);
6550 __isl_give isl_union_map *
6551 isl_union_map_preimage_range_multi_aff(
6552 __isl_take isl_union_map *umap,
6553 __isl_take isl_multi_aff *ma);
6554 __isl_give isl_union_map *
6555 isl_union_map_preimage_domain_pw_multi_aff(
6556 __isl_take isl_union_map *umap,
6557 __isl_take isl_pw_multi_aff *pma);
6558 __isl_give isl_union_map *
6559 isl_union_map_preimage_range_pw_multi_aff(
6560 __isl_take isl_union_map *umap,
6561 __isl_take isl_pw_multi_aff *pma);
6562 __isl_give isl_union_map *
6563 isl_union_map_preimage_domain_union_pw_multi_aff(
6564 __isl_take isl_union_map *umap,
6565 __isl_take isl_union_pw_multi_aff *upma);
6566 __isl_give isl_union_map *
6567 isl_union_map_preimage_range_union_pw_multi_aff(
6568 __isl_take isl_union_map *umap,
6569 __isl_take isl_union_pw_multi_aff *upma);
6571 These functions compute the preimage of the given set or map domain/range under
6572 the given function. In other words, the expression is plugged
6573 into the set description or into the domain/range of the map.
6577 #include <isl/aff.h>
6578 __isl_give isl_aff *isl_aff_pullback_aff(
6579 __isl_take isl_aff *aff1,
6580 __isl_take isl_aff *aff2);
6581 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6582 __isl_take isl_aff *aff,
6583 __isl_take isl_multi_aff *ma);
6584 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6585 __isl_take isl_pw_aff *pa,
6586 __isl_take isl_multi_aff *ma);
6587 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6588 __isl_take isl_pw_aff *pa,
6589 __isl_take isl_pw_multi_aff *pma);
6590 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6591 __isl_take isl_pw_aff *pa,
6592 __isl_take isl_multi_pw_aff *mpa);
6593 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6594 __isl_take isl_multi_aff *ma1,
6595 __isl_take isl_multi_aff *ma2);
6596 __isl_give isl_pw_multi_aff *
6597 isl_pw_multi_aff_pullback_multi_aff(
6598 __isl_take isl_pw_multi_aff *pma,
6599 __isl_take isl_multi_aff *ma);
6600 __isl_give isl_multi_pw_aff *
6601 isl_multi_pw_aff_pullback_multi_aff(
6602 __isl_take isl_multi_pw_aff *mpa,
6603 __isl_take isl_multi_aff *ma);
6604 __isl_give isl_pw_multi_aff *
6605 isl_pw_multi_aff_pullback_pw_multi_aff(
6606 __isl_take isl_pw_multi_aff *pma1,
6607 __isl_take isl_pw_multi_aff *pma2);
6608 __isl_give isl_multi_pw_aff *
6609 isl_multi_pw_aff_pullback_pw_multi_aff(
6610 __isl_take isl_multi_pw_aff *mpa,
6611 __isl_take isl_pw_multi_aff *pma);
6612 __isl_give isl_multi_pw_aff *
6613 isl_multi_pw_aff_pullback_multi_pw_aff(
6614 __isl_take isl_multi_pw_aff *mpa1,
6615 __isl_take isl_multi_pw_aff *mpa2);
6616 __isl_give isl_union_pw_aff *
6617 isl_union_pw_aff_pullback_union_pw_multi_aff(
6618 __isl_take isl_union_pw_aff *upa,
6619 __isl_take isl_union_pw_multi_aff *upma);
6620 __isl_give isl_union_pw_multi_aff *
6621 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6622 __isl_take isl_union_pw_multi_aff *upma1,
6623 __isl_take isl_union_pw_multi_aff *upma2);
6624 __isl_give isl_multi_union_pw_aff *
6625 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6626 __isl_take isl_multi_union_pw_aff *mupa,
6627 __isl_take isl_union_pw_multi_aff *upma);
6629 These functions precompose the first expression by the second function.
6630 In other words, the second function is plugged
6631 into the first expression.
6635 #include <isl/aff.h>
6636 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6637 __isl_take isl_aff *aff1,
6638 __isl_take isl_aff *aff2);
6639 __isl_give isl_set *isl_aff_eq_set(
6640 __isl_take isl_aff *aff1,
6641 __isl_take isl_aff *aff2);
6642 __isl_give isl_set *isl_aff_ne_set(
6643 __isl_take isl_aff *aff1,
6644 __isl_take isl_aff *aff2);
6645 __isl_give isl_basic_set *isl_aff_le_basic_set(
6646 __isl_take isl_aff *aff1,
6647 __isl_take isl_aff *aff2);
6648 __isl_give isl_set *isl_aff_le_set(
6649 __isl_take isl_aff *aff1,
6650 __isl_take isl_aff *aff2);
6651 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6652 __isl_take isl_aff *aff1,
6653 __isl_take isl_aff *aff2);
6654 __isl_give isl_set *isl_aff_lt_set(
6655 __isl_take isl_aff *aff1,
6656 __isl_take isl_aff *aff2);
6657 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6658 __isl_take isl_aff *aff1,
6659 __isl_take isl_aff *aff2);
6660 __isl_give isl_set *isl_aff_ge_set(
6661 __isl_take isl_aff *aff1,
6662 __isl_take isl_aff *aff2);
6663 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6664 __isl_take isl_aff *aff1,
6665 __isl_take isl_aff *aff2);
6666 __isl_give isl_set *isl_aff_gt_set(
6667 __isl_take isl_aff *aff1,
6668 __isl_take isl_aff *aff2);
6669 __isl_give isl_set *isl_pw_aff_eq_set(
6670 __isl_take isl_pw_aff *pwaff1,
6671 __isl_take isl_pw_aff *pwaff2);
6672 __isl_give isl_set *isl_pw_aff_ne_set(
6673 __isl_take isl_pw_aff *pwaff1,
6674 __isl_take isl_pw_aff *pwaff2);
6675 __isl_give isl_set *isl_pw_aff_le_set(
6676 __isl_take isl_pw_aff *pwaff1,
6677 __isl_take isl_pw_aff *pwaff2);
6678 __isl_give isl_set *isl_pw_aff_lt_set(
6679 __isl_take isl_pw_aff *pwaff1,
6680 __isl_take isl_pw_aff *pwaff2);
6681 __isl_give isl_set *isl_pw_aff_ge_set(
6682 __isl_take isl_pw_aff *pwaff1,
6683 __isl_take isl_pw_aff *pwaff2);
6684 __isl_give isl_set *isl_pw_aff_gt_set(
6685 __isl_take isl_pw_aff *pwaff1,
6686 __isl_take isl_pw_aff *pwaff2);
6688 __isl_give isl_set *isl_multi_aff_lex_le_set(
6689 __isl_take isl_multi_aff *ma1,
6690 __isl_take isl_multi_aff *ma2);
6691 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6692 __isl_take isl_multi_aff *ma1,
6693 __isl_take isl_multi_aff *ma2);
6694 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6695 __isl_take isl_multi_aff *ma1,
6696 __isl_take isl_multi_aff *ma2);
6697 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6698 __isl_take isl_multi_aff *ma1,
6699 __isl_take isl_multi_aff *ma2);
6701 __isl_give isl_set *isl_pw_aff_list_eq_set(
6702 __isl_take isl_pw_aff_list *list1,
6703 __isl_take isl_pw_aff_list *list2);
6704 __isl_give isl_set *isl_pw_aff_list_ne_set(
6705 __isl_take isl_pw_aff_list *list1,
6706 __isl_take isl_pw_aff_list *list2);
6707 __isl_give isl_set *isl_pw_aff_list_le_set(
6708 __isl_take isl_pw_aff_list *list1,
6709 __isl_take isl_pw_aff_list *list2);
6710 __isl_give isl_set *isl_pw_aff_list_lt_set(
6711 __isl_take isl_pw_aff_list *list1,
6712 __isl_take isl_pw_aff_list *list2);
6713 __isl_give isl_set *isl_pw_aff_list_ge_set(
6714 __isl_take isl_pw_aff_list *list1,
6715 __isl_take isl_pw_aff_list *list2);
6716 __isl_give isl_set *isl_pw_aff_list_gt_set(
6717 __isl_take isl_pw_aff_list *list1,
6718 __isl_take isl_pw_aff_list *list2);
6720 The function C<isl_aff_ge_basic_set> returns a basic set
6721 containing those elements in the shared space
6722 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6723 The function C<isl_pw_aff_ge_set> returns a set
6724 containing those elements in the shared domain
6725 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6726 greater than or equal to C<pwaff2>.
6727 The function C<isl_multi_aff_lex_le_set> returns a set
6728 containing those elements in the shared domain space
6729 where C<ma1> is lexicographically smaller than or
6731 The functions operating on C<isl_pw_aff_list> apply the corresponding
6732 C<isl_pw_aff> function to each pair of elements in the two lists.
6734 #include <isl/aff.h>
6735 __isl_give isl_map *isl_pw_aff_eq_map(
6736 __isl_take isl_pw_aff *pa1,
6737 __isl_take isl_pw_aff *pa2);
6738 __isl_give isl_map *isl_pw_aff_lt_map(
6739 __isl_take isl_pw_aff *pa1,
6740 __isl_take isl_pw_aff *pa2);
6741 __isl_give isl_map *isl_pw_aff_gt_map(
6742 __isl_take isl_pw_aff *pa1,
6743 __isl_take isl_pw_aff *pa2);
6745 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6746 __isl_take isl_multi_pw_aff *mpa1,
6747 __isl_take isl_multi_pw_aff *mpa2);
6748 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6749 __isl_take isl_multi_pw_aff *mpa1,
6750 __isl_take isl_multi_pw_aff *mpa2);
6751 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6752 __isl_take isl_multi_pw_aff *mpa1,
6753 __isl_take isl_multi_pw_aff *mpa2);
6755 These functions return a map between domain elements of the arguments
6756 where the function values satisfy the given relation.
6758 #include <isl/union_map.h>
6759 __isl_give isl_union_map *
6760 isl_union_map_eq_at_multi_union_pw_aff(
6761 __isl_take isl_union_map *umap,
6762 __isl_take isl_multi_union_pw_aff *mupa);
6763 __isl_give isl_union_map *
6764 isl_union_map_lex_lt_at_multi_union_pw_aff(
6765 __isl_take isl_union_map *umap,
6766 __isl_take isl_multi_union_pw_aff *mupa);
6767 __isl_give isl_union_map *
6768 isl_union_map_lex_gt_at_multi_union_pw_aff(
6769 __isl_take isl_union_map *umap,
6770 __isl_take isl_multi_union_pw_aff *mupa);
6772 These functions select the subset of elements in the union map
6773 that have an equal or lexicographically smaller function value.
6775 =item * Cartesian Product
6777 #include <isl/space.h>
6778 __isl_give isl_space *isl_space_product(
6779 __isl_take isl_space *space1,
6780 __isl_take isl_space *space2);
6781 __isl_give isl_space *isl_space_domain_product(
6782 __isl_take isl_space *space1,
6783 __isl_take isl_space *space2);
6784 __isl_give isl_space *isl_space_range_product(
6785 __isl_take isl_space *space1,
6786 __isl_take isl_space *space2);
6789 C<isl_space_product>, C<isl_space_domain_product>
6790 and C<isl_space_range_product> take pairs or relation spaces and
6791 produce a single relations space, where either the domain, the range
6792 or both domain and range are wrapped spaces of relations between
6793 the domains and/or ranges of the input spaces.
6794 If the product is only constructed over the domain or the range
6795 then the ranges or the domains of the inputs should be the same.
6796 The function C<isl_space_product> also accepts a pair of set spaces,
6797 in which case it returns a wrapped space of a relation between the
6800 #include <isl/set.h>
6801 __isl_give isl_set *isl_set_product(
6802 __isl_take isl_set *set1,
6803 __isl_take isl_set *set2);
6805 #include <isl/map.h>
6806 __isl_give isl_basic_map *isl_basic_map_domain_product(
6807 __isl_take isl_basic_map *bmap1,
6808 __isl_take isl_basic_map *bmap2);
6809 __isl_give isl_basic_map *isl_basic_map_range_product(
6810 __isl_take isl_basic_map *bmap1,
6811 __isl_take isl_basic_map *bmap2);
6812 __isl_give isl_basic_map *isl_basic_map_product(
6813 __isl_take isl_basic_map *bmap1,
6814 __isl_take isl_basic_map *bmap2);
6815 __isl_give isl_map *isl_map_domain_product(
6816 __isl_take isl_map *map1,
6817 __isl_take isl_map *map2);
6818 __isl_give isl_map *isl_map_range_product(
6819 __isl_take isl_map *map1,
6820 __isl_take isl_map *map2);
6821 __isl_give isl_map *isl_map_product(
6822 __isl_take isl_map *map1,
6823 __isl_take isl_map *map2);
6825 #include <isl/union_set.h>
6826 __isl_give isl_union_set *isl_union_set_product(
6827 __isl_take isl_union_set *uset1,
6828 __isl_take isl_union_set *uset2);
6830 #include <isl/union_map.h>
6831 __isl_give isl_union_map *isl_union_map_domain_product(
6832 __isl_take isl_union_map *umap1,
6833 __isl_take isl_union_map *umap2);
6834 __isl_give isl_union_map *isl_union_map_range_product(
6835 __isl_take isl_union_map *umap1,
6836 __isl_take isl_union_map *umap2);
6837 __isl_give isl_union_map *isl_union_map_product(
6838 __isl_take isl_union_map *umap1,
6839 __isl_take isl_union_map *umap2);
6841 #include <isl/val.h>
6842 __isl_give isl_multi_val *isl_multi_val_range_product(
6843 __isl_take isl_multi_val *mv1,
6844 __isl_take isl_multi_val *mv2);
6845 __isl_give isl_multi_val *isl_multi_val_product(
6846 __isl_take isl_multi_val *mv1,
6847 __isl_take isl_multi_val *mv2);
6849 #include <isl/aff.h>
6850 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6851 __isl_take isl_multi_aff *ma1,
6852 __isl_take isl_multi_aff *ma2);
6853 __isl_give isl_multi_aff *isl_multi_aff_product(
6854 __isl_take isl_multi_aff *ma1,
6855 __isl_take isl_multi_aff *ma2);
6856 __isl_give isl_multi_pw_aff *
6857 isl_multi_pw_aff_range_product(
6858 __isl_take isl_multi_pw_aff *mpa1,
6859 __isl_take isl_multi_pw_aff *mpa2);
6860 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6861 __isl_take isl_multi_pw_aff *mpa1,
6862 __isl_take isl_multi_pw_aff *mpa2);
6863 __isl_give isl_pw_multi_aff *
6864 isl_pw_multi_aff_range_product(
6865 __isl_take isl_pw_multi_aff *pma1,
6866 __isl_take isl_pw_multi_aff *pma2);
6867 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6868 __isl_take isl_pw_multi_aff *pma1,
6869 __isl_take isl_pw_multi_aff *pma2);
6870 __isl_give isl_multi_union_pw_aff *
6871 isl_multi_union_pw_aff_range_product(
6872 __isl_take isl_multi_union_pw_aff *mupa1,
6873 __isl_take isl_multi_union_pw_aff *mupa2);
6875 The above functions compute the cross product of the given
6876 sets, relations or functions. The domains and ranges of the results
6877 are wrapped maps between domains and ranges of the inputs.
6878 To obtain a ``flat'' product, use the following functions
6881 #include <isl/set.h>
6882 __isl_give isl_basic_set *isl_basic_set_flat_product(
6883 __isl_take isl_basic_set *bset1,
6884 __isl_take isl_basic_set *bset2);
6885 __isl_give isl_set *isl_set_flat_product(
6886 __isl_take isl_set *set1,
6887 __isl_take isl_set *set2);
6889 #include <isl/map.h>
6890 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6891 __isl_take isl_basic_map *bmap1,
6892 __isl_take isl_basic_map *bmap2);
6893 __isl_give isl_map *isl_map_flat_domain_product(
6894 __isl_take isl_map *map1,
6895 __isl_take isl_map *map2);
6896 __isl_give isl_map *isl_map_flat_range_product(
6897 __isl_take isl_map *map1,
6898 __isl_take isl_map *map2);
6899 __isl_give isl_basic_map *isl_basic_map_flat_product(
6900 __isl_take isl_basic_map *bmap1,
6901 __isl_take isl_basic_map *bmap2);
6902 __isl_give isl_map *isl_map_flat_product(
6903 __isl_take isl_map *map1,
6904 __isl_take isl_map *map2);
6906 #include <isl/union_map.h>
6907 __isl_give isl_union_map *
6908 isl_union_map_flat_domain_product(
6909 __isl_take isl_union_map *umap1,
6910 __isl_take isl_union_map *umap2);
6911 __isl_give isl_union_map *
6912 isl_union_map_flat_range_product(
6913 __isl_take isl_union_map *umap1,
6914 __isl_take isl_union_map *umap2);
6916 #include <isl/val.h>
6917 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6918 __isl_take isl_multi_val *mv1,
6919 __isl_take isl_multi_val *mv2);
6921 #include <isl/aff.h>
6922 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6923 __isl_take isl_multi_aff *ma1,
6924 __isl_take isl_multi_aff *ma2);
6925 __isl_give isl_pw_multi_aff *
6926 isl_pw_multi_aff_flat_range_product(
6927 __isl_take isl_pw_multi_aff *pma1,
6928 __isl_take isl_pw_multi_aff *pma2);
6929 __isl_give isl_multi_pw_aff *
6930 isl_multi_pw_aff_flat_range_product(
6931 __isl_take isl_multi_pw_aff *mpa1,
6932 __isl_take isl_multi_pw_aff *mpa2);
6933 __isl_give isl_union_pw_multi_aff *
6934 isl_union_pw_multi_aff_flat_range_product(
6935 __isl_take isl_union_pw_multi_aff *upma1,
6936 __isl_take isl_union_pw_multi_aff *upma2);
6937 __isl_give isl_multi_union_pw_aff *
6938 isl_multi_union_pw_aff_flat_range_product(
6939 __isl_take isl_multi_union_pw_aff *mupa1,
6940 __isl_take isl_multi_union_pw_aff *mupa2);
6942 #include <isl/space.h>
6943 __isl_give isl_space *isl_space_factor_domain(
6944 __isl_take isl_space *space);
6945 __isl_give isl_space *isl_space_factor_range(
6946 __isl_take isl_space *space);
6947 __isl_give isl_space *isl_space_domain_factor_domain(
6948 __isl_take isl_space *space);
6949 __isl_give isl_space *isl_space_domain_factor_range(
6950 __isl_take isl_space *space);
6951 __isl_give isl_space *isl_space_range_factor_domain(
6952 __isl_take isl_space *space);
6953 __isl_give isl_space *isl_space_range_factor_range(
6954 __isl_take isl_space *space);
6956 The functions C<isl_space_range_factor_domain> and
6957 C<isl_space_range_factor_range> extract the two arguments from
6958 the result of a call to C<isl_space_range_product>.
6960 The arguments of a call to a product can be extracted
6961 from the result using the following functions.
6963 #include <isl/map.h>
6964 __isl_give isl_map *isl_map_factor_domain(
6965 __isl_take isl_map *map);
6966 __isl_give isl_map *isl_map_factor_range(
6967 __isl_take isl_map *map);
6968 __isl_give isl_map *isl_map_domain_factor_domain(
6969 __isl_take isl_map *map);
6970 __isl_give isl_map *isl_map_domain_factor_range(
6971 __isl_take isl_map *map);
6972 __isl_give isl_map *isl_map_range_factor_domain(
6973 __isl_take isl_map *map);
6974 __isl_give isl_map *isl_map_range_factor_range(
6975 __isl_take isl_map *map);
6977 #include <isl/union_map.h>
6978 __isl_give isl_union_map *isl_union_map_factor_domain(
6979 __isl_take isl_union_map *umap);
6980 __isl_give isl_union_map *isl_union_map_factor_range(
6981 __isl_take isl_union_map *umap);
6982 __isl_give isl_union_map *
6983 isl_union_map_domain_factor_domain(
6984 __isl_take isl_union_map *umap);
6985 __isl_give isl_union_map *
6986 isl_union_map_domain_factor_range(
6987 __isl_take isl_union_map *umap);
6988 __isl_give isl_union_map *
6989 isl_union_map_range_factor_domain(
6990 __isl_take isl_union_map *umap);
6991 __isl_give isl_union_map *
6992 isl_union_map_range_factor_range(
6993 __isl_take isl_union_map *umap);
6995 #include <isl/val.h>
6996 __isl_give isl_multi_val *isl_multi_val_factor_range(
6997 __isl_take isl_multi_val *mv);
6998 __isl_give isl_multi_val *
6999 isl_multi_val_range_factor_domain(
7000 __isl_take isl_multi_val *mv);
7001 __isl_give isl_multi_val *
7002 isl_multi_val_range_factor_range(
7003 __isl_take isl_multi_val *mv);
7005 #include <isl/aff.h>
7006 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
7007 __isl_take isl_multi_aff *ma);
7008 __isl_give isl_multi_aff *
7009 isl_multi_aff_range_factor_domain(
7010 __isl_take isl_multi_aff *ma);
7011 __isl_give isl_multi_aff *
7012 isl_multi_aff_range_factor_range(
7013 __isl_take isl_multi_aff *ma);
7014 __isl_give isl_multi_pw_aff *
7015 isl_multi_pw_aff_factor_range(
7016 __isl_take isl_multi_pw_aff *mpa);
7017 __isl_give isl_multi_pw_aff *
7018 isl_multi_pw_aff_range_factor_domain(
7019 __isl_take isl_multi_pw_aff *mpa);
7020 __isl_give isl_multi_pw_aff *
7021 isl_multi_pw_aff_range_factor_range(
7022 __isl_take isl_multi_pw_aff *mpa);
7023 __isl_give isl_multi_union_pw_aff *
7024 isl_multi_union_pw_aff_factor_range(
7025 __isl_take isl_multi_union_pw_aff *mupa);
7026 __isl_give isl_multi_union_pw_aff *
7027 isl_multi_union_pw_aff_range_factor_domain(
7028 __isl_take isl_multi_union_pw_aff *mupa);
7029 __isl_give isl_multi_union_pw_aff *
7030 isl_multi_union_pw_aff_range_factor_range(
7031 __isl_take isl_multi_union_pw_aff *mupa);
7033 The splice functions are a generalization of the flat product functions,
7034 where the second argument may be inserted at any position inside
7035 the first argument rather than being placed at the end.
7036 The functions C<isl_multi_val_factor_range>,
7037 C<isl_multi_aff_factor_range>,
7038 C<isl_multi_pw_aff_factor_range> and
7039 C<isl_multi_union_pw_aff_factor_range>
7040 take functions that live in a set space.
7042 #include <isl/val.h>
7043 __isl_give isl_multi_val *isl_multi_val_range_splice(
7044 __isl_take isl_multi_val *mv1, unsigned pos,
7045 __isl_take isl_multi_val *mv2);
7047 #include <isl/aff.h>
7048 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
7049 __isl_take isl_multi_aff *ma1, unsigned pos,
7050 __isl_take isl_multi_aff *ma2);
7051 __isl_give isl_multi_aff *isl_multi_aff_splice(
7052 __isl_take isl_multi_aff *ma1,
7053 unsigned in_pos, unsigned out_pos,
7054 __isl_take isl_multi_aff *ma2);
7055 __isl_give isl_multi_pw_aff *
7056 isl_multi_pw_aff_range_splice(
7057 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
7058 __isl_take isl_multi_pw_aff *mpa2);
7059 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
7060 __isl_take isl_multi_pw_aff *mpa1,
7061 unsigned in_pos, unsigned out_pos,
7062 __isl_take isl_multi_pw_aff *mpa2);
7063 __isl_give isl_multi_union_pw_aff *
7064 isl_multi_union_pw_aff_range_splice(
7065 __isl_take isl_multi_union_pw_aff *mupa1,
7067 __isl_take isl_multi_union_pw_aff *mupa2);
7069 =item * Simplification
7071 When applied to a set or relation,
7072 the gist operation returns a set or relation that has the
7073 same intersection with the context as the input set or relation.
7074 Any implicit equality in the intersection is made explicit in the result,
7075 while all inequalities that are redundant with respect to the intersection
7077 In case of union sets and relations, the gist operation is performed
7080 When applied to a function,
7081 the gist operation applies the set gist operation to each of
7082 the cells in the domain of the input piecewise expression.
7083 The context is also exploited
7084 to simplify the expression associated to each cell.
7086 #include <isl/set.h>
7087 __isl_give isl_basic_set *isl_basic_set_gist(
7088 __isl_take isl_basic_set *bset,
7089 __isl_take isl_basic_set *context);
7090 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
7091 __isl_take isl_set *context);
7092 __isl_give isl_set *isl_set_gist_params(
7093 __isl_take isl_set *set,
7094 __isl_take isl_set *context);
7096 #include <isl/map.h>
7097 __isl_give isl_basic_map *isl_basic_map_gist(
7098 __isl_take isl_basic_map *bmap,
7099 __isl_take isl_basic_map *context);
7100 __isl_give isl_basic_map *isl_basic_map_gist_domain(
7101 __isl_take isl_basic_map *bmap,
7102 __isl_take isl_basic_set *context);
7103 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
7104 __isl_take isl_map *context);
7105 __isl_give isl_map *isl_map_gist_params(
7106 __isl_take isl_map *map,
7107 __isl_take isl_set *context);
7108 __isl_give isl_map *isl_map_gist_domain(
7109 __isl_take isl_map *map,
7110 __isl_take isl_set *context);
7111 __isl_give isl_map *isl_map_gist_range(
7112 __isl_take isl_map *map,
7113 __isl_take isl_set *context);
7115 #include <isl/union_set.h>
7116 __isl_give isl_union_set *isl_union_set_gist(
7117 __isl_take isl_union_set *uset,
7118 __isl_take isl_union_set *context);
7119 __isl_give isl_union_set *isl_union_set_gist_params(
7120 __isl_take isl_union_set *uset,
7121 __isl_take isl_set *set);
7123 #include <isl/union_map.h>
7124 __isl_give isl_union_map *isl_union_map_gist(
7125 __isl_take isl_union_map *umap,
7126 __isl_take isl_union_map *context);
7127 __isl_give isl_union_map *isl_union_map_gist_params(
7128 __isl_take isl_union_map *umap,
7129 __isl_take isl_set *set);
7130 __isl_give isl_union_map *isl_union_map_gist_domain(
7131 __isl_take isl_union_map *umap,
7132 __isl_take isl_union_set *uset);
7133 __isl_give isl_union_map *isl_union_map_gist_range(
7134 __isl_take isl_union_map *umap,
7135 __isl_take isl_union_set *uset);
7137 #include <isl/aff.h>
7138 __isl_give isl_aff *isl_aff_gist_params(
7139 __isl_take isl_aff *aff,
7140 __isl_take isl_set *context);
7141 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
7142 __isl_take isl_set *context);
7143 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
7144 __isl_take isl_multi_aff *maff,
7145 __isl_take isl_set *context);
7146 __isl_give isl_multi_aff *isl_multi_aff_gist(
7147 __isl_take isl_multi_aff *maff,
7148 __isl_take isl_set *context);
7149 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
7150 __isl_take isl_pw_aff *pwaff,
7151 __isl_take isl_set *context);
7152 __isl_give isl_pw_aff *isl_pw_aff_gist(
7153 __isl_take isl_pw_aff *pwaff,
7154 __isl_take isl_set *context);
7155 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
7156 __isl_take isl_pw_multi_aff *pma,
7157 __isl_take isl_set *set);
7158 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
7159 __isl_take isl_pw_multi_aff *pma,
7160 __isl_take isl_set *set);
7161 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
7162 __isl_take isl_multi_pw_aff *mpa,
7163 __isl_take isl_set *set);
7164 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
7165 __isl_take isl_multi_pw_aff *mpa,
7166 __isl_take isl_set *set);
7167 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
7168 __isl_take isl_union_pw_aff *upa,
7169 __isl_take isl_union_set *context);
7170 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
7171 __isl_take isl_union_pw_aff *upa,
7172 __isl_take isl_set *context);
7173 __isl_give isl_union_pw_multi_aff *
7174 isl_union_pw_multi_aff_gist_params(
7175 __isl_take isl_union_pw_multi_aff *upma,
7176 __isl_take isl_set *context);
7177 __isl_give isl_union_pw_multi_aff *
7178 isl_union_pw_multi_aff_gist(
7179 __isl_take isl_union_pw_multi_aff *upma,
7180 __isl_take isl_union_set *context);
7181 __isl_give isl_multi_union_pw_aff *
7182 isl_multi_union_pw_aff_gist_params(
7183 __isl_take isl_multi_union_pw_aff *aff,
7184 __isl_take isl_set *context);
7185 __isl_give isl_multi_union_pw_aff *
7186 isl_multi_union_pw_aff_gist(
7187 __isl_take isl_multi_union_pw_aff *aff,
7188 __isl_take isl_union_set *context);
7190 #include <isl/polynomial.h>
7191 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
7192 __isl_take isl_qpolynomial *qp,
7193 __isl_take isl_set *context);
7194 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
7195 __isl_take isl_qpolynomial *qp,
7196 __isl_take isl_set *context);
7197 __isl_give isl_qpolynomial_fold *
7198 isl_qpolynomial_fold_gist_params(
7199 __isl_take isl_qpolynomial_fold *fold,
7200 __isl_take isl_set *context);
7201 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7202 __isl_take isl_qpolynomial_fold *fold,
7203 __isl_take isl_set *context);
7204 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7205 __isl_take isl_pw_qpolynomial *pwqp,
7206 __isl_take isl_set *context);
7207 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7208 __isl_take isl_pw_qpolynomial *pwqp,
7209 __isl_take isl_set *context);
7210 __isl_give isl_pw_qpolynomial_fold *
7211 isl_pw_qpolynomial_fold_gist(
7212 __isl_take isl_pw_qpolynomial_fold *pwf,
7213 __isl_take isl_set *context);
7214 __isl_give isl_pw_qpolynomial_fold *
7215 isl_pw_qpolynomial_fold_gist_params(
7216 __isl_take isl_pw_qpolynomial_fold *pwf,
7217 __isl_take isl_set *context);
7218 __isl_give isl_union_pw_qpolynomial *
7219 isl_union_pw_qpolynomial_gist_params(
7220 __isl_take isl_union_pw_qpolynomial *upwqp,
7221 __isl_take isl_set *context);
7222 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7223 __isl_take isl_union_pw_qpolynomial *upwqp,
7224 __isl_take isl_union_set *context);
7225 __isl_give isl_union_pw_qpolynomial_fold *
7226 isl_union_pw_qpolynomial_fold_gist(
7227 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7228 __isl_take isl_union_set *context);
7229 __isl_give isl_union_pw_qpolynomial_fold *
7230 isl_union_pw_qpolynomial_fold_gist_params(
7231 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7232 __isl_take isl_set *context);
7234 =item * Binary Arithmetic Operations
7236 #include <isl/set.h>
7237 __isl_give isl_set *isl_set_sum(
7238 __isl_take isl_set *set1,
7239 __isl_take isl_set *set2);
7240 #include <isl/map.h>
7241 __isl_give isl_map *isl_map_sum(
7242 __isl_take isl_map *map1,
7243 __isl_take isl_map *map2);
7245 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7246 i.e., the set containing the sums of pairs of elements from
7247 C<set1> and C<set2>.
7248 The domain of the result of C<isl_map_sum> is the intersection
7249 of the domains of its two arguments. The corresponding range
7250 elements are the sums of the corresponding range elements
7251 in the two arguments.
7253 #include <isl/val.h>
7254 __isl_give isl_multi_val *isl_multi_val_add(
7255 __isl_take isl_multi_val *mv1,
7256 __isl_take isl_multi_val *mv2);
7257 __isl_give isl_multi_val *isl_multi_val_sub(
7258 __isl_take isl_multi_val *mv1,
7259 __isl_take isl_multi_val *mv2);
7261 #include <isl/aff.h>
7262 __isl_give isl_aff *isl_aff_add(
7263 __isl_take isl_aff *aff1,
7264 __isl_take isl_aff *aff2);
7265 __isl_give isl_multi_aff *isl_multi_aff_add(
7266 __isl_take isl_multi_aff *maff1,
7267 __isl_take isl_multi_aff *maff2);
7268 __isl_give isl_pw_aff *isl_pw_aff_add(
7269 __isl_take isl_pw_aff *pwaff1,
7270 __isl_take isl_pw_aff *pwaff2);
7271 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7272 __isl_take isl_multi_pw_aff *mpa1,
7273 __isl_take isl_multi_pw_aff *mpa2);
7274 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7275 __isl_take isl_pw_multi_aff *pma1,
7276 __isl_take isl_pw_multi_aff *pma2);
7277 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7278 __isl_take isl_union_pw_aff *upa1,
7279 __isl_take isl_union_pw_aff *upa2);
7280 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7281 __isl_take isl_union_pw_multi_aff *upma1,
7282 __isl_take isl_union_pw_multi_aff *upma2);
7283 __isl_give isl_multi_union_pw_aff *
7284 isl_multi_union_pw_aff_add(
7285 __isl_take isl_multi_union_pw_aff *mupa1,
7286 __isl_take isl_multi_union_pw_aff *mupa2);
7287 __isl_give isl_pw_aff *isl_pw_aff_min(
7288 __isl_take isl_pw_aff *pwaff1,
7289 __isl_take isl_pw_aff *pwaff2);
7290 __isl_give isl_pw_aff *isl_pw_aff_max(
7291 __isl_take isl_pw_aff *pwaff1,
7292 __isl_take isl_pw_aff *pwaff2);
7293 __isl_give isl_aff *isl_aff_sub(
7294 __isl_take isl_aff *aff1,
7295 __isl_take isl_aff *aff2);
7296 __isl_give isl_multi_aff *isl_multi_aff_sub(
7297 __isl_take isl_multi_aff *ma1,
7298 __isl_take isl_multi_aff *ma2);
7299 __isl_give isl_pw_aff *isl_pw_aff_sub(
7300 __isl_take isl_pw_aff *pwaff1,
7301 __isl_take isl_pw_aff *pwaff2);
7302 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7303 __isl_take isl_multi_pw_aff *mpa1,
7304 __isl_take isl_multi_pw_aff *mpa2);
7305 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7306 __isl_take isl_pw_multi_aff *pma1,
7307 __isl_take isl_pw_multi_aff *pma2);
7308 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7309 __isl_take isl_union_pw_aff *upa1,
7310 __isl_take isl_union_pw_aff *upa2);
7311 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7312 __isl_take isl_union_pw_multi_aff *upma1,
7313 __isl_take isl_union_pw_multi_aff *upma2);
7314 __isl_give isl_multi_union_pw_aff *
7315 isl_multi_union_pw_aff_sub(
7316 __isl_take isl_multi_union_pw_aff *mupa1,
7317 __isl_take isl_multi_union_pw_aff *mupa2);
7319 C<isl_aff_sub> subtracts the second argument from the first.
7321 #include <isl/polynomial.h>
7322 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7323 __isl_take isl_qpolynomial *qp1,
7324 __isl_take isl_qpolynomial *qp2);
7325 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7326 __isl_take isl_pw_qpolynomial *pwqp1,
7327 __isl_take isl_pw_qpolynomial *pwqp2);
7328 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7329 __isl_take isl_pw_qpolynomial *pwqp1,
7330 __isl_take isl_pw_qpolynomial *pwqp2);
7331 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7332 __isl_take isl_pw_qpolynomial_fold *pwf1,
7333 __isl_take isl_pw_qpolynomial_fold *pwf2);
7334 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7335 __isl_take isl_union_pw_qpolynomial *upwqp1,
7336 __isl_take isl_union_pw_qpolynomial *upwqp2);
7337 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7338 __isl_take isl_qpolynomial *qp1,
7339 __isl_take isl_qpolynomial *qp2);
7340 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7341 __isl_take isl_pw_qpolynomial *pwqp1,
7342 __isl_take isl_pw_qpolynomial *pwqp2);
7343 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7344 __isl_take isl_union_pw_qpolynomial *upwqp1,
7345 __isl_take isl_union_pw_qpolynomial *upwqp2);
7346 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7347 __isl_take isl_pw_qpolynomial_fold *pwf1,
7348 __isl_take isl_pw_qpolynomial_fold *pwf2);
7349 __isl_give isl_union_pw_qpolynomial_fold *
7350 isl_union_pw_qpolynomial_fold_fold(
7351 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7352 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7354 #include <isl/aff.h>
7355 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7356 __isl_take isl_pw_aff *pwaff1,
7357 __isl_take isl_pw_aff *pwaff2);
7358 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7359 __isl_take isl_pw_multi_aff *pma1,
7360 __isl_take isl_pw_multi_aff *pma2);
7361 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7362 __isl_take isl_union_pw_aff *upa1,
7363 __isl_take isl_union_pw_aff *upa2);
7364 __isl_give isl_union_pw_multi_aff *
7365 isl_union_pw_multi_aff_union_add(
7366 __isl_take isl_union_pw_multi_aff *upma1,
7367 __isl_take isl_union_pw_multi_aff *upma2);
7368 __isl_give isl_multi_union_pw_aff *
7369 isl_multi_union_pw_aff_union_add(
7370 __isl_take isl_multi_union_pw_aff *mupa1,
7371 __isl_take isl_multi_union_pw_aff *mupa2);
7372 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7373 __isl_take isl_pw_aff *pwaff1,
7374 __isl_take isl_pw_aff *pwaff2);
7375 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7376 __isl_take isl_pw_aff *pwaff1,
7377 __isl_take isl_pw_aff *pwaff2);
7379 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7380 expression with a domain that is the union of those of C<pwaff1> and
7381 C<pwaff2> and such that on each cell, the quasi-affine expression is
7382 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7383 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7384 associated expression is the defined one.
7385 This in contrast to the C<isl_pw_aff_max> function, which is
7386 only defined on the shared definition domain of the arguments.
7388 #include <isl/val.h>
7389 __isl_give isl_multi_val *isl_multi_val_add_val(
7390 __isl_take isl_multi_val *mv,
7391 __isl_take isl_val *v);
7392 __isl_give isl_multi_val *isl_multi_val_mod_val(
7393 __isl_take isl_multi_val *mv,
7394 __isl_take isl_val *v);
7395 __isl_give isl_multi_val *isl_multi_val_scale_val(
7396 __isl_take isl_multi_val *mv,
7397 __isl_take isl_val *v);
7398 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7399 __isl_take isl_multi_val *mv,
7400 __isl_take isl_val *v);
7402 #include <isl/aff.h>
7403 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7404 __isl_take isl_val *mod);
7405 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7406 __isl_take isl_pw_aff *pa,
7407 __isl_take isl_val *mod);
7408 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7409 __isl_take isl_union_pw_aff *upa,
7410 __isl_take isl_val *f);
7411 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7412 __isl_take isl_val *v);
7413 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7414 __isl_take isl_multi_aff *ma,
7415 __isl_take isl_val *v);
7416 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7417 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7418 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7419 __isl_take isl_multi_pw_aff *mpa,
7420 __isl_take isl_val *v);
7421 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7422 __isl_take isl_pw_multi_aff *pma,
7423 __isl_take isl_val *v);
7424 __isl_give isl_union_pw_multi_aff *
7425 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7426 __isl_take isl_union_pw_aff *upa,
7427 __isl_take isl_val *f);
7428 isl_union_pw_multi_aff_scale_val(
7429 __isl_take isl_union_pw_multi_aff *upma,
7430 __isl_take isl_val *val);
7431 __isl_give isl_multi_union_pw_aff *
7432 isl_multi_union_pw_aff_scale_val(
7433 __isl_take isl_multi_union_pw_aff *mupa,
7434 __isl_take isl_val *v);
7435 __isl_give isl_aff *isl_aff_scale_down_ui(
7436 __isl_take isl_aff *aff, unsigned f);
7437 __isl_give isl_aff *isl_aff_scale_down_val(
7438 __isl_take isl_aff *aff, __isl_take isl_val *v);
7439 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7440 __isl_take isl_multi_aff *ma,
7441 __isl_take isl_val *v);
7442 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7443 __isl_take isl_pw_aff *pa,
7444 __isl_take isl_val *f);
7445 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7446 __isl_take isl_multi_pw_aff *mpa,
7447 __isl_take isl_val *v);
7448 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7449 __isl_take isl_pw_multi_aff *pma,
7450 __isl_take isl_val *v);
7451 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7452 __isl_take isl_union_pw_aff *upa,
7453 __isl_take isl_val *v);
7454 __isl_give isl_union_pw_multi_aff *
7455 isl_union_pw_multi_aff_scale_down_val(
7456 __isl_take isl_union_pw_multi_aff *upma,
7457 __isl_take isl_val *val);
7458 __isl_give isl_multi_union_pw_aff *
7459 isl_multi_union_pw_aff_scale_down_val(
7460 __isl_take isl_multi_union_pw_aff *mupa,
7461 __isl_take isl_val *v);
7463 #include <isl/polynomial.h>
7464 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7465 __isl_take isl_qpolynomial *qp,
7466 __isl_take isl_val *v);
7467 __isl_give isl_qpolynomial_fold *
7468 isl_qpolynomial_fold_scale_val(
7469 __isl_take isl_qpolynomial_fold *fold,
7470 __isl_take isl_val *v);
7471 __isl_give isl_pw_qpolynomial *
7472 isl_pw_qpolynomial_scale_val(
7473 __isl_take isl_pw_qpolynomial *pwqp,
7474 __isl_take isl_val *v);
7475 __isl_give isl_pw_qpolynomial_fold *
7476 isl_pw_qpolynomial_fold_scale_val(
7477 __isl_take isl_pw_qpolynomial_fold *pwf,
7478 __isl_take isl_val *v);
7479 __isl_give isl_union_pw_qpolynomial *
7480 isl_union_pw_qpolynomial_scale_val(
7481 __isl_take isl_union_pw_qpolynomial *upwqp,
7482 __isl_take isl_val *v);
7483 __isl_give isl_union_pw_qpolynomial_fold *
7484 isl_union_pw_qpolynomial_fold_scale_val(
7485 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7486 __isl_take isl_val *v);
7487 __isl_give isl_qpolynomial *
7488 isl_qpolynomial_scale_down_val(
7489 __isl_take isl_qpolynomial *qp,
7490 __isl_take isl_val *v);
7491 __isl_give isl_qpolynomial_fold *
7492 isl_qpolynomial_fold_scale_down_val(
7493 __isl_take isl_qpolynomial_fold *fold,
7494 __isl_take isl_val *v);
7495 __isl_give isl_pw_qpolynomial *
7496 isl_pw_qpolynomial_scale_down_val(
7497 __isl_take isl_pw_qpolynomial *pwqp,
7498 __isl_take isl_val *v);
7499 __isl_give isl_pw_qpolynomial_fold *
7500 isl_pw_qpolynomial_fold_scale_down_val(
7501 __isl_take isl_pw_qpolynomial_fold *pwf,
7502 __isl_take isl_val *v);
7503 __isl_give isl_union_pw_qpolynomial *
7504 isl_union_pw_qpolynomial_scale_down_val(
7505 __isl_take isl_union_pw_qpolynomial *upwqp,
7506 __isl_take isl_val *v);
7507 __isl_give isl_union_pw_qpolynomial_fold *
7508 isl_union_pw_qpolynomial_fold_scale_down_val(
7509 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7510 __isl_take isl_val *v);
7512 #include <isl/val.h>
7513 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7514 __isl_take isl_multi_val *mv1,
7515 __isl_take isl_multi_val *mv2);
7516 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7517 __isl_take isl_multi_val *mv1,
7518 __isl_take isl_multi_val *mv2);
7519 __isl_give isl_multi_val *
7520 isl_multi_val_scale_down_multi_val(
7521 __isl_take isl_multi_val *mv1,
7522 __isl_take isl_multi_val *mv2);
7524 #include <isl/aff.h>
7525 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7526 __isl_take isl_multi_aff *ma,
7527 __isl_take isl_multi_val *mv);
7528 __isl_give isl_multi_union_pw_aff *
7529 isl_multi_union_pw_aff_mod_multi_val(
7530 __isl_take isl_multi_union_pw_aff *upma,
7531 __isl_take isl_multi_val *mv);
7532 __isl_give isl_multi_pw_aff *
7533 isl_multi_pw_aff_mod_multi_val(
7534 __isl_take isl_multi_pw_aff *mpa,
7535 __isl_take isl_multi_val *mv);
7536 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7537 __isl_take isl_multi_aff *ma,
7538 __isl_take isl_multi_val *mv);
7539 __isl_give isl_pw_multi_aff *
7540 isl_pw_multi_aff_scale_multi_val(
7541 __isl_take isl_pw_multi_aff *pma,
7542 __isl_take isl_multi_val *mv);
7543 __isl_give isl_multi_pw_aff *
7544 isl_multi_pw_aff_scale_multi_val(
7545 __isl_take isl_multi_pw_aff *mpa,
7546 __isl_take isl_multi_val *mv);
7547 __isl_give isl_multi_union_pw_aff *
7548 isl_multi_union_pw_aff_scale_multi_val(
7549 __isl_take isl_multi_union_pw_aff *mupa,
7550 __isl_take isl_multi_val *mv);
7551 __isl_give isl_union_pw_multi_aff *
7552 isl_union_pw_multi_aff_scale_multi_val(
7553 __isl_take isl_union_pw_multi_aff *upma,
7554 __isl_take isl_multi_val *mv);
7555 __isl_give isl_multi_aff *
7556 isl_multi_aff_scale_down_multi_val(
7557 __isl_take isl_multi_aff *ma,
7558 __isl_take isl_multi_val *mv);
7559 __isl_give isl_multi_pw_aff *
7560 isl_multi_pw_aff_scale_down_multi_val(
7561 __isl_take isl_multi_pw_aff *mpa,
7562 __isl_take isl_multi_val *mv);
7563 __isl_give isl_multi_union_pw_aff *
7564 isl_multi_union_pw_aff_scale_down_multi_val(
7565 __isl_take isl_multi_union_pw_aff *mupa,
7566 __isl_take isl_multi_val *mv);
7568 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7569 by the corresponding elements of C<mv>.
7571 #include <isl/aff.h>
7572 __isl_give isl_aff *isl_aff_mul(
7573 __isl_take isl_aff *aff1,
7574 __isl_take isl_aff *aff2);
7575 __isl_give isl_aff *isl_aff_div(
7576 __isl_take isl_aff *aff1,
7577 __isl_take isl_aff *aff2);
7578 __isl_give isl_pw_aff *isl_pw_aff_mul(
7579 __isl_take isl_pw_aff *pwaff1,
7580 __isl_take isl_pw_aff *pwaff2);
7581 __isl_give isl_pw_aff *isl_pw_aff_div(
7582 __isl_take isl_pw_aff *pa1,
7583 __isl_take isl_pw_aff *pa2);
7584 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7585 __isl_take isl_pw_aff *pa1,
7586 __isl_take isl_pw_aff *pa2);
7587 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7588 __isl_take isl_pw_aff *pa1,
7589 __isl_take isl_pw_aff *pa2);
7591 When multiplying two affine expressions, at least one of the two needs
7592 to be a constant. Similarly, when dividing an affine expression by another,
7593 the second expression needs to be a constant.
7594 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7595 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7598 #include <isl/polynomial.h>
7599 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7600 __isl_take isl_qpolynomial *qp1,
7601 __isl_take isl_qpolynomial *qp2);
7602 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7603 __isl_take isl_pw_qpolynomial *pwqp1,
7604 __isl_take isl_pw_qpolynomial *pwqp2);
7605 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7606 __isl_take isl_union_pw_qpolynomial *upwqp1,
7607 __isl_take isl_union_pw_qpolynomial *upwqp2);
7611 =head3 Lexicographic Optimization
7613 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7614 the following functions
7615 compute a set that contains the lexicographic minimum or maximum
7616 of the elements in C<set> (or C<bset>) for those values of the parameters
7617 that satisfy C<dom>.
7618 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7619 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7621 In other words, the union of the parameter values
7622 for which the result is non-empty and of C<*empty>
7625 #include <isl/set.h>
7626 __isl_give isl_set *isl_basic_set_partial_lexmin(
7627 __isl_take isl_basic_set *bset,
7628 __isl_take isl_basic_set *dom,
7629 __isl_give isl_set **empty);
7630 __isl_give isl_set *isl_basic_set_partial_lexmax(
7631 __isl_take isl_basic_set *bset,
7632 __isl_take isl_basic_set *dom,
7633 __isl_give isl_set **empty);
7634 __isl_give isl_set *isl_set_partial_lexmin(
7635 __isl_take isl_set *set, __isl_take isl_set *dom,
7636 __isl_give isl_set **empty);
7637 __isl_give isl_set *isl_set_partial_lexmax(
7638 __isl_take isl_set *set, __isl_take isl_set *dom,
7639 __isl_give isl_set **empty);
7641 Given a (basic) set C<set> (or C<bset>), the following functions simply
7642 return a set containing the lexicographic minimum or maximum
7643 of the elements in C<set> (or C<bset>).
7644 In case of union sets, the optimum is computed per space.
7646 #include <isl/set.h>
7647 __isl_give isl_set *isl_basic_set_lexmin(
7648 __isl_take isl_basic_set *bset);
7649 __isl_give isl_set *isl_basic_set_lexmax(
7650 __isl_take isl_basic_set *bset);
7651 __isl_give isl_set *isl_set_lexmin(
7652 __isl_take isl_set *set);
7653 __isl_give isl_set *isl_set_lexmax(
7654 __isl_take isl_set *set);
7655 __isl_give isl_union_set *isl_union_set_lexmin(
7656 __isl_take isl_union_set *uset);
7657 __isl_give isl_union_set *isl_union_set_lexmax(
7658 __isl_take isl_union_set *uset);
7660 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7661 the following functions
7662 compute a relation that maps each element of C<dom>
7663 to the single lexicographic minimum or maximum
7664 of the elements that are associated to that same
7665 element in C<map> (or C<bmap>).
7666 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7667 that contains the elements in C<dom> that do not map
7668 to any elements in C<map> (or C<bmap>).
7669 In other words, the union of the domain of the result and of C<*empty>
7672 #include <isl/map.h>
7673 __isl_give isl_map *isl_basic_map_partial_lexmax(
7674 __isl_take isl_basic_map *bmap,
7675 __isl_take isl_basic_set *dom,
7676 __isl_give isl_set **empty);
7677 __isl_give isl_map *isl_basic_map_partial_lexmin(
7678 __isl_take isl_basic_map *bmap,
7679 __isl_take isl_basic_set *dom,
7680 __isl_give isl_set **empty);
7681 __isl_give isl_map *isl_map_partial_lexmax(
7682 __isl_take isl_map *map, __isl_take isl_set *dom,
7683 __isl_give isl_set **empty);
7684 __isl_give isl_map *isl_map_partial_lexmin(
7685 __isl_take isl_map *map, __isl_take isl_set *dom,
7686 __isl_give isl_set **empty);
7688 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7689 return a map mapping each element in the domain of
7690 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7691 of all elements associated to that element.
7692 In case of union relations, the optimum is computed per space.
7694 #include <isl/map.h>
7695 __isl_give isl_map *isl_basic_map_lexmin(
7696 __isl_take isl_basic_map *bmap);
7697 __isl_give isl_map *isl_basic_map_lexmax(
7698 __isl_take isl_basic_map *bmap);
7699 __isl_give isl_map *isl_map_lexmin(
7700 __isl_take isl_map *map);
7701 __isl_give isl_map *isl_map_lexmax(
7702 __isl_take isl_map *map);
7703 __isl_give isl_union_map *isl_union_map_lexmin(
7704 __isl_take isl_union_map *umap);
7705 __isl_give isl_union_map *isl_union_map_lexmax(
7706 __isl_take isl_union_map *umap);
7708 The following functions return their result in the form of
7709 a piecewise multi-affine expression,
7710 but are otherwise equivalent to the corresponding functions
7711 returning a basic set or relation.
7713 #include <isl/set.h>
7714 __isl_give isl_pw_multi_aff *
7715 isl_basic_set_partial_lexmin_pw_multi_aff(
7716 __isl_take isl_basic_set *bset,
7717 __isl_take isl_basic_set *dom,
7718 __isl_give isl_set **empty);
7719 __isl_give isl_pw_multi_aff *
7720 isl_basic_set_partial_lexmax_pw_multi_aff(
7721 __isl_take isl_basic_set *bset,
7722 __isl_take isl_basic_set *dom,
7723 __isl_give isl_set **empty);
7724 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7725 __isl_take isl_set *set);
7726 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7727 __isl_take isl_set *set);
7729 #include <isl/map.h>
7730 __isl_give isl_pw_multi_aff *
7731 isl_basic_map_lexmin_pw_multi_aff(
7732 __isl_take isl_basic_map *bmap);
7733 __isl_give isl_pw_multi_aff *
7734 isl_basic_map_partial_lexmin_pw_multi_aff(
7735 __isl_take isl_basic_map *bmap,
7736 __isl_take isl_basic_set *dom,
7737 __isl_give isl_set **empty);
7738 __isl_give isl_pw_multi_aff *
7739 isl_basic_map_partial_lexmax_pw_multi_aff(
7740 __isl_take isl_basic_map *bmap,
7741 __isl_take isl_basic_set *dom,
7742 __isl_give isl_set **empty);
7743 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7744 __isl_take isl_map *map);
7745 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7746 __isl_take isl_map *map);
7748 The following functions return the lexicographic minimum or maximum
7749 on the shared domain of the inputs and the single defined function
7750 on those parts of the domain where only a single function is defined.
7752 #include <isl/aff.h>
7753 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7754 __isl_take isl_pw_multi_aff *pma1,
7755 __isl_take isl_pw_multi_aff *pma2);
7756 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7757 __isl_take isl_pw_multi_aff *pma1,
7758 __isl_take isl_pw_multi_aff *pma2);
7760 If the input to a lexicographic optimization problem has
7761 multiple constraints with the same coefficients for the optimized
7762 variables, then, by default, this symmetry is exploited by
7763 replacing those constraints by a single constraint with
7764 an abstract bound, which is in turn bounded by the corresponding terms
7765 in the original constraints.
7766 Without this optimization, the solver would typically consider
7767 all possible orderings of those original bounds, resulting in a needless
7768 decomposition of the domain.
7769 However, the optimization can also result in slowdowns since
7770 an extra parameter is introduced that may get used in additional
7772 The following option determines whether symmetry detection is applied
7773 during lexicographic optimization.
7775 #include <isl/options.h>
7776 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7778 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7782 See also \autoref{s:offline}.
7786 =head2 Ternary Operations
7788 #include <isl/aff.h>
7789 __isl_give isl_pw_aff *isl_pw_aff_cond(
7790 __isl_take isl_pw_aff *cond,
7791 __isl_take isl_pw_aff *pwaff_true,
7792 __isl_take isl_pw_aff *pwaff_false);
7794 The function C<isl_pw_aff_cond> performs a conditional operator
7795 and returns an expression that is equal to C<pwaff_true>
7796 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7797 where C<cond> is zero.
7801 Lists are defined over several element types, including
7802 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
7803 C<isl_union_pw_aff>,
7804 C<isl_union_pw_multi_aff>,
7805 C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
7807 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7808 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7809 Here we take lists of C<isl_set>s as an example.
7810 Lists can be created, copied, modified and freed using the following functions.
7812 #include <isl/set.h>
7813 __isl_give isl_set_list *isl_set_list_from_set(
7814 __isl_take isl_set *el);
7815 __isl_give isl_set_list *isl_set_list_alloc(
7816 isl_ctx *ctx, int n);
7817 __isl_give isl_set_list *isl_set_list_copy(
7818 __isl_keep isl_set_list *list);
7819 __isl_give isl_set_list *isl_set_list_insert(
7820 __isl_take isl_set_list *list, unsigned pos,
7821 __isl_take isl_set *el);
7822 __isl_give isl_set_list *isl_set_list_add(
7823 __isl_take isl_set_list *list,
7824 __isl_take isl_set *el);
7825 __isl_give isl_set_list *isl_set_list_drop(
7826 __isl_take isl_set_list *list,
7827 unsigned first, unsigned n);
7828 __isl_give isl_set_list *isl_set_list_set_set(
7829 __isl_take isl_set_list *list, int index,
7830 __isl_take isl_set *set);
7831 __isl_give isl_set_list *isl_set_list_concat(
7832 __isl_take isl_set_list *list1,
7833 __isl_take isl_set_list *list2);
7834 __isl_give isl_set_list *isl_set_list_map(
7835 __isl_take isl_set_list *list,
7836 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7839 __isl_give isl_set_list *isl_set_list_sort(
7840 __isl_take isl_set_list *list,
7841 int (*cmp)(__isl_keep isl_set *a,
7842 __isl_keep isl_set *b, void *user),
7844 __isl_null isl_set_list *isl_set_list_free(
7845 __isl_take isl_set_list *list);
7847 C<isl_set_list_alloc> creates an empty list with an initial capacity
7848 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7849 add elements to a list, increasing its capacity as needed.
7850 C<isl_set_list_from_set> creates a list with a single element.
7852 Lists can be inspected using the following functions.
7854 #include <isl/set.h>
7855 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7856 __isl_give isl_set *isl_set_list_get_set(
7857 __isl_keep isl_set_list *list, int index);
7858 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7859 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7861 isl_stat isl_set_list_foreach_scc(
7862 __isl_keep isl_set_list *list,
7863 isl_bool (*follows)(__isl_keep isl_set *a,
7864 __isl_keep isl_set *b, void *user),
7866 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7869 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7870 strongly connected components of the graph with as vertices the elements
7871 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7872 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7873 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7875 Lists can be printed using
7877 #include <isl/set.h>
7878 __isl_give isl_printer *isl_printer_print_set_list(
7879 __isl_take isl_printer *p,
7880 __isl_keep isl_set_list *list);
7882 =head2 Associative arrays
7884 Associative arrays map isl objects of a specific type to isl objects
7885 of some (other) specific type. They are defined for several pairs
7886 of types, including (C<isl_map>, C<isl_basic_set>),
7887 (C<isl_id>, C<isl_ast_expr>),
7888 (C<isl_id>, C<isl_id>) and
7889 (C<isl_id>, C<isl_pw_aff>).
7890 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7893 Associative arrays can be created, copied and freed using
7894 the following functions.
7896 #include <isl/id_to_ast_expr.h>
7897 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7898 isl_ctx *ctx, int min_size);
7899 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7900 __isl_keep isl_id_to_ast_expr *id2expr);
7901 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7902 __isl_take isl_id_to_ast_expr *id2expr);
7904 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7905 to specify the expected size of the associative array.
7906 The associative array will be grown automatically as needed.
7908 Associative arrays can be inspected using the following functions.
7910 #include <isl/id_to_ast_expr.h>
7911 __isl_give isl_maybe_isl_ast_expr
7912 isl_id_to_ast_expr_try_get(
7913 __isl_keep isl_id_to_ast_expr *id2expr,
7914 __isl_keep isl_id *key);
7915 isl_bool isl_id_to_ast_expr_has(
7916 __isl_keep isl_id_to_ast_expr *id2expr,
7917 __isl_keep isl_id *key);
7918 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7919 __isl_keep isl_id_to_ast_expr *id2expr,
7920 __isl_take isl_id *key);
7921 isl_stat isl_id_to_ast_expr_foreach(
7922 __isl_keep isl_id_to_ast_expr *id2expr,
7923 isl_stat (*fn)(__isl_take isl_id *key,
7924 __isl_take isl_ast_expr *val, void *user),
7927 The function C<isl_id_to_ast_expr_try_get> returns a structure
7928 containing two elements, C<valid> and C<value>.
7929 If there is a value associated to the key, then C<valid>
7930 is set to C<isl_bool_true> and C<value> contains a copy of
7931 the associated value. Otherwise C<value> is C<NULL> and
7932 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7933 on whether some error has occurred or there simply is no associated value.
7934 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7935 in the structure and
7936 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7938 Associative arrays can be modified using the following functions.
7940 #include <isl/id_to_ast_expr.h>
7941 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7942 __isl_take isl_id_to_ast_expr *id2expr,
7943 __isl_take isl_id *key,
7944 __isl_take isl_ast_expr *val);
7945 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7946 __isl_take isl_id_to_ast_expr *id2expr,
7947 __isl_take isl_id *key);
7949 Associative arrays can be printed using the following function.
7951 #include <isl/id_to_ast_expr.h>
7952 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7953 __isl_take isl_printer *p,
7954 __isl_keep isl_id_to_ast_expr *id2expr);
7958 Vectors can be created, copied and freed using the following functions.
7960 #include <isl/vec.h>
7961 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7963 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
7965 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7966 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7968 Note that the elements of a vector created by C<isl_vec_alloc>
7969 may have arbitrary values.
7970 A vector created by C<isl_vec_zero> has elements with value zero.
7971 The elements can be changed and inspected using the following functions.
7973 int isl_vec_size(__isl_keep isl_vec *vec);
7974 __isl_give isl_val *isl_vec_get_element_val(
7975 __isl_keep isl_vec *vec, int pos);
7976 __isl_give isl_vec *isl_vec_set_element_si(
7977 __isl_take isl_vec *vec, int pos, int v);
7978 __isl_give isl_vec *isl_vec_set_element_val(
7979 __isl_take isl_vec *vec, int pos,
7980 __isl_take isl_val *v);
7981 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7983 __isl_give isl_vec *isl_vec_set_val(
7984 __isl_take isl_vec *vec, __isl_take isl_val *v);
7985 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7986 __isl_keep isl_vec *vec2, int pos);
7988 C<isl_vec_get_element> will return a negative value if anything went wrong.
7989 In that case, the value of C<*v> is undefined.
7991 The following function can be used to concatenate two vectors.
7993 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7994 __isl_take isl_vec *vec2);
7998 Matrices can be created, copied and freed using the following functions.
8000 #include <isl/mat.h>
8001 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
8002 unsigned n_row, unsigned n_col);
8003 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
8004 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
8006 Note that the elements of a newly created matrix may have arbitrary values.
8007 The elements can be changed and inspected using the following functions.
8009 int isl_mat_rows(__isl_keep isl_mat *mat);
8010 int isl_mat_cols(__isl_keep isl_mat *mat);
8011 __isl_give isl_val *isl_mat_get_element_val(
8012 __isl_keep isl_mat *mat, int row, int col);
8013 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
8014 int row, int col, int v);
8015 __isl_give isl_mat *isl_mat_set_element_val(
8016 __isl_take isl_mat *mat, int row, int col,
8017 __isl_take isl_val *v);
8019 The following function computes the rank of a matrix.
8020 The return value may be -1 if some error occurred.
8022 #include <isl/mat.h>
8023 int isl_mat_rank(__isl_keep isl_mat *mat);
8025 The following function can be used to compute the (right) inverse
8026 of a matrix, i.e., a matrix such that the product of the original
8027 and the inverse (in that order) is a multiple of the identity matrix.
8028 The input matrix is assumed to be of full row-rank.
8030 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
8032 The following function can be used to compute the (right) kernel
8033 (or null space) of a matrix, i.e., a matrix such that the product of
8034 the original and the kernel (in that order) is the zero matrix.
8036 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
8038 The following function computes a basis for the space spanned
8039 by the rows of a matrix.
8041 __isl_give isl_mat *isl_mat_row_basis(
8042 __isl_take isl_mat *mat);
8044 The following function computes rows that extend a basis of C<mat1>
8045 to a basis that also covers C<mat2>.
8047 __isl_give isl_mat *isl_mat_row_basis_extension(
8048 __isl_take isl_mat *mat1,
8049 __isl_take isl_mat *mat2);
8051 The following function checks whether there is no linear dependence
8052 among the combined rows of "mat1" and "mat2" that is not already present
8053 in "mat1" or "mat2" individually.
8054 If "mat1" and "mat2" have linearly independent rows by themselves,
8055 then this means that there is no linear dependence among all rows together.
8057 isl_bool isl_mat_has_linearly_independent_rows(
8058 __isl_keep isl_mat *mat1,
8059 __isl_keep isl_mat *mat2);
8061 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
8063 The following functions determine
8064 an upper or lower bound on a quasipolynomial over its domain.
8066 __isl_give isl_pw_qpolynomial_fold *
8067 isl_pw_qpolynomial_bound(
8068 __isl_take isl_pw_qpolynomial *pwqp,
8069 enum isl_fold type, int *tight);
8071 __isl_give isl_union_pw_qpolynomial_fold *
8072 isl_union_pw_qpolynomial_bound(
8073 __isl_take isl_union_pw_qpolynomial *upwqp,
8074 enum isl_fold type, int *tight);
8076 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
8077 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
8078 is the returned bound is known be tight, i.e., for each value
8079 of the parameters there is at least
8080 one element in the domain that reaches the bound.
8081 If the domain of C<pwqp> is not wrapping, then the bound is computed
8082 over all elements in that domain and the result has a purely parametric
8083 domain. If the domain of C<pwqp> is wrapping, then the bound is
8084 computed over the range of the wrapped relation. The domain of the
8085 wrapped relation becomes the domain of the result.
8087 =head2 Parametric Vertex Enumeration
8089 The parametric vertex enumeration described in this section
8090 is mainly intended to be used internally and by the C<barvinok>
8093 #include <isl/vertices.h>
8094 __isl_give isl_vertices *isl_basic_set_compute_vertices(
8095 __isl_keep isl_basic_set *bset);
8097 The function C<isl_basic_set_compute_vertices> performs the
8098 actual computation of the parametric vertices and the chamber
8099 decomposition and stores the result in an C<isl_vertices> object.
8100 This information can be queried by either iterating over all
8101 the vertices or iterating over all the chambers or cells
8102 and then iterating over all vertices that are active on the chamber.
8104 isl_stat isl_vertices_foreach_vertex(
8105 __isl_keep isl_vertices *vertices,
8106 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8107 void *user), void *user);
8109 isl_stat isl_vertices_foreach_cell(
8110 __isl_keep isl_vertices *vertices,
8111 isl_stat (*fn)(__isl_take isl_cell *cell,
8112 void *user), void *user);
8113 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
8114 isl_stat (*fn)(__isl_take isl_vertex *vertex,
8115 void *user), void *user);
8117 Other operations that can be performed on an C<isl_vertices> object are
8120 int isl_vertices_get_n_vertices(
8121 __isl_keep isl_vertices *vertices);
8122 __isl_null isl_vertices *isl_vertices_free(
8123 __isl_take isl_vertices *vertices);
8125 Vertices can be inspected and destroyed using the following functions.
8127 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
8128 __isl_give isl_basic_set *isl_vertex_get_domain(
8129 __isl_keep isl_vertex *vertex);
8130 __isl_give isl_multi_aff *isl_vertex_get_expr(
8131 __isl_keep isl_vertex *vertex);
8132 void isl_vertex_free(__isl_take isl_vertex *vertex);
8134 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
8135 describing the vertex in terms of the parameters,
8136 while C<isl_vertex_get_domain> returns the activity domain
8139 Chambers can be inspected and destroyed using the following functions.
8141 __isl_give isl_basic_set *isl_cell_get_domain(
8142 __isl_keep isl_cell *cell);
8143 void isl_cell_free(__isl_take isl_cell *cell);
8145 =head1 Polyhedral Compilation Library
8147 This section collects functionality in C<isl> that has been specifically
8148 designed for use during polyhedral compilation.
8150 =head2 Schedule Trees
8152 A schedule tree is a structured representation of a schedule,
8153 assigning a relative order to a set of domain elements.
8154 The relative order expressed by the schedule tree is
8155 defined recursively. In particular, the order between
8156 two domain elements is determined by the node that is closest
8157 to the root that refers to both elements and that orders them apart.
8158 Each node in the tree is of one of several types.
8159 The root node is always of type C<isl_schedule_node_domain>
8160 (or C<isl_schedule_node_extension>)
8161 and it describes the (extra) domain elements to which the schedule applies.
8162 The other types of nodes are as follows.
8166 =item C<isl_schedule_node_band>
8168 A band of schedule dimensions. Each schedule dimension is represented
8169 by a union piecewise quasi-affine expression. If this expression
8170 assigns a different value to two domain elements, while all previous
8171 schedule dimensions in the same band assign them the same value,
8172 then the two domain elements are ordered according to these two
8174 Each expression is required to be total in the domain elements
8175 that reach the band node.
8177 =item C<isl_schedule_node_expansion>
8179 An expansion node maps each of the domain elements that reach the node
8180 to one or more domain elements. The image of this mapping forms
8181 the set of domain elements that reach the child of the expansion node.
8182 The function that maps each of the expanded domain elements
8183 to the original domain element from which it was expanded
8184 is called the contraction.
8186 =item C<isl_schedule_node_filter>
8188 A filter node does not impose any ordering, but rather intersects
8189 the set of domain elements that the current subtree refers to
8190 with a given union set. The subtree of the filter node only
8191 refers to domain elements in the intersection.
8192 A filter node is typically only used as a child of a sequence or
8195 =item C<isl_schedule_node_leaf>
8197 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
8199 =item C<isl_schedule_node_mark>
8201 A mark node can be used to attach any kind of information to a subtree
8202 of the schedule tree.
8204 =item C<isl_schedule_node_sequence>
8206 A sequence node has one or more children, each of which is a filter node.
8207 The filters on these filter nodes form a partition of
8208 the domain elements that the current subtree refers to.
8209 If two domain elements appear in distinct filters then the sequence
8210 node orders them according to the child positions of the corresponding
8213 =item C<isl_schedule_node_set>
8215 A set node is similar to a sequence node, except that
8216 it expresses that domain elements appearing in distinct filters
8217 may have any order. The order of the children of a set node
8218 is therefore also immaterial.
8222 The following node types are only supported by the AST generator.
8226 =item C<isl_schedule_node_context>
8228 The context describes constraints on the parameters and
8229 the schedule dimensions of outer
8230 bands that the AST generator may assume to hold. It is also the only
8231 kind of node that may introduce additional parameters.
8232 The space of the context is that of the flat product of the outer
8233 band nodes. In particular, if there are no outer band nodes, then
8234 this space is the unnamed zero-dimensional space.
8235 Since a context node references the outer band nodes, any tree
8236 containing a context node is considered to be anchored.
8238 =item C<isl_schedule_node_extension>
8240 An extension node instructs the AST generator to add additional
8241 domain elements that need to be scheduled.
8242 The additional domain elements are described by the range of
8243 the extension map in terms of the outer schedule dimensions,
8244 i.e., the flat product of the outer band nodes.
8245 Note that domain elements are added whenever the AST generator
8246 reaches the extension node, meaning that there are still some
8247 active domain elements for which an AST needs to be generated.
8248 The conditions under which some domain elements are still active
8249 may however not be completely described by the outer AST nodes
8250 generated at that point.
8251 Since an extension node references the outer band nodes, any tree
8252 containing an extension node is considered to be anchored.
8254 An extension node may also appear as the root of a schedule tree,
8255 when it is intended to be inserted into another tree
8256 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8257 In this case, the domain of the extension node should
8258 correspond to the flat product of the outer band nodes
8259 in this other schedule tree at the point where the extension tree
8262 =item C<isl_schedule_node_guard>
8264 The guard describes constraints on the parameters and
8265 the schedule dimensions of outer
8266 bands that need to be enforced by the outer nodes
8267 in the generated AST.
8268 That is, the part of the AST that is generated from descendants
8269 of the guard node can assume that these constraints are satisfied.
8270 The space of the guard is that of the flat product of the outer
8271 band nodes. In particular, if there are no outer band nodes, then
8272 this space is the unnamed zero-dimensional space.
8273 Since a guard node references the outer band nodes, any tree
8274 containing a guard node is considered to be anchored.
8278 Except for the C<isl_schedule_node_context> nodes,
8279 none of the nodes may introduce any parameters that were not
8280 already present in the root domain node.
8282 A schedule tree is encapsulated in an C<isl_schedule> object.
8283 The simplest such objects, those with a tree consisting of single domain node,
8284 can be created using the following functions with either an empty
8285 domain or a given domain.
8287 #include <isl/schedule.h>
8288 __isl_give isl_schedule *isl_schedule_empty(
8289 __isl_take isl_space *space);
8290 __isl_give isl_schedule *isl_schedule_from_domain(
8291 __isl_take isl_union_set *domain);
8293 The function C<isl_schedule_constraints_compute_schedule> described
8294 in L</"Scheduling"> can also be used to construct schedules.
8296 C<isl_schedule> objects may be copied and freed using the following functions.
8298 #include <isl/schedule.h>
8299 __isl_give isl_schedule *isl_schedule_copy(
8300 __isl_keep isl_schedule *sched);
8301 __isl_null isl_schedule *isl_schedule_free(
8302 __isl_take isl_schedule *sched);
8304 The following functions checks whether two C<isl_schedule> objects
8305 are obviously the same.
8307 #include <isl/schedule.h>
8308 isl_bool isl_schedule_plain_is_equal(
8309 __isl_keep isl_schedule *schedule1,
8310 __isl_keep isl_schedule *schedule2);
8312 The domain of the schedule, i.e., the domain described by the root node,
8313 can be obtained using the following function.
8315 #include <isl/schedule.h>
8316 __isl_give isl_union_set *isl_schedule_get_domain(
8317 __isl_keep isl_schedule *schedule);
8319 An extra top-level band node (right underneath the domain node) can
8320 be introduced into the schedule using the following function.
8321 The schedule tree is assumed not to have any anchored nodes.
8323 #include <isl/schedule.h>
8324 __isl_give isl_schedule *
8325 isl_schedule_insert_partial_schedule(
8326 __isl_take isl_schedule *schedule,
8327 __isl_take isl_multi_union_pw_aff *partial);
8329 A top-level context node (right underneath the domain node) can
8330 be introduced into the schedule using the following function.
8332 #include <isl/schedule.h>
8333 __isl_give isl_schedule *isl_schedule_insert_context(
8334 __isl_take isl_schedule *schedule,
8335 __isl_take isl_set *context)
8337 A top-level guard node (right underneath the domain node) can
8338 be introduced into the schedule using the following function.
8340 #include <isl/schedule.h>
8341 __isl_give isl_schedule *isl_schedule_insert_guard(
8342 __isl_take isl_schedule *schedule,
8343 __isl_take isl_set *guard)
8345 A schedule that combines two schedules either in the given
8346 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8347 or an C<isl_schedule_node_set> node,
8348 can be created using the following functions.
8350 #include <isl/schedule.h>
8351 __isl_give isl_schedule *isl_schedule_sequence(
8352 __isl_take isl_schedule *schedule1,
8353 __isl_take isl_schedule *schedule2);
8354 __isl_give isl_schedule *isl_schedule_set(
8355 __isl_take isl_schedule *schedule1,
8356 __isl_take isl_schedule *schedule2);
8358 The domains of the two input schedules need to be disjoint.
8360 The following function can be used to restrict the domain
8361 of a schedule with a domain node as root to be a subset of the given union set.
8362 This operation may remove nodes in the tree that have become
8365 #include <isl/schedule.h>
8366 __isl_give isl_schedule *isl_schedule_intersect_domain(
8367 __isl_take isl_schedule *schedule,
8368 __isl_take isl_union_set *domain);
8370 The following function can be used to simplify the domain
8371 of a schedule with a domain node as root with respect to the given
8374 #include <isl/schedule.h>
8375 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8376 __isl_take isl_schedule *schedule,
8377 __isl_take isl_set *context);
8379 The following function resets the user pointers on all parameter
8380 and tuple identifiers referenced by the nodes of the given schedule.
8382 #include <isl/schedule.h>
8383 __isl_give isl_schedule *isl_schedule_reset_user(
8384 __isl_take isl_schedule *schedule);
8386 The following function aligns the parameters of all nodes
8387 in the given schedule to the given space.
8389 #include <isl/schedule.h>
8390 __isl_give isl_schedule *isl_schedule_align_params(
8391 __isl_take isl_schedule *schedule,
8392 __isl_take isl_space *space);
8394 The following function allows the user to plug in a given function
8395 in the iteration domains. The input schedule is not allowed to contain
8396 any expansion nodes.
8398 #include <isl/schedule.h>
8399 __isl_give isl_schedule *
8400 isl_schedule_pullback_union_pw_multi_aff(
8401 __isl_take isl_schedule *schedule,
8402 __isl_take isl_union_pw_multi_aff *upma);
8404 The following function can be used to plug in the schedule C<expansion>
8405 in the leaves of C<schedule>, where C<contraction> describes how
8406 the domain elements of C<expansion> map to the domain elements
8407 at the original leaves of C<schedule>.
8408 The resulting schedule will contain expansion nodes, unless
8409 C<contraction> is an identity function.
8411 #include <isl/schedule.h>
8412 __isl_give isl_schedule *isl_schedule_expand(
8413 __isl_take isl_schedule *schedule,
8414 __isl_take isl_union_pw_multi_aff *contraction,
8415 __isl_take isl_schedule *expansion);
8417 An C<isl_union_map> representation of the schedule can be obtained
8418 from an C<isl_schedule> using the following function.
8420 #include <isl/schedule.h>
8421 __isl_give isl_union_map *isl_schedule_get_map(
8422 __isl_keep isl_schedule *sched);
8424 The resulting relation encodes the same relative ordering as
8425 the schedule by mapping the domain elements to a common schedule space.
8426 If the schedule_separate_components option is set, then the order
8427 of the children of a set node is explicitly encoded in the result.
8428 If the tree contains any expansion nodes, then the relation
8429 is formulated in terms of the expanded domain elements.
8431 Schedules can be read from input using the following functions.
8433 #include <isl/schedule.h>
8434 __isl_give isl_schedule *isl_schedule_read_from_file(
8435 isl_ctx *ctx, FILE *input);
8436 __isl_give isl_schedule *isl_schedule_read_from_str(
8437 isl_ctx *ctx, const char *str);
8439 A representation of the schedule can be printed using
8441 #include <isl/schedule.h>
8442 __isl_give isl_printer *isl_printer_print_schedule(
8443 __isl_take isl_printer *p,
8444 __isl_keep isl_schedule *schedule);
8445 __isl_give char *isl_schedule_to_str(
8446 __isl_keep isl_schedule *schedule);
8448 C<isl_schedule_to_str> prints the schedule in flow format.
8450 The schedule tree can be traversed through the use of
8451 C<isl_schedule_node> objects that point to a particular
8452 position in the schedule tree. Whenever a C<isl_schedule_node>
8453 is used to modify a node in the schedule tree, the original schedule
8454 tree is left untouched and the modifications are performed to a copy
8455 of the tree. The returned C<isl_schedule_node> then points to
8456 this modified copy of the tree.
8458 The root of the schedule tree can be obtained using the following function.
8460 #include <isl/schedule.h>
8461 __isl_give isl_schedule_node *isl_schedule_get_root(
8462 __isl_keep isl_schedule *schedule);
8464 A pointer to a newly created schedule tree with a single domain
8465 node can be created using the following functions.
8467 #include <isl/schedule_node.h>
8468 __isl_give isl_schedule_node *
8469 isl_schedule_node_from_domain(
8470 __isl_take isl_union_set *domain);
8471 __isl_give isl_schedule_node *
8472 isl_schedule_node_from_extension(
8473 __isl_take isl_union_map *extension);
8475 C<isl_schedule_node_from_extension> creates a tree with an extension
8478 Schedule nodes can be copied and freed using the following functions.
8480 #include <isl/schedule_node.h>
8481 __isl_give isl_schedule_node *isl_schedule_node_copy(
8482 __isl_keep isl_schedule_node *node);
8483 __isl_null isl_schedule_node *isl_schedule_node_free(
8484 __isl_take isl_schedule_node *node);
8486 The following functions can be used to check if two schedule
8487 nodes point to the same position in the same schedule.
8489 #include <isl/schedule_node.h>
8490 isl_bool isl_schedule_node_is_equal(
8491 __isl_keep isl_schedule_node *node1,
8492 __isl_keep isl_schedule_node *node2);
8494 The following properties can be obtained from a schedule node.
8496 #include <isl/schedule_node.h>
8497 enum isl_schedule_node_type isl_schedule_node_get_type(
8498 __isl_keep isl_schedule_node *node);
8499 enum isl_schedule_node_type
8500 isl_schedule_node_get_parent_type(
8501 __isl_keep isl_schedule_node *node);
8502 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8503 __isl_keep isl_schedule_node *node);
8505 The function C<isl_schedule_node_get_type> returns the type of
8506 the node, while C<isl_schedule_node_get_parent_type> returns
8507 type of the parent of the node, which is required to exist.
8508 The function C<isl_schedule_node_get_schedule> returns a copy
8509 to the schedule to which the node belongs.
8511 The following functions can be used to move the schedule node
8512 to a different position in the tree or to check if such a position
8515 #include <isl/schedule_node.h>
8516 isl_bool isl_schedule_node_has_parent(
8517 __isl_keep isl_schedule_node *node);
8518 __isl_give isl_schedule_node *isl_schedule_node_parent(
8519 __isl_take isl_schedule_node *node);
8520 __isl_give isl_schedule_node *isl_schedule_node_root(
8521 __isl_take isl_schedule_node *node);
8522 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8523 __isl_take isl_schedule_node *node,
8525 int isl_schedule_node_n_children(
8526 __isl_keep isl_schedule_node *node);
8527 __isl_give isl_schedule_node *isl_schedule_node_child(
8528 __isl_take isl_schedule_node *node, int pos);
8529 isl_bool isl_schedule_node_has_children(
8530 __isl_keep isl_schedule_node *node);
8531 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8532 __isl_take isl_schedule_node *node);
8533 isl_bool isl_schedule_node_has_previous_sibling(
8534 __isl_keep isl_schedule_node *node);
8535 __isl_give isl_schedule_node *
8536 isl_schedule_node_previous_sibling(
8537 __isl_take isl_schedule_node *node);
8538 isl_bool isl_schedule_node_has_next_sibling(
8539 __isl_keep isl_schedule_node *node);
8540 __isl_give isl_schedule_node *
8541 isl_schedule_node_next_sibling(
8542 __isl_take isl_schedule_node *node);
8544 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8545 is the node itself, the ancestor of generation 1 is its parent and so on.
8547 It is also possible to query the number of ancestors of a node,
8548 the position of the current node
8549 within the children of its parent, the position of the subtree
8550 containing a node within the children of an ancestor
8551 or to obtain a copy of a given
8552 child without destroying the current node.
8553 Given two nodes that point to the same schedule, their closest
8554 shared ancestor can be obtained using
8555 C<isl_schedule_node_get_shared_ancestor>.
8557 #include <isl/schedule_node.h>
8558 int isl_schedule_node_get_tree_depth(
8559 __isl_keep isl_schedule_node *node);
8560 int isl_schedule_node_get_child_position(
8561 __isl_keep isl_schedule_node *node);
8562 int isl_schedule_node_get_ancestor_child_position(
8563 __isl_keep isl_schedule_node *node,
8564 __isl_keep isl_schedule_node *ancestor);
8565 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8566 __isl_keep isl_schedule_node *node, int pos);
8567 __isl_give isl_schedule_node *
8568 isl_schedule_node_get_shared_ancestor(
8569 __isl_keep isl_schedule_node *node1,
8570 __isl_keep isl_schedule_node *node2);
8572 All nodes in a schedule tree or
8573 all descendants of a specific node (including the node) can be visited
8574 in depth-first pre-order using the following functions.
8576 #include <isl/schedule.h>
8577 isl_stat isl_schedule_foreach_schedule_node_top_down(
8578 __isl_keep isl_schedule *sched,
8579 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8580 void *user), void *user);
8582 #include <isl/schedule_node.h>
8583 isl_stat isl_schedule_node_foreach_descendant_top_down(
8584 __isl_keep isl_schedule_node *node,
8585 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8586 void *user), void *user);
8588 The callback function is slightly different from the usual
8589 callbacks in that it not only indicates success (non-negative result)
8590 or failure (negative result), but also indicates whether the children
8591 of the given node should be visited. In particular, if the callback
8592 returns a positive value, then the children are visited, but if
8593 the callback returns zero, then the children are not visited.
8595 The following functions checks whether
8596 all descendants of a specific node (including the node itself)
8597 satisfy a user-specified test.
8599 #include <isl/schedule_node.h>
8600 isl_bool isl_schedule_node_every_descendant(
8601 __isl_keep isl_schedule_node *node,
8602 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8603 void *user), void *user)
8605 The ancestors of a node in a schedule tree can be visited from
8606 the root down to and including the parent of the node using
8607 the following function.
8609 #include <isl/schedule_node.h>
8610 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8611 __isl_keep isl_schedule_node *node,
8612 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8613 void *user), void *user);
8615 The following functions allows for a depth-first post-order
8616 traversal of the nodes in a schedule tree or
8617 of the descendants of a specific node (including the node
8618 itself), where the user callback is allowed to modify the
8621 #include <isl/schedule.h>
8622 __isl_give isl_schedule *
8623 isl_schedule_map_schedule_node_bottom_up(
8624 __isl_take isl_schedule *schedule,
8625 __isl_give isl_schedule_node *(*fn)(
8626 __isl_take isl_schedule_node *node,
8627 void *user), void *user);
8629 #include <isl/schedule_node.h>
8630 __isl_give isl_schedule_node *
8631 isl_schedule_node_map_descendant_bottom_up(
8632 __isl_take isl_schedule_node *node,
8633 __isl_give isl_schedule_node *(*fn)(
8634 __isl_take isl_schedule_node *node,
8635 void *user), void *user);
8637 The traversal continues from the node returned by the callback function.
8638 It is the responsibility of the user to ensure that this does not
8639 lead to an infinite loop. It is safest to always return a pointer
8640 to the same position (same ancestors and child positions) as the input node.
8642 The following function removes a node (along with its descendants)
8643 from a schedule tree and returns a pointer to the leaf at the
8644 same position in the updated tree.
8645 It is not allowed to remove the root of a schedule tree or
8646 a child of a set or sequence node.
8648 #include <isl/schedule_node.h>
8649 __isl_give isl_schedule_node *isl_schedule_node_cut(
8650 __isl_take isl_schedule_node *node);
8652 The following function removes a single node
8653 from a schedule tree and returns a pointer to the child
8654 of the node, now located at the position of the original node
8655 or to a leaf node at that position if there was no child.
8656 It is not allowed to remove the root of a schedule tree,
8657 a set or sequence node, a child of a set or sequence node or
8658 a band node with an anchored subtree.
8660 #include <isl/schedule_node.h>
8661 __isl_give isl_schedule_node *isl_schedule_node_delete(
8662 __isl_take isl_schedule_node *node);
8664 Most nodes in a schedule tree only contain local information.
8665 In some cases, however, a node may also refer to the schedule dimensions
8666 of its outer band nodes.
8667 This means that the position of the node within the tree should
8668 not be changed, or at least that no changes are performed to the
8669 outer band nodes. The following function can be used to test
8670 whether the subtree rooted at a given node contains any such nodes.
8672 #include <isl/schedule_node.h>
8673 isl_bool isl_schedule_node_is_subtree_anchored(
8674 __isl_keep isl_schedule_node *node);
8676 The following function resets the user pointers on all parameter
8677 and tuple identifiers referenced by the given schedule node.
8679 #include <isl/schedule_node.h>
8680 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8681 __isl_take isl_schedule_node *node);
8683 The following function aligns the parameters of the given schedule
8684 node to the given space.
8686 #include <isl/schedule_node.h>
8687 __isl_give isl_schedule_node *
8688 isl_schedule_node_align_params(
8689 __isl_take isl_schedule_node *node,
8690 __isl_take isl_space *space);
8692 Several node types have their own functions for querying
8693 (and in some cases setting) some node type specific properties.
8695 #include <isl/schedule_node.h>
8696 __isl_give isl_space *isl_schedule_node_band_get_space(
8697 __isl_keep isl_schedule_node *node);
8698 __isl_give isl_multi_union_pw_aff *
8699 isl_schedule_node_band_get_partial_schedule(
8700 __isl_keep isl_schedule_node *node);
8701 __isl_give isl_union_map *
8702 isl_schedule_node_band_get_partial_schedule_union_map(
8703 __isl_keep isl_schedule_node *node);
8704 unsigned isl_schedule_node_band_n_member(
8705 __isl_keep isl_schedule_node *node);
8706 isl_bool isl_schedule_node_band_member_get_coincident(
8707 __isl_keep isl_schedule_node *node, int pos);
8708 __isl_give isl_schedule_node *
8709 isl_schedule_node_band_member_set_coincident(
8710 __isl_take isl_schedule_node *node, int pos,
8712 isl_bool isl_schedule_node_band_get_permutable(
8713 __isl_keep isl_schedule_node *node);
8714 __isl_give isl_schedule_node *
8715 isl_schedule_node_band_set_permutable(
8716 __isl_take isl_schedule_node *node, int permutable);
8717 enum isl_ast_loop_type
8718 isl_schedule_node_band_member_get_ast_loop_type(
8719 __isl_keep isl_schedule_node *node, int pos);
8720 __isl_give isl_schedule_node *
8721 isl_schedule_node_band_member_set_ast_loop_type(
8722 __isl_take isl_schedule_node *node, int pos,
8723 enum isl_ast_loop_type type);
8724 __isl_give isl_union_set *
8725 enum isl_ast_loop_type
8726 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8727 __isl_keep isl_schedule_node *node, int pos);
8728 __isl_give isl_schedule_node *
8729 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8730 __isl_take isl_schedule_node *node, int pos,
8731 enum isl_ast_loop_type type);
8732 isl_schedule_node_band_get_ast_build_options(
8733 __isl_keep isl_schedule_node *node);
8734 __isl_give isl_schedule_node *
8735 isl_schedule_node_band_set_ast_build_options(
8736 __isl_take isl_schedule_node *node,
8737 __isl_take isl_union_set *options);
8738 __isl_give isl_set *
8739 isl_schedule_node_band_get_ast_isolate_option(
8740 __isl_keep isl_schedule_node *node);
8742 The function C<isl_schedule_node_band_get_space> returns the space
8743 of the partial schedule of the band.
8744 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8745 returns a representation of the partial schedule of the band node
8746 in the form of an C<isl_union_map>.
8747 The coincident and permutable properties are set by
8748 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8750 A scheduling dimension is considered to be ``coincident''
8751 if it satisfies the coincidence constraints within its band.
8752 That is, if the dependence distances of the coincidence
8753 constraints are all zero in that direction (for fixed
8754 iterations of outer bands).
8755 A band is marked permutable if it was produced using the Pluto-like scheduler.
8756 Note that the scheduler may have to resort to a Feautrier style scheduling
8757 step even if the default scheduler is used.
8758 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8759 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8760 For the meaning of these loop AST generation types and the difference
8761 between the regular loop AST generation type and the isolate
8762 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8763 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8764 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8765 may return C<isl_ast_loop_error> if an error occurs.
8766 The AST build options govern how an AST is generated for
8767 the individual schedule dimensions during AST generation.
8768 See L</"AST Generation Options (Schedule Tree)">.
8769 The isolate option for the given node can be extracted from these
8770 AST build options using the function
8771 C<isl_schedule_node_band_get_ast_isolate_option>.
8773 #include <isl/schedule_node.h>
8774 __isl_give isl_set *
8775 isl_schedule_node_context_get_context(
8776 __isl_keep isl_schedule_node *node);
8778 #include <isl/schedule_node.h>
8779 __isl_give isl_union_set *
8780 isl_schedule_node_domain_get_domain(
8781 __isl_keep isl_schedule_node *node);
8783 #include <isl/schedule_node.h>
8784 __isl_give isl_union_map *
8785 isl_schedule_node_expansion_get_expansion(
8786 __isl_keep isl_schedule_node *node);
8787 __isl_give isl_union_pw_multi_aff *
8788 isl_schedule_node_expansion_get_contraction(
8789 __isl_keep isl_schedule_node *node);
8791 #include <isl/schedule_node.h>
8792 __isl_give isl_union_map *
8793 isl_schedule_node_extension_get_extension(
8794 __isl_keep isl_schedule_node *node);
8796 #include <isl/schedule_node.h>
8797 __isl_give isl_union_set *
8798 isl_schedule_node_filter_get_filter(
8799 __isl_keep isl_schedule_node *node);
8801 #include <isl/schedule_node.h>
8802 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8803 __isl_keep isl_schedule_node *node);
8805 #include <isl/schedule_node.h>
8806 __isl_give isl_id *isl_schedule_node_mark_get_id(
8807 __isl_keep isl_schedule_node *node);
8809 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8810 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8811 partial schedules related to the node.
8813 #include <isl/schedule_node.h>
8814 __isl_give isl_multi_union_pw_aff *
8815 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8816 __isl_keep isl_schedule_node *node);
8817 __isl_give isl_union_pw_multi_aff *
8818 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8819 __isl_keep isl_schedule_node *node);
8820 __isl_give isl_union_map *
8821 isl_schedule_node_get_prefix_schedule_union_map(
8822 __isl_keep isl_schedule_node *node);
8823 __isl_give isl_union_map *
8824 isl_schedule_node_get_prefix_schedule_relation(
8825 __isl_keep isl_schedule_node *node);
8826 __isl_give isl_union_map *
8827 isl_schedule_node_get_subtree_schedule_union_map(
8828 __isl_keep isl_schedule_node *node);
8830 In particular, the functions
8831 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8832 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8833 and C<isl_schedule_node_get_prefix_schedule_union_map>
8834 return a relative ordering on the domain elements that reach the given
8835 node determined by its ancestors.
8836 The function C<isl_schedule_node_get_prefix_schedule_relation>
8837 additionally includes the domain constraints in the result.
8838 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8839 returns a representation of the partial schedule defined by the
8840 subtree rooted at the given node.
8841 If the tree contains any expansion nodes, then the subtree schedule
8842 is formulated in terms of the expanded domain elements.
8843 The tree passed to functions returning a prefix schedule
8844 may only contain extension nodes if these would not affect
8845 the result of these functions. That is, if one of the ancestors
8846 is an extension node, then all of the domain elements that were
8847 added by the extension node need to have been filtered out
8848 by filter nodes between the extension node and the input node.
8849 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8850 may not contain in extension nodes in the selected subtree.
8852 The expansion/contraction defined by an entire subtree, combining
8853 the expansions/contractions
8854 on the expansion nodes in the subtree, can be obtained using
8855 the following functions.
8857 #include <isl/schedule_node.h>
8858 __isl_give isl_union_map *
8859 isl_schedule_node_get_subtree_expansion(
8860 __isl_keep isl_schedule_node *node);
8861 __isl_give isl_union_pw_multi_aff *
8862 isl_schedule_node_get_subtree_contraction(
8863 __isl_keep isl_schedule_node *node);
8865 The total number of outer band members of given node, i.e.,
8866 the shared output dimension of the maps in the result
8867 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8868 using the following function.
8870 #include <isl/schedule_node.h>
8871 int isl_schedule_node_get_schedule_depth(
8872 __isl_keep isl_schedule_node *node);
8874 The following functions return the elements that reach the given node
8875 or the union of universes in the spaces that contain these elements.
8877 #include <isl/schedule_node.h>
8878 __isl_give isl_union_set *
8879 isl_schedule_node_get_domain(
8880 __isl_keep isl_schedule_node *node);
8881 __isl_give isl_union_set *
8882 isl_schedule_node_get_universe_domain(
8883 __isl_keep isl_schedule_node *node);
8885 The input tree of C<isl_schedule_node_get_domain>
8886 may only contain extension nodes if these would not affect
8887 the result of this function. That is, if one of the ancestors
8888 is an extension node, then all of the domain elements that were
8889 added by the extension node need to have been filtered out
8890 by filter nodes between the extension node and the input node.
8892 The following functions can be used to introduce additional nodes
8893 in the schedule tree. The new node is introduced at the point
8894 in the tree where the C<isl_schedule_node> points to and
8895 the results points to the new node.
8897 #include <isl/schedule_node.h>
8898 __isl_give isl_schedule_node *
8899 isl_schedule_node_insert_partial_schedule(
8900 __isl_take isl_schedule_node *node,
8901 __isl_take isl_multi_union_pw_aff *schedule);
8903 This function inserts a new band node with (the greatest integer
8904 part of) the given partial schedule.
8905 The subtree rooted at the given node is assumed not to have
8908 #include <isl/schedule_node.h>
8909 __isl_give isl_schedule_node *
8910 isl_schedule_node_insert_context(
8911 __isl_take isl_schedule_node *node,
8912 __isl_take isl_set *context);
8914 This function inserts a new context node with the given context constraints.
8916 #include <isl/schedule_node.h>
8917 __isl_give isl_schedule_node *
8918 isl_schedule_node_insert_filter(
8919 __isl_take isl_schedule_node *node,
8920 __isl_take isl_union_set *filter);
8922 This function inserts a new filter node with the given filter.
8923 If the original node already pointed to a filter node, then the
8924 two filter nodes are merged into one.
8926 #include <isl/schedule_node.h>
8927 __isl_give isl_schedule_node *
8928 isl_schedule_node_insert_guard(
8929 __isl_take isl_schedule_node *node,
8930 __isl_take isl_set *guard);
8932 This function inserts a new guard node with the given guard constraints.
8934 #include <isl/schedule_node.h>
8935 __isl_give isl_schedule_node *
8936 isl_schedule_node_insert_mark(
8937 __isl_take isl_schedule_node *node,
8938 __isl_take isl_id *mark);
8940 This function inserts a new mark node with the give mark identifier.
8942 #include <isl/schedule_node.h>
8943 __isl_give isl_schedule_node *
8944 isl_schedule_node_insert_sequence(
8945 __isl_take isl_schedule_node *node,
8946 __isl_take isl_union_set_list *filters);
8947 __isl_give isl_schedule_node *
8948 isl_schedule_node_insert_set(
8949 __isl_take isl_schedule_node *node,
8950 __isl_take isl_union_set_list *filters);
8952 These functions insert a new sequence or set node with the given
8953 filters as children.
8955 #include <isl/schedule_node.h>
8956 __isl_give isl_schedule_node *isl_schedule_node_group(
8957 __isl_take isl_schedule_node *node,
8958 __isl_take isl_id *group_id);
8960 This function introduces an expansion node in between the current
8961 node and its parent that expands instances of a space with tuple
8962 identifier C<group_id> to the original domain elements that reach
8963 the node. The group instances are identified by the prefix schedule
8964 of those domain elements. The ancestors of the node are adjusted
8965 to refer to the group instances instead of the original domain
8966 elements. The return value points to the same node in the updated
8967 schedule tree as the input node, i.e., to the child of the newly
8968 introduced expansion node. Grouping instances of different statements
8969 ensures that they will be treated as a single statement by the
8970 AST generator up to the point of the expansion node.
8972 The following function can be used to flatten a nested
8975 #include <isl/schedule_node.h>
8976 __isl_give isl_schedule_node *
8977 isl_schedule_node_sequence_splice_child(
8978 __isl_take isl_schedule_node *node, int pos);
8980 That is, given a sequence node C<node> that has another sequence node
8981 in its child at position C<pos> (in particular, the child of that filter
8982 node is a sequence node), attach the children of that other sequence
8983 node as children of C<node>, replacing the original child at position
8986 The partial schedule of a band node can be scaled (down) or reduced using
8987 the following functions.
8989 #include <isl/schedule_node.h>
8990 __isl_give isl_schedule_node *
8991 isl_schedule_node_band_scale(
8992 __isl_take isl_schedule_node *node,
8993 __isl_take isl_multi_val *mv);
8994 __isl_give isl_schedule_node *
8995 isl_schedule_node_band_scale_down(
8996 __isl_take isl_schedule_node *node,
8997 __isl_take isl_multi_val *mv);
8998 __isl_give isl_schedule_node *
8999 isl_schedule_node_band_mod(
9000 __isl_take isl_schedule_node *node,
9001 __isl_take isl_multi_val *mv);
9003 The spaces of the two arguments need to match.
9004 After scaling, the partial schedule is replaced by its greatest
9005 integer part to ensure that the schedule remains integral.
9007 The partial schedule of a band node can be shifted by an
9008 C<isl_multi_union_pw_aff> with a domain that is a superset
9009 of the domain of the partial schedule using
9010 the following function.
9012 #include <isl/schedule_node.h>
9013 __isl_give isl_schedule_node *
9014 isl_schedule_node_band_shift(
9015 __isl_take isl_schedule_node *node,
9016 __isl_take isl_multi_union_pw_aff *shift);
9018 A band node can be tiled using the following function.
9020 #include <isl/schedule_node.h>
9021 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
9022 __isl_take isl_schedule_node *node,
9023 __isl_take isl_multi_val *sizes);
9025 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
9027 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
9028 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
9030 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
9032 The C<isl_schedule_node_band_tile> function tiles
9033 the band using the given tile sizes inside its schedule.
9034 A new child band node is created to represent the point loops and it is
9035 inserted between the modified band and its children.
9036 The subtree rooted at the given node is assumed not to have
9038 The C<tile_scale_tile_loops> option specifies whether the tile
9039 loops iterators should be scaled by the tile sizes.
9040 If the C<tile_shift_point_loops> option is set, then the point loops
9041 are shifted to start at zero.
9043 A band node can be split into two nested band nodes
9044 using the following function.
9046 #include <isl/schedule_node.h>
9047 __isl_give isl_schedule_node *isl_schedule_node_band_split(
9048 __isl_take isl_schedule_node *node, int pos);
9050 The resulting outer band node contains the first C<pos> dimensions of
9051 the schedule of C<node> while the inner band contains the remaining dimensions.
9052 The schedules of the two band nodes live in anonymous spaces.
9053 The loop AST generation type options and the isolate option
9054 are split over the two band nodes.
9056 A band node can be moved down to the leaves of the subtree rooted
9057 at the band node using the following function.
9059 #include <isl/schedule_node.h>
9060 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
9061 __isl_take isl_schedule_node *node);
9063 The subtree rooted at the given node is assumed not to have
9065 The result points to the node in the resulting tree that is in the same
9066 position as the node pointed to by C<node> in the original tree.
9068 #include <isl/schedule_node.h>
9069 __isl_give isl_schedule_node *
9070 isl_schedule_node_order_before(
9071 __isl_take isl_schedule_node *node,
9072 __isl_take isl_union_set *filter);
9073 __isl_give isl_schedule_node *
9074 isl_schedule_node_order_after(
9075 __isl_take isl_schedule_node *node,
9076 __isl_take isl_union_set *filter);
9078 These functions split the domain elements that reach C<node>
9079 into those that satisfy C<filter> and those that do not and
9080 arranges for the elements that do satisfy the filter to be
9081 executed before (in case of C<isl_schedule_node_order_before>)
9082 or after (in case of C<isl_schedule_node_order_after>)
9083 those that do not. The order is imposed by
9084 a sequence node, possibly reusing the grandparent of C<node>
9085 on two copies of the subtree attached to the original C<node>.
9086 Both copies are simplified with respect to their filter.
9088 Return a pointer to the copy of the subtree that does not
9089 satisfy C<filter>. If there is no such copy (because all
9090 reaching domain elements satisfy the filter), then return
9091 the original pointer.
9093 #include <isl/schedule_node.h>
9094 __isl_give isl_schedule_node *
9095 isl_schedule_node_graft_before(
9096 __isl_take isl_schedule_node *node,
9097 __isl_take isl_schedule_node *graft);
9098 __isl_give isl_schedule_node *
9099 isl_schedule_node_graft_after(
9100 __isl_take isl_schedule_node *node,
9101 __isl_take isl_schedule_node *graft);
9103 This function inserts the C<graft> tree into the tree containing C<node>
9104 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
9105 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
9106 The root node of C<graft>
9107 should be an extension node where the domain of the extension
9108 is the flat product of all outer band nodes of C<node>.
9109 The root node may also be a domain node.
9110 The elements of the domain or the range of the extension may not
9111 intersect with the domain elements that reach "node".
9112 The schedule tree of C<graft> may not be anchored.
9114 The schedule tree of C<node> is modified to include an extension node
9115 corresponding to the root node of C<graft> as a child of the original
9116 parent of C<node>. The original node that C<node> points to and the
9117 child of the root node of C<graft> are attached to this extension node
9118 through a sequence, with appropriate filters and with the child
9119 of C<graft> appearing before or after the original C<node>.
9121 If C<node> already appears inside a sequence that is the child of
9122 an extension node and if the spaces of the new domain elements
9123 do not overlap with those of the original domain elements,
9124 then that extension node is extended with the new extension
9125 rather than introducing a new segment of extension and sequence nodes.
9127 Return a pointer to the same node in the modified tree that
9128 C<node> pointed to in the original tree.
9130 A representation of the schedule node can be printed using
9132 #include <isl/schedule_node.h>
9133 __isl_give isl_printer *isl_printer_print_schedule_node(
9134 __isl_take isl_printer *p,
9135 __isl_keep isl_schedule_node *node);
9136 __isl_give char *isl_schedule_node_to_str(
9137 __isl_keep isl_schedule_node *node);
9139 C<isl_schedule_node_to_str> prints the schedule node in block format.
9141 =head2 Dependence Analysis
9143 C<isl> contains specialized functionality for performing
9144 array dataflow analysis. That is, given a I<sink> access relation,
9145 a collection of possible I<source> accesses and
9146 a collection of I<kill> accesses,
9147 C<isl> can compute relations that describe
9148 for each iteration of the sink access, which iterations
9149 of which of the source access relations may have
9150 accessed the same data element before the given iteration
9151 of the sink access without any intermediate kill of that data element.
9152 The resulting dependence relations map source iterations
9153 to either the corresponding sink iterations or
9154 pairs of corresponding sink iterations and accessed data elements.
9155 To compute standard flow dependences, the sink should be
9156 a read, while the sources should be writes.
9157 If no kills are specified,
9158 then memory based dependence analysis is performed.
9159 If, on the other hand, all sources are also kills,
9160 then value based dependence analysis is performed.
9161 If any of the source accesses are marked as being I<must>
9162 accesses, then they are also treated as kills.
9163 Furthermore, the specification of must-sources results
9164 in the computation of must-dependences.
9165 Only dependences originating in a must access not coscheduled
9166 with any other access to the same element and without
9167 any may accesses between the must access and the sink access
9168 are considered to be must dependences.
9170 =head3 High-level Interface
9172 A high-level interface to dependence analysis is provided
9173 by the following function.
9175 #include <isl/flow.h>
9176 __isl_give isl_union_flow *
9177 isl_union_access_info_compute_flow(
9178 __isl_take isl_union_access_info *access);
9180 The input C<isl_union_access_info> object describes the sink
9181 access relations, the source access relations and a schedule,
9182 while the output C<isl_union_flow> object describes
9183 the resulting dependence relations and the subsets of the
9184 sink relations for which no source was found.
9186 An C<isl_union_access_info> is created, modified, copied and freed using
9187 the following functions.
9189 #include <isl/flow.h>
9190 __isl_give isl_union_access_info *
9191 isl_union_access_info_from_sink(
9192 __isl_take isl_union_map *sink);
9193 __isl_give isl_union_access_info *
9194 isl_union_access_info_set_kill(
9195 __isl_take isl_union_access_info *access,
9196 __isl_take isl_union_map *kill);
9197 __isl_give isl_union_access_info *
9198 isl_union_access_info_set_may_source(
9199 __isl_take isl_union_access_info *access,
9200 __isl_take isl_union_map *may_source);
9201 __isl_give isl_union_access_info *
9202 isl_union_access_info_set_must_source(
9203 __isl_take isl_union_access_info *access,
9204 __isl_take isl_union_map *must_source);
9205 __isl_give isl_union_access_info *
9206 isl_union_access_info_set_schedule(
9207 __isl_take isl_union_access_info *access,
9208 __isl_take isl_schedule *schedule);
9209 __isl_give isl_union_access_info *
9210 isl_union_access_info_set_schedule_map(
9211 __isl_take isl_union_access_info *access,
9212 __isl_take isl_union_map *schedule_map);
9213 __isl_give isl_union_access_info *
9214 isl_union_access_info_copy(
9215 __isl_keep isl_union_access_info *access);
9216 __isl_null isl_union_access_info *
9217 isl_union_access_info_free(
9218 __isl_take isl_union_access_info *access);
9220 The may sources set by C<isl_union_access_info_set_may_source>
9221 do not need to include the must sources set by
9222 C<isl_union_access_info_set_must_source> as a subset.
9223 The kills set by C<isl_union_access_info_set_kill> may overlap
9224 with the may-sources and/or must-sources.
9225 The user is free not to call one (or more) of these functions,
9226 in which case the corresponding set is kept to its empty default.
9227 Similarly, the default schedule initialized by
9228 C<isl_union_access_info_from_sink> is empty.
9229 The current schedule is determined by the last call to either
9230 C<isl_union_access_info_set_schedule> or
9231 C<isl_union_access_info_set_schedule_map>.
9232 The domain of the schedule corresponds to the domains of
9233 the access relations. In particular, the domains of the access
9234 relations are effectively intersected with the domain of the schedule
9235 and only the resulting accesses are considered by the dependence analysis.
9237 An C<isl_union_access_info> object can be read from input
9238 using the following function.
9240 #include <isl/flow.h>
9241 __isl_give isl_union_access_info *
9242 isl_union_access_info_read_from_file(isl_ctx *ctx,
9245 A representation of the information contained in an object
9246 of type C<isl_union_access_info> can be obtained using
9248 #include <isl/flow.h>
9249 __isl_give isl_printer *
9250 isl_printer_print_union_access_info(
9251 __isl_take isl_printer *p,
9252 __isl_keep isl_union_access_info *access);
9253 __isl_give char *isl_union_access_info_to_str(
9254 __isl_keep isl_union_access_info *access);
9256 C<isl_union_access_info_to_str> prints the information in flow format.
9258 The output of C<isl_union_access_info_compute_flow> can be examined,
9259 copied, and freed using the following functions.
9261 #include <isl/flow.h>
9262 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9263 __isl_keep isl_union_flow *flow);
9264 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9265 __isl_keep isl_union_flow *flow);
9266 __isl_give isl_union_map *
9267 isl_union_flow_get_full_must_dependence(
9268 __isl_keep isl_union_flow *flow);
9269 __isl_give isl_union_map *
9270 isl_union_flow_get_full_may_dependence(
9271 __isl_keep isl_union_flow *flow);
9272 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9273 __isl_keep isl_union_flow *flow);
9274 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9275 __isl_keep isl_union_flow *flow);
9276 __isl_give isl_union_flow *isl_union_flow_copy(
9277 __isl_keep isl_union_flow *flow);
9278 __isl_null isl_union_flow *isl_union_flow_free(
9279 __isl_take isl_union_flow *flow);
9281 The relation returned by C<isl_union_flow_get_must_dependence>
9282 relates domain elements of must sources to domain elements of the sink.
9283 The relation returned by C<isl_union_flow_get_may_dependence>
9284 relates domain elements of must or may sources to domain elements of the sink
9285 and includes the previous relation as a subset.
9286 The relation returned by C<isl_union_flow_get_full_must_dependence>
9287 relates domain elements of must sources to pairs of domain elements of the sink
9288 and accessed data elements.
9289 The relation returned by C<isl_union_flow_get_full_may_dependence>
9290 relates domain elements of must or may sources to pairs of
9291 domain elements of the sink and accessed data elements.
9292 This relation includes the previous relation as a subset.
9293 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9294 of the sink relation for which no dependences have been found.
9295 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9296 of the sink relation for which no definite dependences have been found.
9297 That is, it contains those sink access that do not contribute to any
9298 of the elements in the relation returned
9299 by C<isl_union_flow_get_must_dependence>.
9301 A representation of the information contained in an object
9302 of type C<isl_union_flow> can be obtained using
9304 #include <isl/flow.h>
9305 __isl_give isl_printer *isl_printer_print_union_flow(
9306 __isl_take isl_printer *p,
9307 __isl_keep isl_union_flow *flow);
9308 __isl_give char *isl_union_flow_to_str(
9309 __isl_keep isl_union_flow *flow);
9311 C<isl_union_flow_to_str> prints the information in flow format.
9313 =head3 Low-level Interface
9315 A lower-level interface is provided by the following functions.
9317 #include <isl/flow.h>
9319 typedef int (*isl_access_level_before)(void *first, void *second);
9321 __isl_give isl_access_info *isl_access_info_alloc(
9322 __isl_take isl_map *sink,
9323 void *sink_user, isl_access_level_before fn,
9325 __isl_give isl_access_info *isl_access_info_add_source(
9326 __isl_take isl_access_info *acc,
9327 __isl_take isl_map *source, int must,
9329 __isl_null isl_access_info *isl_access_info_free(
9330 __isl_take isl_access_info *acc);
9332 __isl_give isl_flow *isl_access_info_compute_flow(
9333 __isl_take isl_access_info *acc);
9335 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9336 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9337 void *dep_user, void *user),
9339 __isl_give isl_map *isl_flow_get_no_source(
9340 __isl_keep isl_flow *deps, int must);
9341 void isl_flow_free(__isl_take isl_flow *deps);
9343 The function C<isl_access_info_compute_flow> performs the actual
9344 dependence analysis. The other functions are used to construct
9345 the input for this function or to read off the output.
9347 The input is collected in an C<isl_access_info>, which can
9348 be created through a call to C<isl_access_info_alloc>.
9349 The arguments to this functions are the sink access relation
9350 C<sink>, a token C<sink_user> used to identify the sink
9351 access to the user, a callback function for specifying the
9352 relative order of source and sink accesses, and the number
9353 of source access relations that will be added.
9355 The callback function has type C<int (*)(void *first, void *second)>.
9356 The function is called with two user supplied tokens identifying
9357 either a source or the sink and it should return the shared nesting
9358 level and the relative order of the two accesses.
9359 In particular, let I<n> be the number of loops shared by
9360 the two accesses. If C<first> precedes C<second> textually,
9361 then the function should return I<2 * n + 1>; otherwise,
9362 it should return I<2 * n>.
9363 The low-level interface assumes that no sources are coscheduled.
9364 If the information returned by the callback does not allow
9365 the relative order to be determined, then one of the sources
9366 is arbitrarily taken to be executed after the other(s).
9368 The sources can be added to the C<isl_access_info> object by performing
9369 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9370 C<must> indicates whether the source is a I<must> access
9371 or a I<may> access. Note that a multi-valued access relation
9372 should only be marked I<must> if every iteration in the domain
9373 of the relation accesses I<all> elements in its image.
9374 The C<source_user> token is again used to identify
9375 the source access. The range of the source access relation
9376 C<source> should have the same dimension as the range
9377 of the sink access relation.
9378 The C<isl_access_info_free> function should usually not be
9379 called explicitly, because it is already called implicitly by
9380 C<isl_access_info_compute_flow>.
9382 The result of the dependence analysis is collected in an
9383 C<isl_flow>. There may be elements of
9384 the sink access for which no preceding source access could be
9385 found or for which all preceding sources are I<may> accesses.
9386 The relations containing these elements can be obtained through
9387 calls to C<isl_flow_get_no_source>, the first with C<must> set
9388 and the second with C<must> unset.
9389 In the case of standard flow dependence analysis,
9390 with the sink a read and the sources I<must> writes,
9391 the first relation corresponds to the reads from uninitialized
9392 array elements and the second relation is empty.
9393 The actual flow dependences can be extracted using
9394 C<isl_flow_foreach>. This function will call the user-specified
9395 callback function C<fn> for each B<non-empty> dependence between
9396 a source and the sink. The callback function is called
9397 with four arguments, the actual flow dependence relation
9398 mapping source iterations to sink iterations, a boolean that
9399 indicates whether it is a I<must> or I<may> dependence, a token
9400 identifying the source and an additional C<void *> with value
9401 equal to the third argument of the C<isl_flow_foreach> call.
9402 A dependence is marked I<must> if it originates from a I<must>
9403 source and if it is not followed by any I<may> sources.
9405 After finishing with an C<isl_flow>, the user should call
9406 C<isl_flow_free> to free all associated memory.
9408 =head3 Interaction with the Low-level Interface
9410 During the dependence analysis, we frequently need to perform
9411 the following operation. Given a relation between sink iterations
9412 and potential source iterations from a particular source domain,
9413 what is the last potential source iteration corresponding to each
9414 sink iteration. It can sometimes be convenient to adjust
9415 the set of potential source iterations before or after each such operation.
9416 The prototypical example is fuzzy array dataflow analysis,
9417 where we need to analyze if, based on data-dependent constraints,
9418 the sink iteration can ever be executed without one or more of
9419 the corresponding potential source iterations being executed.
9420 If so, we can introduce extra parameters and select an unknown
9421 but fixed source iteration from the potential source iterations.
9422 To be able to perform such manipulations, C<isl> provides the following
9425 #include <isl/flow.h>
9427 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9428 __isl_keep isl_map *source_map,
9429 __isl_keep isl_set *sink, void *source_user,
9431 __isl_give isl_access_info *isl_access_info_set_restrict(
9432 __isl_take isl_access_info *acc,
9433 isl_access_restrict fn, void *user);
9435 The function C<isl_access_info_set_restrict> should be called
9436 before calling C<isl_access_info_compute_flow> and registers a callback function
9437 that will be called any time C<isl> is about to compute the last
9438 potential source. The first argument is the (reverse) proto-dependence,
9439 mapping sink iterations to potential source iterations.
9440 The second argument represents the sink iterations for which
9441 we want to compute the last source iteration.
9442 The third argument is the token corresponding to the source
9443 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9444 The callback is expected to return a restriction on either the input or
9445 the output of the operation computing the last potential source.
9446 If the input needs to be restricted then restrictions are needed
9447 for both the source and the sink iterations. The sink iterations
9448 and the potential source iterations will be intersected with these sets.
9449 If the output needs to be restricted then only a restriction on the source
9450 iterations is required.
9451 If any error occurs, the callback should return C<NULL>.
9452 An C<isl_restriction> object can be created, freed and inspected
9453 using the following functions.
9455 #include <isl/flow.h>
9457 __isl_give isl_restriction *isl_restriction_input(
9458 __isl_take isl_set *source_restr,
9459 __isl_take isl_set *sink_restr);
9460 __isl_give isl_restriction *isl_restriction_output(
9461 __isl_take isl_set *source_restr);
9462 __isl_give isl_restriction *isl_restriction_none(
9463 __isl_take isl_map *source_map);
9464 __isl_give isl_restriction *isl_restriction_empty(
9465 __isl_take isl_map *source_map);
9466 __isl_null isl_restriction *isl_restriction_free(
9467 __isl_take isl_restriction *restr);
9469 C<isl_restriction_none> and C<isl_restriction_empty> are special
9470 cases of C<isl_restriction_input>. C<isl_restriction_none>
9471 is essentially equivalent to
9473 isl_restriction_input(isl_set_universe(
9474 isl_space_range(isl_map_get_space(source_map))),
9476 isl_space_domain(isl_map_get_space(source_map))));
9478 whereas C<isl_restriction_empty> is essentially equivalent to
9480 isl_restriction_input(isl_set_empty(
9481 isl_space_range(isl_map_get_space(source_map))),
9483 isl_space_domain(isl_map_get_space(source_map))));
9487 #include <isl/schedule.h>
9488 __isl_give isl_schedule *
9489 isl_schedule_constraints_compute_schedule(
9490 __isl_take isl_schedule_constraints *sc);
9492 The function C<isl_schedule_constraints_compute_schedule> can be
9493 used to compute a schedule that satisfies the given schedule constraints.
9494 These schedule constraints include the iteration domain for which
9495 a schedule should be computed and dependences between pairs of
9496 iterations. In particular, these dependences include
9497 I<validity> dependences and I<proximity> dependences.
9498 By default, the algorithm used to construct the schedule is similar
9499 to that of C<Pluto>.
9500 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9502 The generated schedule respects all validity dependences.
9503 That is, all dependence distances over these dependences in the
9504 scheduled space are lexicographically positive.
9506 The default algorithm tries to ensure that the dependence distances
9507 over coincidence constraints are zero and to minimize the
9508 dependence distances over proximity dependences.
9509 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9510 for groups of domains where the dependence distances over validity
9511 dependences have only non-negative values.
9512 Note that when minimizing the maximal dependence distance
9513 over proximity dependences, a single affine expression in the parameters
9514 is constructed that bounds all dependence distances. If no such expression
9515 exists, then the algorithm will fail and resort to an alternative
9516 scheduling algorithm. In particular, this means that adding proximity
9517 dependences may eliminate valid solutions. A typical example where this
9518 phenomenon may occur is when some subset of the proximity dependences
9519 has no restriction on some parameter, forcing the coefficient of that
9520 parameter to be zero, while some other subset forces the dependence
9521 distance to depend on that parameter, requiring the same coefficient
9523 When using Feautrier's algorithm, the coincidence and proximity constraints
9524 are only taken into account during the extension to a
9525 full-dimensional schedule.
9527 An C<isl_schedule_constraints> object can be constructed
9528 and manipulated using the following functions.
9530 #include <isl/schedule.h>
9531 __isl_give isl_schedule_constraints *
9532 isl_schedule_constraints_copy(
9533 __isl_keep isl_schedule_constraints *sc);
9534 __isl_give isl_schedule_constraints *
9535 isl_schedule_constraints_on_domain(
9536 __isl_take isl_union_set *domain);
9537 __isl_give isl_schedule_constraints *
9538 isl_schedule_constraints_set_context(
9539 __isl_take isl_schedule_constraints *sc,
9540 __isl_take isl_set *context);
9541 __isl_give isl_schedule_constraints *
9542 isl_schedule_constraints_set_validity(
9543 __isl_take isl_schedule_constraints *sc,
9544 __isl_take isl_union_map *validity);
9545 __isl_give isl_schedule_constraints *
9546 isl_schedule_constraints_set_coincidence(
9547 __isl_take isl_schedule_constraints *sc,
9548 __isl_take isl_union_map *coincidence);
9549 __isl_give isl_schedule_constraints *
9550 isl_schedule_constraints_set_proximity(
9551 __isl_take isl_schedule_constraints *sc,
9552 __isl_take isl_union_map *proximity);
9553 __isl_give isl_schedule_constraints *
9554 isl_schedule_constraints_set_conditional_validity(
9555 __isl_take isl_schedule_constraints *sc,
9556 __isl_take isl_union_map *condition,
9557 __isl_take isl_union_map *validity);
9558 __isl_give isl_schedule_constraints *
9559 isl_schedule_constraints_apply(
9560 __isl_take isl_schedule_constraints *sc,
9561 __isl_take isl_union_map *umap);
9562 __isl_null isl_schedule_constraints *
9563 isl_schedule_constraints_free(
9564 __isl_take isl_schedule_constraints *sc);
9566 The initial C<isl_schedule_constraints> object created by
9567 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9568 That is, it has an empty set of dependences.
9569 The function C<isl_schedule_constraints_set_context> allows the user
9570 to specify additional constraints on the parameters that may
9571 be assumed to hold during the construction of the schedule.
9572 The function C<isl_schedule_constraints_set_validity> replaces the
9573 validity dependences, mapping domain elements I<i> to domain
9574 elements that should be scheduled after I<i>.
9575 The function C<isl_schedule_constraints_set_coincidence> replaces the
9576 coincidence dependences, mapping domain elements I<i> to domain
9577 elements that should be scheduled together with I<I>, if possible.
9578 The function C<isl_schedule_constraints_set_proximity> replaces the
9579 proximity dependences, mapping domain elements I<i> to domain
9580 elements that should be scheduled either before I<I>
9581 or as early as possible after I<i>.
9583 The function C<isl_schedule_constraints_set_conditional_validity>
9584 replaces the conditional validity constraints.
9585 A conditional validity constraint is only imposed when any of the corresponding
9586 conditions is satisfied, i.e., when any of them is non-zero.
9587 That is, the scheduler ensures that within each band if the dependence
9588 distances over the condition constraints are not all zero
9589 then all corresponding conditional validity constraints are respected.
9590 A conditional validity constraint corresponds to a condition
9591 if the two are adjacent, i.e., if the domain of one relation intersect
9592 the range of the other relation.
9593 The typical use case of conditional validity constraints is
9594 to allow order constraints between live ranges to be violated
9595 as long as the live ranges themselves are local to the band.
9596 To allow more fine-grained control over which conditions correspond
9597 to which conditional validity constraints, the domains and ranges
9598 of these relations may include I<tags>. That is, the domains and
9599 ranges of those relation may themselves be wrapped relations
9600 where the iteration domain appears in the domain of those wrapped relations
9601 and the range of the wrapped relations can be arbitrarily chosen
9602 by the user. Conditions and conditional validity constraints are only
9603 considered adjacent to each other if the entire wrapped relation matches.
9604 In particular, a relation with a tag will never be considered adjacent
9605 to a relation without a tag.
9607 The function C<isl_schedule_constraints_apply> takes
9608 schedule constraints that are defined on some set of domain elements
9609 and transforms them to schedule constraints on the elements
9610 to which these domain elements are mapped by the given transformation.
9612 An C<isl_schedule_constraints> object can be inspected
9613 using the following functions.
9615 #include <isl/schedule.h>
9616 __isl_give isl_union_set *
9617 isl_schedule_constraints_get_domain(
9618 __isl_keep isl_schedule_constraints *sc);
9619 __isl_give isl_set *isl_schedule_constraints_get_context(
9620 __isl_keep isl_schedule_constraints *sc);
9621 __isl_give isl_union_map *
9622 isl_schedule_constraints_get_validity(
9623 __isl_keep isl_schedule_constraints *sc);
9624 __isl_give isl_union_map *
9625 isl_schedule_constraints_get_coincidence(
9626 __isl_keep isl_schedule_constraints *sc);
9627 __isl_give isl_union_map *
9628 isl_schedule_constraints_get_proximity(
9629 __isl_keep isl_schedule_constraints *sc);
9630 __isl_give isl_union_map *
9631 isl_schedule_constraints_get_conditional_validity(
9632 __isl_keep isl_schedule_constraints *sc);
9633 __isl_give isl_union_map *
9634 isl_schedule_constraints_get_conditional_validity_condition(
9635 __isl_keep isl_schedule_constraints *sc);
9637 An C<isl_schedule_constraints> object can be read from input
9638 using the following functions.
9640 #include <isl/schedule.h>
9641 __isl_give isl_schedule_constraints *
9642 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9644 __isl_give isl_schedule_constraints *
9645 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9648 The contents of an C<isl_schedule_constraints> object can be printed
9649 using the following functions.
9651 #include <isl/schedule.h>
9652 __isl_give isl_printer *
9653 isl_printer_print_schedule_constraints(
9654 __isl_take isl_printer *p,
9655 __isl_keep isl_schedule_constraints *sc);
9656 __isl_give char *isl_schedule_constraints_to_str(
9657 __isl_keep isl_schedule_constraints *sc);
9659 The following function computes a schedule directly from
9660 an iteration domain and validity and proximity dependences
9661 and is implemented in terms of the functions described above.
9662 The use of C<isl_union_set_compute_schedule> is discouraged.
9664 #include <isl/schedule.h>
9665 __isl_give isl_schedule *isl_union_set_compute_schedule(
9666 __isl_take isl_union_set *domain,
9667 __isl_take isl_union_map *validity,
9668 __isl_take isl_union_map *proximity);
9670 The generated schedule represents a schedule tree.
9671 For more information on schedule trees, see
9672 L</"Schedule Trees">.
9676 #include <isl/schedule.h>
9677 isl_stat isl_options_set_schedule_max_coefficient(
9678 isl_ctx *ctx, int val);
9679 int isl_options_get_schedule_max_coefficient(
9681 isl_stat isl_options_set_schedule_max_constant_term(
9682 isl_ctx *ctx, int val);
9683 int isl_options_get_schedule_max_constant_term(
9685 isl_stat isl_options_set_schedule_serialize_sccs(
9686 isl_ctx *ctx, int val);
9687 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9688 isl_stat isl_options_set_schedule_whole_component(
9689 isl_ctx *ctx, int val);
9690 int isl_options_get_schedule_whole_component(
9692 isl_stat isl_options_set_schedule_maximize_band_depth(
9693 isl_ctx *ctx, int val);
9694 int isl_options_get_schedule_maximize_band_depth(
9696 isl_stat isl_options_set_schedule_maximize_coincidence(
9697 isl_ctx *ctx, int val);
9698 int isl_options_get_schedule_maximize_coincidence(
9700 isl_stat isl_options_set_schedule_outer_coincidence(
9701 isl_ctx *ctx, int val);
9702 int isl_options_get_schedule_outer_coincidence(
9704 isl_stat isl_options_set_schedule_split_scaled(
9705 isl_ctx *ctx, int val);
9706 int isl_options_get_schedule_split_scaled(
9708 isl_stat isl_options_set_schedule_treat_coalescing(
9709 isl_ctx *ctx, int val);
9710 int isl_options_get_schedule_treat_coalescing(
9712 isl_stat isl_options_set_schedule_algorithm(
9713 isl_ctx *ctx, int val);
9714 int isl_options_get_schedule_algorithm(
9716 isl_stat isl_options_set_schedule_carry_self_first(
9717 isl_ctx *ctx, int val);
9718 int isl_options_get_schedule_carry_self_first(
9720 isl_stat isl_options_set_schedule_separate_components(
9721 isl_ctx *ctx, int val);
9722 int isl_options_get_schedule_separate_components(
9727 =item * schedule_max_coefficient
9729 This option enforces that the coefficients for variable and parameter
9730 dimensions in the calculated schedule are not larger than the specified value.
9731 This option can significantly increase the speed of the scheduling calculation
9732 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9733 this option does not introduce bounds on the variable or parameter
9736 =item * schedule_max_constant_term
9738 This option enforces that the constant coefficients in the calculated schedule
9739 are not larger than the maximal constant term. This option can significantly
9740 increase the speed of the scheduling calculation and may also prevent fusing of
9741 unrelated dimensions. A value of -1 means that this option does not introduce
9742 bounds on the constant coefficients.
9744 =item * schedule_serialize_sccs
9746 If this option is set, then all strongly connected components
9747 in the dependence graph are serialized as soon as they are detected.
9748 This means in particular that instances of statements will only
9749 appear in the same band node if these statements belong
9750 to the same strongly connected component at the point where
9751 the band node is constructed.
9753 =item * schedule_whole_component
9755 If this option is set, then entire (weakly) connected
9756 components in the dependence graph are scheduled together
9758 Otherwise, each strongly connected component within
9759 such a weakly connected component is first scheduled separately
9760 and then combined with other strongly connected components.
9761 This option has no effect if C<schedule_serialize_sccs> is set.
9763 =item * schedule_maximize_band_depth
9765 If this option is set, then the scheduler tries to maximize
9766 the width of the bands. Wider bands give more possibilities for tiling.
9767 In particular, if the C<schedule_whole_component> option is set,
9768 then bands are split if this might result in wider bands.
9769 Otherwise, the effect of this option is to only allow
9770 strongly connected components to be combined if this does
9771 not reduce the width of the bands.
9772 Note that if the C<schedule_serialize_sccs> options is set, then
9773 the C<schedule_maximize_band_depth> option therefore has no effect.
9775 =item * schedule_maximize_coincidence
9777 This option is only effective if the C<schedule_whole_component>
9778 option is turned off.
9779 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9780 strongly connected components are only combined with each other
9781 if this does not reduce the number of coincident band members.
9783 =item * schedule_outer_coincidence
9785 If this option is set, then we try to construct schedules
9786 where the outermost scheduling dimension in each band
9787 satisfies the coincidence constraints.
9789 =item * schedule_algorithm
9791 Selects the scheduling algorithm to be used.
9792 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9793 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9795 =item * schedule_split_scaled
9797 If this option is set, then we try to construct schedules in which the
9798 constant term is split off from the linear part if the linear parts of
9799 the scheduling rows for all nodes in the graph have a common non-trivial
9801 The constant term is then dropped and the linear
9803 This option is only effective when the Feautrier style scheduler is
9804 being used, either as the main scheduler or as a fallback for the
9805 Pluto-like scheduler.
9807 =item * schedule_treat_coalescing
9809 If this option is set, then the scheduler will try and avoid
9810 producing schedules that perform loop coalescing.
9811 In particular, for the Pluto-like scheduler, this option places
9812 bounds on the schedule coefficients based on the sizes of the instance sets.
9813 For the Feautrier style scheduler, this option detects potentially
9814 coalescing schedules and then tries to adjust the schedule to avoid
9817 =item * schedule_carry_self_first
9819 If this option is set, then the Feautrier style scheduler
9820 (when used as a fallback for the Pluto-like scheduler) will
9821 first try to only carry self-dependences.
9823 =item * schedule_separate_components
9825 If this option is set then the function C<isl_schedule_get_map>
9826 will treat set nodes in the same way as sequence nodes.
9830 =head2 AST Generation
9832 This section describes the C<isl> functionality for generating
9833 ASTs that visit all the elements
9834 in a domain in an order specified by a schedule tree or
9836 In case the schedule given as a C<isl_union_map>, an AST is generated
9837 that visits all the elements in the domain of the C<isl_union_map>
9838 according to the lexicographic order of the corresponding image
9839 element(s). If the range of the C<isl_union_map> consists of
9840 elements in more than one space, then each of these spaces is handled
9841 separately in an arbitrary order.
9842 It should be noted that the schedule tree or the image elements
9843 in a schedule map only specify the I<order>
9844 in which the corresponding domain elements should be visited.
9845 No direct relation between the partial schedule values
9846 or the image elements on the one hand and the loop iterators
9847 in the generated AST on the other hand should be assumed.
9849 Each AST is generated within a build. The initial build
9850 simply specifies the constraints on the parameters (if any)
9851 and can be created, inspected, copied and freed using the following functions.
9853 #include <isl/ast_build.h>
9854 __isl_give isl_ast_build *isl_ast_build_alloc(
9856 __isl_give isl_ast_build *isl_ast_build_from_context(
9857 __isl_take isl_set *set);
9858 __isl_give isl_ast_build *isl_ast_build_copy(
9859 __isl_keep isl_ast_build *build);
9860 __isl_null isl_ast_build *isl_ast_build_free(
9861 __isl_take isl_ast_build *build);
9863 The C<set> argument is usually a parameter set with zero or more parameters.
9864 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9865 this set is required to be a parameter set.
9866 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9867 specify any parameter constraints.
9868 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9869 and L</"Fine-grained Control over AST Generation">.
9870 Finally, the AST itself can be constructed using one of the following
9873 #include <isl/ast_build.h>
9874 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9875 __isl_keep isl_ast_build *build,
9876 __isl_take isl_schedule *schedule);
9877 __isl_give isl_ast_node *
9878 isl_ast_build_node_from_schedule_map(
9879 __isl_keep isl_ast_build *build,
9880 __isl_take isl_union_map *schedule);
9882 =head3 Inspecting the AST
9884 The basic properties of an AST node can be obtained as follows.
9886 #include <isl/ast.h>
9887 enum isl_ast_node_type isl_ast_node_get_type(
9888 __isl_keep isl_ast_node *node);
9890 The type of an AST node is one of
9891 C<isl_ast_node_for>,
9893 C<isl_ast_node_block>,
9894 C<isl_ast_node_mark> or
9895 C<isl_ast_node_user>.
9896 An C<isl_ast_node_for> represents a for node.
9897 An C<isl_ast_node_if> represents an if node.
9898 An C<isl_ast_node_block> represents a compound node.
9899 An C<isl_ast_node_mark> introduces a mark in the AST.
9900 An C<isl_ast_node_user> represents an expression statement.
9901 An expression statement typically corresponds to a domain element, i.e.,
9902 one of the elements that is visited by the AST.
9904 Each type of node has its own additional properties.
9906 #include <isl/ast.h>
9907 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9908 __isl_keep isl_ast_node *node);
9909 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9910 __isl_keep isl_ast_node *node);
9911 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9912 __isl_keep isl_ast_node *node);
9913 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9914 __isl_keep isl_ast_node *node);
9915 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9916 __isl_keep isl_ast_node *node);
9917 isl_bool isl_ast_node_for_is_degenerate(
9918 __isl_keep isl_ast_node *node);
9920 An C<isl_ast_for> is considered degenerate if it is known to execute
9923 #include <isl/ast.h>
9924 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9925 __isl_keep isl_ast_node *node);
9926 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9927 __isl_keep isl_ast_node *node);
9928 isl_bool isl_ast_node_if_has_else(
9929 __isl_keep isl_ast_node *node);
9930 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9931 __isl_keep isl_ast_node *node);
9933 __isl_give isl_ast_node_list *
9934 isl_ast_node_block_get_children(
9935 __isl_keep isl_ast_node *node);
9937 __isl_give isl_id *isl_ast_node_mark_get_id(
9938 __isl_keep isl_ast_node *node);
9939 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9940 __isl_keep isl_ast_node *node);
9942 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9943 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9945 #include <isl/ast.h>
9946 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9947 __isl_keep isl_ast_node *node);
9949 All descendants of a specific node in the AST (including the node itself)
9951 in depth-first pre-order using the following function.
9953 #include <isl/ast.h>
9954 isl_stat isl_ast_node_foreach_descendant_top_down(
9955 __isl_keep isl_ast_node *node,
9956 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9957 void *user), void *user);
9959 The callback function should return C<isl_bool_true> if the children
9960 of the given node should be visited and C<isl_bool_false> if they should not.
9961 It should return C<isl_bool_error> in case of failure, in which case
9962 the entire traversal is aborted.
9964 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9965 the following functions.
9967 #include <isl/ast.h>
9968 enum isl_ast_expr_type isl_ast_expr_get_type(
9969 __isl_keep isl_ast_expr *expr);
9971 The type of an AST expression is one of
9973 C<isl_ast_expr_id> or
9974 C<isl_ast_expr_int>.
9975 An C<isl_ast_expr_op> represents the result of an operation.
9976 An C<isl_ast_expr_id> represents an identifier.
9977 An C<isl_ast_expr_int> represents an integer value.
9979 Each type of expression has its own additional properties.
9981 #include <isl/ast.h>
9982 enum isl_ast_op_type isl_ast_expr_get_op_type(
9983 __isl_keep isl_ast_expr *expr);
9984 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9985 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9986 __isl_keep isl_ast_expr *expr, int pos);
9987 isl_stat isl_ast_expr_foreach_ast_op_type(
9988 __isl_keep isl_ast_expr *expr,
9989 isl_stat (*fn)(enum isl_ast_op_type type,
9990 void *user), void *user);
9991 isl_stat isl_ast_node_foreach_ast_op_type(
9992 __isl_keep isl_ast_node *node,
9993 isl_stat (*fn)(enum isl_ast_op_type type,
9994 void *user), void *user);
9996 C<isl_ast_expr_get_op_type> returns the type of the operation
9997 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9998 arguments. C<isl_ast_expr_get_op_arg> returns the specified
10000 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
10001 C<isl_ast_op_type> that appears in C<expr>.
10002 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
10003 C<isl_ast_op_type> that appears in C<node>.
10004 The operation type is one of the following.
10008 =item C<isl_ast_op_and>
10010 Logical I<and> of two arguments.
10011 Both arguments can be evaluated.
10013 =item C<isl_ast_op_and_then>
10015 Logical I<and> of two arguments.
10016 The second argument can only be evaluated if the first evaluates to true.
10018 =item C<isl_ast_op_or>
10020 Logical I<or> of two arguments.
10021 Both arguments can be evaluated.
10023 =item C<isl_ast_op_or_else>
10025 Logical I<or> of two arguments.
10026 The second argument can only be evaluated if the first evaluates to false.
10028 =item C<isl_ast_op_max>
10030 Maximum of two or more arguments.
10032 =item C<isl_ast_op_min>
10034 Minimum of two or more arguments.
10036 =item C<isl_ast_op_minus>
10040 =item C<isl_ast_op_add>
10042 Sum of two arguments.
10044 =item C<isl_ast_op_sub>
10046 Difference of two arguments.
10048 =item C<isl_ast_op_mul>
10050 Product of two arguments.
10052 =item C<isl_ast_op_div>
10054 Exact division. That is, the result is known to be an integer.
10056 =item C<isl_ast_op_fdiv_q>
10058 Result of integer division, rounded towards negative
10060 The divisor is known to be positive.
10062 =item C<isl_ast_op_pdiv_q>
10064 Result of integer division, where dividend is known to be non-negative.
10065 The divisor is known to be positive.
10067 =item C<isl_ast_op_pdiv_r>
10069 Remainder of integer division, where dividend is known to be non-negative.
10070 The divisor is known to be positive.
10072 =item C<isl_ast_op_zdiv_r>
10074 Equal to zero iff the remainder on integer division is zero.
10075 The divisor is known to be positive.
10077 =item C<isl_ast_op_cond>
10079 Conditional operator defined on three arguments.
10080 If the first argument evaluates to true, then the result
10081 is equal to the second argument. Otherwise, the result
10082 is equal to the third argument.
10083 The second and third argument may only be evaluated if
10084 the first argument evaluates to true and false, respectively.
10085 Corresponds to C<a ? b : c> in C.
10087 =item C<isl_ast_op_select>
10089 Conditional operator defined on three arguments.
10090 If the first argument evaluates to true, then the result
10091 is equal to the second argument. Otherwise, the result
10092 is equal to the third argument.
10093 The second and third argument may be evaluated independently
10094 of the value of the first argument.
10095 Corresponds to C<a * b + (1 - a) * c> in C.
10097 =item C<isl_ast_op_eq>
10101 =item C<isl_ast_op_le>
10103 Less than or equal relation.
10105 =item C<isl_ast_op_lt>
10107 Less than relation.
10109 =item C<isl_ast_op_ge>
10111 Greater than or equal relation.
10113 =item C<isl_ast_op_gt>
10115 Greater than relation.
10117 =item C<isl_ast_op_call>
10120 The number of arguments of the C<isl_ast_expr> is one more than
10121 the number of arguments in the function call, the first argument
10122 representing the function being called.
10124 =item C<isl_ast_op_access>
10127 The number of arguments of the C<isl_ast_expr> is one more than
10128 the number of index expressions in the array access, the first argument
10129 representing the array being accessed.
10131 =item C<isl_ast_op_member>
10134 This operation has two arguments, a structure and the name of
10135 the member of the structure being accessed.
10139 #include <isl/ast.h>
10140 __isl_give isl_id *isl_ast_expr_get_id(
10141 __isl_keep isl_ast_expr *expr);
10143 Return the identifier represented by the AST expression.
10145 #include <isl/ast.h>
10146 __isl_give isl_val *isl_ast_expr_get_val(
10147 __isl_keep isl_ast_expr *expr);
10149 Return the integer represented by the AST expression.
10151 =head3 Properties of ASTs
10153 #include <isl/ast.h>
10154 isl_bool isl_ast_expr_is_equal(
10155 __isl_keep isl_ast_expr *expr1,
10156 __isl_keep isl_ast_expr *expr2);
10158 Check if two C<isl_ast_expr>s are equal to each other.
10160 =head3 Manipulating and printing the AST
10162 AST nodes can be copied and freed using the following functions.
10164 #include <isl/ast.h>
10165 __isl_give isl_ast_node *isl_ast_node_copy(
10166 __isl_keep isl_ast_node *node);
10167 __isl_null isl_ast_node *isl_ast_node_free(
10168 __isl_take isl_ast_node *node);
10170 AST expressions can be copied and freed using the following functions.
10172 #include <isl/ast.h>
10173 __isl_give isl_ast_expr *isl_ast_expr_copy(
10174 __isl_keep isl_ast_expr *expr);
10175 __isl_null isl_ast_expr *isl_ast_expr_free(
10176 __isl_take isl_ast_expr *expr);
10178 New AST expressions can be created either directly or within
10179 the context of an C<isl_ast_build>.
10181 #include <isl/ast.h>
10182 __isl_give isl_ast_expr *isl_ast_expr_from_val(
10183 __isl_take isl_val *v);
10184 __isl_give isl_ast_expr *isl_ast_expr_from_id(
10185 __isl_take isl_id *id);
10186 __isl_give isl_ast_expr *isl_ast_expr_neg(
10187 __isl_take isl_ast_expr *expr);
10188 __isl_give isl_ast_expr *isl_ast_expr_address_of(
10189 __isl_take isl_ast_expr *expr);
10190 __isl_give isl_ast_expr *isl_ast_expr_add(
10191 __isl_take isl_ast_expr *expr1,
10192 __isl_take isl_ast_expr *expr2);
10193 __isl_give isl_ast_expr *isl_ast_expr_sub(
10194 __isl_take isl_ast_expr *expr1,
10195 __isl_take isl_ast_expr *expr2);
10196 __isl_give isl_ast_expr *isl_ast_expr_mul(
10197 __isl_take isl_ast_expr *expr1,
10198 __isl_take isl_ast_expr *expr2);
10199 __isl_give isl_ast_expr *isl_ast_expr_div(
10200 __isl_take isl_ast_expr *expr1,
10201 __isl_take isl_ast_expr *expr2);
10202 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
10203 __isl_take isl_ast_expr *expr1,
10204 __isl_take isl_ast_expr *expr2);
10205 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
10206 __isl_take isl_ast_expr *expr1,
10207 __isl_take isl_ast_expr *expr2);
10208 __isl_give isl_ast_expr *isl_ast_expr_and(
10209 __isl_take isl_ast_expr *expr1,
10210 __isl_take isl_ast_expr *expr2)
10211 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10212 __isl_take isl_ast_expr *expr1,
10213 __isl_take isl_ast_expr *expr2)
10214 __isl_give isl_ast_expr *isl_ast_expr_or(
10215 __isl_take isl_ast_expr *expr1,
10216 __isl_take isl_ast_expr *expr2)
10217 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10218 __isl_take isl_ast_expr *expr1,
10219 __isl_take isl_ast_expr *expr2)
10220 __isl_give isl_ast_expr *isl_ast_expr_eq(
10221 __isl_take isl_ast_expr *expr1,
10222 __isl_take isl_ast_expr *expr2);
10223 __isl_give isl_ast_expr *isl_ast_expr_le(
10224 __isl_take isl_ast_expr *expr1,
10225 __isl_take isl_ast_expr *expr2);
10226 __isl_give isl_ast_expr *isl_ast_expr_lt(
10227 __isl_take isl_ast_expr *expr1,
10228 __isl_take isl_ast_expr *expr2);
10229 __isl_give isl_ast_expr *isl_ast_expr_ge(
10230 __isl_take isl_ast_expr *expr1,
10231 __isl_take isl_ast_expr *expr2);
10232 __isl_give isl_ast_expr *isl_ast_expr_gt(
10233 __isl_take isl_ast_expr *expr1,
10234 __isl_take isl_ast_expr *expr2);
10235 __isl_give isl_ast_expr *isl_ast_expr_access(
10236 __isl_take isl_ast_expr *array,
10237 __isl_take isl_ast_expr_list *indices);
10238 __isl_give isl_ast_expr *isl_ast_expr_call(
10239 __isl_take isl_ast_expr *function,
10240 __isl_take isl_ast_expr_list *arguments);
10242 The function C<isl_ast_expr_address_of> can be applied to an
10243 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10244 to represent the address of the C<isl_ast_expr_access>.
10245 The second argument of the functions C<isl_ast_expr_pdiv_q> and
10246 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
10248 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10249 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10251 #include <isl/ast_build.h>
10252 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10253 __isl_keep isl_ast_build *build,
10254 __isl_take isl_set *set);
10255 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10256 __isl_keep isl_ast_build *build,
10257 __isl_take isl_pw_aff *pa);
10258 __isl_give isl_ast_expr *
10259 isl_ast_build_access_from_pw_multi_aff(
10260 __isl_keep isl_ast_build *build,
10261 __isl_take isl_pw_multi_aff *pma);
10262 __isl_give isl_ast_expr *
10263 isl_ast_build_access_from_multi_pw_aff(
10264 __isl_keep isl_ast_build *build,
10265 __isl_take isl_multi_pw_aff *mpa);
10266 __isl_give isl_ast_expr *
10267 isl_ast_build_call_from_pw_multi_aff(
10268 __isl_keep isl_ast_build *build,
10269 __isl_take isl_pw_multi_aff *pma);
10270 __isl_give isl_ast_expr *
10271 isl_ast_build_call_from_multi_pw_aff(
10272 __isl_keep isl_ast_build *build,
10273 __isl_take isl_multi_pw_aff *mpa);
10276 the domains of C<pa>, C<mpa> and C<pma> should correspond
10277 to the schedule space of C<build>.
10278 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10279 the function being called.
10280 If the accessed space is a nested relation, then it is taken
10281 to represent an access of the member specified by the range
10282 of this nested relation of the structure specified by the domain
10283 of the nested relation.
10285 The following functions can be used to modify an C<isl_ast_expr>.
10287 #include <isl/ast.h>
10288 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10289 __isl_take isl_ast_expr *expr, int pos,
10290 __isl_take isl_ast_expr *arg);
10292 Replace the argument of C<expr> at position C<pos> by C<arg>.
10294 #include <isl/ast.h>
10295 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10296 __isl_take isl_ast_expr *expr,
10297 __isl_take isl_id_to_ast_expr *id2expr);
10299 The function C<isl_ast_expr_substitute_ids> replaces the
10300 subexpressions of C<expr> of type C<isl_ast_expr_id>
10301 by the corresponding expression in C<id2expr>, if there is any.
10304 User specified data can be attached to an C<isl_ast_node> and obtained
10305 from the same C<isl_ast_node> using the following functions.
10307 #include <isl/ast.h>
10308 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10309 __isl_take isl_ast_node *node,
10310 __isl_take isl_id *annotation);
10311 __isl_give isl_id *isl_ast_node_get_annotation(
10312 __isl_keep isl_ast_node *node);
10314 Basic printing can be performed using the following functions.
10316 #include <isl/ast.h>
10317 __isl_give isl_printer *isl_printer_print_ast_expr(
10318 __isl_take isl_printer *p,
10319 __isl_keep isl_ast_expr *expr);
10320 __isl_give isl_printer *isl_printer_print_ast_node(
10321 __isl_take isl_printer *p,
10322 __isl_keep isl_ast_node *node);
10323 __isl_give char *isl_ast_expr_to_str(
10324 __isl_keep isl_ast_expr *expr);
10325 __isl_give char *isl_ast_node_to_str(
10326 __isl_keep isl_ast_node *node);
10327 __isl_give char *isl_ast_expr_to_C_str(
10328 __isl_keep isl_ast_expr *expr);
10329 __isl_give char *isl_ast_node_to_C_str(
10330 __isl_keep isl_ast_node *node);
10332 The functions C<isl_ast_expr_to_C_str> and
10333 C<isl_ast_node_to_C_str> are convenience functions
10334 that return a string representation of the input in C format.
10336 More advanced printing can be performed using the following functions.
10338 #include <isl/ast.h>
10339 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10340 __isl_take isl_printer *p,
10341 enum isl_ast_op_type type,
10342 __isl_keep const char *name);
10343 isl_stat isl_options_set_ast_print_macro_once(
10344 isl_ctx *ctx, int val);
10345 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10346 __isl_give isl_printer *isl_ast_op_type_print_macro(
10347 enum isl_ast_op_type type,
10348 __isl_take isl_printer *p);
10349 __isl_give isl_printer *isl_ast_expr_print_macros(
10350 __isl_keep isl_ast_expr *expr,
10351 __isl_take isl_printer *p);
10352 __isl_give isl_printer *isl_ast_node_print_macros(
10353 __isl_keep isl_ast_node *node,
10354 __isl_take isl_printer *p);
10355 __isl_give isl_printer *isl_ast_node_print(
10356 __isl_keep isl_ast_node *node,
10357 __isl_take isl_printer *p,
10358 __isl_take isl_ast_print_options *options);
10359 __isl_give isl_printer *isl_ast_node_for_print(
10360 __isl_keep isl_ast_node *node,
10361 __isl_take isl_printer *p,
10362 __isl_take isl_ast_print_options *options);
10363 __isl_give isl_printer *isl_ast_node_if_print(
10364 __isl_keep isl_ast_node *node,
10365 __isl_take isl_printer *p,
10366 __isl_take isl_ast_print_options *options);
10368 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10369 C<isl> may print out an AST that makes use of macros such
10370 as C<floord>, C<min> and C<max>.
10371 The names of these macros may be modified by a call
10372 to C<isl_ast_op_type_set_print_name>. The user-specified
10373 names are associated to the printer object.
10374 C<isl_ast_op_type_print_macro> prints out the macro
10375 corresponding to a specific C<isl_ast_op_type>.
10376 If the print-macro-once option is set, then a given macro definition
10377 is only printed once to any given printer object.
10378 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10379 for subexpressions where these macros would be used and prints
10380 out the required macro definitions.
10381 Essentially, C<isl_ast_expr_print_macros> calls
10382 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10383 as function argument.
10384 C<isl_ast_node_print_macros> does the same
10385 for expressions in its C<isl_ast_node> argument.
10386 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10387 C<isl_ast_node_if_print> print an C<isl_ast_node>
10388 in C<ISL_FORMAT_C>, but allow for some extra control
10389 through an C<isl_ast_print_options> object.
10390 This object can be created using the following functions.
10392 #include <isl/ast.h>
10393 __isl_give isl_ast_print_options *
10394 isl_ast_print_options_alloc(isl_ctx *ctx);
10395 __isl_give isl_ast_print_options *
10396 isl_ast_print_options_copy(
10397 __isl_keep isl_ast_print_options *options);
10398 __isl_null isl_ast_print_options *
10399 isl_ast_print_options_free(
10400 __isl_take isl_ast_print_options *options);
10402 __isl_give isl_ast_print_options *
10403 isl_ast_print_options_set_print_user(
10404 __isl_take isl_ast_print_options *options,
10405 __isl_give isl_printer *(*print_user)(
10406 __isl_take isl_printer *p,
10407 __isl_take isl_ast_print_options *options,
10408 __isl_keep isl_ast_node *node, void *user),
10410 __isl_give isl_ast_print_options *
10411 isl_ast_print_options_set_print_for(
10412 __isl_take isl_ast_print_options *options,
10413 __isl_give isl_printer *(*print_for)(
10414 __isl_take isl_printer *p,
10415 __isl_take isl_ast_print_options *options,
10416 __isl_keep isl_ast_node *node, void *user),
10419 The callback set by C<isl_ast_print_options_set_print_user>
10420 is called whenever a node of type C<isl_ast_node_user> needs to
10422 The callback set by C<isl_ast_print_options_set_print_for>
10423 is called whenever a node of type C<isl_ast_node_for> needs to
10425 Note that C<isl_ast_node_for_print> will I<not> call the
10426 callback set by C<isl_ast_print_options_set_print_for> on the node
10427 on which C<isl_ast_node_for_print> is called, but only on nested
10428 nodes of type C<isl_ast_node_for>. It is therefore safe to
10429 call C<isl_ast_node_for_print> from within the callback set by
10430 C<isl_ast_print_options_set_print_for>.
10432 The following option determines the type to be used for iterators
10433 while printing the AST.
10435 isl_stat isl_options_set_ast_iterator_type(
10436 isl_ctx *ctx, const char *val);
10437 const char *isl_options_get_ast_iterator_type(
10440 The AST printer only prints body nodes as blocks if these
10441 blocks cannot be safely omitted.
10442 For example, a C<for> node with one body node will not be
10443 surrounded with braces in C<ISL_FORMAT_C>.
10444 A block will always be printed by setting the following option.
10446 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10448 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10452 #include <isl/ast_build.h>
10453 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10454 isl_ctx *ctx, int val);
10455 int isl_options_get_ast_build_atomic_upper_bound(
10457 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10459 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10460 isl_stat isl_options_set_ast_build_detect_min_max(
10461 isl_ctx *ctx, int val);
10462 int isl_options_get_ast_build_detect_min_max(
10464 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10465 isl_ctx *ctx, int val);
10466 int isl_options_get_ast_build_exploit_nested_bounds(
10468 isl_stat isl_options_set_ast_build_group_coscheduled(
10469 isl_ctx *ctx, int val);
10470 int isl_options_get_ast_build_group_coscheduled(
10472 isl_stat isl_options_set_ast_build_separation_bounds(
10473 isl_ctx *ctx, int val);
10474 int isl_options_get_ast_build_separation_bounds(
10476 isl_stat isl_options_set_ast_build_scale_strides(
10477 isl_ctx *ctx, int val);
10478 int isl_options_get_ast_build_scale_strides(
10480 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10482 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10483 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10485 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10489 =item * ast_build_atomic_upper_bound
10491 Generate loop upper bounds that consist of the current loop iterator,
10492 an operator and an expression not involving the iterator.
10493 If this option is not set, then the current loop iterator may appear
10494 several times in the upper bound.
10495 For example, when this option is turned off, AST generation
10498 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10502 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10505 When the option is turned on, the following AST is generated
10507 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10510 =item * ast_build_prefer_pdiv
10512 If this option is turned off, then the AST generation will
10513 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10514 operators, but no C<isl_ast_op_pdiv_q> or
10515 C<isl_ast_op_pdiv_r> operators.
10516 If this option is turned on, then C<isl> will try to convert
10517 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10518 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10520 =item * ast_build_detect_min_max
10522 If this option is turned on, then C<isl> will try and detect
10523 min or max-expressions when building AST expressions from
10524 piecewise affine expressions.
10526 =item * ast_build_exploit_nested_bounds
10528 Simplify conditions based on bounds of nested for loops.
10529 In particular, remove conditions that are implied by the fact
10530 that one or more nested loops have at least one iteration,
10531 meaning that the upper bound is at least as large as the lower bound.
10532 For example, when this option is turned off, AST generation
10535 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10541 for (int c0 = 0; c0 <= N; c0 += 1)
10542 for (int c1 = 0; c1 <= M; c1 += 1)
10545 When the option is turned on, the following AST is generated
10547 for (int c0 = 0; c0 <= N; c0 += 1)
10548 for (int c1 = 0; c1 <= M; c1 += 1)
10551 =item * ast_build_group_coscheduled
10553 If two domain elements are assigned the same schedule point, then
10554 they may be executed in any order and they may even appear in different
10555 loops. If this options is set, then the AST generator will make
10556 sure that coscheduled domain elements do not appear in separate parts
10557 of the AST. This is useful in case of nested AST generation
10558 if the outer AST generation is given only part of a schedule
10559 and the inner AST generation should handle the domains that are
10560 coscheduled by this initial part of the schedule together.
10561 For example if an AST is generated for a schedule
10563 { A[i] -> [0]; B[i] -> [0] }
10565 then the C<isl_ast_build_set_create_leaf> callback described
10566 below may get called twice, once for each domain.
10567 Setting this option ensures that the callback is only called once
10568 on both domains together.
10570 =item * ast_build_separation_bounds
10572 This option specifies which bounds to use during separation.
10573 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10574 then all (possibly implicit) bounds on the current dimension will
10575 be used during separation.
10576 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10577 then only those bounds that are explicitly available will
10578 be used during separation.
10580 =item * ast_build_scale_strides
10582 This option specifies whether the AST generator is allowed
10583 to scale down iterators of strided loops.
10585 =item * ast_build_allow_else
10587 This option specifies whether the AST generator is allowed
10588 to construct if statements with else branches.
10590 =item * ast_build_allow_or
10592 This option specifies whether the AST generator is allowed
10593 to construct if conditions with disjunctions.
10597 =head3 AST Generation Options (Schedule Tree)
10599 In case of AST construction from a schedule tree, the options
10600 that control how an AST is created from the individual schedule
10601 dimensions are stored in the band nodes of the tree
10602 (see L</"Schedule Trees">).
10604 In particular, a schedule dimension can be handled in four
10605 different ways, atomic, separate, unroll or the default.
10606 This loop AST generation type can be set using
10607 C<isl_schedule_node_band_member_set_ast_loop_type>.
10609 the first three can be selected by including a one-dimensional
10610 element with as value the position of the schedule dimension
10611 within the band and as name one of C<atomic>, C<separate>
10612 or C<unroll> in the options
10613 set by C<isl_schedule_node_band_set_ast_build_options>.
10614 Only one of these three may be specified for
10615 any given schedule dimension within a band node.
10616 If none of these is specified, then the default
10617 is used. The meaning of the options is as follows.
10623 When this option is specified, the AST generator will make
10624 sure that a given domains space only appears in a single
10625 loop at the specified level.
10627 For example, for the schedule tree
10629 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10631 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10632 options: "{ atomic[x] }"
10634 the following AST will be generated
10636 for (int c0 = 0; c0 <= 10; c0 += 1) {
10643 On the other hand, for the schedule tree
10645 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10647 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10648 options: "{ separate[x] }"
10650 the following AST will be generated
10654 for (int c0 = 1; c0 <= 9; c0 += 1) {
10661 If neither C<atomic> nor C<separate> is specified, then the AST generator
10662 may produce either of these two results or some intermediate form.
10666 When this option is specified, the AST generator will
10667 split the domain of the specified schedule dimension
10668 into pieces with a fixed set of statements for which
10669 instances need to be executed by the iterations in
10670 the schedule domain part. This option tends to avoid
10671 the generation of guards inside the corresponding loops.
10672 See also the C<atomic> option.
10676 When this option is specified, the AST generator will
10677 I<completely> unroll the corresponding schedule dimension.
10678 It is the responsibility of the user to ensure that such
10679 unrolling is possible.
10680 To obtain a partial unrolling, the user should apply an additional
10681 strip-mining to the schedule and fully unroll the inner schedule
10686 The C<isolate> option is a bit more involved. It allows the user
10687 to isolate a range of schedule dimension values from smaller and
10688 greater values. Additionally, the user may specify a different
10689 atomic/separate/unroll choice for the isolated part and the remaining
10690 parts. The typical use case of the C<isolate> option is to isolate
10691 full tiles from partial tiles.
10692 The part that needs to be isolated may depend on outer schedule dimensions.
10693 The option therefore needs to be able to reference those outer schedule
10694 dimensions. In particular, the space of the C<isolate> option is that
10695 of a wrapped map with as domain the flat product of all outer band nodes
10696 and as range the space of the current band node.
10697 The atomic/separate/unroll choice for the isolated part is determined
10698 by an option that lives in an unnamed wrapped space with as domain
10699 a zero-dimensional C<isolate> space and as range the regular
10700 C<atomic>, C<separate> or C<unroll> space.
10701 This option may also be set directly using
10702 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10703 The atomic/separate/unroll choice for the remaining part is determined
10704 by the regular C<atomic>, C<separate> or C<unroll> option.
10705 Since the C<isolate> option references outer schedule dimensions,
10706 its use in a band node causes any tree containing the node
10707 to be considered anchored.
10709 As an example, consider the isolation of full tiles from partial tiles
10710 in a tiling of a triangular domain. The original schedule is as follows.
10712 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10714 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10715 { A[i,j] -> [floor(j/10)] }, \
10716 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10720 for (int c0 = 0; c0 <= 10; c0 += 1)
10721 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10722 for (int c2 = 10 * c0;
10723 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10724 for (int c3 = 10 * c1;
10725 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10728 Isolating the full tiles, we have the following input
10730 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10732 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10733 { A[i,j] -> [floor(j/10)] }, \
10734 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10735 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10736 10a+9+10b+9 <= 100 }"
10741 for (int c0 = 0; c0 <= 8; c0 += 1) {
10742 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10743 for (int c2 = 10 * c0;
10744 c2 <= 10 * c0 + 9; c2 += 1)
10745 for (int c3 = 10 * c1;
10746 c3 <= 10 * c1 + 9; c3 += 1)
10748 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10749 for (int c2 = 10 * c0;
10750 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10751 for (int c3 = 10 * c1;
10752 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10755 for (int c0 = 9; c0 <= 10; c0 += 1)
10756 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10757 for (int c2 = 10 * c0;
10758 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10759 for (int c3 = 10 * c1;
10760 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10764 We may then additionally unroll the innermost loop of the isolated part
10766 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10768 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10769 { A[i,j] -> [floor(j/10)] }, \
10770 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10771 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10772 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10777 for (int c0 = 0; c0 <= 8; c0 += 1) {
10778 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10779 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10781 A(c2, 10 * c1 + 1);
10782 A(c2, 10 * c1 + 2);
10783 A(c2, 10 * c1 + 3);
10784 A(c2, 10 * c1 + 4);
10785 A(c2, 10 * c1 + 5);
10786 A(c2, 10 * c1 + 6);
10787 A(c2, 10 * c1 + 7);
10788 A(c2, 10 * c1 + 8);
10789 A(c2, 10 * c1 + 9);
10791 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10792 for (int c2 = 10 * c0;
10793 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10794 for (int c3 = 10 * c1;
10795 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10798 for (int c0 = 9; c0 <= 10; c0 += 1)
10799 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10800 for (int c2 = 10 * c0;
10801 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10802 for (int c3 = 10 * c1;
10803 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10808 =head3 AST Generation Options (Schedule Map)
10810 In case of AST construction using
10811 C<isl_ast_build_node_from_schedule_map>, the options
10812 that control how an AST is created from the individual schedule
10813 dimensions are stored in the C<isl_ast_build>.
10814 They can be set using the following function.
10816 #include <isl/ast_build.h>
10817 __isl_give isl_ast_build *
10818 isl_ast_build_set_options(
10819 __isl_take isl_ast_build *build,
10820 __isl_take isl_union_map *options);
10822 The options are encoded in an C<isl_union_map>.
10823 The domain of this union relation refers to the schedule domain,
10824 i.e., the range of the schedule passed
10825 to C<isl_ast_build_node_from_schedule_map>.
10826 In the case of nested AST generation (see L</"Nested AST Generation">),
10827 the domain of C<options> should refer to the extra piece of the schedule.
10828 That is, it should be equal to the range of the wrapped relation in the
10829 range of the schedule.
10830 The range of the options can consist of elements in one or more spaces,
10831 the names of which determine the effect of the option.
10832 The values of the range typically also refer to the schedule dimension
10833 to which the option applies, with value C<0> representing
10834 the outermost schedule dimension. In case of nested AST generation
10835 (see L</"Nested AST Generation">), these values refer to the position
10836 of the schedule dimension within the innermost AST generation.
10837 The constraints on the domain elements of
10838 the option should only refer to this dimension and earlier dimensions.
10839 We consider the following spaces.
10843 =item C<separation_class>
10845 B<This option has been deprecated. Use the isolate option on
10846 schedule trees instead.>
10848 This space is a wrapped relation between two one dimensional spaces.
10849 The input space represents the schedule dimension to which the option
10850 applies and the output space represents the separation class.
10851 While constructing a loop corresponding to the specified schedule
10852 dimension(s), the AST generator will try to generate separate loops
10853 for domain elements that are assigned different classes.
10854 If only some of the elements are assigned a class, then those elements
10855 that are not assigned any class will be treated as belonging to a class
10856 that is separate from the explicitly assigned classes.
10857 The typical use case for this option is to separate full tiles from
10859 The other options, described below, are applied after the separation
10862 As an example, consider the separation into full and partial tiles
10863 of a tiling of a triangular domain.
10864 Take, for example, the domain
10866 { A[i,j] : 0 <= i,j and i + j <= 100 }
10868 and a tiling into tiles of 10 by 10. The input to the AST generator
10869 is then the schedule
10871 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10874 Without any options, the following AST is generated
10876 for (int c0 = 0; c0 <= 10; c0 += 1)
10877 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10878 for (int c2 = 10 * c0;
10879 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10881 for (int c3 = 10 * c1;
10882 c3 <= min(10 * c1 + 9, -c2 + 100);
10886 Separation into full and partial tiles can be obtained by assigning
10887 a class, say C<0>, to the full tiles. The full tiles are represented by those
10888 values of the first and second schedule dimensions for which there are
10889 values of the third and fourth dimensions to cover an entire tile.
10890 That is, we need to specify the following option
10892 { [a,b,c,d] -> separation_class[[0]->[0]] :
10893 exists b': 0 <= 10a,10b' and
10894 10a+9+10b'+9 <= 100;
10895 [a,b,c,d] -> separation_class[[1]->[0]] :
10896 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10898 which simplifies to
10900 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10901 a >= 0 and b >= 0 and b <= 8 - a;
10902 [a, b, c, d] -> separation_class[[0] -> [0]] :
10903 a >= 0 and a <= 8 }
10905 With this option, the generated AST is as follows
10908 for (int c0 = 0; c0 <= 8; c0 += 1) {
10909 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10910 for (int c2 = 10 * c0;
10911 c2 <= 10 * c0 + 9; c2 += 1)
10912 for (int c3 = 10 * c1;
10913 c3 <= 10 * c1 + 9; c3 += 1)
10915 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10916 for (int c2 = 10 * c0;
10917 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10919 for (int c3 = 10 * c1;
10920 c3 <= min(-c2 + 100, 10 * c1 + 9);
10924 for (int c0 = 9; c0 <= 10; c0 += 1)
10925 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10926 for (int c2 = 10 * c0;
10927 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10929 for (int c3 = 10 * c1;
10930 c3 <= min(10 * c1 + 9, -c2 + 100);
10937 This is a single-dimensional space representing the schedule dimension(s)
10938 to which ``separation'' should be applied. Separation tries to split
10939 a loop into several pieces if this can avoid the generation of guards
10941 See also the C<atomic> option.
10945 This is a single-dimensional space representing the schedule dimension(s)
10946 for which the domains should be considered ``atomic''. That is, the
10947 AST generator will make sure that any given domain space will only appear
10948 in a single loop at the specified level.
10950 Consider the following schedule
10952 { a[i] -> [i] : 0 <= i < 10;
10953 b[i] -> [i+1] : 0 <= i < 10 }
10955 If the following option is specified
10957 { [i] -> separate[x] }
10959 then the following AST will be generated
10963 for (int c0 = 1; c0 <= 9; c0 += 1) {
10970 If, on the other hand, the following option is specified
10972 { [i] -> atomic[x] }
10974 then the following AST will be generated
10976 for (int c0 = 0; c0 <= 10; c0 += 1) {
10983 If neither C<atomic> nor C<separate> is specified, then the AST generator
10984 may produce either of these two results or some intermediate form.
10988 This is a single-dimensional space representing the schedule dimension(s)
10989 that should be I<completely> unrolled.
10990 To obtain a partial unrolling, the user should apply an additional
10991 strip-mining to the schedule and fully unroll the inner loop.
10995 =head3 Fine-grained Control over AST Generation
10997 Besides specifying the constraints on the parameters,
10998 an C<isl_ast_build> object can be used to control
10999 various aspects of the AST generation process.
11000 In case of AST construction using
11001 C<isl_ast_build_node_from_schedule_map>,
11002 the most prominent way of control is through ``options'',
11003 as explained above.
11005 Additional control is available through the following functions.
11007 #include <isl/ast_build.h>
11008 __isl_give isl_ast_build *
11009 isl_ast_build_set_iterators(
11010 __isl_take isl_ast_build *build,
11011 __isl_take isl_id_list *iterators);
11013 The function C<isl_ast_build_set_iterators> allows the user to
11014 specify a list of iterator C<isl_id>s to be used as iterators.
11015 If the input schedule is injective, then
11016 the number of elements in this list should be as large as the dimension
11017 of the schedule space, but no direct correspondence should be assumed
11018 between dimensions and elements.
11019 If the input schedule is not injective, then an additional number
11020 of C<isl_id>s equal to the largest dimension of the input domains
11022 If the number of provided C<isl_id>s is insufficient, then additional
11023 names are automatically generated.
11025 #include <isl/ast_build.h>
11026 __isl_give isl_ast_build *
11027 isl_ast_build_set_create_leaf(
11028 __isl_take isl_ast_build *build,
11029 __isl_give isl_ast_node *(*fn)(
11030 __isl_take isl_ast_build *build,
11031 void *user), void *user);
11034 C<isl_ast_build_set_create_leaf> function allows for the
11035 specification of a callback that should be called whenever the AST
11036 generator arrives at an element of the schedule domain.
11037 The callback should return an AST node that should be inserted
11038 at the corresponding position of the AST. The default action (when
11039 the callback is not set) is to continue generating parts of the AST to scan
11040 all the domain elements associated to the schedule domain element
11041 and to insert user nodes, ``calling'' the domain element, for each of them.
11042 The C<build> argument contains the current state of the C<isl_ast_build>.
11043 To ease nested AST generation (see L</"Nested AST Generation">),
11044 all control information that is
11045 specific to the current AST generation such as the options and
11046 the callbacks has been removed from this C<isl_ast_build>.
11047 The callback would typically return the result of a nested
11048 AST generation or a
11049 user defined node created using the following function.
11051 #include <isl/ast.h>
11052 __isl_give isl_ast_node *isl_ast_node_alloc_user(
11053 __isl_take isl_ast_expr *expr);
11055 #include <isl/ast_build.h>
11056 __isl_give isl_ast_build *
11057 isl_ast_build_set_at_each_domain(
11058 __isl_take isl_ast_build *build,
11059 __isl_give isl_ast_node *(*fn)(
11060 __isl_take isl_ast_node *node,
11061 __isl_keep isl_ast_build *build,
11062 void *user), void *user);
11063 __isl_give isl_ast_build *
11064 isl_ast_build_set_before_each_for(
11065 __isl_take isl_ast_build *build,
11066 __isl_give isl_id *(*fn)(
11067 __isl_keep isl_ast_build *build,
11068 void *user), void *user);
11069 __isl_give isl_ast_build *
11070 isl_ast_build_set_after_each_for(
11071 __isl_take isl_ast_build *build,
11072 __isl_give isl_ast_node *(*fn)(
11073 __isl_take isl_ast_node *node,
11074 __isl_keep isl_ast_build *build,
11075 void *user), void *user);
11076 __isl_give isl_ast_build *
11077 isl_ast_build_set_before_each_mark(
11078 __isl_take isl_ast_build *build,
11079 isl_stat (*fn)(__isl_keep isl_id *mark,
11080 __isl_keep isl_ast_build *build,
11081 void *user), void *user);
11082 __isl_give isl_ast_build *
11083 isl_ast_build_set_after_each_mark(
11084 __isl_take isl_ast_build *build,
11085 __isl_give isl_ast_node *(*fn)(
11086 __isl_take isl_ast_node *node,
11087 __isl_keep isl_ast_build *build,
11088 void *user), void *user);
11090 The callback set by C<isl_ast_build_set_at_each_domain> will
11091 be called for each domain AST node.
11092 The callbacks set by C<isl_ast_build_set_before_each_for>
11093 and C<isl_ast_build_set_after_each_for> will be called
11094 for each for AST node. The first will be called in depth-first
11095 pre-order, while the second will be called in depth-first post-order.
11096 Since C<isl_ast_build_set_before_each_for> is called before the for
11097 node is actually constructed, it is only passed an C<isl_ast_build>.
11098 The returned C<isl_id> will be added as an annotation (using
11099 C<isl_ast_node_set_annotation>) to the constructed for node.
11100 In particular, if the user has also specified an C<after_each_for>
11101 callback, then the annotation can be retrieved from the node passed to
11102 that callback using C<isl_ast_node_get_annotation>.
11103 The callbacks set by C<isl_ast_build_set_before_each_mark>
11104 and C<isl_ast_build_set_after_each_mark> will be called for each
11105 mark AST node that is created, i.e., for each mark schedule node
11106 in the input schedule tree. The first will be called in depth-first
11107 pre-order, while the second will be called in depth-first post-order.
11108 Since the callback set by C<isl_ast_build_set_before_each_mark>
11109 is called before the mark AST node is actually constructed, it is passed
11110 the identifier of the mark node.
11111 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
11112 The given C<isl_ast_build> can be used to create new
11113 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
11114 or C<isl_ast_build_call_from_pw_multi_aff>.
11116 =head3 Nested AST Generation
11118 C<isl> allows the user to create an AST within the context
11119 of another AST. These nested ASTs are created using the
11120 same C<isl_ast_build_node_from_schedule_map> function that is used to create
11121 the outer AST. The C<build> argument should be an C<isl_ast_build>
11122 passed to a callback set by
11123 C<isl_ast_build_set_create_leaf>.
11124 The space of the range of the C<schedule> argument should refer
11125 to this build. In particular, the space should be a wrapped
11126 relation and the domain of this wrapped relation should be the
11127 same as that of the range of the schedule returned by
11128 C<isl_ast_build_get_schedule> below.
11129 In practice, the new schedule is typically
11130 created by calling C<isl_union_map_range_product> on the old schedule
11131 and some extra piece of the schedule.
11132 The space of the schedule domain is also available from
11133 the C<isl_ast_build>.
11135 #include <isl/ast_build.h>
11136 __isl_give isl_union_map *isl_ast_build_get_schedule(
11137 __isl_keep isl_ast_build *build);
11138 __isl_give isl_space *isl_ast_build_get_schedule_space(
11139 __isl_keep isl_ast_build *build);
11140 __isl_give isl_ast_build *isl_ast_build_restrict(
11141 __isl_take isl_ast_build *build,
11142 __isl_take isl_set *set);
11144 The C<isl_ast_build_get_schedule> function returns a (partial)
11145 schedule for the domains elements for which part of the AST still needs to
11146 be generated in the current build.
11147 In particular, the domain elements are mapped to those iterations of the loops
11148 enclosing the current point of the AST generation inside which
11149 the domain elements are executed.
11150 No direct correspondence between
11151 the input schedule and this schedule should be assumed.
11152 The space obtained from C<isl_ast_build_get_schedule_space> can be used
11153 to create a set for C<isl_ast_build_restrict> to intersect
11154 with the current build. In particular, the set passed to
11155 C<isl_ast_build_restrict> can have additional parameters.
11156 The ids of the set dimensions in the space returned by
11157 C<isl_ast_build_get_schedule_space> correspond to the
11158 iterators of the already generated loops.
11159 The user should not rely on the ids of the output dimensions
11160 of the relations in the union relation returned by
11161 C<isl_ast_build_get_schedule> having any particular value.
11163 =head1 Applications
11165 Although C<isl> is mainly meant to be used as a library,
11166 it also contains some basic applications that use some
11167 of the functionality of C<isl>.
11168 For applications that take one or more polytopes or polyhedra
11169 as input, this input may be specified in either the L<isl format>
11170 or the L<PolyLib format>.
11172 =head2 C<isl_polyhedron_sample>
11174 C<isl_polyhedron_sample> takes a polyhedron as input and prints
11175 an integer element of the polyhedron, if there is any.
11176 The first column in the output is the denominator and is always
11177 equal to 1. If the polyhedron contains no integer points,
11178 then a vector of length zero is printed.
11182 C<isl_pip> takes the same input as the C<example> program
11183 from the C<piplib> distribution, i.e., a set of constraints
11184 on the parameters, a line containing only -1 and finally a set
11185 of constraints on a parametric polyhedron.
11186 The coefficients of the parameters appear in the last columns
11187 (but before the final constant column).
11188 The output is the lexicographic minimum of the parametric polyhedron.
11189 As C<isl> currently does not have its own output format, the output
11190 is just a dump of the internal state.
11192 =head2 C<isl_polyhedron_minimize>
11194 C<isl_polyhedron_minimize> computes the minimum of some linear
11195 or affine objective function over the integer points in a polyhedron.
11196 If an affine objective function
11197 is given, then the constant should appear in the last column.
11199 =head2 C<isl_polytope_scan>
11201 Given a polytope, C<isl_polytope_scan> prints
11202 all integer points in the polytope.
11206 Given an C<isl_union_access_info> object as input,
11207 C<isl_flow> prints out the corresponding dependences,
11208 as computed by C<isl_union_access_info_compute_flow>.
11210 =head2 C<isl_codegen>
11212 Given either a schedule tree or a sequence consisting of
11213 a schedule map, a context set and an options relation,
11214 C<isl_codegen> prints out an AST that scans the domain elements
11215 of the schedule in the order of their image(s) taking into account
11216 the constraints in the context set.
11218 =head2 C<isl_schedule>
11220 Given an C<isl_schedule_constraints> object as input,
11221 C<isl_schedule> prints out a schedule that satisfies the given