3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
273 =head3 Changes since isl-0.19
277 =item * Zero-dimensional objects of type C<isl_multi_pw_aff> or
278 C<isl_multi_union_pw_aff> can now keep track of an explicit domain.
279 This explicit domain, if present, is taken into account
280 by various operations that take such objects as input.
286 C<isl> is released under the MIT license.
290 Permission is hereby granted, free of charge, to any person obtaining a copy of
291 this software and associated documentation files (the "Software"), to deal in
292 the Software without restriction, including without limitation the rights to
293 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
294 of the Software, and to permit persons to whom the Software is furnished to do
295 so, subject to the following conditions:
297 The above copyright notice and this permission notice shall be included in all
298 copies or substantial portions of the Software.
300 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
301 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
302 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
303 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
304 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
305 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
310 Note that by default C<isl> requires C<GMP>, which is released
311 under the GNU Lesser General Public License (LGPL). This means
312 that code linked against C<isl> is also linked against LGPL code.
314 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
315 will link against C<imath>, a library for exact integer arithmetic released
316 under the MIT license.
320 The source of C<isl> can be obtained either as a tarball
321 or from the git repository. Both are available from
322 L<http://isl.gforge.inria.fr/>.
323 The installation process depends on how you obtained
326 =head2 Installation from the git repository
330 =item 1 Clone or update the repository
332 The first time the source is obtained, you need to clone
335 git clone git://repo.or.cz/isl.git
337 To obtain updates, you need to pull in the latest changes
341 =item 2 Optionally get C<imath> submodule
343 To build C<isl> with C<imath>, you need to obtain the C<imath>
344 submodule by running in the git source tree of C<isl>
349 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
351 =item 2 Generate C<configure>
357 After performing the above steps, continue
358 with the L<Common installation instructions>.
360 =head2 Common installation instructions
364 =item 1 Obtain C<GMP>
366 By default, building C<isl> requires C<GMP>, including its headers files.
367 Your distribution may not provide these header files by default
368 and you may need to install a package called C<gmp-devel> or something
369 similar. Alternatively, C<GMP> can be built from
370 source, available from L<http://gmplib.org/>.
371 C<GMP> is not needed if you build C<isl> with C<imath>.
375 C<isl> uses the standard C<autoconf> C<configure> script.
380 optionally followed by some configure options.
381 A complete list of options can be obtained by running
385 Below we discuss some of the more common options.
391 Installation prefix for C<isl>
393 =item C<--with-int=[gmp|imath|imath-32]>
395 Select the integer library to be used by C<isl>, the default is C<gmp>.
396 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
397 for values out of the 32 bit range. In most applications, C<isl> will run
398 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
401 =item C<--with-gmp-prefix>
403 Installation prefix for C<GMP> (architecture-independent files).
405 =item C<--with-gmp-exec-prefix>
407 Installation prefix for C<GMP> (architecture-dependent files).
415 =item 4 Install (optional)
421 =head1 Integer Set Library
423 =head2 Memory Management
425 Since a high-level operation on isl objects usually involves
426 several substeps and since the user is usually not interested in
427 the intermediate results, most functions that return a new object
428 will also release all the objects passed as arguments.
429 If the user still wants to use one or more of these arguments
430 after the function call, she should pass along a copy of the
431 object rather than the object itself.
432 The user is then responsible for making sure that the original
433 object gets used somewhere else or is explicitly freed.
435 The arguments and return values of all documented functions are
436 annotated to make clear which arguments are released and which
437 arguments are preserved. In particular, the following annotations
444 C<__isl_give> means that a new object is returned.
445 The user should make sure that the returned pointer is
446 used exactly once as a value for an C<__isl_take> argument.
447 In between, it can be used as a value for as many
448 C<__isl_keep> arguments as the user likes.
449 There is one exception, and that is the case where the
450 pointer returned is C<NULL>. Is this case, the user
451 is free to use it as an C<__isl_take> argument or not.
452 When applied to a C<char *>, the returned pointer needs to be
457 C<__isl_null> means that a C<NULL> value is returned.
461 C<__isl_take> means that the object the argument points to
462 is taken over by the function and may no longer be used
463 by the user as an argument to any other function.
464 The pointer value must be one returned by a function
465 returning an C<__isl_give> pointer.
466 If the user passes in a C<NULL> value, then this will
467 be treated as an error in the sense that the function will
468 not perform its usual operation. However, it will still
469 make sure that all the other C<__isl_take> arguments
474 C<__isl_keep> means that the function will only use the object
475 temporarily. After the function has finished, the user
476 can still use it as an argument to other functions.
477 A C<NULL> value will be treated in the same way as
478 a C<NULL> value for an C<__isl_take> argument.
479 This annotation may also be used on return values of
480 type C<const char *>, in which case the returned pointer should
481 not be freed by the user and is only valid until the object
482 from which it was derived is updated or freed.
486 =head2 Initialization
488 All manipulations of integer sets and relations occur within
489 the context of an C<isl_ctx>.
490 A given C<isl_ctx> can only be used within a single thread.
491 All arguments of a function are required to have been allocated
492 within the same context.
493 There are currently no functions available for moving an object
494 from one C<isl_ctx> to another C<isl_ctx>. This means that
495 there is currently no way of safely moving an object from one
496 thread to another, unless the whole C<isl_ctx> is moved.
498 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
499 freed using C<isl_ctx_free>.
500 All objects allocated within an C<isl_ctx> should be freed
501 before the C<isl_ctx> itself is freed.
503 isl_ctx *isl_ctx_alloc();
504 void isl_ctx_free(isl_ctx *ctx);
506 The user can impose a bound on the number of low-level I<operations>
507 that can be performed by an C<isl_ctx>. This bound can be set and
508 retrieved using the following functions. A bound of zero means that
509 no bound is imposed. The number of operations performed can be
510 reset using C<isl_ctx_reset_operations>. Note that the number
511 of low-level operations needed to perform a high-level computation
512 may differ significantly across different versions
513 of C<isl>, but it should be the same across different platforms
514 for the same version of C<isl>.
516 Warning: This feature is experimental. C<isl> has good support to abort and
517 bail out during the computation, but this feature may exercise error code paths
518 that are normally not used that much. Consequently, it is not unlikely that
519 hidden bugs will be exposed.
521 void isl_ctx_set_max_operations(isl_ctx *ctx,
522 unsigned long max_operations);
523 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
524 void isl_ctx_reset_operations(isl_ctx *ctx);
526 In order to be able to create an object in the same context
527 as another object, most object types (described later in
528 this document) provide a function to obtain the context
529 in which the object was created.
532 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
533 isl_ctx *isl_multi_val_get_ctx(
534 __isl_keep isl_multi_val *mv);
537 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
539 #include <isl/local_space.h>
540 isl_ctx *isl_local_space_get_ctx(
541 __isl_keep isl_local_space *ls);
544 isl_ctx *isl_set_list_get_ctx(
545 __isl_keep isl_set_list *list);
548 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
549 isl_ctx *isl_multi_aff_get_ctx(
550 __isl_keep isl_multi_aff *maff);
551 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
552 isl_ctx *isl_pw_multi_aff_get_ctx(
553 __isl_keep isl_pw_multi_aff *pma);
554 isl_ctx *isl_multi_pw_aff_get_ctx(
555 __isl_keep isl_multi_pw_aff *mpa);
556 isl_ctx *isl_union_pw_aff_get_ctx(
557 __isl_keep isl_union_pw_aff *upa);
558 isl_ctx *isl_union_pw_multi_aff_get_ctx(
559 __isl_keep isl_union_pw_multi_aff *upma);
560 isl_ctx *isl_multi_union_pw_aff_get_ctx(
561 __isl_keep isl_multi_union_pw_aff *mupa);
563 #include <isl/id_to_ast_expr.h>
564 isl_ctx *isl_id_to_ast_expr_get_ctx(
565 __isl_keep isl_id_to_ast_expr *id2expr);
567 #include <isl/point.h>
568 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
571 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
574 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
576 #include <isl/vertices.h>
577 isl_ctx *isl_vertices_get_ctx(
578 __isl_keep isl_vertices *vertices);
579 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
580 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
582 #include <isl/flow.h>
583 isl_ctx *isl_restriction_get_ctx(
584 __isl_keep isl_restriction *restr);
585 isl_ctx *isl_union_access_info_get_ctx(
586 __isl_keep isl_union_access_info *access);
587 isl_ctx *isl_union_flow_get_ctx(
588 __isl_keep isl_union_flow *flow);
590 #include <isl/schedule.h>
591 isl_ctx *isl_schedule_get_ctx(
592 __isl_keep isl_schedule *sched);
593 isl_ctx *isl_schedule_constraints_get_ctx(
594 __isl_keep isl_schedule_constraints *sc);
596 #include <isl/schedule_node.h>
597 isl_ctx *isl_schedule_node_get_ctx(
598 __isl_keep isl_schedule_node *node);
600 #include <isl/ast_build.h>
601 isl_ctx *isl_ast_build_get_ctx(
602 __isl_keep isl_ast_build *build);
605 isl_ctx *isl_ast_expr_get_ctx(
606 __isl_keep isl_ast_expr *expr);
607 isl_ctx *isl_ast_node_get_ctx(
608 __isl_keep isl_ast_node *node);
612 C<isl> uses two special return types for functions that either return
613 a boolean or that in principle do not return anything.
614 In particular, the C<isl_bool> type has three possible values:
615 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
616 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
617 C<isl_bool_error> (a negative integer value), indicating that something
618 went wrong. The following function can be used to negate an C<isl_bool>,
619 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
622 isl_bool isl_bool_not(isl_bool b);
624 The C<isl_stat> type has two possible values:
625 C<isl_stat_ok> (the integer value zero), indicating a successful
627 C<isl_stat_error> (a negative integer value), indicating that something
629 See L</"Error Handling"> for more information on
630 C<isl_bool_error> and C<isl_stat_error>.
634 An C<isl_val> represents an integer value, a rational value
635 or one of three special values, infinity, negative infinity and NaN.
636 Some predefined values can be created using the following functions.
639 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
640 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
641 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
642 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
643 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
644 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
646 Specific integer values can be created using the following functions.
649 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
651 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
653 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
654 size_t n, size_t size, const void *chunks);
656 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
657 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
658 The least significant digit is assumed to be stored first.
660 Value objects can be copied and freed using the following functions.
663 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
664 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
666 They can be inspected using the following functions.
669 long isl_val_get_num_si(__isl_keep isl_val *v);
670 long isl_val_get_den_si(__isl_keep isl_val *v);
671 __isl_give isl_val *isl_val_get_den_val(
672 __isl_keep isl_val *v);
673 double isl_val_get_d(__isl_keep isl_val *v);
674 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
676 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
677 size_t size, void *chunks);
679 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
680 of C<size> bytes needed to store the absolute value of the
682 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
683 which is assumed to have been preallocated by the caller.
684 The least significant digit is stored first.
685 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
686 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
687 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
689 An C<isl_val> can be modified using the following function.
692 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
695 The following unary properties are defined on C<isl_val>s.
698 int isl_val_sgn(__isl_keep isl_val *v);
699 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
700 isl_bool isl_val_is_one(__isl_keep isl_val *v);
701 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
702 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
703 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
704 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
705 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
706 isl_bool isl_val_is_int(__isl_keep isl_val *v);
707 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
708 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
709 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
710 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
712 Note that the sign of NaN is undefined.
714 The following binary properties are defined on pairs of C<isl_val>s.
717 isl_bool isl_val_lt(__isl_keep isl_val *v1,
718 __isl_keep isl_val *v2);
719 isl_bool isl_val_le(__isl_keep isl_val *v1,
720 __isl_keep isl_val *v2);
721 isl_bool isl_val_gt(__isl_keep isl_val *v1,
722 __isl_keep isl_val *v2);
723 isl_bool isl_val_ge(__isl_keep isl_val *v1,
724 __isl_keep isl_val *v2);
725 isl_bool isl_val_eq(__isl_keep isl_val *v1,
726 __isl_keep isl_val *v2);
727 isl_bool isl_val_ne(__isl_keep isl_val *v1,
728 __isl_keep isl_val *v2);
729 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
730 __isl_keep isl_val *v2);
732 Comparisons to NaN always return false.
733 That is, a NaN is not considered to hold any relative position
734 with respect to any value. In particular, a NaN
735 is neither considered to be equal to nor to be different from
736 any value (including another NaN).
737 The function C<isl_val_abs_eq> checks whether its two arguments
738 are equal in absolute value.
740 For integer C<isl_val>s we additionally have the following binary property.
743 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
744 __isl_keep isl_val *v2);
746 An C<isl_val> can also be compared to an integer using the following
747 functions. The result of C<isl_val_cmp_si> undefined for NaN.
750 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
751 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
753 The following unary operations are available on C<isl_val>s.
756 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
757 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
758 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
759 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
760 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
761 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
762 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
764 The following binary operations are available on C<isl_val>s.
767 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
768 __isl_take isl_val *v2);
769 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
770 __isl_take isl_val *v2);
771 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
772 __isl_take isl_val *v2);
773 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
775 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
776 __isl_take isl_val *v2);
777 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
779 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
780 __isl_take isl_val *v2);
781 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
783 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
784 __isl_take isl_val *v2);
785 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
788 On integer values, we additionally have the following operations.
791 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
792 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
793 __isl_take isl_val *v2);
794 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
795 __isl_take isl_val *v2);
796 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
797 __isl_take isl_val *v2, __isl_give isl_val **x,
798 __isl_give isl_val **y);
800 The function C<isl_val_gcdext> returns the greatest common divisor g
801 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
802 that C<*x> * C<v1> + C<*y> * C<v2> = g.
804 =head3 GMP specific functions
806 These functions are only available if C<isl> has been compiled with C<GMP>
809 Specific integer and rational values can be created from C<GMP> values using
810 the following functions.
812 #include <isl/val_gmp.h>
813 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
815 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
816 const mpz_t n, const mpz_t d);
818 The numerator and denominator of a rational value can be extracted as
819 C<GMP> values using the following functions.
821 #include <isl/val_gmp.h>
822 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
823 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
825 =head2 Sets and Relations
827 C<isl> uses six types of objects for representing sets and relations,
828 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
829 C<isl_union_set> and C<isl_union_map>.
830 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
831 can be described as a conjunction of affine constraints, while
832 C<isl_set> and C<isl_map> represent unions of
833 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
834 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
835 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
836 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
837 where spaces are considered different if they have a different number
838 of dimensions and/or different names (see L<"Spaces">).
839 The difference between sets and relations (maps) is that sets have
840 one set of variables, while relations have two sets of variables,
841 input variables and output variables.
843 =head2 Error Handling
845 C<isl> supports different ways to react in case a runtime error is triggered.
846 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
847 with two maps that have incompatible spaces. There are three possible ways
848 to react on error: to warn, to continue or to abort.
850 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
851 the last error in the corresponding C<isl_ctx> and the function in which the
852 error was triggered returns a value indicating that some error has
853 occurred. In case of functions returning a pointer, this value is
854 C<NULL>. In case of functions returning an C<isl_bool> or an
855 C<isl_stat>, this value is C<isl_bool_error> or C<isl_stat_error>.
856 An error does not corrupt internal state,
857 such that isl can continue to be used. C<isl> also provides functions to
858 read the last error, including the specific error message,
859 the isl source file where the error occurred and the line number,
860 and to reset all information about the last error. The
861 last error is only stored for information purposes. Its presence does not
862 change the behavior of C<isl>. Hence, resetting an error is not required to
863 continue to use isl, but only to observe new errors.
866 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
867 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
868 const char *isl_ctx_last_error_file(isl_ctx *ctx);
869 int isl_ctx_last_error_line(isl_ctx *ctx);
870 void isl_ctx_reset_error(isl_ctx *ctx);
872 If no error has occurred since the last call to C<isl_ctx_reset_error>,
873 then the functions C<isl_ctx_last_error_msg> and
874 C<isl_ctx_last_error_file> return C<NULL>.
876 Another option is to continue on error. This is similar to warn on error mode,
877 except that C<isl> does not print any warning. This allows a program to
878 implement its own error reporting.
880 The last option is to directly abort the execution of the program from within
881 the isl library. This makes it obviously impossible to recover from an error,
882 but it allows to directly spot the error location. By aborting on error,
883 debuggers break at the location the error occurred and can provide a stack
884 trace. Other tools that automatically provide stack traces on abort or that do
885 not want to continue execution after an error was triggered may also prefer to
888 The on error behavior of isl can be specified by calling
889 C<isl_options_set_on_error> or by setting the command line option
890 C<--isl-on-error>. Valid arguments for the function call are
891 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
892 choices for the command line option are C<warn>, C<continue> and C<abort>.
893 It is also possible to query the current error mode.
895 #include <isl/options.h>
896 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
897 int isl_options_get_on_error(isl_ctx *ctx);
901 Identifiers are used to identify both individual dimensions
902 and tuples of dimensions. They consist of an optional name and an optional
903 user pointer. The name and the user pointer cannot both be C<NULL>, however.
904 Identifiers with the same name but different pointer values
905 are considered to be distinct.
906 Similarly, identifiers with different names but the same pointer value
907 are also considered to be distinct.
908 Equal identifiers are represented using the same object.
909 Pairs of identifiers can therefore be tested for equality using the
911 Identifiers can be constructed, copied, freed, inspected and printed
912 using the following functions.
915 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
916 __isl_keep const char *name, void *user);
917 __isl_give isl_id *isl_id_set_free_user(
918 __isl_take isl_id *id,
919 void (*free_user)(void *user));
920 __isl_give isl_id *isl_id_copy(isl_id *id);
921 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
923 void *isl_id_get_user(__isl_keep isl_id *id);
924 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
926 __isl_give isl_printer *isl_printer_print_id(
927 __isl_take isl_printer *p, __isl_keep isl_id *id);
929 The callback set by C<isl_id_set_free_user> is called on the user
930 pointer when the last reference to the C<isl_id> is freed.
931 Note that C<isl_id_get_name> returns a pointer to some internal
932 data structure, so the result can only be used while the
933 corresponding C<isl_id> is alive.
937 Whenever a new set, relation or similar object is created from scratch,
938 the space in which it lives needs to be specified using an C<isl_space>.
939 Each space involves zero or more parameters and zero, one or two
940 tuples of set or input/output dimensions. The parameters and dimensions
941 are identified by an C<isl_dim_type> and a position.
942 The type C<isl_dim_param> refers to parameters,
943 the type C<isl_dim_set> refers to set dimensions (for spaces
944 with a single tuple of dimensions) and the types C<isl_dim_in>
945 and C<isl_dim_out> refer to input and output dimensions
946 (for spaces with two tuples of dimensions).
947 Local spaces (see L</"Local Spaces">) also contain dimensions
948 of type C<isl_dim_div>.
949 Note that parameters are only identified by their position within
950 a given object. Across different objects, parameters are (usually)
951 identified by their names or identifiers. Only unnamed parameters
952 are identified by their positions across objects. The use of unnamed
953 parameters is discouraged.
955 #include <isl/space.h>
956 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
957 unsigned nparam, unsigned n_in, unsigned n_out);
958 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
960 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
961 unsigned nparam, unsigned dim);
962 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
963 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
965 The space used for creating a parameter domain
966 needs to be created using C<isl_space_params_alloc>.
967 For other sets, the space
968 needs to be created using C<isl_space_set_alloc>, while
969 for a relation, the space
970 needs to be created using C<isl_space_alloc>.
972 To check whether a given space is that of a set or a map
973 or whether it is a parameter space, use these functions:
975 #include <isl/space.h>
976 isl_bool isl_space_is_params(__isl_keep isl_space *space);
977 isl_bool isl_space_is_set(__isl_keep isl_space *space);
978 isl_bool isl_space_is_map(__isl_keep isl_space *space);
980 Spaces can be compared using the following functions:
982 #include <isl/space.h>
983 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
984 __isl_keep isl_space *space2);
985 isl_bool isl_space_has_equal_params(
986 __isl_keep isl_space *space1,
987 __isl_keep isl_space *space2);
988 isl_bool isl_space_has_equal_tuples(
989 __isl_keep isl_space *space1,
990 __isl_keep isl_space *space2);
991 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
992 __isl_keep isl_space *space2);
993 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
994 __isl_keep isl_space *space2);
995 isl_bool isl_space_tuple_is_equal(
996 __isl_keep isl_space *space1,
997 enum isl_dim_type type1,
998 __isl_keep isl_space *space2,
999 enum isl_dim_type type2);
1001 C<isl_space_is_domain> checks whether the first argument is equal
1002 to the domain of the second argument. This requires in particular that
1003 the first argument is a set space and that the second argument
1004 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1005 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1006 spaces are the same. That is, it checks if they have the same
1007 identifier (if any), the same dimension and the same internal structure
1010 C<isl_space_has_equal_params> checks whether two spaces
1011 have the same parameters in the same order.
1012 C<isl_space_has_equal_tuples> check whether two spaces have
1013 the same tuples. In contrast to C<isl_space_is_equal> below,
1014 it does not check the
1015 parameters. This is useful because many C<isl> functions align the
1016 parameters before they perform their operations, such that equivalence
1018 C<isl_space_is_equal> checks whether two spaces are identical,
1019 meaning that they have the same parameters and the same tuples.
1020 That is, it checks whether both C<isl_space_has_equal_params> and
1021 C<isl_space_has_equal_tuples> hold.
1023 It is often useful to create objects that live in the
1024 same space as some other object. This can be accomplished
1025 by creating the new objects
1026 (see L</"Creating New Sets and Relations"> or
1027 L</"Functions">) based on the space
1028 of the original object.
1030 #include <isl/set.h>
1031 __isl_give isl_space *isl_basic_set_get_space(
1032 __isl_keep isl_basic_set *bset);
1033 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1035 #include <isl/union_set.h>
1036 __isl_give isl_space *isl_union_set_get_space(
1037 __isl_keep isl_union_set *uset);
1039 #include <isl/map.h>
1040 __isl_give isl_space *isl_basic_map_get_space(
1041 __isl_keep isl_basic_map *bmap);
1042 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1044 #include <isl/union_map.h>
1045 __isl_give isl_space *isl_union_map_get_space(
1046 __isl_keep isl_union_map *umap);
1048 #include <isl/constraint.h>
1049 __isl_give isl_space *isl_constraint_get_space(
1050 __isl_keep isl_constraint *constraint);
1052 #include <isl/polynomial.h>
1053 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1054 __isl_keep isl_qpolynomial *qp);
1055 __isl_give isl_space *isl_qpolynomial_get_space(
1056 __isl_keep isl_qpolynomial *qp);
1057 __isl_give isl_space *
1058 isl_qpolynomial_fold_get_domain_space(
1059 __isl_keep isl_qpolynomial_fold *fold);
1060 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1061 __isl_keep isl_qpolynomial_fold *fold);
1062 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1063 __isl_keep isl_pw_qpolynomial *pwqp);
1064 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1065 __isl_keep isl_pw_qpolynomial *pwqp);
1066 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1067 __isl_keep isl_pw_qpolynomial_fold *pwf);
1068 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1069 __isl_keep isl_pw_qpolynomial_fold *pwf);
1070 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1071 __isl_keep isl_union_pw_qpolynomial *upwqp);
1072 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1073 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1075 #include <isl/val.h>
1076 __isl_give isl_space *isl_multi_val_get_space(
1077 __isl_keep isl_multi_val *mv);
1079 #include <isl/aff.h>
1080 __isl_give isl_space *isl_aff_get_domain_space(
1081 __isl_keep isl_aff *aff);
1082 __isl_give isl_space *isl_aff_get_space(
1083 __isl_keep isl_aff *aff);
1084 __isl_give isl_space *isl_pw_aff_get_domain_space(
1085 __isl_keep isl_pw_aff *pwaff);
1086 __isl_give isl_space *isl_pw_aff_get_space(
1087 __isl_keep isl_pw_aff *pwaff);
1088 __isl_give isl_space *isl_multi_aff_get_domain_space(
1089 __isl_keep isl_multi_aff *maff);
1090 __isl_give isl_space *isl_multi_aff_get_space(
1091 __isl_keep isl_multi_aff *maff);
1092 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1093 __isl_keep isl_pw_multi_aff *pma);
1094 __isl_give isl_space *isl_pw_multi_aff_get_space(
1095 __isl_keep isl_pw_multi_aff *pma);
1096 __isl_give isl_space *isl_union_pw_aff_get_space(
1097 __isl_keep isl_union_pw_aff *upa);
1098 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1099 __isl_keep isl_union_pw_multi_aff *upma);
1100 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1101 __isl_keep isl_multi_pw_aff *mpa);
1102 __isl_give isl_space *isl_multi_pw_aff_get_space(
1103 __isl_keep isl_multi_pw_aff *mpa);
1104 __isl_give isl_space *
1105 isl_multi_union_pw_aff_get_domain_space(
1106 __isl_keep isl_multi_union_pw_aff *mupa);
1107 __isl_give isl_space *
1108 isl_multi_union_pw_aff_get_space(
1109 __isl_keep isl_multi_union_pw_aff *mupa);
1111 #include <isl/point.h>
1112 __isl_give isl_space *isl_point_get_space(
1113 __isl_keep isl_point *pnt);
1115 The number of dimensions of a given type of space
1116 may be read off from a space or an object that lives
1117 in a space using the following functions.
1118 In case of C<isl_space_dim>, type may be
1119 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1120 C<isl_dim_out> (only for relations), C<isl_dim_set>
1121 (only for sets) or C<isl_dim_all>.
1123 #include <isl/space.h>
1124 unsigned isl_space_dim(__isl_keep isl_space *space,
1125 enum isl_dim_type type);
1127 #include <isl/local_space.h>
1128 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1129 enum isl_dim_type type);
1131 #include <isl/set.h>
1132 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1133 enum isl_dim_type type);
1134 unsigned isl_set_dim(__isl_keep isl_set *set,
1135 enum isl_dim_type type);
1137 #include <isl/union_set.h>
1138 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1139 enum isl_dim_type type);
1141 #include <isl/map.h>
1142 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1143 enum isl_dim_type type);
1144 unsigned isl_map_dim(__isl_keep isl_map *map,
1145 enum isl_dim_type type);
1147 #include <isl/union_map.h>
1148 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1149 enum isl_dim_type type);
1151 #include <isl/val.h>
1152 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1153 enum isl_dim_type type);
1155 #include <isl/aff.h>
1156 int isl_aff_dim(__isl_keep isl_aff *aff,
1157 enum isl_dim_type type);
1158 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1159 enum isl_dim_type type);
1160 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1161 enum isl_dim_type type);
1162 unsigned isl_pw_multi_aff_dim(
1163 __isl_keep isl_pw_multi_aff *pma,
1164 enum isl_dim_type type);
1165 unsigned isl_multi_pw_aff_dim(
1166 __isl_keep isl_multi_pw_aff *mpa,
1167 enum isl_dim_type type);
1168 unsigned isl_union_pw_aff_dim(
1169 __isl_keep isl_union_pw_aff *upa,
1170 enum isl_dim_type type);
1171 unsigned isl_union_pw_multi_aff_dim(
1172 __isl_keep isl_union_pw_multi_aff *upma,
1173 enum isl_dim_type type);
1174 unsigned isl_multi_union_pw_aff_dim(
1175 __isl_keep isl_multi_union_pw_aff *mupa,
1176 enum isl_dim_type type);
1178 #include <isl/polynomial.h>
1179 unsigned isl_union_pw_qpolynomial_dim(
1180 __isl_keep isl_union_pw_qpolynomial *upwqp,
1181 enum isl_dim_type type);
1182 unsigned isl_union_pw_qpolynomial_fold_dim(
1183 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1184 enum isl_dim_type type);
1186 Note that an C<isl_union_set>, an C<isl_union_map>,
1187 an C<isl_union_pw_multi_aff>,
1188 an C<isl_union_pw_qpolynomial> and
1189 an C<isl_union_pw_qpolynomial_fold>
1190 only have parameters.
1192 Additional parameters can be added to a space using the following function.
1194 #include <isl/space.h>
1195 __isl_give isl_space *isl_space_add_param_id(
1196 __isl_take isl_space *space,
1197 __isl_take isl_id *id);
1199 If a parameter with the given identifier already appears in the space,
1200 then it is not added again.
1202 The identifiers or names of the individual dimensions of spaces
1203 may be set or read off using the following functions on spaces
1204 or objects that live in spaces.
1205 These functions are mostly useful to obtain the identifiers, positions
1206 or names of the parameters. Identifiers of individual dimensions are
1207 essentially only useful for printing. They are ignored by all other
1208 operations and may not be preserved across those operations.
1210 #include <isl/space.h>
1211 __isl_give isl_space *isl_space_set_dim_id(
1212 __isl_take isl_space *space,
1213 enum isl_dim_type type, unsigned pos,
1214 __isl_take isl_id *id);
1215 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1216 enum isl_dim_type type, unsigned pos);
1217 __isl_give isl_id *isl_space_get_dim_id(
1218 __isl_keep isl_space *space,
1219 enum isl_dim_type type, unsigned pos);
1220 __isl_give isl_space *isl_space_set_dim_name(
1221 __isl_take isl_space *space,
1222 enum isl_dim_type type, unsigned pos,
1223 __isl_keep const char *name);
1224 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1225 enum isl_dim_type type, unsigned pos);
1226 __isl_keep const char *isl_space_get_dim_name(
1227 __isl_keep isl_space *space,
1228 enum isl_dim_type type, unsigned pos);
1230 #include <isl/local_space.h>
1231 __isl_give isl_local_space *isl_local_space_set_dim_id(
1232 __isl_take isl_local_space *ls,
1233 enum isl_dim_type type, unsigned pos,
1234 __isl_take isl_id *id);
1235 isl_bool isl_local_space_has_dim_id(
1236 __isl_keep isl_local_space *ls,
1237 enum isl_dim_type type, unsigned pos);
1238 __isl_give isl_id *isl_local_space_get_dim_id(
1239 __isl_keep isl_local_space *ls,
1240 enum isl_dim_type type, unsigned pos);
1241 __isl_give isl_local_space *isl_local_space_set_dim_name(
1242 __isl_take isl_local_space *ls,
1243 enum isl_dim_type type, unsigned pos, const char *s);
1244 isl_bool isl_local_space_has_dim_name(
1245 __isl_keep isl_local_space *ls,
1246 enum isl_dim_type type, unsigned pos)
1247 const char *isl_local_space_get_dim_name(
1248 __isl_keep isl_local_space *ls,
1249 enum isl_dim_type type, unsigned pos);
1251 #include <isl/constraint.h>
1252 const char *isl_constraint_get_dim_name(
1253 __isl_keep isl_constraint *constraint,
1254 enum isl_dim_type type, unsigned pos);
1256 #include <isl/set.h>
1257 __isl_give isl_id *isl_basic_set_get_dim_id(
1258 __isl_keep isl_basic_set *bset,
1259 enum isl_dim_type type, unsigned pos);
1260 __isl_give isl_set *isl_set_set_dim_id(
1261 __isl_take isl_set *set, enum isl_dim_type type,
1262 unsigned pos, __isl_take isl_id *id);
1263 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1264 enum isl_dim_type type, unsigned pos);
1265 __isl_give isl_id *isl_set_get_dim_id(
1266 __isl_keep isl_set *set, enum isl_dim_type type,
1268 const char *isl_basic_set_get_dim_name(
1269 __isl_keep isl_basic_set *bset,
1270 enum isl_dim_type type, unsigned pos);
1271 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1272 enum isl_dim_type type, unsigned pos);
1273 const char *isl_set_get_dim_name(
1274 __isl_keep isl_set *set,
1275 enum isl_dim_type type, unsigned pos);
1277 #include <isl/map.h>
1278 __isl_give isl_map *isl_map_set_dim_id(
1279 __isl_take isl_map *map, enum isl_dim_type type,
1280 unsigned pos, __isl_take isl_id *id);
1281 isl_bool isl_basic_map_has_dim_id(
1282 __isl_keep isl_basic_map *bmap,
1283 enum isl_dim_type type, unsigned pos);
1284 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1285 enum isl_dim_type type, unsigned pos);
1286 __isl_give isl_id *isl_map_get_dim_id(
1287 __isl_keep isl_map *map, enum isl_dim_type type,
1289 __isl_give isl_id *isl_union_map_get_dim_id(
1290 __isl_keep isl_union_map *umap,
1291 enum isl_dim_type type, unsigned pos);
1292 const char *isl_basic_map_get_dim_name(
1293 __isl_keep isl_basic_map *bmap,
1294 enum isl_dim_type type, unsigned pos);
1295 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1296 enum isl_dim_type type, unsigned pos);
1297 const char *isl_map_get_dim_name(
1298 __isl_keep isl_map *map,
1299 enum isl_dim_type type, unsigned pos);
1301 #include <isl/val.h>
1302 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1303 __isl_take isl_multi_val *mv,
1304 enum isl_dim_type type, unsigned pos,
1305 __isl_take isl_id *id);
1306 __isl_give isl_id *isl_multi_val_get_dim_id(
1307 __isl_keep isl_multi_val *mv,
1308 enum isl_dim_type type, unsigned pos);
1309 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1310 __isl_take isl_multi_val *mv,
1311 enum isl_dim_type type, unsigned pos, const char *s);
1313 #include <isl/aff.h>
1314 __isl_give isl_aff *isl_aff_set_dim_id(
1315 __isl_take isl_aff *aff, enum isl_dim_type type,
1316 unsigned pos, __isl_take isl_id *id);
1317 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1318 __isl_take isl_multi_aff *maff,
1319 enum isl_dim_type type, unsigned pos,
1320 __isl_take isl_id *id);
1321 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1322 __isl_take isl_pw_aff *pma,
1323 enum isl_dim_type type, unsigned pos,
1324 __isl_take isl_id *id);
1325 __isl_give isl_multi_pw_aff *
1326 isl_multi_pw_aff_set_dim_id(
1327 __isl_take isl_multi_pw_aff *mpa,
1328 enum isl_dim_type type, unsigned pos,
1329 __isl_take isl_id *id);
1330 __isl_give isl_multi_union_pw_aff *
1331 isl_multi_union_pw_aff_set_dim_id(
1332 __isl_take isl_multi_union_pw_aff *mupa,
1333 enum isl_dim_type type, unsigned pos,
1334 __isl_take isl_id *id);
1335 __isl_give isl_id *isl_multi_aff_get_dim_id(
1336 __isl_keep isl_multi_aff *ma,
1337 enum isl_dim_type type, unsigned pos);
1338 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1339 enum isl_dim_type type, unsigned pos);
1340 __isl_give isl_id *isl_pw_aff_get_dim_id(
1341 __isl_keep isl_pw_aff *pa,
1342 enum isl_dim_type type, unsigned pos);
1343 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1344 __isl_keep isl_pw_multi_aff *pma,
1345 enum isl_dim_type type, unsigned pos);
1346 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1347 __isl_keep isl_multi_pw_aff *mpa,
1348 enum isl_dim_type type, unsigned pos);
1349 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1350 __isl_keep isl_multi_union_pw_aff *mupa,
1351 enum isl_dim_type type, unsigned pos);
1352 __isl_give isl_aff *isl_aff_set_dim_name(
1353 __isl_take isl_aff *aff, enum isl_dim_type type,
1354 unsigned pos, const char *s);
1355 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1356 __isl_take isl_multi_aff *maff,
1357 enum isl_dim_type type, unsigned pos, const char *s);
1358 __isl_give isl_multi_pw_aff *
1359 isl_multi_pw_aff_set_dim_name(
1360 __isl_take isl_multi_pw_aff *mpa,
1361 enum isl_dim_type type, unsigned pos, const char *s);
1362 __isl_give isl_union_pw_aff *
1363 isl_union_pw_aff_set_dim_name(
1364 __isl_take isl_union_pw_aff *upa,
1365 enum isl_dim_type type, unsigned pos,
1367 __isl_give isl_union_pw_multi_aff *
1368 isl_union_pw_multi_aff_set_dim_name(
1369 __isl_take isl_union_pw_multi_aff *upma,
1370 enum isl_dim_type type, unsigned pos,
1372 __isl_give isl_multi_union_pw_aff *
1373 isl_multi_union_pw_aff_set_dim_name(
1374 __isl_take isl_multi_union_pw_aff *mupa,
1375 enum isl_dim_type type, unsigned pos,
1376 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1377 enum isl_dim_type type, unsigned pos);
1378 const char *isl_pw_aff_get_dim_name(
1379 __isl_keep isl_pw_aff *pa,
1380 enum isl_dim_type type, unsigned pos);
1381 const char *isl_pw_multi_aff_get_dim_name(
1382 __isl_keep isl_pw_multi_aff *pma,
1383 enum isl_dim_type type, unsigned pos);
1385 #include <isl/polynomial.h>
1386 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1387 __isl_take isl_qpolynomial *qp,
1388 enum isl_dim_type type, unsigned pos,
1390 __isl_give isl_pw_qpolynomial *
1391 isl_pw_qpolynomial_set_dim_name(
1392 __isl_take isl_pw_qpolynomial *pwqp,
1393 enum isl_dim_type type, unsigned pos,
1395 __isl_give isl_pw_qpolynomial_fold *
1396 isl_pw_qpolynomial_fold_set_dim_name(
1397 __isl_take isl_pw_qpolynomial_fold *pwf,
1398 enum isl_dim_type type, unsigned pos,
1400 __isl_give isl_union_pw_qpolynomial *
1401 isl_union_pw_qpolynomial_set_dim_name(
1402 __isl_take isl_union_pw_qpolynomial *upwqp,
1403 enum isl_dim_type type, unsigned pos,
1405 __isl_give isl_union_pw_qpolynomial_fold *
1406 isl_union_pw_qpolynomial_fold_set_dim_name(
1407 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1408 enum isl_dim_type type, unsigned pos,
1411 Note that C<isl_space_get_name> returns a pointer to some internal
1412 data structure, so the result can only be used while the
1413 corresponding C<isl_space> is alive.
1414 Also note that every function that operates on two sets or relations
1415 requires that both arguments have the same parameters. This also
1416 means that if one of the arguments has named parameters, then the
1417 other needs to have named parameters too and the names need to match.
1418 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1419 arguments may have different parameters (as long as they are named),
1420 in which case the result will have as parameters the union of the parameters of
1423 Given the identifier or name of a dimension (typically a parameter),
1424 its position can be obtained from the following functions.
1426 #include <isl/space.h>
1427 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1428 enum isl_dim_type type, __isl_keep isl_id *id);
1429 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1430 enum isl_dim_type type, const char *name);
1432 #include <isl/local_space.h>
1433 int isl_local_space_find_dim_by_name(
1434 __isl_keep isl_local_space *ls,
1435 enum isl_dim_type type, const char *name);
1437 #include <isl/val.h>
1438 int isl_multi_val_find_dim_by_id(
1439 __isl_keep isl_multi_val *mv,
1440 enum isl_dim_type type, __isl_keep isl_id *id);
1441 int isl_multi_val_find_dim_by_name(
1442 __isl_keep isl_multi_val *mv,
1443 enum isl_dim_type type, const char *name);
1445 #include <isl/set.h>
1446 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1447 enum isl_dim_type type, __isl_keep isl_id *id);
1448 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1449 enum isl_dim_type type, const char *name);
1451 #include <isl/map.h>
1452 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1453 enum isl_dim_type type, __isl_keep isl_id *id);
1454 int isl_basic_map_find_dim_by_name(
1455 __isl_keep isl_basic_map *bmap,
1456 enum isl_dim_type type, const char *name);
1457 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1458 enum isl_dim_type type, const char *name);
1459 int isl_union_map_find_dim_by_name(
1460 __isl_keep isl_union_map *umap,
1461 enum isl_dim_type type, const char *name);
1463 #include <isl/aff.h>
1464 int isl_multi_aff_find_dim_by_id(
1465 __isl_keep isl_multi_aff *ma,
1466 enum isl_dim_type type, __isl_keep isl_id *id);
1467 int isl_multi_pw_aff_find_dim_by_id(
1468 __isl_keep isl_multi_pw_aff *mpa,
1469 enum isl_dim_type type, __isl_keep isl_id *id);
1470 int isl_multi_union_pw_aff_find_dim_by_id(
1471 __isl_keep isl_union_multi_pw_aff *mupa,
1472 enum isl_dim_type type, __isl_keep isl_id *id);
1473 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1474 enum isl_dim_type type, const char *name);
1475 int isl_multi_aff_find_dim_by_name(
1476 __isl_keep isl_multi_aff *ma,
1477 enum isl_dim_type type, const char *name);
1478 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1479 enum isl_dim_type type, const char *name);
1480 int isl_multi_pw_aff_find_dim_by_name(
1481 __isl_keep isl_multi_pw_aff *mpa,
1482 enum isl_dim_type type, const char *name);
1483 int isl_pw_multi_aff_find_dim_by_name(
1484 __isl_keep isl_pw_multi_aff *pma,
1485 enum isl_dim_type type, const char *name);
1486 int isl_union_pw_aff_find_dim_by_name(
1487 __isl_keep isl_union_pw_aff *upa,
1488 enum isl_dim_type type, const char *name);
1489 int isl_union_pw_multi_aff_find_dim_by_name(
1490 __isl_keep isl_union_pw_multi_aff *upma,
1491 enum isl_dim_type type, const char *name);
1492 int isl_multi_union_pw_aff_find_dim_by_name(
1493 __isl_keep isl_multi_union_pw_aff *mupa,
1494 enum isl_dim_type type, const char *name);
1496 #include <isl/polynomial.h>
1497 int isl_pw_qpolynomial_find_dim_by_name(
1498 __isl_keep isl_pw_qpolynomial *pwqp,
1499 enum isl_dim_type type, const char *name);
1500 int isl_pw_qpolynomial_fold_find_dim_by_name(
1501 __isl_keep isl_pw_qpolynomial_fold *pwf,
1502 enum isl_dim_type type, const char *name);
1503 int isl_union_pw_qpolynomial_find_dim_by_name(
1504 __isl_keep isl_union_pw_qpolynomial *upwqp,
1505 enum isl_dim_type type, const char *name);
1506 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1507 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1508 enum isl_dim_type type, const char *name);
1510 The identifiers or names of entire spaces may be set or read off
1511 using the following functions.
1513 #include <isl/space.h>
1514 __isl_give isl_space *isl_space_set_tuple_id(
1515 __isl_take isl_space *space,
1516 enum isl_dim_type type, __isl_take isl_id *id);
1517 __isl_give isl_space *isl_space_reset_tuple_id(
1518 __isl_take isl_space *space, enum isl_dim_type type);
1519 isl_bool isl_space_has_tuple_id(
1520 __isl_keep isl_space *space,
1521 enum isl_dim_type type);
1522 __isl_give isl_id *isl_space_get_tuple_id(
1523 __isl_keep isl_space *space, enum isl_dim_type type);
1524 __isl_give isl_space *isl_space_set_tuple_name(
1525 __isl_take isl_space *space,
1526 enum isl_dim_type type, const char *s);
1527 isl_bool isl_space_has_tuple_name(
1528 __isl_keep isl_space *space,
1529 enum isl_dim_type type);
1530 __isl_keep const char *isl_space_get_tuple_name(
1531 __isl_keep isl_space *space,
1532 enum isl_dim_type type);
1534 #include <isl/local_space.h>
1535 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1536 __isl_take isl_local_space *ls,
1537 enum isl_dim_type type, __isl_take isl_id *id);
1539 #include <isl/set.h>
1540 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1541 __isl_take isl_basic_set *bset,
1542 __isl_take isl_id *id);
1543 __isl_give isl_set *isl_set_set_tuple_id(
1544 __isl_take isl_set *set, __isl_take isl_id *id);
1545 __isl_give isl_set *isl_set_reset_tuple_id(
1546 __isl_take isl_set *set);
1547 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1548 __isl_give isl_id *isl_set_get_tuple_id(
1549 __isl_keep isl_set *set);
1550 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1551 __isl_take isl_basic_set *set, const char *s);
1552 __isl_give isl_set *isl_set_set_tuple_name(
1553 __isl_take isl_set *set, const char *s);
1554 const char *isl_basic_set_get_tuple_name(
1555 __isl_keep isl_basic_set *bset);
1556 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1557 const char *isl_set_get_tuple_name(
1558 __isl_keep isl_set *set);
1560 #include <isl/map.h>
1561 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1562 __isl_take isl_basic_map *bmap,
1563 enum isl_dim_type type, __isl_take isl_id *id);
1564 __isl_give isl_map *isl_map_set_tuple_id(
1565 __isl_take isl_map *map, enum isl_dim_type type,
1566 __isl_take isl_id *id);
1567 __isl_give isl_map *isl_map_reset_tuple_id(
1568 __isl_take isl_map *map, enum isl_dim_type type);
1569 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1570 enum isl_dim_type type);
1571 __isl_give isl_id *isl_map_get_tuple_id(
1572 __isl_keep isl_map *map, enum isl_dim_type type);
1573 __isl_give isl_map *isl_map_set_tuple_name(
1574 __isl_take isl_map *map,
1575 enum isl_dim_type type, const char *s);
1576 const char *isl_basic_map_get_tuple_name(
1577 __isl_keep isl_basic_map *bmap,
1578 enum isl_dim_type type);
1579 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1580 __isl_take isl_basic_map *bmap,
1581 enum isl_dim_type type, const char *s);
1582 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1583 enum isl_dim_type type);
1584 const char *isl_map_get_tuple_name(
1585 __isl_keep isl_map *map,
1586 enum isl_dim_type type);
1588 #include <isl/val.h>
1589 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1590 __isl_take isl_multi_val *mv,
1591 enum isl_dim_type type, __isl_take isl_id *id);
1592 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1593 __isl_take isl_multi_val *mv,
1594 enum isl_dim_type type);
1595 isl_bool isl_multi_val_has_tuple_id(
1596 __isl_keep isl_multi_val *mv,
1597 enum isl_dim_type type);
1598 __isl_give isl_id *isl_multi_val_get_tuple_id(
1599 __isl_keep isl_multi_val *mv,
1600 enum isl_dim_type type);
1601 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1602 __isl_take isl_multi_val *mv,
1603 enum isl_dim_type type, const char *s);
1604 const char *isl_multi_val_get_tuple_name(
1605 __isl_keep isl_multi_val *mv,
1606 enum isl_dim_type type);
1608 #include <isl/aff.h>
1609 __isl_give isl_aff *isl_aff_set_tuple_id(
1610 __isl_take isl_aff *aff,
1611 enum isl_dim_type type, __isl_take isl_id *id);
1612 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1613 __isl_take isl_multi_aff *maff,
1614 enum isl_dim_type type, __isl_take isl_id *id);
1615 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1616 __isl_take isl_pw_aff *pwaff,
1617 enum isl_dim_type type, __isl_take isl_id *id);
1618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1619 __isl_take isl_pw_multi_aff *pma,
1620 enum isl_dim_type type, __isl_take isl_id *id);
1621 __isl_give isl_multi_union_pw_aff *
1622 isl_multi_union_pw_aff_set_tuple_id(
1623 __isl_take isl_multi_union_pw_aff *mupa,
1624 enum isl_dim_type type, __isl_take isl_id *id);
1625 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1626 __isl_take isl_multi_aff *ma,
1627 enum isl_dim_type type);
1628 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1629 __isl_take isl_pw_aff *pa,
1630 enum isl_dim_type type);
1631 __isl_give isl_multi_pw_aff *
1632 isl_multi_pw_aff_reset_tuple_id(
1633 __isl_take isl_multi_pw_aff *mpa,
1634 enum isl_dim_type type);
1635 __isl_give isl_pw_multi_aff *
1636 isl_pw_multi_aff_reset_tuple_id(
1637 __isl_take isl_pw_multi_aff *pma,
1638 enum isl_dim_type type);
1639 __isl_give isl_multi_union_pw_aff *
1640 isl_multi_union_pw_aff_reset_tuple_id(
1641 __isl_take isl_multi_union_pw_aff *mupa,
1642 enum isl_dim_type type);
1643 isl_bool isl_multi_aff_has_tuple_id(
1644 __isl_keep isl_multi_aff *ma,
1645 enum isl_dim_type type);
1646 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1647 __isl_keep isl_multi_aff *ma,
1648 enum isl_dim_type type);
1649 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1650 enum isl_dim_type type);
1651 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1652 __isl_keep isl_pw_aff *pa,
1653 enum isl_dim_type type);
1654 isl_bool isl_pw_multi_aff_has_tuple_id(
1655 __isl_keep isl_pw_multi_aff *pma,
1656 enum isl_dim_type type);
1657 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1658 __isl_keep isl_pw_multi_aff *pma,
1659 enum isl_dim_type type);
1660 isl_bool isl_multi_pw_aff_has_tuple_id(
1661 __isl_keep isl_multi_pw_aff *mpa,
1662 enum isl_dim_type type);
1663 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1664 __isl_keep isl_multi_pw_aff *mpa,
1665 enum isl_dim_type type);
1666 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1667 __isl_keep isl_multi_union_pw_aff *mupa,
1668 enum isl_dim_type type);
1669 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1670 __isl_keep isl_multi_union_pw_aff *mupa,
1671 enum isl_dim_type type);
1672 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1673 __isl_take isl_multi_aff *maff,
1674 enum isl_dim_type type, const char *s);
1675 __isl_give isl_multi_pw_aff *
1676 isl_multi_pw_aff_set_tuple_name(
1677 __isl_take isl_multi_pw_aff *mpa,
1678 enum isl_dim_type type, const char *s);
1679 __isl_give isl_multi_union_pw_aff *
1680 isl_multi_union_pw_aff_set_tuple_name(
1681 __isl_take isl_multi_union_pw_aff *mupa,
1682 enum isl_dim_type type, const char *s);
1683 const char *isl_multi_aff_get_tuple_name(
1684 __isl_keep isl_multi_aff *multi,
1685 enum isl_dim_type type);
1686 isl_bool isl_pw_multi_aff_has_tuple_name(
1687 __isl_keep isl_pw_multi_aff *pma,
1688 enum isl_dim_type type);
1689 const char *isl_pw_multi_aff_get_tuple_name(
1690 __isl_keep isl_pw_multi_aff *pma,
1691 enum isl_dim_type type);
1692 const char *isl_multi_union_pw_aff_get_tuple_name(
1693 __isl_keep isl_multi_union_pw_aff *mupa,
1694 enum isl_dim_type type);
1696 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1697 or C<isl_dim_set>. As with C<isl_space_get_name>,
1698 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1700 Binary operations require the corresponding spaces of their arguments
1701 to have the same name.
1703 To keep the names of all parameters and tuples, but reset the user pointers
1704 of all the corresponding identifiers, use the following function.
1706 #include <isl/space.h>
1707 __isl_give isl_space *isl_space_reset_user(
1708 __isl_take isl_space *space);
1710 #include <isl/set.h>
1711 __isl_give isl_set *isl_set_reset_user(
1712 __isl_take isl_set *set);
1714 #include <isl/map.h>
1715 __isl_give isl_map *isl_map_reset_user(
1716 __isl_take isl_map *map);
1718 #include <isl/union_set.h>
1719 __isl_give isl_union_set *isl_union_set_reset_user(
1720 __isl_take isl_union_set *uset);
1722 #include <isl/union_map.h>
1723 __isl_give isl_union_map *isl_union_map_reset_user(
1724 __isl_take isl_union_map *umap);
1726 #include <isl/val.h>
1727 __isl_give isl_multi_val *isl_multi_val_reset_user(
1728 __isl_take isl_multi_val *mv);
1730 #include <isl/aff.h>
1731 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1732 __isl_take isl_multi_aff *ma);
1733 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1734 __isl_take isl_pw_aff *pa);
1735 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1736 __isl_take isl_multi_pw_aff *mpa);
1737 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1738 __isl_take isl_pw_multi_aff *pma);
1739 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1740 __isl_take isl_union_pw_aff *upa);
1741 __isl_give isl_multi_union_pw_aff *
1742 isl_multi_union_pw_aff_reset_user(
1743 __isl_take isl_multi_union_pw_aff *mupa);
1744 __isl_give isl_union_pw_multi_aff *
1745 isl_union_pw_multi_aff_reset_user(
1746 __isl_take isl_union_pw_multi_aff *upma);
1748 #include <isl/polynomial.h>
1749 __isl_give isl_pw_qpolynomial *
1750 isl_pw_qpolynomial_reset_user(
1751 __isl_take isl_pw_qpolynomial *pwqp);
1752 __isl_give isl_union_pw_qpolynomial *
1753 isl_union_pw_qpolynomial_reset_user(
1754 __isl_take isl_union_pw_qpolynomial *upwqp);
1755 __isl_give isl_pw_qpolynomial_fold *
1756 isl_pw_qpolynomial_fold_reset_user(
1757 __isl_take isl_pw_qpolynomial_fold *pwf);
1758 __isl_give isl_union_pw_qpolynomial_fold *
1759 isl_union_pw_qpolynomial_fold_reset_user(
1760 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1762 Spaces can be nested. In particular, the domain of a set or
1763 the domain or range of a relation can be a nested relation.
1764 This process is also called I<wrapping>.
1765 The functions for detecting, constructing and deconstructing
1766 such nested spaces can be found in the wrapping properties
1767 of L</"Unary Properties">, the wrapping operations
1768 of L</"Unary Operations"> and the Cartesian product operations
1769 of L</"Basic Operations">.
1771 Spaces can be created from other spaces
1772 using the functions described in L</"Unary Operations">
1773 and L</"Binary Operations">.
1777 A local space is essentially a space with
1778 zero or more existentially quantified variables.
1779 The local space of various objects can be obtained
1780 using the following functions.
1782 #include <isl/constraint.h>
1783 __isl_give isl_local_space *isl_constraint_get_local_space(
1784 __isl_keep isl_constraint *constraint);
1786 #include <isl/set.h>
1787 __isl_give isl_local_space *isl_basic_set_get_local_space(
1788 __isl_keep isl_basic_set *bset);
1790 #include <isl/map.h>
1791 __isl_give isl_local_space *isl_basic_map_get_local_space(
1792 __isl_keep isl_basic_map *bmap);
1794 #include <isl/aff.h>
1795 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1796 __isl_keep isl_aff *aff);
1797 __isl_give isl_local_space *isl_aff_get_local_space(
1798 __isl_keep isl_aff *aff);
1800 A new local space can be created from a space using
1802 #include <isl/local_space.h>
1803 __isl_give isl_local_space *isl_local_space_from_space(
1804 __isl_take isl_space *space);
1806 They can be inspected, modified, copied and freed using the following functions.
1808 #include <isl/local_space.h>
1809 isl_bool isl_local_space_is_params(
1810 __isl_keep isl_local_space *ls);
1811 isl_bool isl_local_space_is_set(
1812 __isl_keep isl_local_space *ls);
1813 __isl_give isl_space *isl_local_space_get_space(
1814 __isl_keep isl_local_space *ls);
1815 __isl_give isl_aff *isl_local_space_get_div(
1816 __isl_keep isl_local_space *ls, int pos);
1817 __isl_give isl_local_space *isl_local_space_copy(
1818 __isl_keep isl_local_space *ls);
1819 __isl_null isl_local_space *isl_local_space_free(
1820 __isl_take isl_local_space *ls);
1822 Note that C<isl_local_space_get_div> can only be used on local spaces
1825 Two local spaces can be compared using
1827 isl_bool isl_local_space_is_equal(
1828 __isl_keep isl_local_space *ls1,
1829 __isl_keep isl_local_space *ls2);
1831 Local spaces can be created from other local spaces
1832 using the functions described in L</"Unary Operations">
1833 and L</"Binary Operations">.
1835 =head2 Creating New Sets and Relations
1837 C<isl> has functions for creating some standard sets and relations.
1841 =item * Empty sets and relations
1843 __isl_give isl_basic_set *isl_basic_set_empty(
1844 __isl_take isl_space *space);
1845 __isl_give isl_basic_map *isl_basic_map_empty(
1846 __isl_take isl_space *space);
1847 __isl_give isl_set *isl_set_empty(
1848 __isl_take isl_space *space);
1849 __isl_give isl_map *isl_map_empty(
1850 __isl_take isl_space *space);
1851 __isl_give isl_union_set *isl_union_set_empty(
1852 __isl_take isl_space *space);
1853 __isl_give isl_union_map *isl_union_map_empty(
1854 __isl_take isl_space *space);
1856 For C<isl_union_set>s and C<isl_union_map>s, the space
1857 is only used to specify the parameters.
1859 =item * Universe sets and relations
1861 __isl_give isl_basic_set *isl_basic_set_universe(
1862 __isl_take isl_space *space);
1863 __isl_give isl_basic_map *isl_basic_map_universe(
1864 __isl_take isl_space *space);
1865 __isl_give isl_set *isl_set_universe(
1866 __isl_take isl_space *space);
1867 __isl_give isl_map *isl_map_universe(
1868 __isl_take isl_space *space);
1869 __isl_give isl_union_set *isl_union_set_universe(
1870 __isl_take isl_union_set *uset);
1871 __isl_give isl_union_map *isl_union_map_universe(
1872 __isl_take isl_union_map *umap);
1874 The sets and relations constructed by the functions above
1875 contain all integer values, while those constructed by the
1876 functions below only contain non-negative values.
1878 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1879 __isl_take isl_space *space);
1880 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1881 __isl_take isl_space *space);
1882 __isl_give isl_set *isl_set_nat_universe(
1883 __isl_take isl_space *space);
1884 __isl_give isl_map *isl_map_nat_universe(
1885 __isl_take isl_space *space);
1887 =item * Identity relations
1889 __isl_give isl_basic_map *isl_basic_map_identity(
1890 __isl_take isl_space *space);
1891 __isl_give isl_map *isl_map_identity(
1892 __isl_take isl_space *space);
1894 The number of input and output dimensions in C<space> needs
1897 =item * Lexicographic order
1899 __isl_give isl_map *isl_map_lex_lt(
1900 __isl_take isl_space *set_space);
1901 __isl_give isl_map *isl_map_lex_le(
1902 __isl_take isl_space *set_space);
1903 __isl_give isl_map *isl_map_lex_gt(
1904 __isl_take isl_space *set_space);
1905 __isl_give isl_map *isl_map_lex_ge(
1906 __isl_take isl_space *set_space);
1907 __isl_give isl_map *isl_map_lex_lt_first(
1908 __isl_take isl_space *space, unsigned n);
1909 __isl_give isl_map *isl_map_lex_le_first(
1910 __isl_take isl_space *space, unsigned n);
1911 __isl_give isl_map *isl_map_lex_gt_first(
1912 __isl_take isl_space *space, unsigned n);
1913 __isl_give isl_map *isl_map_lex_ge_first(
1914 __isl_take isl_space *space, unsigned n);
1916 The first four functions take a space for a B<set>
1917 and return relations that express that the elements in the domain
1918 are lexicographically less
1919 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1920 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1921 than the elements in the range.
1922 The last four functions take a space for a map
1923 and return relations that express that the first C<n> dimensions
1924 in the domain are lexicographically less
1925 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1926 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1927 than the first C<n> dimensions in the range.
1931 A basic set or relation can be converted to a set or relation
1932 using the following functions.
1934 __isl_give isl_set *isl_set_from_basic_set(
1935 __isl_take isl_basic_set *bset);
1936 __isl_give isl_map *isl_map_from_basic_map(
1937 __isl_take isl_basic_map *bmap);
1939 Sets and relations can be converted to union sets and relations
1940 using the following functions.
1942 __isl_give isl_union_set *isl_union_set_from_basic_set(
1943 __isl_take isl_basic_set *bset);
1944 __isl_give isl_union_map *isl_union_map_from_basic_map(
1945 __isl_take isl_basic_map *bmap);
1946 __isl_give isl_union_set *isl_union_set_from_set(
1947 __isl_take isl_set *set);
1948 __isl_give isl_union_map *isl_union_map_from_map(
1949 __isl_take isl_map *map);
1951 The inverse conversions below can only be used if the input
1952 union set or relation is known to contain elements in exactly one
1955 __isl_give isl_set *isl_set_from_union_set(
1956 __isl_take isl_union_set *uset);
1957 __isl_give isl_map *isl_map_from_union_map(
1958 __isl_take isl_union_map *umap);
1960 Sets and relations can be copied and freed again using the following
1963 __isl_give isl_basic_set *isl_basic_set_copy(
1964 __isl_keep isl_basic_set *bset);
1965 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1966 __isl_give isl_union_set *isl_union_set_copy(
1967 __isl_keep isl_union_set *uset);
1968 __isl_give isl_basic_map *isl_basic_map_copy(
1969 __isl_keep isl_basic_map *bmap);
1970 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1971 __isl_give isl_union_map *isl_union_map_copy(
1972 __isl_keep isl_union_map *umap);
1973 __isl_null isl_basic_set *isl_basic_set_free(
1974 __isl_take isl_basic_set *bset);
1975 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1976 __isl_null isl_union_set *isl_union_set_free(
1977 __isl_take isl_union_set *uset);
1978 __isl_null isl_basic_map *isl_basic_map_free(
1979 __isl_take isl_basic_map *bmap);
1980 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1981 __isl_null isl_union_map *isl_union_map_free(
1982 __isl_take isl_union_map *umap);
1984 Other sets and relations can be constructed by starting
1985 from a universe set or relation, adding equality and/or
1986 inequality constraints and then projecting out the
1987 existentially quantified variables, if any.
1988 Constraints can be constructed, manipulated and
1989 added to (or removed from) (basic) sets and relations
1990 using the following functions.
1992 #include <isl/constraint.h>
1993 __isl_give isl_constraint *isl_constraint_alloc_equality(
1994 __isl_take isl_local_space *ls);
1995 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1996 __isl_take isl_local_space *ls);
1997 __isl_give isl_constraint *isl_constraint_set_constant_si(
1998 __isl_take isl_constraint *constraint, int v);
1999 __isl_give isl_constraint *isl_constraint_set_constant_val(
2000 __isl_take isl_constraint *constraint,
2001 __isl_take isl_val *v);
2002 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2003 __isl_take isl_constraint *constraint,
2004 enum isl_dim_type type, int pos, int v);
2005 __isl_give isl_constraint *
2006 isl_constraint_set_coefficient_val(
2007 __isl_take isl_constraint *constraint,
2008 enum isl_dim_type type, int pos,
2009 __isl_take isl_val *v);
2010 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2011 __isl_take isl_basic_map *bmap,
2012 __isl_take isl_constraint *constraint);
2013 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2014 __isl_take isl_basic_set *bset,
2015 __isl_take isl_constraint *constraint);
2016 __isl_give isl_map *isl_map_add_constraint(
2017 __isl_take isl_map *map,
2018 __isl_take isl_constraint *constraint);
2019 __isl_give isl_set *isl_set_add_constraint(
2020 __isl_take isl_set *set,
2021 __isl_take isl_constraint *constraint);
2023 For example, to create a set containing the even integers
2024 between 10 and 42, you would use the following code.
2027 isl_local_space *ls;
2029 isl_basic_set *bset;
2031 space = isl_space_set_alloc(ctx, 0, 2);
2032 bset = isl_basic_set_universe(isl_space_copy(space));
2033 ls = isl_local_space_from_space(space);
2035 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2036 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2037 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2038 bset = isl_basic_set_add_constraint(bset, c);
2040 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2041 c = isl_constraint_set_constant_si(c, -10);
2042 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2043 bset = isl_basic_set_add_constraint(bset, c);
2045 c = isl_constraint_alloc_inequality(ls);
2046 c = isl_constraint_set_constant_si(c, 42);
2047 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2048 bset = isl_basic_set_add_constraint(bset, c);
2050 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2054 isl_basic_set *bset;
2055 bset = isl_basic_set_read_from_str(ctx,
2056 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2058 A basic set or relation can also be constructed from two matrices
2059 describing the equalities and the inequalities.
2061 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2062 __isl_take isl_space *space,
2063 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2064 enum isl_dim_type c1,
2065 enum isl_dim_type c2, enum isl_dim_type c3,
2066 enum isl_dim_type c4);
2067 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2068 __isl_take isl_space *space,
2069 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2070 enum isl_dim_type c1,
2071 enum isl_dim_type c2, enum isl_dim_type c3,
2072 enum isl_dim_type c4, enum isl_dim_type c5);
2074 The C<isl_dim_type> arguments indicate the order in which
2075 different kinds of variables appear in the input matrices
2076 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2077 C<isl_dim_set> and C<isl_dim_div> for sets and
2078 of C<isl_dim_cst>, C<isl_dim_param>,
2079 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2081 A (basic or union) set or relation can also be constructed from a
2082 (union) (piecewise) (multiple) affine expression
2083 or a list of affine expressions
2084 (See L</"Functions">), provided these affine expressions do not
2087 __isl_give isl_basic_map *isl_basic_map_from_aff(
2088 __isl_take isl_aff *aff);
2089 __isl_give isl_map *isl_map_from_aff(
2090 __isl_take isl_aff *aff);
2091 __isl_give isl_set *isl_set_from_pw_aff(
2092 __isl_take isl_pw_aff *pwaff);
2093 __isl_give isl_map *isl_map_from_pw_aff(
2094 __isl_take isl_pw_aff *pwaff);
2095 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2096 __isl_take isl_space *domain_space,
2097 __isl_take isl_aff_list *list);
2098 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2099 __isl_take isl_multi_aff *maff)
2100 __isl_give isl_map *isl_map_from_multi_aff(
2101 __isl_take isl_multi_aff *maff)
2102 __isl_give isl_set *isl_set_from_pw_multi_aff(
2103 __isl_take isl_pw_multi_aff *pma);
2104 __isl_give isl_map *isl_map_from_pw_multi_aff(
2105 __isl_take isl_pw_multi_aff *pma);
2106 __isl_give isl_set *isl_set_from_multi_pw_aff(
2107 __isl_take isl_multi_pw_aff *mpa);
2108 __isl_give isl_map *isl_map_from_multi_pw_aff(
2109 __isl_take isl_multi_pw_aff *mpa);
2110 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2111 __isl_take isl_union_pw_aff *upa);
2112 __isl_give isl_union_map *
2113 isl_union_map_from_union_pw_multi_aff(
2114 __isl_take isl_union_pw_multi_aff *upma);
2115 __isl_give isl_union_map *
2116 isl_union_map_from_multi_union_pw_aff(
2117 __isl_take isl_multi_union_pw_aff *mupa);
2119 The C<domain_space> argument describes the domain of the resulting
2120 basic relation. It is required because the C<list> may consist
2121 of zero affine expressions.
2122 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2123 is not allowed to be zero-dimensional. The domain of the result
2124 is the shared domain of the union piecewise affine elements.
2126 =head2 Inspecting Sets and Relations
2128 Usually, the user should not have to care about the actual constraints
2129 of the sets and maps, but should instead apply the abstract operations
2130 explained in the following sections.
2131 Occasionally, however, it may be required to inspect the individual
2132 coefficients of the constraints. This section explains how to do so.
2133 In these cases, it may also be useful to have C<isl> compute
2134 an explicit representation of the existentially quantified variables.
2136 __isl_give isl_set *isl_set_compute_divs(
2137 __isl_take isl_set *set);
2138 __isl_give isl_map *isl_map_compute_divs(
2139 __isl_take isl_map *map);
2140 __isl_give isl_union_set *isl_union_set_compute_divs(
2141 __isl_take isl_union_set *uset);
2142 __isl_give isl_union_map *isl_union_map_compute_divs(
2143 __isl_take isl_union_map *umap);
2145 This explicit representation defines the existentially quantified
2146 variables as integer divisions of the other variables, possibly
2147 including earlier existentially quantified variables.
2148 An explicitly represented existentially quantified variable therefore
2149 has a unique value when the values of the other variables are known.
2151 Alternatively, the existentially quantified variables can be removed
2152 using the following functions, which compute an overapproximation.
2154 #include <isl/set.h>
2155 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2156 __isl_take isl_basic_set *bset);
2157 __isl_give isl_set *isl_set_remove_divs(
2158 __isl_take isl_set *set);
2160 #include <isl/map.h>
2161 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2162 __isl_take isl_basic_map *bmap);
2163 __isl_give isl_map *isl_map_remove_divs(
2164 __isl_take isl_map *map);
2166 #include <isl/union_set.h>
2167 __isl_give isl_union_set *isl_union_set_remove_divs(
2168 __isl_take isl_union_set *bset);
2170 #include <isl/union_map.h>
2171 __isl_give isl_union_map *isl_union_map_remove_divs(
2172 __isl_take isl_union_map *bmap);
2174 It is also possible to only remove those divs that are defined
2175 in terms of a given range of dimensions or only those for which
2176 no explicit representation is known.
2178 __isl_give isl_basic_set *
2179 isl_basic_set_remove_divs_involving_dims(
2180 __isl_take isl_basic_set *bset,
2181 enum isl_dim_type type,
2182 unsigned first, unsigned n);
2183 __isl_give isl_basic_map *
2184 isl_basic_map_remove_divs_involving_dims(
2185 __isl_take isl_basic_map *bmap,
2186 enum isl_dim_type type,
2187 unsigned first, unsigned n);
2188 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2189 __isl_take isl_set *set, enum isl_dim_type type,
2190 unsigned first, unsigned n);
2191 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2192 __isl_take isl_map *map, enum isl_dim_type type,
2193 unsigned first, unsigned n);
2195 __isl_give isl_basic_set *
2196 isl_basic_set_remove_unknown_divs(
2197 __isl_take isl_basic_set *bset);
2198 __isl_give isl_set *isl_set_remove_unknown_divs(
2199 __isl_take isl_set *set);
2200 __isl_give isl_map *isl_map_remove_unknown_divs(
2201 __isl_take isl_map *map);
2203 To iterate over all the sets or maps in a union set or map, use
2205 #include <isl/union_set.h>
2206 isl_stat isl_union_set_foreach_set(
2207 __isl_keep isl_union_set *uset,
2208 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2211 #include <isl/union_map.h>
2212 isl_stat isl_union_map_foreach_map(
2213 __isl_keep isl_union_map *umap,
2214 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2216 isl_bool isl_union_map_every_map(
2217 __isl_keep isl_union_map *umap,
2218 isl_bool (*test)(__isl_keep isl_map *map,
2222 These functions call the callback function once for each
2223 (pair of) space(s) for which there are elements in the input.
2224 The argument to the callback contains all elements in the input
2225 with that (pair of) space(s).
2226 The C<isl_union_map_every_map> variant check whether each
2227 call to the callback returns true and stops checking as soon as one
2228 of these calls returns false.
2230 The number of sets or maps in a union set or map can be obtained
2233 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2234 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2236 To extract the set or map in a given space from a union, use
2238 __isl_give isl_set *isl_union_set_extract_set(
2239 __isl_keep isl_union_set *uset,
2240 __isl_take isl_space *space);
2241 __isl_give isl_map *isl_union_map_extract_map(
2242 __isl_keep isl_union_map *umap,
2243 __isl_take isl_space *space);
2245 To iterate over all the basic sets or maps in a set or map, use
2247 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2248 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2251 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2252 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2256 The callback function C<fn> should return C<isl_stat_ok> if successful and
2257 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2258 occurs, the above functions will return C<isl_stat_error>.
2260 It should be noted that C<isl> does not guarantee that
2261 the basic sets or maps passed to C<fn> are disjoint.
2262 If this is required, then the user should call one of
2263 the following functions first.
2265 __isl_give isl_set *isl_set_make_disjoint(
2266 __isl_take isl_set *set);
2267 __isl_give isl_map *isl_map_make_disjoint(
2268 __isl_take isl_map *map);
2270 The number of basic sets in a set can be obtained
2271 or the number of basic maps in a map can be obtained
2274 #include <isl/set.h>
2275 int isl_set_n_basic_set(__isl_keep isl_set *set);
2277 #include <isl/map.h>
2278 int isl_map_n_basic_map(__isl_keep isl_map *map);
2280 It is also possible to obtain a list of basic sets from a set
2283 #include <isl/set.h>
2284 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2285 __isl_keep isl_set *set);
2287 #include <isl/union_set.h>
2288 __isl_give isl_basic_set_list *
2289 isl_union_set_get_basic_set_list(
2290 __isl_keep isl_union_set *uset);
2292 The returned list can be manipulated using the functions in L<"Lists">.
2294 To iterate over the constraints of a basic set or map, use
2296 #include <isl/constraint.h>
2298 int isl_basic_set_n_constraint(
2299 __isl_keep isl_basic_set *bset);
2300 isl_stat isl_basic_set_foreach_constraint(
2301 __isl_keep isl_basic_set *bset,
2302 isl_stat (*fn)(__isl_take isl_constraint *c,
2305 int isl_basic_map_n_constraint(
2306 __isl_keep isl_basic_map *bmap);
2307 isl_stat isl_basic_map_foreach_constraint(
2308 __isl_keep isl_basic_map *bmap,
2309 isl_stat (*fn)(__isl_take isl_constraint *c,
2312 __isl_null isl_constraint *isl_constraint_free(
2313 __isl_take isl_constraint *c);
2315 Again, the callback function C<fn> should return C<isl_stat_ok>
2317 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2318 occurs, the above functions will return C<isl_stat_error>.
2319 The constraint C<c> represents either an equality or an inequality.
2320 Use the following function to find out whether a constraint
2321 represents an equality. If not, it represents an inequality.
2323 isl_bool isl_constraint_is_equality(
2324 __isl_keep isl_constraint *constraint);
2326 It is also possible to obtain a list of constraints from a basic
2329 #include <isl/constraint.h>
2330 __isl_give isl_constraint_list *
2331 isl_basic_map_get_constraint_list(
2332 __isl_keep isl_basic_map *bmap);
2333 __isl_give isl_constraint_list *
2334 isl_basic_set_get_constraint_list(
2335 __isl_keep isl_basic_set *bset);
2337 These functions require that all existentially quantified variables
2338 have an explicit representation.
2339 The returned list can be manipulated using the functions in L<"Lists">.
2341 The coefficients of the constraints can be inspected using
2342 the following functions.
2344 isl_bool isl_constraint_is_lower_bound(
2345 __isl_keep isl_constraint *constraint,
2346 enum isl_dim_type type, unsigned pos);
2347 isl_bool isl_constraint_is_upper_bound(
2348 __isl_keep isl_constraint *constraint,
2349 enum isl_dim_type type, unsigned pos);
2350 __isl_give isl_val *isl_constraint_get_constant_val(
2351 __isl_keep isl_constraint *constraint);
2352 __isl_give isl_val *isl_constraint_get_coefficient_val(
2353 __isl_keep isl_constraint *constraint,
2354 enum isl_dim_type type, int pos);
2356 The explicit representations of the existentially quantified
2357 variables can be inspected using the following function.
2358 Note that the user is only allowed to use this function
2359 if the inspected set or map is the result of a call
2360 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2361 The existentially quantified variable is equal to the floor
2362 of the returned affine expression. The affine expression
2363 itself can be inspected using the functions in
2366 __isl_give isl_aff *isl_constraint_get_div(
2367 __isl_keep isl_constraint *constraint, int pos);
2369 To obtain the constraints of a basic set or map in matrix
2370 form, use the following functions.
2372 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2373 __isl_keep isl_basic_set *bset,
2374 enum isl_dim_type c1, enum isl_dim_type c2,
2375 enum isl_dim_type c3, enum isl_dim_type c4);
2376 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2377 __isl_keep isl_basic_set *bset,
2378 enum isl_dim_type c1, enum isl_dim_type c2,
2379 enum isl_dim_type c3, enum isl_dim_type c4);
2380 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2381 __isl_keep isl_basic_map *bmap,
2382 enum isl_dim_type c1,
2383 enum isl_dim_type c2, enum isl_dim_type c3,
2384 enum isl_dim_type c4, enum isl_dim_type c5);
2385 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2386 __isl_keep isl_basic_map *bmap,
2387 enum isl_dim_type c1,
2388 enum isl_dim_type c2, enum isl_dim_type c3,
2389 enum isl_dim_type c4, enum isl_dim_type c5);
2391 The C<isl_dim_type> arguments dictate the order in which
2392 different kinds of variables appear in the resulting matrix.
2393 For set inputs, they should be a permutation of
2394 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2395 For map inputs, they should be a permutation of
2396 C<isl_dim_cst>, C<isl_dim_param>,
2397 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2401 Points are elements of a set. They can be used to construct
2402 simple sets (boxes) or they can be used to represent the
2403 individual elements of a set.
2404 The zero point (the origin) can be created using
2406 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2408 The coordinates of a point can be inspected, set and changed
2411 __isl_give isl_val *isl_point_get_coordinate_val(
2412 __isl_keep isl_point *pnt,
2413 enum isl_dim_type type, int pos);
2414 __isl_give isl_point *isl_point_set_coordinate_val(
2415 __isl_take isl_point *pnt,
2416 enum isl_dim_type type, int pos,
2417 __isl_take isl_val *v);
2419 __isl_give isl_point *isl_point_add_ui(
2420 __isl_take isl_point *pnt,
2421 enum isl_dim_type type, int pos, unsigned val);
2422 __isl_give isl_point *isl_point_sub_ui(
2423 __isl_take isl_point *pnt,
2424 enum isl_dim_type type, int pos, unsigned val);
2426 Points can be copied or freed using
2428 __isl_give isl_point *isl_point_copy(
2429 __isl_keep isl_point *pnt);
2430 __isl_null isl_point *isl_point_free(
2431 __isl_take isl_point *pnt);
2433 A singleton set can be created from a point using
2435 __isl_give isl_basic_set *isl_basic_set_from_point(
2436 __isl_take isl_point *pnt);
2437 __isl_give isl_set *isl_set_from_point(
2438 __isl_take isl_point *pnt);
2439 __isl_give isl_union_set *isl_union_set_from_point(
2440 __isl_take isl_point *pnt);
2442 and a box can be created from two opposite extremal points using
2444 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2445 __isl_take isl_point *pnt1,
2446 __isl_take isl_point *pnt2);
2447 __isl_give isl_set *isl_set_box_from_points(
2448 __isl_take isl_point *pnt1,
2449 __isl_take isl_point *pnt2);
2451 All elements of a B<bounded> (union) set can be enumerated using
2452 the following functions.
2454 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2455 isl_stat (*fn)(__isl_take isl_point *pnt,
2458 isl_stat isl_union_set_foreach_point(
2459 __isl_keep isl_union_set *uset,
2460 isl_stat (*fn)(__isl_take isl_point *pnt,
2464 The function C<fn> is called for each integer point in
2465 C<set> with as second argument the last argument of
2466 the C<isl_set_foreach_point> call. The function C<fn>
2467 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2468 In the latter case, C<isl_set_foreach_point> will stop
2469 enumerating and return C<isl_stat_error> as well.
2470 If the enumeration is performed successfully and to completion,
2471 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2473 To obtain a single point of a (basic or union) set, use
2475 __isl_give isl_point *isl_basic_set_sample_point(
2476 __isl_take isl_basic_set *bset);
2477 __isl_give isl_point *isl_set_sample_point(
2478 __isl_take isl_set *set);
2479 __isl_give isl_point *isl_union_set_sample_point(
2480 __isl_take isl_union_set *uset);
2482 If C<set> does not contain any (integer) points, then the
2483 resulting point will be ``void'', a property that can be
2486 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2490 Besides sets and relation, C<isl> also supports various types of functions.
2491 Each of these types is derived from the value type (see L</"Values">)
2492 or from one of two primitive function types
2493 through the application of zero or more type constructors.
2494 We first describe the primitive type and then we describe
2495 the types derived from these primitive types.
2497 =head3 Primitive Functions
2499 C<isl> support two primitive function types, quasi-affine
2500 expressions and quasipolynomials.
2501 A quasi-affine expression is defined either over a parameter
2502 space or over a set and is composed of integer constants,
2503 parameters and set variables, addition, subtraction and
2504 integer division by an integer constant.
2505 For example, the quasi-affine expression
2507 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2509 maps C<x> to C<2*floor((4 n + x)/9>.
2510 A quasipolynomial is a polynomial expression in quasi-affine
2511 expression. That is, it additionally allows for multiplication.
2512 Note, though, that it is not allowed to construct an integer
2513 division of an expression involving multiplications.
2514 Here is an example of a quasipolynomial that is not
2515 quasi-affine expression
2517 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2519 Note that the external representations of quasi-affine expressions
2520 and quasipolynomials are different. Quasi-affine expressions
2521 use a notation with square brackets just like binary relations,
2522 while quasipolynomials do not. This might change at some point.
2524 If a primitive function is defined over a parameter space,
2525 then the space of the function itself is that of a set.
2526 If it is defined over a set, then the space of the function
2527 is that of a relation. In both cases, the set space (or
2528 the output space) is single-dimensional, anonymous and unstructured.
2529 To create functions with multiple dimensions or with other kinds
2530 of set or output spaces, use multiple expressions
2531 (see L</"Multiple Expressions">).
2535 =item * Quasi-affine Expressions
2537 Besides the expressions described above, a quasi-affine
2538 expression can also be set to NaN. Such expressions
2539 typically represent a failure to represent a result
2540 as a quasi-affine expression.
2542 The zero quasi affine expression or the quasi affine expression
2543 that is equal to a given value, parameter or
2544 a specified dimension on a given domain can be created using
2546 #include <isl/aff.h>
2547 __isl_give isl_aff *isl_aff_zero_on_domain(
2548 __isl_take isl_local_space *ls);
2549 __isl_give isl_aff *isl_aff_val_on_domain(
2550 __isl_take isl_local_space *ls,
2551 __isl_take isl_val *val);
2552 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2553 __isl_take isl_space *space,
2554 __isl_take isl_id *id);
2555 __isl_give isl_aff *isl_aff_var_on_domain(
2556 __isl_take isl_local_space *ls,
2557 enum isl_dim_type type, unsigned pos);
2558 __isl_give isl_aff *isl_aff_nan_on_domain(
2559 __isl_take isl_local_space *ls);
2561 The space passed to C<isl_aff_param_on_domain_space_id>
2562 is required to have a parameter with the given identifier.
2564 Quasi affine expressions can be copied and freed using
2566 #include <isl/aff.h>
2567 __isl_give isl_aff *isl_aff_copy(
2568 __isl_keep isl_aff *aff);
2569 __isl_null isl_aff *isl_aff_free(
2570 __isl_take isl_aff *aff);
2572 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2573 using the following function. The constraint is required to have
2574 a non-zero coefficient for the specified dimension.
2576 #include <isl/constraint.h>
2577 __isl_give isl_aff *isl_constraint_get_bound(
2578 __isl_keep isl_constraint *constraint,
2579 enum isl_dim_type type, int pos);
2581 The entire affine expression of the constraint can also be extracted
2582 using the following function.
2584 #include <isl/constraint.h>
2585 __isl_give isl_aff *isl_constraint_get_aff(
2586 __isl_keep isl_constraint *constraint);
2588 Conversely, an equality constraint equating
2589 the affine expression to zero or an inequality constraint enforcing
2590 the affine expression to be non-negative, can be constructed using
2592 __isl_give isl_constraint *isl_equality_from_aff(
2593 __isl_take isl_aff *aff);
2594 __isl_give isl_constraint *isl_inequality_from_aff(
2595 __isl_take isl_aff *aff);
2597 The coefficients and the integer divisions of an affine expression
2598 can be inspected using the following functions.
2600 #include <isl/aff.h>
2601 __isl_give isl_val *isl_aff_get_constant_val(
2602 __isl_keep isl_aff *aff);
2603 __isl_give isl_val *isl_aff_get_coefficient_val(
2604 __isl_keep isl_aff *aff,
2605 enum isl_dim_type type, int pos);
2606 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2607 enum isl_dim_type type, int pos);
2608 __isl_give isl_val *isl_aff_get_denominator_val(
2609 __isl_keep isl_aff *aff);
2610 __isl_give isl_aff *isl_aff_get_div(
2611 __isl_keep isl_aff *aff, int pos);
2613 They can be modified using the following functions.
2615 #include <isl/aff.h>
2616 __isl_give isl_aff *isl_aff_set_constant_si(
2617 __isl_take isl_aff *aff, int v);
2618 __isl_give isl_aff *isl_aff_set_constant_val(
2619 __isl_take isl_aff *aff, __isl_take isl_val *v);
2620 __isl_give isl_aff *isl_aff_set_coefficient_si(
2621 __isl_take isl_aff *aff,
2622 enum isl_dim_type type, int pos, int v);
2623 __isl_give isl_aff *isl_aff_set_coefficient_val(
2624 __isl_take isl_aff *aff,
2625 enum isl_dim_type type, int pos,
2626 __isl_take isl_val *v);
2628 __isl_give isl_aff *isl_aff_add_constant_si(
2629 __isl_take isl_aff *aff, int v);
2630 __isl_give isl_aff *isl_aff_add_constant_val(
2631 __isl_take isl_aff *aff, __isl_take isl_val *v);
2632 __isl_give isl_aff *isl_aff_add_constant_num_si(
2633 __isl_take isl_aff *aff, int v);
2634 __isl_give isl_aff *isl_aff_add_coefficient_si(
2635 __isl_take isl_aff *aff,
2636 enum isl_dim_type type, int pos, int v);
2637 __isl_give isl_aff *isl_aff_add_coefficient_val(
2638 __isl_take isl_aff *aff,
2639 enum isl_dim_type type, int pos,
2640 __isl_take isl_val *v);
2642 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2643 set the I<numerator> of the constant or coefficient, while
2644 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2645 the constant or coefficient as a whole.
2646 The C<add_constant> and C<add_coefficient> functions add an integer
2647 or rational value to
2648 the possibly rational constant or coefficient.
2649 The C<add_constant_num> functions add an integer value to
2652 =item * Quasipolynomials
2654 Some simple quasipolynomials can be created using the following functions.
2656 #include <isl/polynomial.h>
2657 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2658 __isl_take isl_space *domain);
2659 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2660 __isl_take isl_space *domain);
2661 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2662 __isl_take isl_space *domain);
2663 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2664 __isl_take isl_space *domain);
2665 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2666 __isl_take isl_space *domain);
2667 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2668 __isl_take isl_space *domain,
2669 __isl_take isl_val *val);
2670 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2671 __isl_take isl_space *domain,
2672 enum isl_dim_type type, unsigned pos);
2673 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2674 __isl_take isl_aff *aff);
2676 Recall that the space in which a quasipolynomial lives is a map space
2677 with a one-dimensional range. The C<domain> argument in some of
2678 the functions above corresponds to the domain of this map space.
2680 Quasipolynomials can be copied and freed again using the following
2683 #include <isl/polynomial.h>
2684 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2685 __isl_keep isl_qpolynomial *qp);
2686 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2687 __isl_take isl_qpolynomial *qp);
2689 The constant term of a quasipolynomial can be extracted using
2691 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2692 __isl_keep isl_qpolynomial *qp);
2694 To iterate over all terms in a quasipolynomial,
2697 isl_stat isl_qpolynomial_foreach_term(
2698 __isl_keep isl_qpolynomial *qp,
2699 isl_stat (*fn)(__isl_take isl_term *term,
2700 void *user), void *user);
2702 The terms themselves can be inspected and freed using
2705 unsigned isl_term_dim(__isl_keep isl_term *term,
2706 enum isl_dim_type type);
2707 __isl_give isl_val *isl_term_get_coefficient_val(
2708 __isl_keep isl_term *term);
2709 int isl_term_get_exp(__isl_keep isl_term *term,
2710 enum isl_dim_type type, unsigned pos);
2711 __isl_give isl_aff *isl_term_get_div(
2712 __isl_keep isl_term *term, unsigned pos);
2713 void isl_term_free(__isl_take isl_term *term);
2715 Each term is a product of parameters, set variables and
2716 integer divisions. The function C<isl_term_get_exp>
2717 returns the exponent of a given dimensions in the given term.
2723 A reduction represents a maximum or a minimum of its
2725 The only reduction type defined by C<isl> is
2726 C<isl_qpolynomial_fold>.
2728 There are currently no functions to directly create such
2729 objects, but they do appear in the piecewise quasipolynomial
2730 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2732 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2734 Reductions can be copied and freed using
2735 the following functions.
2737 #include <isl/polynomial.h>
2738 __isl_give isl_qpolynomial_fold *
2739 isl_qpolynomial_fold_copy(
2740 __isl_keep isl_qpolynomial_fold *fold);
2741 void isl_qpolynomial_fold_free(
2742 __isl_take isl_qpolynomial_fold *fold);
2744 To iterate over all quasipolynomials in a reduction, use
2746 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2747 __isl_keep isl_qpolynomial_fold *fold,
2748 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2749 void *user), void *user);
2751 =head3 Multiple Expressions
2753 A multiple expression represents a sequence of zero or
2754 more base expressions, all defined on the same domain space.
2755 The domain space of the multiple expression is the same
2756 as that of the base expressions, but the range space
2757 can be any space. In case the base expressions have
2758 a set space, the corresponding multiple expression
2759 also has a set space.
2760 Objects of the value type do not have an associated space.
2761 The space of a multiple value is therefore always a set space.
2762 Similarly, the space of a multiple union piecewise
2763 affine expression is always a set space.
2764 If the base expressions are not total, then
2765 a corresponding zero-dimensional multiple expression may
2766 have an explicit domain that keeps track of the domain
2767 outside of any base expressions.
2769 The multiple expression types defined by C<isl>
2770 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2771 C<isl_multi_union_pw_aff>.
2773 A multiple expression with the value zero for
2774 each output (or set) dimension can be created
2775 using the following functions.
2777 #include <isl/val.h>
2778 __isl_give isl_multi_val *isl_multi_val_zero(
2779 __isl_take isl_space *space);
2781 #include <isl/aff.h>
2782 __isl_give isl_multi_aff *isl_multi_aff_zero(
2783 __isl_take isl_space *space);
2784 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2785 __isl_take isl_space *space);
2786 __isl_give isl_multi_union_pw_aff *
2787 isl_multi_union_pw_aff_zero(
2788 __isl_take isl_space *space);
2790 Since there is no canonical way of representing a zero
2791 value of type C<isl_union_pw_aff>, the space passed
2792 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2794 An identity function can be created using the following
2795 functions. The space needs to be that of a relation
2796 with the same number of input and output dimensions.
2798 #include <isl/aff.h>
2799 __isl_give isl_multi_aff *isl_multi_aff_identity(
2800 __isl_take isl_space *space);
2801 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2802 __isl_take isl_space *space);
2804 A function that performs a projection on a universe
2805 relation or set can be created using the following functions.
2806 See also the corresponding
2807 projection operations in L</"Unary Operations">.
2809 #include <isl/aff.h>
2810 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2811 __isl_take isl_space *space);
2812 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2813 __isl_take isl_space *space);
2814 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2815 __isl_take isl_space *space,
2816 enum isl_dim_type type,
2817 unsigned first, unsigned n);
2819 A multiple expression can be created from a single
2820 base expression using the following functions.
2821 The space of the created multiple expression is the same
2822 as that of the base expression, except for
2823 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2824 lives in a parameter space and the output lives
2825 in a single-dimensional set space.
2827 #include <isl/aff.h>
2828 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2829 __isl_take isl_aff *aff);
2830 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2831 __isl_take isl_pw_aff *pa);
2832 __isl_give isl_multi_union_pw_aff *
2833 isl_multi_union_pw_aff_from_union_pw_aff(
2834 __isl_take isl_union_pw_aff *upa);
2836 A multiple expression can be created from a list
2837 of base expression in a specified space.
2838 The domain of this space needs to be the same
2839 as the domains of the base expressions in the list.
2840 If the base expressions have a set space (or no associated space),
2841 then this space also needs to be a set space.
2843 #include <isl/val.h>
2844 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2845 __isl_take isl_space *space,
2846 __isl_take isl_val_list *list);
2848 #include <isl/aff.h>
2849 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2850 __isl_take isl_space *space,
2851 __isl_take isl_aff_list *list);
2852 __isl_give isl_multi_pw_aff *
2853 isl_multi_pw_aff_from_pw_aff_list(
2854 __isl_take isl_space *space,
2855 __isl_take isl_pw_aff_list *list);
2856 __isl_give isl_multi_union_pw_aff *
2857 isl_multi_union_pw_aff_from_union_pw_aff_list(
2858 __isl_take isl_space *space,
2859 __isl_take isl_union_pw_aff_list *list);
2861 As a convenience, a multiple piecewise expression can
2862 also be created from a multiple expression.
2863 Each piecewise expression in the result has a single
2866 #include <isl/aff.h>
2867 __isl_give isl_multi_pw_aff *
2868 isl_multi_pw_aff_from_multi_aff(
2869 __isl_take isl_multi_aff *ma);
2871 Similarly, a multiple union expression can be
2872 created from a multiple expression.
2874 #include <isl/aff.h>
2875 __isl_give isl_multi_union_pw_aff *
2876 isl_multi_union_pw_aff_from_multi_aff(
2877 __isl_take isl_multi_aff *ma);
2878 __isl_give isl_multi_union_pw_aff *
2879 isl_multi_union_pw_aff_from_multi_pw_aff(
2880 __isl_take isl_multi_pw_aff *mpa);
2882 A multiple quasi-affine expression can be created from
2883 a multiple value with a given domain space using the following
2886 #include <isl/aff.h>
2887 __isl_give isl_multi_aff *
2888 isl_multi_aff_multi_val_on_space(
2889 __isl_take isl_space *space,
2890 __isl_take isl_multi_val *mv);
2893 a multiple union piecewise affine expression can be created from
2894 a multiple value with a given domain or
2895 a (piecewise) multiple affine expression with a given domain
2896 using the following functions.
2898 #include <isl/aff.h>
2899 __isl_give isl_multi_union_pw_aff *
2900 isl_multi_union_pw_aff_multi_val_on_domain(
2901 __isl_take isl_union_set *domain,
2902 __isl_take isl_multi_val *mv);
2903 __isl_give isl_multi_union_pw_aff *
2904 isl_multi_union_pw_aff_multi_aff_on_domain(
2905 __isl_take isl_union_set *domain,
2906 __isl_take isl_multi_aff *ma);
2907 __isl_give isl_multi_union_pw_aff *
2908 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2909 __isl_take isl_union_set *domain,
2910 __isl_take isl_pw_multi_aff *pma);
2912 Multiple expressions can be copied and freed using
2913 the following functions.
2915 #include <isl/val.h>
2916 __isl_give isl_multi_val *isl_multi_val_copy(
2917 __isl_keep isl_multi_val *mv);
2918 __isl_null isl_multi_val *isl_multi_val_free(
2919 __isl_take isl_multi_val *mv);
2921 #include <isl/aff.h>
2922 __isl_give isl_multi_aff *isl_multi_aff_copy(
2923 __isl_keep isl_multi_aff *maff);
2924 __isl_null isl_multi_aff *isl_multi_aff_free(
2925 __isl_take isl_multi_aff *maff);
2926 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2927 __isl_keep isl_multi_pw_aff *mpa);
2928 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2929 __isl_take isl_multi_pw_aff *mpa);
2930 __isl_give isl_multi_union_pw_aff *
2931 isl_multi_union_pw_aff_copy(
2932 __isl_keep isl_multi_union_pw_aff *mupa);
2933 __isl_null isl_multi_union_pw_aff *
2934 isl_multi_union_pw_aff_free(
2935 __isl_take isl_multi_union_pw_aff *mupa);
2937 The base expression at a given position of a multiple
2938 expression can be extracted using the following functions.
2940 #include <isl/val.h>
2941 __isl_give isl_val *isl_multi_val_get_val(
2942 __isl_keep isl_multi_val *mv, int pos);
2944 #include <isl/aff.h>
2945 __isl_give isl_aff *isl_multi_aff_get_aff(
2946 __isl_keep isl_multi_aff *multi, int pos);
2947 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2948 __isl_keep isl_multi_pw_aff *mpa, int pos);
2949 __isl_give isl_union_pw_aff *
2950 isl_multi_union_pw_aff_get_union_pw_aff(
2951 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2953 It can be replaced using the following functions.
2955 #include <isl/val.h>
2956 __isl_give isl_multi_val *isl_multi_val_set_val(
2957 __isl_take isl_multi_val *mv, int pos,
2958 __isl_take isl_val *val);
2960 #include <isl/aff.h>
2961 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2962 __isl_take isl_multi_aff *multi, int pos,
2963 __isl_take isl_aff *aff);
2964 __isl_give isl_multi_union_pw_aff *
2965 isl_multi_union_pw_aff_set_union_pw_aff(
2966 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2967 __isl_take isl_union_pw_aff *upa);
2969 As a convenience, a sequence of base expressions that have
2970 their domains in a given space can be extracted from a sequence
2971 of union expressions using the following function.
2973 #include <isl/aff.h>
2974 __isl_give isl_multi_pw_aff *
2975 isl_multi_union_pw_aff_extract_multi_pw_aff(
2976 __isl_keep isl_multi_union_pw_aff *mupa,
2977 __isl_take isl_space *space);
2979 Note that there is a difference between C<isl_multi_union_pw_aff>
2980 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2981 of unions of piecewise expressions, while the second is a union
2982 of piecewise sequences. In particular, multiple affine expressions
2983 in an C<isl_union_pw_multi_aff> may live in different spaces,
2984 while there is only a single multiple expression in
2985 an C<isl_multi_union_pw_aff>, which can therefore only live
2986 in a single space. This means that not every
2987 C<isl_union_pw_multi_aff> can be converted to
2988 an C<isl_multi_union_pw_aff>. Conversely, the elements
2989 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2990 while each multiple expression inside an C<isl_union_pw_multi_aff>
2991 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2992 of dimension greater than one may therefore not be exact.
2993 The following functions can
2994 be used to perform these conversions when they are possible.
2996 #include <isl/aff.h>
2997 __isl_give isl_multi_union_pw_aff *
2998 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2999 __isl_take isl_union_pw_multi_aff *upma);
3000 __isl_give isl_union_pw_multi_aff *
3001 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3002 __isl_take isl_multi_union_pw_aff *mupa);
3004 =head3 Piecewise Expressions
3006 A piecewise expression is an expression that is described
3007 using zero or more base expression defined over the same
3008 number of cells in the domain space of the base expressions.
3009 All base expressions are defined over the same
3010 domain space and the cells are disjoint.
3011 The space of a piecewise expression is the same as
3012 that of the base expressions.
3013 If the union of the cells is a strict subset of the domain
3014 space, then the value of the piecewise expression outside
3015 this union is different for types derived from quasi-affine
3016 expressions and those derived from quasipolynomials.
3017 Piecewise expressions derived from quasi-affine expressions
3018 are considered to be undefined outside the union of their cells.
3019 Piecewise expressions derived from quasipolynomials
3020 are considered to be zero outside the union of their cells.
3022 Piecewise quasipolynomials are mainly used by the C<barvinok>
3023 library for representing the number of elements in a parametric set or map.
3024 For example, the piecewise quasipolynomial
3026 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3028 represents the number of points in the map
3030 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3032 The piecewise expression types defined by C<isl>
3033 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3034 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3036 A piecewise expression with no cells can be created using
3037 the following functions.
3039 #include <isl/aff.h>
3040 __isl_give isl_pw_aff *isl_pw_aff_empty(
3041 __isl_take isl_space *space);
3042 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3043 __isl_take isl_space *space);
3045 A piecewise expression with a single universe cell can be
3046 created using the following functions.
3048 #include <isl/aff.h>
3049 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3050 __isl_take isl_aff *aff);
3051 __isl_give isl_pw_multi_aff *
3052 isl_pw_multi_aff_from_multi_aff(
3053 __isl_take isl_multi_aff *ma);
3055 #include <isl/polynomial.h>
3056 __isl_give isl_pw_qpolynomial *
3057 isl_pw_qpolynomial_from_qpolynomial(
3058 __isl_take isl_qpolynomial *qp);
3060 A piecewise expression with a single specified cell can be
3061 created using the following functions.
3063 #include <isl/aff.h>
3064 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3065 __isl_take isl_set *set, __isl_take isl_aff *aff);
3066 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3067 __isl_take isl_set *set,
3068 __isl_take isl_multi_aff *maff);
3070 #include <isl/polynomial.h>
3071 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3072 __isl_take isl_set *set,
3073 __isl_take isl_qpolynomial *qp);
3075 The following convenience functions first create a base expression and
3076 then create a piecewise expression over a universe domain.
3078 #include <isl/aff.h>
3079 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3080 __isl_take isl_local_space *ls);
3081 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3082 __isl_take isl_local_space *ls,
3083 enum isl_dim_type type, unsigned pos);
3084 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3085 __isl_take isl_local_space *ls);
3086 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3087 __isl_take isl_space *space);
3088 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3089 __isl_take isl_space *space);
3090 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3091 __isl_take isl_space *space);
3092 __isl_give isl_pw_multi_aff *
3093 isl_pw_multi_aff_project_out_map(
3094 __isl_take isl_space *space,
3095 enum isl_dim_type type,
3096 unsigned first, unsigned n);
3098 #include <isl/polynomial.h>
3099 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3100 __isl_take isl_space *space);
3102 The following convenience functions first create a base expression and
3103 then create a piecewise expression over a given domain.
3105 #include <isl/aff.h>
3106 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3107 __isl_take isl_set *domain,
3108 __isl_take isl_val *v);
3109 __isl_give isl_pw_multi_aff *
3110 isl_pw_multi_aff_multi_val_on_domain(
3111 __isl_take isl_set *domain,
3112 __isl_take isl_multi_val *mv);
3114 As a convenience, a piecewise multiple expression can
3115 also be created from a piecewise expression.
3116 Each multiple expression in the result is derived
3117 from the corresponding base expression.
3119 #include <isl/aff.h>
3120 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3121 __isl_take isl_pw_aff *pa);
3123 Similarly, a piecewise quasipolynomial can be
3124 created from a piecewise quasi-affine expression using
3125 the following function.
3127 #include <isl/polynomial.h>
3128 __isl_give isl_pw_qpolynomial *
3129 isl_pw_qpolynomial_from_pw_aff(
3130 __isl_take isl_pw_aff *pwaff);
3132 Piecewise expressions can be copied and freed using the following functions.
3134 #include <isl/aff.h>
3135 __isl_give isl_pw_aff *isl_pw_aff_copy(
3136 __isl_keep isl_pw_aff *pwaff);
3137 __isl_null isl_pw_aff *isl_pw_aff_free(
3138 __isl_take isl_pw_aff *pwaff);
3139 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3140 __isl_keep isl_pw_multi_aff *pma);
3141 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3142 __isl_take isl_pw_multi_aff *pma);
3144 #include <isl/polynomial.h>
3145 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3146 __isl_keep isl_pw_qpolynomial *pwqp);
3147 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3148 __isl_take isl_pw_qpolynomial *pwqp);
3149 __isl_give isl_pw_qpolynomial_fold *
3150 isl_pw_qpolynomial_fold_copy(
3151 __isl_keep isl_pw_qpolynomial_fold *pwf);
3152 __isl_null isl_pw_qpolynomial_fold *
3153 isl_pw_qpolynomial_fold_free(
3154 __isl_take isl_pw_qpolynomial_fold *pwf);
3156 To iterate over the different cells of a piecewise expression,
3157 use the following functions.
3159 #include <isl/aff.h>
3160 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3161 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3162 isl_stat isl_pw_aff_foreach_piece(
3163 __isl_keep isl_pw_aff *pwaff,
3164 isl_stat (*fn)(__isl_take isl_set *set,
3165 __isl_take isl_aff *aff,
3166 void *user), void *user);
3167 int isl_pw_multi_aff_n_piece(
3168 __isl_keep isl_pw_multi_aff *pma);
3169 isl_stat isl_pw_multi_aff_foreach_piece(
3170 __isl_keep isl_pw_multi_aff *pma,
3171 isl_stat (*fn)(__isl_take isl_set *set,
3172 __isl_take isl_multi_aff *maff,
3173 void *user), void *user);
3175 #include <isl/polynomial.h>
3176 int isl_pw_qpolynomial_n_piece(
3177 __isl_keep isl_pw_qpolynomial *pwqp);
3178 isl_stat isl_pw_qpolynomial_foreach_piece(
3179 __isl_keep isl_pw_qpolynomial *pwqp,
3180 isl_stat (*fn)(__isl_take isl_set *set,
3181 __isl_take isl_qpolynomial *qp,
3182 void *user), void *user);
3183 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3184 __isl_keep isl_pw_qpolynomial *pwqp,
3185 isl_stat (*fn)(__isl_take isl_set *set,
3186 __isl_take isl_qpolynomial *qp,
3187 void *user), void *user);
3188 int isl_pw_qpolynomial_fold_n_piece(
3189 __isl_keep isl_pw_qpolynomial_fold *pwf);
3190 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3191 __isl_keep isl_pw_qpolynomial_fold *pwf,
3192 isl_stat (*fn)(__isl_take isl_set *set,
3193 __isl_take isl_qpolynomial_fold *fold,
3194 void *user), void *user);
3195 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3196 __isl_keep isl_pw_qpolynomial_fold *pwf,
3197 isl_stat (*fn)(__isl_take isl_set *set,
3198 __isl_take isl_qpolynomial_fold *fold,
3199 void *user), void *user);
3201 As usual, the function C<fn> should return C<isl_stat_ok> on success
3202 and C<isl_stat_error> on failure. The difference between
3203 C<isl_pw_qpolynomial_foreach_piece> and
3204 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3205 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3206 compute unique representations for all existentially quantified
3207 variables and then turn these existentially quantified variables
3208 into extra set variables, adapting the associated quasipolynomial
3209 accordingly. This means that the C<set> passed to C<fn>
3210 will not have any existentially quantified variables, but that
3211 the dimensions of the sets may be different for different
3212 invocations of C<fn>.
3213 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3214 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3216 A piecewise expression consisting of the expressions at a given
3217 position of a piecewise multiple expression can be extracted
3218 using the following function.
3220 #include <isl/aff.h>
3221 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3222 __isl_keep isl_pw_multi_aff *pma, int pos);
3224 These expressions can be replaced using the following function.
3226 #include <isl/aff.h>
3227 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3228 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3229 __isl_take isl_pw_aff *pa);
3231 Note that there is a difference between C<isl_multi_pw_aff> and
3232 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3233 affine expressions, while the second is a piecewise sequence
3234 of affine expressions. In particular, each of the piecewise
3235 affine expressions in an C<isl_multi_pw_aff> may have a different
3236 domain, while all multiple expressions associated to a cell
3237 in an C<isl_pw_multi_aff> have the same domain.
3238 It is possible to convert between the two, but when converting
3239 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3240 of the result is the intersection of the domains of the input.
3241 The reverse conversion is exact.
3243 #include <isl/aff.h>
3244 __isl_give isl_pw_multi_aff *
3245 isl_pw_multi_aff_from_multi_pw_aff(
3246 __isl_take isl_multi_pw_aff *mpa);
3247 __isl_give isl_multi_pw_aff *
3248 isl_multi_pw_aff_from_pw_multi_aff(
3249 __isl_take isl_pw_multi_aff *pma);
3251 =head3 Union Expressions
3253 A union expression collects base expressions defined
3254 over different domains. The space of a union expression
3255 is that of the shared parameter space.
3257 The union expression types defined by C<isl>
3258 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3259 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3261 C<isl_union_pw_aff>,
3262 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3263 there can be at most one base expression for a given domain space.
3265 C<isl_union_pw_multi_aff>,
3266 there can be multiple such expressions for a given domain space,
3267 but the domains of these expressions need to be disjoint.
3269 An empty union expression can be created using the following functions.
3271 #include <isl/aff.h>
3272 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3273 __isl_take isl_space *space);
3274 __isl_give isl_union_pw_multi_aff *
3275 isl_union_pw_multi_aff_empty(
3276 __isl_take isl_space *space);
3278 #include <isl/polynomial.h>
3279 __isl_give isl_union_pw_qpolynomial *
3280 isl_union_pw_qpolynomial_zero(
3281 __isl_take isl_space *space);
3283 A union expression containing a single base expression
3284 can be created using the following functions.
3286 #include <isl/aff.h>
3287 __isl_give isl_union_pw_aff *
3288 isl_union_pw_aff_from_pw_aff(
3289 __isl_take isl_pw_aff *pa);
3290 __isl_give isl_union_pw_multi_aff *
3291 isl_union_pw_multi_aff_from_aff(
3292 __isl_take isl_aff *aff);
3293 __isl_give isl_union_pw_multi_aff *
3294 isl_union_pw_multi_aff_from_pw_multi_aff(
3295 __isl_take isl_pw_multi_aff *pma);
3297 #include <isl/polynomial.h>
3298 __isl_give isl_union_pw_qpolynomial *
3299 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3300 __isl_take isl_pw_qpolynomial *pwqp);
3302 The following functions create a base expression on each
3303 of the sets in the union set and collect the results.
3305 #include <isl/aff.h>
3306 __isl_give isl_union_pw_multi_aff *
3307 isl_union_pw_multi_aff_from_union_pw_aff(
3308 __isl_take isl_union_pw_aff *upa);
3309 __isl_give isl_union_pw_aff *
3310 isl_union_pw_multi_aff_get_union_pw_aff(
3311 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3312 __isl_give isl_union_pw_aff *
3313 isl_union_pw_aff_val_on_domain(
3314 __isl_take isl_union_set *domain,
3315 __isl_take isl_val *v);
3316 __isl_give isl_union_pw_multi_aff *
3317 isl_union_pw_multi_aff_multi_val_on_domain(
3318 __isl_take isl_union_set *domain,
3319 __isl_take isl_multi_val *mv);
3320 __isl_give isl_union_pw_aff *
3321 isl_union_pw_aff_param_on_domain_id(
3322 __isl_take isl_union_set *domain,
3323 __isl_take isl_id *id);
3325 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3326 is the identifier of a parameter that may or may not already
3327 be present in C<domain>.
3329 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3331 expression on a given domain can be created using the following
3334 #include <isl/aff.h>
3335 __isl_give isl_union_pw_aff *
3336 isl_union_pw_aff_aff_on_domain(
3337 __isl_take isl_union_set *domain,
3338 __isl_take isl_aff *aff);
3339 __isl_give isl_union_pw_aff *
3340 isl_union_pw_aff_pw_aff_on_domain(
3341 __isl_take isl_union_set *domain,
3342 __isl_take isl_pw_aff *pa);
3344 A base expression can be added to a union expression using
3345 the following functions.
3347 #include <isl/aff.h>
3348 __isl_give isl_union_pw_aff *
3349 isl_union_pw_aff_add_pw_aff(
3350 __isl_take isl_union_pw_aff *upa,
3351 __isl_take isl_pw_aff *pa);
3352 __isl_give isl_union_pw_multi_aff *
3353 isl_union_pw_multi_aff_add_pw_multi_aff(
3354 __isl_take isl_union_pw_multi_aff *upma,
3355 __isl_take isl_pw_multi_aff *pma);
3357 #include <isl/polynomial.h>
3358 __isl_give isl_union_pw_qpolynomial *
3359 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3360 __isl_take isl_union_pw_qpolynomial *upwqp,
3361 __isl_take isl_pw_qpolynomial *pwqp);
3363 Union expressions can be copied and freed using
3364 the following functions.
3366 #include <isl/aff.h>
3367 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3368 __isl_keep isl_union_pw_aff *upa);
3369 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3370 __isl_take isl_union_pw_aff *upa);
3371 __isl_give isl_union_pw_multi_aff *
3372 isl_union_pw_multi_aff_copy(
3373 __isl_keep isl_union_pw_multi_aff *upma);
3374 __isl_null isl_union_pw_multi_aff *
3375 isl_union_pw_multi_aff_free(
3376 __isl_take isl_union_pw_multi_aff *upma);
3378 #include <isl/polynomial.h>
3379 __isl_give isl_union_pw_qpolynomial *
3380 isl_union_pw_qpolynomial_copy(
3381 __isl_keep isl_union_pw_qpolynomial *upwqp);
3382 __isl_null isl_union_pw_qpolynomial *
3383 isl_union_pw_qpolynomial_free(
3384 __isl_take isl_union_pw_qpolynomial *upwqp);
3385 __isl_give isl_union_pw_qpolynomial_fold *
3386 isl_union_pw_qpolynomial_fold_copy(
3387 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3388 __isl_null isl_union_pw_qpolynomial_fold *
3389 isl_union_pw_qpolynomial_fold_free(
3390 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3392 To iterate over the base expressions in a union expression,
3393 use the following functions.
3395 #include <isl/aff.h>
3396 int isl_union_pw_aff_n_pw_aff(
3397 __isl_keep isl_union_pw_aff *upa);
3398 isl_stat isl_union_pw_aff_foreach_pw_aff(
3399 __isl_keep isl_union_pw_aff *upa,
3400 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3401 void *user), void *user);
3402 int isl_union_pw_multi_aff_n_pw_multi_aff(
3403 __isl_keep isl_union_pw_multi_aff *upma);
3404 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3405 __isl_keep isl_union_pw_multi_aff *upma,
3406 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3407 void *user), void *user);
3409 #include <isl/polynomial.h>
3410 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3411 __isl_keep isl_union_pw_qpolynomial *upwqp);
3412 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3413 __isl_keep isl_union_pw_qpolynomial *upwqp,
3414 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3415 void *user), void *user);
3416 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3417 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3418 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3419 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3420 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3421 void *user), void *user);
3423 To extract the base expression in a given space from a union, use
3424 the following functions.
3426 #include <isl/aff.h>
3427 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3428 __isl_keep isl_union_pw_aff *upa,
3429 __isl_take isl_space *space);
3430 __isl_give isl_pw_multi_aff *
3431 isl_union_pw_multi_aff_extract_pw_multi_aff(
3432 __isl_keep isl_union_pw_multi_aff *upma,
3433 __isl_take isl_space *space);
3435 #include <isl/polynomial.h>
3436 __isl_give isl_pw_qpolynomial *
3437 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3438 __isl_keep isl_union_pw_qpolynomial *upwqp,
3439 __isl_take isl_space *space);
3441 =head2 Input and Output
3443 For set and relation,
3444 C<isl> supports its own input/output format, which is similar
3445 to the C<Omega> format, but also supports the C<PolyLib> format
3447 For other object types, typically only an C<isl> format is supported.
3449 =head3 C<isl> format
3451 The C<isl> format is similar to that of C<Omega>, but has a different
3452 syntax for describing the parameters and allows for the definition
3453 of an existentially quantified variable as the integer division
3454 of an affine expression.
3455 For example, the set of integers C<i> between C<0> and C<n>
3456 such that C<i % 10 <= 6> can be described as
3458 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3461 A set or relation can have several disjuncts, separated
3462 by the keyword C<or>. Each disjunct is either a conjunction
3463 of constraints or a projection (C<exists>) of a conjunction
3464 of constraints. The constraints are separated by the keyword
3467 =head3 C<PolyLib> format
3469 If the represented set is a union, then the first line
3470 contains a single number representing the number of disjuncts.
3471 Otherwise, a line containing the number C<1> is optional.
3473 Each disjunct is represented by a matrix of constraints.
3474 The first line contains two numbers representing
3475 the number of rows and columns,
3476 where the number of rows is equal to the number of constraints
3477 and the number of columns is equal to two plus the number of variables.
3478 The following lines contain the actual rows of the constraint matrix.
3479 In each row, the first column indicates whether the constraint
3480 is an equality (C<0>) or inequality (C<1>). The final column
3481 corresponds to the constant term.
3483 If the set is parametric, then the coefficients of the parameters
3484 appear in the last columns before the constant column.
3485 The coefficients of any existentially quantified variables appear
3486 between those of the set variables and those of the parameters.
3488 =head3 Extended C<PolyLib> format
3490 The extended C<PolyLib> format is nearly identical to the
3491 C<PolyLib> format. The only difference is that the line
3492 containing the number of rows and columns of a constraint matrix
3493 also contains four additional numbers:
3494 the number of output dimensions, the number of input dimensions,
3495 the number of local dimensions (i.e., the number of existentially
3496 quantified variables) and the number of parameters.
3497 For sets, the number of ``output'' dimensions is equal
3498 to the number of set dimensions, while the number of ``input''
3503 Objects can be read from input using the following functions.
3505 #include <isl/val.h>
3506 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3508 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3509 isl_ctx *ctx, const char *str);
3511 #include <isl/set.h>
3512 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3513 isl_ctx *ctx, FILE *input);
3514 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3515 isl_ctx *ctx, const char *str);
3516 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3518 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3521 #include <isl/map.h>
3522 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3523 isl_ctx *ctx, FILE *input);
3524 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3525 isl_ctx *ctx, const char *str);
3526 __isl_give isl_map *isl_map_read_from_file(
3527 isl_ctx *ctx, FILE *input);
3528 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3531 #include <isl/union_set.h>
3532 __isl_give isl_union_set *isl_union_set_read_from_file(
3533 isl_ctx *ctx, FILE *input);
3534 __isl_give isl_union_set *isl_union_set_read_from_str(
3535 isl_ctx *ctx, const char *str);
3537 #include <isl/union_map.h>
3538 __isl_give isl_union_map *isl_union_map_read_from_file(
3539 isl_ctx *ctx, FILE *input);
3540 __isl_give isl_union_map *isl_union_map_read_from_str(
3541 isl_ctx *ctx, const char *str);
3543 #include <isl/aff.h>
3544 __isl_give isl_aff *isl_aff_read_from_str(
3545 isl_ctx *ctx, const char *str);
3546 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3547 isl_ctx *ctx, const char *str);
3548 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3549 isl_ctx *ctx, const char *str);
3550 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3551 isl_ctx *ctx, const char *str);
3552 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3553 isl_ctx *ctx, const char *str);
3554 __isl_give isl_union_pw_aff *
3555 isl_union_pw_aff_read_from_str(
3556 isl_ctx *ctx, const char *str);
3557 __isl_give isl_union_pw_multi_aff *
3558 isl_union_pw_multi_aff_read_from_str(
3559 isl_ctx *ctx, const char *str);
3560 __isl_give isl_multi_union_pw_aff *
3561 isl_multi_union_pw_aff_read_from_str(
3562 isl_ctx *ctx, const char *str);
3564 #include <isl/polynomial.h>
3565 __isl_give isl_union_pw_qpolynomial *
3566 isl_union_pw_qpolynomial_read_from_str(
3567 isl_ctx *ctx, const char *str);
3569 For sets and relations,
3570 the input format is autodetected and may be either the C<PolyLib> format
3571 or the C<isl> format.
3575 Before anything can be printed, an C<isl_printer> needs to
3578 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3580 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3581 __isl_null isl_printer *isl_printer_free(
3582 __isl_take isl_printer *printer);
3584 C<isl_printer_to_file> prints to the given file, while
3585 C<isl_printer_to_str> prints to a string that can be extracted
3586 using the following function.
3588 #include <isl/printer.h>
3589 __isl_give char *isl_printer_get_str(
3590 __isl_keep isl_printer *printer);
3592 The printer can be inspected using the following functions.
3594 FILE *isl_printer_get_file(
3595 __isl_keep isl_printer *printer);
3596 int isl_printer_get_output_format(
3597 __isl_keep isl_printer *p);
3598 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3600 The behavior of the printer can be modified in various ways
3602 __isl_give isl_printer *isl_printer_set_output_format(
3603 __isl_take isl_printer *p, int output_format);
3604 __isl_give isl_printer *isl_printer_set_indent(
3605 __isl_take isl_printer *p, int indent);
3606 __isl_give isl_printer *isl_printer_set_indent_prefix(
3607 __isl_take isl_printer *p, const char *prefix);
3608 __isl_give isl_printer *isl_printer_indent(
3609 __isl_take isl_printer *p, int indent);
3610 __isl_give isl_printer *isl_printer_set_prefix(
3611 __isl_take isl_printer *p, const char *prefix);
3612 __isl_give isl_printer *isl_printer_set_suffix(
3613 __isl_take isl_printer *p, const char *suffix);
3614 __isl_give isl_printer *isl_printer_set_yaml_style(
3615 __isl_take isl_printer *p, int yaml_style);
3617 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3618 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3619 and defaults to C<ISL_FORMAT_ISL>.
3620 Each line in the output is prefixed by C<indent_prefix>,
3621 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3622 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3623 In the C<PolyLib> format output,
3624 the coefficients of the existentially quantified variables
3625 appear between those of the set variables and those
3627 The function C<isl_printer_indent> increases the indentation
3628 by the specified amount (which may be negative).
3629 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3630 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3633 To actually print something, use
3635 #include <isl/printer.h>
3636 __isl_give isl_printer *isl_printer_print_double(
3637 __isl_take isl_printer *p, double d);
3639 #include <isl/val.h>
3640 __isl_give isl_printer *isl_printer_print_val(
3641 __isl_take isl_printer *p, __isl_keep isl_val *v);
3643 #include <isl/set.h>
3644 __isl_give isl_printer *isl_printer_print_basic_set(
3645 __isl_take isl_printer *printer,
3646 __isl_keep isl_basic_set *bset);
3647 __isl_give isl_printer *isl_printer_print_set(
3648 __isl_take isl_printer *printer,
3649 __isl_keep isl_set *set);
3651 #include <isl/map.h>
3652 __isl_give isl_printer *isl_printer_print_basic_map(
3653 __isl_take isl_printer *printer,
3654 __isl_keep isl_basic_map *bmap);
3655 __isl_give isl_printer *isl_printer_print_map(
3656 __isl_take isl_printer *printer,
3657 __isl_keep isl_map *map);
3659 #include <isl/union_set.h>
3660 __isl_give isl_printer *isl_printer_print_union_set(
3661 __isl_take isl_printer *p,
3662 __isl_keep isl_union_set *uset);
3664 #include <isl/union_map.h>
3665 __isl_give isl_printer *isl_printer_print_union_map(
3666 __isl_take isl_printer *p,
3667 __isl_keep isl_union_map *umap);
3669 #include <isl/val.h>
3670 __isl_give isl_printer *isl_printer_print_multi_val(
3671 __isl_take isl_printer *p,
3672 __isl_keep isl_multi_val *mv);
3674 #include <isl/aff.h>
3675 __isl_give isl_printer *isl_printer_print_aff(
3676 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3677 __isl_give isl_printer *isl_printer_print_multi_aff(
3678 __isl_take isl_printer *p,
3679 __isl_keep isl_multi_aff *maff);
3680 __isl_give isl_printer *isl_printer_print_pw_aff(
3681 __isl_take isl_printer *p,
3682 __isl_keep isl_pw_aff *pwaff);
3683 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3684 __isl_take isl_printer *p,
3685 __isl_keep isl_pw_multi_aff *pma);
3686 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3687 __isl_take isl_printer *p,
3688 __isl_keep isl_multi_pw_aff *mpa);
3689 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3690 __isl_take isl_printer *p,
3691 __isl_keep isl_union_pw_aff *upa);
3692 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3693 __isl_take isl_printer *p,
3694 __isl_keep isl_union_pw_multi_aff *upma);
3695 __isl_give isl_printer *
3696 isl_printer_print_multi_union_pw_aff(
3697 __isl_take isl_printer *p,
3698 __isl_keep isl_multi_union_pw_aff *mupa);
3700 #include <isl/polynomial.h>
3701 __isl_give isl_printer *isl_printer_print_qpolynomial(
3702 __isl_take isl_printer *p,
3703 __isl_keep isl_qpolynomial *qp);
3704 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3705 __isl_take isl_printer *p,
3706 __isl_keep isl_pw_qpolynomial *pwqp);
3707 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3708 __isl_take isl_printer *p,
3709 __isl_keep isl_union_pw_qpolynomial *upwqp);
3711 __isl_give isl_printer *
3712 isl_printer_print_pw_qpolynomial_fold(
3713 __isl_take isl_printer *p,
3714 __isl_keep isl_pw_qpolynomial_fold *pwf);
3715 __isl_give isl_printer *
3716 isl_printer_print_union_pw_qpolynomial_fold(
3717 __isl_take isl_printer *p,
3718 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3720 For C<isl_printer_print_qpolynomial>,
3721 C<isl_printer_print_pw_qpolynomial> and
3722 C<isl_printer_print_pw_qpolynomial_fold>,
3723 the output format of the printer
3724 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3725 For C<isl_printer_print_union_pw_qpolynomial> and
3726 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3728 In case of printing in C<ISL_FORMAT_C>, the user may want
3729 to set the names of all dimensions first.
3731 C<isl> also provides limited support for printing YAML documents,
3732 just enough for the internal use for printing such documents.
3734 #include <isl/printer.h>
3735 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3736 __isl_take isl_printer *p);
3737 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3738 __isl_take isl_printer *p);
3739 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3740 __isl_take isl_printer *p);
3741 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3742 __isl_take isl_printer *p);
3743 __isl_give isl_printer *isl_printer_yaml_next(
3744 __isl_take isl_printer *p);
3746 A document is started by a call to either
3747 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3748 Anything printed to the printer after such a call belong to the
3749 first key of the mapping or the first element in the sequence.
3750 The function C<isl_printer_yaml_next> moves to the value if
3751 we are currently printing a mapping key, the next key if we
3752 are printing a value or the next element if we are printing
3753 an element in a sequence.
3754 Nested mappings and sequences are initiated by the same
3755 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3756 Each call to these functions needs to have a corresponding call to
3757 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3759 When called on a file printer, the following function flushes
3760 the file. When called on a string printer, the buffer is cleared.
3762 __isl_give isl_printer *isl_printer_flush(
3763 __isl_take isl_printer *p);
3765 The following functions allow the user to attach
3766 notes to a printer in order to keep track of additional state.
3768 #include <isl/printer.h>
3769 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3770 __isl_keep isl_id *id);
3771 __isl_give isl_id *isl_printer_get_note(
3772 __isl_keep isl_printer *p, __isl_take isl_id *id);
3773 __isl_give isl_printer *isl_printer_set_note(
3774 __isl_take isl_printer *p,
3775 __isl_take isl_id *id, __isl_take isl_id *note);
3777 C<isl_printer_set_note> associates the given note to the given
3778 identifier in the printer.
3779 C<isl_printer_get_note> retrieves a note associated to an
3781 C<isl_printer_has_note> checks if there is such a note.
3782 C<isl_printer_get_note> fails if the requested note does not exist.
3784 Alternatively, a string representation can be obtained
3785 directly using the following functions, which always print
3789 __isl_give char *isl_id_to_str(
3790 __isl_keep isl_id *id);
3792 #include <isl/space.h>
3793 __isl_give char *isl_space_to_str(
3794 __isl_keep isl_space *space);
3796 #include <isl/val.h>
3797 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3798 __isl_give char *isl_multi_val_to_str(
3799 __isl_keep isl_multi_val *mv);
3801 #include <isl/set.h>
3802 __isl_give char *isl_basic_set_to_str(
3803 __isl_keep isl_basic_set *bset);
3804 __isl_give char *isl_set_to_str(
3805 __isl_keep isl_set *set);
3807 #include <isl/union_set.h>
3808 __isl_give char *isl_union_set_to_str(
3809 __isl_keep isl_union_set *uset);
3811 #include <isl/map.h>
3812 __isl_give char *isl_basic_map_to_str(
3813 __isl_keep isl_basic_map *bmap);
3814 __isl_give char *isl_map_to_str(
3815 __isl_keep isl_map *map);
3817 #include <isl/union_map.h>
3818 __isl_give char *isl_union_map_to_str(
3819 __isl_keep isl_union_map *umap);
3821 #include <isl/aff.h>
3822 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3823 __isl_give char *isl_pw_aff_to_str(
3824 __isl_keep isl_pw_aff *pa);
3825 __isl_give char *isl_multi_aff_to_str(
3826 __isl_keep isl_multi_aff *ma);
3827 __isl_give char *isl_pw_multi_aff_to_str(
3828 __isl_keep isl_pw_multi_aff *pma);
3829 __isl_give char *isl_multi_pw_aff_to_str(
3830 __isl_keep isl_multi_pw_aff *mpa);
3831 __isl_give char *isl_union_pw_aff_to_str(
3832 __isl_keep isl_union_pw_aff *upa);
3833 __isl_give char *isl_union_pw_multi_aff_to_str(
3834 __isl_keep isl_union_pw_multi_aff *upma);
3835 __isl_give char *isl_multi_union_pw_aff_to_str(
3836 __isl_keep isl_multi_union_pw_aff *mupa);
3838 #include <isl/point.h>
3839 __isl_give char *isl_point_to_str(
3840 __isl_keep isl_point *pnt);
3842 #include <isl/polynomial.h>
3843 __isl_give char *isl_pw_qpolynomial_to_str(
3844 __isl_keep isl_pw_qpolynomial *pwqp);
3845 __isl_give char *isl_union_pw_qpolynomial_to_str(
3846 __isl_keep isl_union_pw_qpolynomial *upwqp);
3850 =head3 Unary Properties
3856 The following functions test whether the given set or relation
3857 contains any integer points. The ``plain'' variants do not perform
3858 any computations, but simply check if the given set or relation
3859 is already known to be empty.
3861 #include <isl/set.h>
3862 isl_bool isl_basic_set_plain_is_empty(
3863 __isl_keep isl_basic_set *bset);
3864 isl_bool isl_basic_set_is_empty(
3865 __isl_keep isl_basic_set *bset);
3866 isl_bool isl_set_plain_is_empty(
3867 __isl_keep isl_set *set);
3868 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3870 #include <isl/union_set.h>
3871 isl_bool isl_union_set_is_empty(
3872 __isl_keep isl_union_set *uset);
3874 #include <isl/map.h>
3875 isl_bool isl_basic_map_plain_is_empty(
3876 __isl_keep isl_basic_map *bmap);
3877 isl_bool isl_basic_map_is_empty(
3878 __isl_keep isl_basic_map *bmap);
3879 isl_bool isl_map_plain_is_empty(
3880 __isl_keep isl_map *map);
3881 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3883 #include <isl/union_map.h>
3884 isl_bool isl_union_map_plain_is_empty(
3885 __isl_keep isl_union_map *umap);
3886 isl_bool isl_union_map_is_empty(
3887 __isl_keep isl_union_map *umap);
3889 =item * Universality
3891 isl_bool isl_basic_set_plain_is_universe(
3892 __isl_keep isl_basic_set *bset);
3893 isl_bool isl_basic_set_is_universe(
3894 __isl_keep isl_basic_set *bset);
3895 isl_bool isl_basic_map_plain_is_universe(
3896 __isl_keep isl_basic_map *bmap);
3897 isl_bool isl_basic_map_is_universe(
3898 __isl_keep isl_basic_map *bmap);
3899 isl_bool isl_set_plain_is_universe(
3900 __isl_keep isl_set *set);
3901 isl_bool isl_map_plain_is_universe(
3902 __isl_keep isl_map *map);
3904 =item * Single-valuedness
3906 #include <isl/set.h>
3907 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3909 #include <isl/map.h>
3910 isl_bool isl_basic_map_is_single_valued(
3911 __isl_keep isl_basic_map *bmap);
3912 isl_bool isl_map_plain_is_single_valued(
3913 __isl_keep isl_map *map);
3914 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3916 #include <isl/union_map.h>
3917 isl_bool isl_union_map_is_single_valued(
3918 __isl_keep isl_union_map *umap);
3922 isl_bool isl_map_plain_is_injective(
3923 __isl_keep isl_map *map);
3924 isl_bool isl_map_is_injective(
3925 __isl_keep isl_map *map);
3926 isl_bool isl_union_map_plain_is_injective(
3927 __isl_keep isl_union_map *umap);
3928 isl_bool isl_union_map_is_injective(
3929 __isl_keep isl_union_map *umap);
3933 isl_bool isl_map_is_bijective(
3934 __isl_keep isl_map *map);
3935 isl_bool isl_union_map_is_bijective(
3936 __isl_keep isl_union_map *umap);
3940 The following functions test whether the given relation
3941 only maps elements to themselves.
3943 #include <isl/map.h>
3944 isl_bool isl_map_is_identity(
3945 __isl_keep isl_map *map);
3947 #include <isl/union_map.h>
3948 isl_bool isl_union_map_is_identity(
3949 __isl_keep isl_union_map *umap);
3953 __isl_give isl_val *
3954 isl_basic_map_plain_get_val_if_fixed(
3955 __isl_keep isl_basic_map *bmap,
3956 enum isl_dim_type type, unsigned pos);
3957 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3958 __isl_keep isl_set *set,
3959 enum isl_dim_type type, unsigned pos);
3960 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3961 __isl_keep isl_map *map,
3962 enum isl_dim_type type, unsigned pos);
3964 If the set or relation obviously lies on a hyperplane where the given dimension
3965 has a fixed value, then return that value.
3966 Otherwise return NaN.
3970 isl_stat isl_set_dim_residue_class_val(
3971 __isl_keep isl_set *set,
3972 int pos, __isl_give isl_val **modulo,
3973 __isl_give isl_val **residue);
3975 Check if the values of the given set dimension are equal to a fixed
3976 value modulo some integer value. If so, assign the modulo to C<*modulo>
3977 and the fixed value to C<*residue>. If the given dimension attains only
3978 a single value, then assign C<0> to C<*modulo> and the fixed value to
3980 If the dimension does not attain only a single value and if no modulo
3981 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3983 #include <isl/set.h>
3984 __isl_give isl_stride_info *isl_set_get_stride_info(
3985 __isl_keep isl_set *set, int pos);
3986 __isl_give isl_val *isl_set_get_stride(
3987 __isl_keep isl_set *set, int pos);
3989 #include <isl/map.h>
3990 __isl_give isl_stride_info *
3991 isl_map_get_range_stride_info(
3992 __isl_keep isl_map *map, int pos);
3994 Check if the values of the given set dimension are equal to
3995 some affine expression of the other dimensions (the offset)
3996 modulo some integer stride or
3997 check if the values of the given output dimensions are equal to
3998 some affine expression of the input dimensions (the offset)
3999 modulo some integer stride.
4000 If no more specific information can be found, then the stride
4001 is taken to be one and the offset is taken to be the zero expression.
4002 The function C<isl_set_get_stride> performs the same
4003 computation as C<isl_set_get_stride_info> but only returns the stride.
4004 For the other functions,
4005 the stride and offset can be extracted from the returned object
4006 using the following functions.
4008 #include <isl/stride_info.h>
4009 __isl_give isl_val *isl_stride_info_get_stride(
4010 __isl_keep isl_stride_info *si);
4011 __isl_give isl_aff *isl_stride_info_get_offset(
4012 __isl_keep isl_stride_info *si);
4014 The stride info object can be released using the following function.
4016 #include <isl/stride_info.h>
4017 __isl_null isl_stride_info *isl_stride_info_free(
4018 __isl_take isl_stride_info *si);
4022 To check whether the description of a set, relation or function depends
4023 on one or more given dimensions,
4024 the following functions can be used.
4026 #include <isl/constraint.h>
4027 isl_bool isl_constraint_involves_dims(
4028 __isl_keep isl_constraint *constraint,
4029 enum isl_dim_type type, unsigned first, unsigned n);
4031 #include <isl/set.h>
4032 isl_bool isl_basic_set_involves_dims(
4033 __isl_keep isl_basic_set *bset,
4034 enum isl_dim_type type, unsigned first, unsigned n);
4035 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4036 enum isl_dim_type type, unsigned first, unsigned n);
4038 #include <isl/map.h>
4039 isl_bool isl_basic_map_involves_dims(
4040 __isl_keep isl_basic_map *bmap,
4041 enum isl_dim_type type, unsigned first, unsigned n);
4042 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4043 enum isl_dim_type type, unsigned first, unsigned n);
4045 #include <isl/union_map.h>
4046 isl_bool isl_union_map_involves_dims(
4047 __isl_keep isl_union_map *umap,
4048 enum isl_dim_type type, unsigned first, unsigned n);
4050 #include <isl/aff.h>
4051 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4052 enum isl_dim_type type, unsigned first, unsigned n);
4053 isl_bool isl_pw_aff_involves_dims(
4054 __isl_keep isl_pw_aff *pwaff,
4055 enum isl_dim_type type, unsigned first, unsigned n);
4056 isl_bool isl_multi_aff_involves_dims(
4057 __isl_keep isl_multi_aff *ma,
4058 enum isl_dim_type type, unsigned first, unsigned n);
4059 isl_bool isl_multi_pw_aff_involves_dims(
4060 __isl_keep isl_multi_pw_aff *mpa,
4061 enum isl_dim_type type, unsigned first, unsigned n);
4063 #include <isl/polynomial.h>
4064 isl_bool isl_qpolynomial_involves_dims(
4065 __isl_keep isl_qpolynomial *qp,
4066 enum isl_dim_type type, unsigned first, unsigned n);
4068 Similarly, the following functions can be used to check whether
4069 a given dimension is involved in any lower or upper bound.
4071 #include <isl/set.h>
4072 isl_bool isl_set_dim_has_any_lower_bound(
4073 __isl_keep isl_set *set,
4074 enum isl_dim_type type, unsigned pos);
4075 isl_bool isl_set_dim_has_any_upper_bound(
4076 __isl_keep isl_set *set,
4077 enum isl_dim_type type, unsigned pos);
4079 Note that these functions return true even if there is a bound on
4080 the dimension on only some of the basic sets of C<set>.
4081 To check if they have a bound for all of the basic sets in C<set>,
4082 use the following functions instead.
4084 #include <isl/set.h>
4085 isl_bool isl_set_dim_has_lower_bound(
4086 __isl_keep isl_set *set,
4087 enum isl_dim_type type, unsigned pos);
4088 isl_bool isl_set_dim_has_upper_bound(
4089 __isl_keep isl_set *set,
4090 enum isl_dim_type type, unsigned pos);
4094 To check whether a set is a parameter domain, use this function:
4096 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4097 isl_bool isl_union_set_is_params(
4098 __isl_keep isl_union_set *uset);
4102 The following functions check whether the space of the given
4103 (basic) set or relation domain and/or range is a wrapped relation.
4105 #include <isl/space.h>
4106 isl_bool isl_space_is_wrapping(
4107 __isl_keep isl_space *space);
4108 isl_bool isl_space_domain_is_wrapping(
4109 __isl_keep isl_space *space);
4110 isl_bool isl_space_range_is_wrapping(
4111 __isl_keep isl_space *space);
4112 isl_bool isl_space_is_product(
4113 __isl_keep isl_space *space);
4115 #include <isl/set.h>
4116 isl_bool isl_basic_set_is_wrapping(
4117 __isl_keep isl_basic_set *bset);
4118 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4120 #include <isl/map.h>
4121 isl_bool isl_map_domain_is_wrapping(
4122 __isl_keep isl_map *map);
4123 isl_bool isl_map_range_is_wrapping(
4124 __isl_keep isl_map *map);
4125 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4127 #include <isl/val.h>
4128 isl_bool isl_multi_val_range_is_wrapping(
4129 __isl_keep isl_multi_val *mv);
4131 #include <isl/aff.h>
4132 isl_bool isl_multi_aff_range_is_wrapping(
4133 __isl_keep isl_multi_aff *ma);
4134 isl_bool isl_multi_pw_aff_range_is_wrapping(
4135 __isl_keep isl_multi_pw_aff *mpa);
4136 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4137 __isl_keep isl_multi_union_pw_aff *mupa);
4139 The input to C<isl_space_is_wrapping> should
4140 be the space of a set, while that of
4141 C<isl_space_domain_is_wrapping> and
4142 C<isl_space_range_is_wrapping> should be the space of a relation.
4143 The input to C<isl_space_is_product> can be either the space
4144 of a set or that of a binary relation.
4145 In case the input is the space of a binary relation, it checks
4146 whether both domain and range are wrapping.
4148 =item * Internal Product
4150 isl_bool isl_basic_map_can_zip(
4151 __isl_keep isl_basic_map *bmap);
4152 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4154 Check whether the product of domain and range of the given relation
4156 i.e., whether both domain and range are nested relations.
4160 #include <isl/space.h>
4161 isl_bool isl_space_can_curry(
4162 __isl_keep isl_space *space);
4164 #include <isl/map.h>
4165 isl_bool isl_basic_map_can_curry(
4166 __isl_keep isl_basic_map *bmap);
4167 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4169 Check whether the domain of the (basic) relation is a wrapped relation.
4171 #include <isl/space.h>
4172 __isl_give isl_space *isl_space_uncurry(
4173 __isl_take isl_space *space);
4175 #include <isl/map.h>
4176 isl_bool isl_basic_map_can_uncurry(
4177 __isl_keep isl_basic_map *bmap);
4178 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4180 Check whether the range of the (basic) relation is a wrapped relation.
4182 #include <isl/space.h>
4183 isl_bool isl_space_can_range_curry(
4184 __isl_keep isl_space *space);
4186 #include <isl/map.h>
4187 isl_bool isl_map_can_range_curry(
4188 __isl_keep isl_map *map);
4190 Check whether the domain of the relation wrapped in the range of
4191 the input is itself a wrapped relation.
4193 =item * Special Values
4195 #include <isl/aff.h>
4196 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4197 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4198 isl_bool isl_multi_pw_aff_is_cst(
4199 __isl_keep isl_multi_pw_aff *mpa);
4201 Check whether the given expression is a constant.
4203 #include <isl/val.h>
4204 isl_bool isl_multi_val_involves_nan(
4205 __isl_keep isl_multi_val *mv);
4207 #include <isl/aff.h>
4208 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4209 isl_bool isl_multi_aff_involves_nan(
4210 __isl_keep isl_multi_aff *ma);
4211 isl_bool isl_pw_aff_involves_nan(
4212 __isl_keep isl_pw_aff *pa);
4213 isl_bool isl_pw_multi_aff_involves_nan(
4214 __isl_keep isl_pw_multi_aff *pma);
4215 isl_bool isl_multi_pw_aff_involves_nan(
4216 __isl_keep isl_multi_pw_aff *mpa);
4217 isl_bool isl_union_pw_aff_involves_nan(
4218 __isl_keep isl_union_pw_aff *upa);
4219 isl_bool isl_union_pw_multi_aff_involves_nan(
4220 __isl_keep isl_union_pw_multi_aff *upma);
4221 isl_bool isl_multi_union_pw_aff_involves_nan(
4222 __isl_keep isl_multi_union_pw_aff *mupa);
4224 #include <isl/polynomial.h>
4225 isl_bool isl_qpolynomial_is_nan(
4226 __isl_keep isl_qpolynomial *qp);
4227 isl_bool isl_qpolynomial_fold_is_nan(
4228 __isl_keep isl_qpolynomial_fold *fold);
4229 isl_bool isl_pw_qpolynomial_involves_nan(
4230 __isl_keep isl_pw_qpolynomial *pwqp);
4231 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4232 __isl_keep isl_pw_qpolynomial_fold *pwf);
4233 isl_bool isl_union_pw_qpolynomial_involves_nan(
4234 __isl_keep isl_union_pw_qpolynomial *upwqp);
4235 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4236 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4238 Check whether the given expression is equal to or involves NaN.
4240 #include <isl/aff.h>
4241 isl_bool isl_aff_plain_is_zero(
4242 __isl_keep isl_aff *aff);
4244 Check whether the affine expression is obviously zero.
4248 =head3 Binary Properties
4254 The following functions check whether two objects
4255 represent the same set, relation or function.
4256 The C<plain> variants only return true if the objects
4257 are obviously the same. That is, they may return false
4258 even if the objects are the same, but they will never
4259 return true if the objects are not the same.
4261 #include <isl/set.h>
4262 isl_bool isl_basic_set_plain_is_equal(
4263 __isl_keep isl_basic_set *bset1,
4264 __isl_keep isl_basic_set *bset2);
4265 isl_bool isl_basic_set_is_equal(
4266 __isl_keep isl_basic_set *bset1,
4267 __isl_keep isl_basic_set *bset2);
4268 isl_bool isl_set_plain_is_equal(
4269 __isl_keep isl_set *set1,
4270 __isl_keep isl_set *set2);
4271 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4272 __isl_keep isl_set *set2);
4274 #include <isl/map.h>
4275 isl_bool isl_basic_map_is_equal(
4276 __isl_keep isl_basic_map *bmap1,
4277 __isl_keep isl_basic_map *bmap2);
4278 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4279 __isl_keep isl_map *map2);
4280 isl_bool isl_map_plain_is_equal(
4281 __isl_keep isl_map *map1,
4282 __isl_keep isl_map *map2);
4284 #include <isl/union_set.h>
4285 isl_bool isl_union_set_is_equal(
4286 __isl_keep isl_union_set *uset1,
4287 __isl_keep isl_union_set *uset2);
4289 #include <isl/union_map.h>
4290 isl_bool isl_union_map_is_equal(
4291 __isl_keep isl_union_map *umap1,
4292 __isl_keep isl_union_map *umap2);
4294 #include <isl/aff.h>
4295 isl_bool isl_aff_plain_is_equal(
4296 __isl_keep isl_aff *aff1,
4297 __isl_keep isl_aff *aff2);
4298 isl_bool isl_multi_aff_plain_is_equal(
4299 __isl_keep isl_multi_aff *maff1,
4300 __isl_keep isl_multi_aff *maff2);
4301 isl_bool isl_pw_aff_plain_is_equal(
4302 __isl_keep isl_pw_aff *pwaff1,
4303 __isl_keep isl_pw_aff *pwaff2);
4304 isl_bool isl_pw_aff_is_equal(
4305 __isl_keep isl_pw_aff *pa1,
4306 __isl_keep isl_pw_aff *pa2);
4307 isl_bool isl_pw_multi_aff_plain_is_equal(
4308 __isl_keep isl_pw_multi_aff *pma1,
4309 __isl_keep isl_pw_multi_aff *pma2);
4310 isl_bool isl_pw_multi_aff_is_equal(
4311 __isl_keep isl_pw_multi_aff *pma1,
4312 __isl_keep isl_pw_multi_aff *pma2);
4313 isl_bool isl_multi_pw_aff_plain_is_equal(
4314 __isl_keep isl_multi_pw_aff *mpa1,
4315 __isl_keep isl_multi_pw_aff *mpa2);
4316 isl_bool isl_multi_pw_aff_is_equal(
4317 __isl_keep isl_multi_pw_aff *mpa1,
4318 __isl_keep isl_multi_pw_aff *mpa2);
4319 isl_bool isl_union_pw_aff_plain_is_equal(
4320 __isl_keep isl_union_pw_aff *upa1,
4321 __isl_keep isl_union_pw_aff *upa2);
4322 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4323 __isl_keep isl_union_pw_multi_aff *upma1,
4324 __isl_keep isl_union_pw_multi_aff *upma2);
4325 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4326 __isl_keep isl_multi_union_pw_aff *mupa1,
4327 __isl_keep isl_multi_union_pw_aff *mupa2);
4329 #include <isl/polynomial.h>
4330 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4331 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4332 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4333 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4334 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4335 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4337 =item * Disjointness
4339 #include <isl/set.h>
4340 isl_bool isl_basic_set_is_disjoint(
4341 __isl_keep isl_basic_set *bset1,
4342 __isl_keep isl_basic_set *bset2);
4343 isl_bool isl_set_plain_is_disjoint(
4344 __isl_keep isl_set *set1,
4345 __isl_keep isl_set *set2);
4346 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4347 __isl_keep isl_set *set2);
4349 #include <isl/map.h>
4350 isl_bool isl_basic_map_is_disjoint(
4351 __isl_keep isl_basic_map *bmap1,
4352 __isl_keep isl_basic_map *bmap2);
4353 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4354 __isl_keep isl_map *map2);
4356 #include <isl/union_set.h>
4357 isl_bool isl_union_set_is_disjoint(
4358 __isl_keep isl_union_set *uset1,
4359 __isl_keep isl_union_set *uset2);
4361 #include <isl/union_map.h>
4362 isl_bool isl_union_map_is_disjoint(
4363 __isl_keep isl_union_map *umap1,
4364 __isl_keep isl_union_map *umap2);
4368 isl_bool isl_basic_set_is_subset(
4369 __isl_keep isl_basic_set *bset1,
4370 __isl_keep isl_basic_set *bset2);
4371 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4372 __isl_keep isl_set *set2);
4373 isl_bool isl_set_is_strict_subset(
4374 __isl_keep isl_set *set1,
4375 __isl_keep isl_set *set2);
4376 isl_bool isl_union_set_is_subset(
4377 __isl_keep isl_union_set *uset1,
4378 __isl_keep isl_union_set *uset2);
4379 isl_bool isl_union_set_is_strict_subset(
4380 __isl_keep isl_union_set *uset1,
4381 __isl_keep isl_union_set *uset2);
4382 isl_bool isl_basic_map_is_subset(
4383 __isl_keep isl_basic_map *bmap1,
4384 __isl_keep isl_basic_map *bmap2);
4385 isl_bool isl_basic_map_is_strict_subset(
4386 __isl_keep isl_basic_map *bmap1,
4387 __isl_keep isl_basic_map *bmap2);
4388 isl_bool isl_map_is_subset(
4389 __isl_keep isl_map *map1,
4390 __isl_keep isl_map *map2);
4391 isl_bool isl_map_is_strict_subset(
4392 __isl_keep isl_map *map1,
4393 __isl_keep isl_map *map2);
4394 isl_bool isl_union_map_is_subset(
4395 __isl_keep isl_union_map *umap1,
4396 __isl_keep isl_union_map *umap2);
4397 isl_bool isl_union_map_is_strict_subset(
4398 __isl_keep isl_union_map *umap1,
4399 __isl_keep isl_union_map *umap2);
4401 Check whether the first argument is a (strict) subset of the
4406 Every comparison function returns a negative value if the first
4407 argument is considered smaller than the second, a positive value
4408 if the first argument is considered greater and zero if the two
4409 constraints are considered the same by the comparison criterion.
4411 #include <isl/constraint.h>
4412 int isl_constraint_plain_cmp(
4413 __isl_keep isl_constraint *c1,
4414 __isl_keep isl_constraint *c2);
4416 This function is useful for sorting C<isl_constraint>s.
4417 The order depends on the internal representation of the inputs.
4418 The order is fixed over different calls to the function (assuming
4419 the internal representation of the inputs has not changed), but may
4420 change over different versions of C<isl>.
4422 #include <isl/constraint.h>
4423 int isl_constraint_cmp_last_non_zero(
4424 __isl_keep isl_constraint *c1,
4425 __isl_keep isl_constraint *c2);
4427 This function can be used to sort constraints that live in the same
4428 local space. Constraints that involve ``earlier'' dimensions or
4429 that have a smaller coefficient for the shared latest dimension
4430 are considered smaller than other constraints.
4431 This function only defines a B<partial> order.
4433 #include <isl/set.h>
4434 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4435 __isl_keep isl_set *set2);
4437 This function is useful for sorting C<isl_set>s.
4438 The order depends on the internal representation of the inputs.
4439 The order is fixed over different calls to the function (assuming
4440 the internal representation of the inputs has not changed), but may
4441 change over different versions of C<isl>.
4443 #include <isl/aff.h>
4444 int isl_multi_aff_plain_cmp(
4445 __isl_keep isl_multi_aff *ma1,
4446 __isl_keep isl_multi_aff *ma2);
4447 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4448 __isl_keep isl_pw_aff *pa2);
4450 The functions C<isl_multi_aff_plain_cmp> and
4451 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4452 C<isl_pw_aff>s. The order is not strictly defined.
4453 The current order sorts expressions that only involve
4454 earlier dimensions before those that involve later dimensions.
4458 =head2 Unary Operations
4464 __isl_give isl_set *isl_set_complement(
4465 __isl_take isl_set *set);
4466 __isl_give isl_map *isl_map_complement(
4467 __isl_take isl_map *map);
4471 #include <isl/space.h>
4472 __isl_give isl_space *isl_space_reverse(
4473 __isl_take isl_space *space);
4475 #include <isl/map.h>
4476 __isl_give isl_basic_map *isl_basic_map_reverse(
4477 __isl_take isl_basic_map *bmap);
4478 __isl_give isl_map *isl_map_reverse(
4479 __isl_take isl_map *map);
4481 #include <isl/union_map.h>
4482 __isl_give isl_union_map *isl_union_map_reverse(
4483 __isl_take isl_union_map *umap);
4487 #include <isl/space.h>
4488 __isl_give isl_space *isl_space_domain(
4489 __isl_take isl_space *space);
4490 __isl_give isl_space *isl_space_range(
4491 __isl_take isl_space *space);
4492 __isl_give isl_space *isl_space_params(
4493 __isl_take isl_space *space);
4495 #include <isl/local_space.h>
4496 __isl_give isl_local_space *isl_local_space_domain(
4497 __isl_take isl_local_space *ls);
4498 __isl_give isl_local_space *isl_local_space_range(
4499 __isl_take isl_local_space *ls);
4501 #include <isl/set.h>
4502 __isl_give isl_basic_set *isl_basic_set_project_out(
4503 __isl_take isl_basic_set *bset,
4504 enum isl_dim_type type, unsigned first, unsigned n);
4505 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4506 enum isl_dim_type type, unsigned first, unsigned n);
4507 __isl_give isl_map *isl_set_project_onto_map(
4508 __isl_take isl_set *set,
4509 enum isl_dim_type type, unsigned first,
4511 __isl_give isl_basic_set *isl_basic_set_params(
4512 __isl_take isl_basic_set *bset);
4513 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4515 The function C<isl_set_project_onto_map> returns a relation
4516 that projects the input set onto the given set dimensions.
4518 #include <isl/map.h>
4519 __isl_give isl_basic_map *isl_basic_map_project_out(
4520 __isl_take isl_basic_map *bmap,
4521 enum isl_dim_type type, unsigned first, unsigned n);
4522 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4523 enum isl_dim_type type, unsigned first, unsigned n);
4524 __isl_give isl_basic_set *isl_basic_map_domain(
4525 __isl_take isl_basic_map *bmap);
4526 __isl_give isl_basic_set *isl_basic_map_range(
4527 __isl_take isl_basic_map *bmap);
4528 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4529 __isl_give isl_set *isl_map_domain(
4530 __isl_take isl_map *bmap);
4531 __isl_give isl_set *isl_map_range(
4532 __isl_take isl_map *map);
4534 #include <isl/union_set.h>
4535 __isl_give isl_union_set *isl_union_set_project_out(
4536 __isl_take isl_union_set *uset,
4537 enum isl_dim_type type,
4538 unsigned first, unsigned n);
4539 __isl_give isl_set *isl_union_set_params(
4540 __isl_take isl_union_set *uset);
4542 The function C<isl_union_set_project_out> can only project out
4545 #include <isl/union_map.h>
4546 __isl_give isl_union_map *isl_union_map_project_out(
4547 __isl_take isl_union_map *umap,
4548 enum isl_dim_type type, unsigned first, unsigned n);
4549 __isl_give isl_union_map *
4550 isl_union_map_project_out_all_params(
4551 __isl_take isl_union_map *umap);
4552 __isl_give isl_set *isl_union_map_params(
4553 __isl_take isl_union_map *umap);
4554 __isl_give isl_union_set *isl_union_map_domain(
4555 __isl_take isl_union_map *umap);
4556 __isl_give isl_union_set *isl_union_map_range(
4557 __isl_take isl_union_map *umap);
4559 The function C<isl_union_map_project_out> can only project out
4562 #include <isl/aff.h>
4563 __isl_give isl_aff *isl_aff_project_domain_on_params(
4564 __isl_take isl_aff *aff);
4565 __isl_give isl_multi_aff *
4566 isl_multi_aff_project_domain_on_params(
4567 __isl_take isl_multi_aff *ma);
4568 __isl_give isl_pw_aff *
4569 isl_pw_aff_project_domain_on_params(
4570 __isl_take isl_pw_aff *pa);
4571 __isl_give isl_multi_pw_aff *
4572 isl_multi_pw_aff_project_domain_on_params(
4573 __isl_take isl_multi_pw_aff *mpa);
4574 __isl_give isl_pw_multi_aff *
4575 isl_pw_multi_aff_project_domain_on_params(
4576 __isl_take isl_pw_multi_aff *pma);
4577 __isl_give isl_set *isl_pw_aff_domain(
4578 __isl_take isl_pw_aff *pwaff);
4579 __isl_give isl_set *isl_pw_multi_aff_domain(
4580 __isl_take isl_pw_multi_aff *pma);
4581 __isl_give isl_set *isl_multi_pw_aff_domain(
4582 __isl_take isl_multi_pw_aff *mpa);
4583 __isl_give isl_union_set *isl_union_pw_aff_domain(
4584 __isl_take isl_union_pw_aff *upa);
4585 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4586 __isl_take isl_union_pw_multi_aff *upma);
4587 __isl_give isl_union_set *
4588 isl_multi_union_pw_aff_domain(
4589 __isl_take isl_multi_union_pw_aff *mupa);
4590 __isl_give isl_set *isl_pw_aff_params(
4591 __isl_take isl_pw_aff *pwa);
4593 If no explicit domain was set on a zero-dimensional input to
4594 C<isl_multi_union_pw_aff_domain>, then this function will
4595 return a parameter set.
4597 #include <isl/polynomial.h>
4598 __isl_give isl_qpolynomial *
4599 isl_qpolynomial_project_domain_on_params(
4600 __isl_take isl_qpolynomial *qp);
4601 __isl_give isl_pw_qpolynomial *
4602 isl_pw_qpolynomial_project_domain_on_params(
4603 __isl_take isl_pw_qpolynomial *pwqp);
4604 __isl_give isl_pw_qpolynomial_fold *
4605 isl_pw_qpolynomial_fold_project_domain_on_params(
4606 __isl_take isl_pw_qpolynomial_fold *pwf);
4607 __isl_give isl_set *isl_pw_qpolynomial_domain(
4608 __isl_take isl_pw_qpolynomial *pwqp);
4609 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4610 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4611 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4612 __isl_take isl_union_pw_qpolynomial *upwqp);
4614 #include <isl/space.h>
4615 __isl_give isl_space *isl_space_domain_map(
4616 __isl_take isl_space *space);
4617 __isl_give isl_space *isl_space_range_map(
4618 __isl_take isl_space *space);
4620 #include <isl/map.h>
4621 __isl_give isl_map *isl_set_wrapped_domain_map(
4622 __isl_take isl_set *set);
4623 __isl_give isl_basic_map *isl_basic_map_domain_map(
4624 __isl_take isl_basic_map *bmap);
4625 __isl_give isl_basic_map *isl_basic_map_range_map(
4626 __isl_take isl_basic_map *bmap);
4627 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4628 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4630 #include <isl/union_map.h>
4631 __isl_give isl_union_map *isl_union_map_domain_map(
4632 __isl_take isl_union_map *umap);
4633 __isl_give isl_union_pw_multi_aff *
4634 isl_union_map_domain_map_union_pw_multi_aff(
4635 __isl_take isl_union_map *umap);
4636 __isl_give isl_union_map *isl_union_map_range_map(
4637 __isl_take isl_union_map *umap);
4638 __isl_give isl_union_map *
4639 isl_union_set_wrapped_domain_map(
4640 __isl_take isl_union_set *uset);
4642 The functions above construct a (basic, regular or union) relation
4643 that maps (a wrapped version of) the input relation to its domain or range.
4644 C<isl_set_wrapped_domain_map> maps the input set to the domain
4645 of its wrapped relation.
4649 __isl_give isl_basic_set *isl_basic_set_eliminate(
4650 __isl_take isl_basic_set *bset,
4651 enum isl_dim_type type,
4652 unsigned first, unsigned n);
4653 __isl_give isl_set *isl_set_eliminate(
4654 __isl_take isl_set *set, enum isl_dim_type type,
4655 unsigned first, unsigned n);
4656 __isl_give isl_basic_map *isl_basic_map_eliminate(
4657 __isl_take isl_basic_map *bmap,
4658 enum isl_dim_type type,
4659 unsigned first, unsigned n);
4660 __isl_give isl_map *isl_map_eliminate(
4661 __isl_take isl_map *map, enum isl_dim_type type,
4662 unsigned first, unsigned n);
4664 Eliminate the coefficients for the given dimensions from the constraints,
4665 without removing the dimensions.
4667 =item * Constructing a set from a parameter domain
4669 A zero-dimensional (local) space or (basic) set can be constructed
4670 on a given parameter domain using the following functions.
4672 #include <isl/space.h>
4673 __isl_give isl_space *isl_space_set_from_params(
4674 __isl_take isl_space *space);
4676 #include <isl/local_space.h>
4677 __isl_give isl_local_space *
4678 isl_local_space_set_from_params(
4679 __isl_take isl_local_space *ls);
4681 #include <isl/set.h>
4682 __isl_give isl_basic_set *isl_basic_set_from_params(
4683 __isl_take isl_basic_set *bset);
4684 __isl_give isl_set *isl_set_from_params(
4685 __isl_take isl_set *set);
4687 =item * Constructing a relation from one or two sets
4689 Create a relation with the given set(s) as domain and/or range.
4690 If only the domain or the range is specified, then
4691 the range or domain of the created relation is a zero-dimensional
4692 flat anonymous space.
4694 #include <isl/space.h>
4695 __isl_give isl_space *isl_space_from_domain(
4696 __isl_take isl_space *space);
4697 __isl_give isl_space *isl_space_from_range(
4698 __isl_take isl_space *space);
4699 __isl_give isl_space *isl_space_map_from_set(
4700 __isl_take isl_space *space);
4701 __isl_give isl_space *isl_space_map_from_domain_and_range(
4702 __isl_take isl_space *domain,
4703 __isl_take isl_space *range);
4705 #include <isl/local_space.h>
4706 __isl_give isl_local_space *isl_local_space_from_domain(
4707 __isl_take isl_local_space *ls);
4709 #include <isl/map.h>
4710 __isl_give isl_map *isl_map_from_domain(
4711 __isl_take isl_set *set);
4712 __isl_give isl_map *isl_map_from_range(
4713 __isl_take isl_set *set);
4715 #include <isl/union_map.h>
4716 __isl_give isl_union_map *isl_union_map_from_domain(
4717 __isl_take isl_union_set *uset);
4718 __isl_give isl_union_map *isl_union_map_from_range(
4719 __isl_take isl_union_set *uset);
4720 __isl_give isl_union_map *
4721 isl_union_map_from_domain_and_range(
4722 __isl_take isl_union_set *domain,
4723 __isl_take isl_union_set *range);
4725 #include <isl/val.h>
4726 __isl_give isl_multi_val *isl_multi_val_from_range(
4727 __isl_take isl_multi_val *mv);
4729 #include <isl/aff.h>
4730 __isl_give isl_aff *isl_aff_from_range(
4731 __isl_take isl_aff *aff);
4732 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4733 __isl_take isl_multi_aff *ma);
4734 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4735 __isl_take isl_pw_aff *pwa);
4736 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4737 __isl_take isl_multi_pw_aff *mpa);
4738 __isl_give isl_multi_union_pw_aff *
4739 isl_multi_union_pw_aff_from_range(
4740 __isl_take isl_multi_union_pw_aff *mupa);
4741 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4742 __isl_take isl_set *set);
4743 __isl_give isl_union_pw_multi_aff *
4744 isl_union_pw_multi_aff_from_domain(
4745 __isl_take isl_union_set *uset);
4747 #include <isl/polynomial.h>
4748 __isl_give isl_pw_qpolynomial *
4749 isl_pw_qpolynomial_from_range(
4750 __isl_take isl_pw_qpolynomial *pwqp);
4751 __isl_give isl_pw_qpolynomial_fold *
4752 isl_pw_qpolynomial_fold_from_range(
4753 __isl_take isl_pw_qpolynomial_fold *pwf);
4757 #include <isl/set.h>
4758 __isl_give isl_basic_set *isl_basic_set_fix_si(
4759 __isl_take isl_basic_set *bset,
4760 enum isl_dim_type type, unsigned pos, int value);
4761 __isl_give isl_basic_set *isl_basic_set_fix_val(
4762 __isl_take isl_basic_set *bset,
4763 enum isl_dim_type type, unsigned pos,
4764 __isl_take isl_val *v);
4765 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4766 enum isl_dim_type type, unsigned pos, int value);
4767 __isl_give isl_set *isl_set_fix_val(
4768 __isl_take isl_set *set,
4769 enum isl_dim_type type, unsigned pos,
4770 __isl_take isl_val *v);
4772 #include <isl/map.h>
4773 __isl_give isl_basic_map *isl_basic_map_fix_si(
4774 __isl_take isl_basic_map *bmap,
4775 enum isl_dim_type type, unsigned pos, int value);
4776 __isl_give isl_basic_map *isl_basic_map_fix_val(
4777 __isl_take isl_basic_map *bmap,
4778 enum isl_dim_type type, unsigned pos,
4779 __isl_take isl_val *v);
4780 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4781 enum isl_dim_type type, unsigned pos, int value);
4782 __isl_give isl_map *isl_map_fix_val(
4783 __isl_take isl_map *map,
4784 enum isl_dim_type type, unsigned pos,
4785 __isl_take isl_val *v);
4787 #include <isl/aff.h>
4788 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4789 __isl_take isl_pw_multi_aff *pma,
4790 enum isl_dim_type type, unsigned pos, int value);
4792 #include <isl/polynomial.h>
4793 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4794 __isl_take isl_pw_qpolynomial *pwqp,
4795 enum isl_dim_type type, unsigned n,
4796 __isl_take isl_val *v);
4797 __isl_give isl_pw_qpolynomial_fold *
4798 isl_pw_qpolynomial_fold_fix_val(
4799 __isl_take isl_pw_qpolynomial_fold *pwf,
4800 enum isl_dim_type type, unsigned n,
4801 __isl_take isl_val *v);
4803 Intersect the set, relation or function domain
4804 with the hyperplane where the given
4805 dimension has the fixed given value.
4807 #include <isl/set.h>
4808 __isl_give isl_basic_set *
4809 isl_basic_set_lower_bound_val(
4810 __isl_take isl_basic_set *bset,
4811 enum isl_dim_type type, unsigned pos,
4812 __isl_take isl_val *value);
4813 __isl_give isl_basic_set *
4814 isl_basic_set_upper_bound_val(
4815 __isl_take isl_basic_set *bset,
4816 enum isl_dim_type type, unsigned pos,
4817 __isl_take isl_val *value);
4818 __isl_give isl_set *isl_set_lower_bound_si(
4819 __isl_take isl_set *set,
4820 enum isl_dim_type type, unsigned pos, int value);
4821 __isl_give isl_set *isl_set_lower_bound_val(
4822 __isl_take isl_set *set,
4823 enum isl_dim_type type, unsigned pos,
4824 __isl_take isl_val *value);
4825 __isl_give isl_set *isl_set_upper_bound_si(
4826 __isl_take isl_set *set,
4827 enum isl_dim_type type, unsigned pos, int value);
4828 __isl_give isl_set *isl_set_upper_bound_val(
4829 __isl_take isl_set *set,
4830 enum isl_dim_type type, unsigned pos,
4831 __isl_take isl_val *value);
4833 #include <isl/map.h>
4834 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4835 __isl_take isl_basic_map *bmap,
4836 enum isl_dim_type type, unsigned pos, int value);
4837 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4838 __isl_take isl_basic_map *bmap,
4839 enum isl_dim_type type, unsigned pos, int value);
4840 __isl_give isl_map *isl_map_lower_bound_si(
4841 __isl_take isl_map *map,
4842 enum isl_dim_type type, unsigned pos, int value);
4843 __isl_give isl_map *isl_map_upper_bound_si(
4844 __isl_take isl_map *map,
4845 enum isl_dim_type type, unsigned pos, int value);
4847 Intersect the set or relation with the half-space where the given
4848 dimension has a value bounded by the fixed given integer value.
4850 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4851 enum isl_dim_type type1, int pos1,
4852 enum isl_dim_type type2, int pos2);
4853 __isl_give isl_basic_map *isl_basic_map_equate(
4854 __isl_take isl_basic_map *bmap,
4855 enum isl_dim_type type1, int pos1,
4856 enum isl_dim_type type2, int pos2);
4857 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4858 enum isl_dim_type type1, int pos1,
4859 enum isl_dim_type type2, int pos2);
4861 Intersect the set or relation with the hyperplane where the given
4862 dimensions are equal to each other.
4864 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4865 enum isl_dim_type type1, int pos1,
4866 enum isl_dim_type type2, int pos2);
4868 Intersect the relation with the hyperplane where the given
4869 dimensions have opposite values.
4871 __isl_give isl_map *isl_map_order_le(
4872 __isl_take isl_map *map,
4873 enum isl_dim_type type1, int pos1,
4874 enum isl_dim_type type2, int pos2);
4875 __isl_give isl_basic_map *isl_basic_map_order_ge(
4876 __isl_take isl_basic_map *bmap,
4877 enum isl_dim_type type1, int pos1,
4878 enum isl_dim_type type2, int pos2);
4879 __isl_give isl_map *isl_map_order_ge(
4880 __isl_take isl_map *map,
4881 enum isl_dim_type type1, int pos1,
4882 enum isl_dim_type type2, int pos2);
4883 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4884 enum isl_dim_type type1, int pos1,
4885 enum isl_dim_type type2, int pos2);
4886 __isl_give isl_basic_map *isl_basic_map_order_gt(
4887 __isl_take isl_basic_map *bmap,
4888 enum isl_dim_type type1, int pos1,
4889 enum isl_dim_type type2, int pos2);
4890 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4891 enum isl_dim_type type1, int pos1,
4892 enum isl_dim_type type2, int pos2);
4894 Intersect the relation with the half-space where the given
4895 dimensions satisfy the given ordering.
4897 #include <isl/union_set.h>
4898 __isl_give isl_union_map *isl_union_map_remove_map_if(
4899 __isl_take isl_union_map *umap,
4900 isl_bool (*fn)(__isl_keep isl_map *map,
4901 void *user), void *user);
4903 This function calls the callback function once for each
4904 pair of spaces for which there are elements in the input.
4905 If the callback returns C<isl_bool_true>, then all those elements
4906 are removed from the result. The only remaining elements in the output
4907 are then those for which the callback returns C<isl_bool_false>.
4911 #include <isl/aff.h>
4912 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4913 __isl_take isl_aff *aff);
4914 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4915 __isl_take isl_aff *aff);
4916 __isl_give isl_set *isl_pw_aff_pos_set(
4917 __isl_take isl_pw_aff *pa);
4918 __isl_give isl_set *isl_pw_aff_nonneg_set(
4919 __isl_take isl_pw_aff *pwaff);
4920 __isl_give isl_set *isl_pw_aff_zero_set(
4921 __isl_take isl_pw_aff *pwaff);
4922 __isl_give isl_set *isl_pw_aff_non_zero_set(
4923 __isl_take isl_pw_aff *pwaff);
4924 __isl_give isl_union_set *
4925 isl_union_pw_aff_zero_union_set(
4926 __isl_take isl_union_pw_aff *upa);
4927 __isl_give isl_union_set *
4928 isl_multi_union_pw_aff_zero_union_set(
4929 __isl_take isl_multi_union_pw_aff *mupa);
4931 The function C<isl_aff_neg_basic_set> returns a basic set
4932 containing those elements in the domain space
4933 of C<aff> where C<aff> is negative.
4934 The function C<isl_pw_aff_nonneg_set> returns a set
4935 containing those elements in the domain
4936 of C<pwaff> where C<pwaff> is non-negative.
4937 The function C<isl_multi_union_pw_aff_zero_union_set>
4938 returns a union set containing those elements
4939 in the domains of its elements where they are all zero.
4943 __isl_give isl_map *isl_set_identity(
4944 __isl_take isl_set *set);
4945 __isl_give isl_union_map *isl_union_set_identity(
4946 __isl_take isl_union_set *uset);
4947 __isl_give isl_union_pw_multi_aff *
4948 isl_union_set_identity_union_pw_multi_aff(
4949 __isl_take isl_union_set *uset);
4951 Construct an identity relation on the given (union) set.
4953 =item * Function Extraction
4955 A piecewise quasi affine expression that is equal to 1 on a set
4956 and 0 outside the set can be created using the following function.
4958 #include <isl/aff.h>
4959 __isl_give isl_pw_aff *isl_set_indicator_function(
4960 __isl_take isl_set *set);
4962 A piecewise multiple quasi affine expression can be extracted
4963 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4964 and the C<isl_map> is single-valued.
4965 In case of a conversion from an C<isl_union_map>
4966 to an C<isl_union_pw_multi_aff>, these properties need to hold
4967 in each domain space.
4968 A conversion to a C<isl_multi_union_pw_aff> additionally
4969 requires that the input is non-empty and involves only a single
4972 #include <isl/aff.h>
4973 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4974 __isl_take isl_set *set);
4975 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4976 __isl_take isl_map *map);
4978 __isl_give isl_union_pw_multi_aff *
4979 isl_union_pw_multi_aff_from_union_set(
4980 __isl_take isl_union_set *uset);
4981 __isl_give isl_union_pw_multi_aff *
4982 isl_union_pw_multi_aff_from_union_map(
4983 __isl_take isl_union_map *umap);
4985 __isl_give isl_multi_union_pw_aff *
4986 isl_multi_union_pw_aff_from_union_map(
4987 __isl_take isl_union_map *umap);
4991 __isl_give isl_basic_set *isl_basic_map_deltas(
4992 __isl_take isl_basic_map *bmap);
4993 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4994 __isl_give isl_union_set *isl_union_map_deltas(
4995 __isl_take isl_union_map *umap);
4997 These functions return a (basic) set containing the differences
4998 between image elements and corresponding domain elements in the input.
5000 __isl_give isl_basic_map *isl_basic_map_deltas_map(
5001 __isl_take isl_basic_map *bmap);
5002 __isl_give isl_map *isl_map_deltas_map(
5003 __isl_take isl_map *map);
5004 __isl_give isl_union_map *isl_union_map_deltas_map(
5005 __isl_take isl_union_map *umap);
5007 The functions above construct a (basic, regular or union) relation
5008 that maps (a wrapped version of) the input relation to its delta set.
5012 Simplify the representation of a set, relation or functions by trying
5013 to combine pairs of basic sets or relations into a single
5014 basic set or relation.
5016 #include <isl/set.h>
5017 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
5019 #include <isl/map.h>
5020 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5022 #include <isl/union_set.h>
5023 __isl_give isl_union_set *isl_union_set_coalesce(
5024 __isl_take isl_union_set *uset);
5026 #include <isl/union_map.h>
5027 __isl_give isl_union_map *isl_union_map_coalesce(
5028 __isl_take isl_union_map *umap);
5030 #include <isl/aff.h>
5031 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5032 __isl_take isl_pw_aff *pwqp);
5033 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5034 __isl_take isl_pw_multi_aff *pma);
5035 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5036 __isl_take isl_multi_pw_aff *mpa);
5037 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5038 __isl_take isl_union_pw_aff *upa);
5039 __isl_give isl_union_pw_multi_aff *
5040 isl_union_pw_multi_aff_coalesce(
5041 __isl_take isl_union_pw_multi_aff *upma);
5042 __isl_give isl_multi_union_pw_aff *
5043 isl_multi_union_pw_aff_coalesce(
5044 __isl_take isl_multi_union_pw_aff *aff);
5046 #include <isl/polynomial.h>
5047 __isl_give isl_pw_qpolynomial_fold *
5048 isl_pw_qpolynomial_fold_coalesce(
5049 __isl_take isl_pw_qpolynomial_fold *pwf);
5050 __isl_give isl_union_pw_qpolynomial *
5051 isl_union_pw_qpolynomial_coalesce(
5052 __isl_take isl_union_pw_qpolynomial *upwqp);
5053 __isl_give isl_union_pw_qpolynomial_fold *
5054 isl_union_pw_qpolynomial_fold_coalesce(
5055 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5057 One of the methods for combining pairs of basic sets or relations
5058 can result in coefficients that are much larger than those that appear
5059 in the constraints of the input. By default, the coefficients are
5060 not allowed to grow larger, but this can be changed by unsetting
5061 the following option.
5063 isl_stat isl_options_set_coalesce_bounded_wrapping(
5064 isl_ctx *ctx, int val);
5065 int isl_options_get_coalesce_bounded_wrapping(
5068 =item * Detecting equalities
5070 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5071 __isl_take isl_basic_set *bset);
5072 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5073 __isl_take isl_basic_map *bmap);
5074 __isl_give isl_set *isl_set_detect_equalities(
5075 __isl_take isl_set *set);
5076 __isl_give isl_map *isl_map_detect_equalities(
5077 __isl_take isl_map *map);
5078 __isl_give isl_union_set *isl_union_set_detect_equalities(
5079 __isl_take isl_union_set *uset);
5080 __isl_give isl_union_map *isl_union_map_detect_equalities(
5081 __isl_take isl_union_map *umap);
5083 Simplify the representation of a set or relation by detecting implicit
5086 =item * Removing redundant constraints
5088 #include <isl/set.h>
5089 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5090 __isl_take isl_basic_set *bset);
5091 __isl_give isl_set *isl_set_remove_redundancies(
5092 __isl_take isl_set *set);
5094 #include <isl/union_set.h>
5095 __isl_give isl_union_set *
5096 isl_union_set_remove_redundancies(
5097 __isl_take isl_union_set *uset);
5099 #include <isl/map.h>
5100 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5101 __isl_take isl_basic_map *bmap);
5102 __isl_give isl_map *isl_map_remove_redundancies(
5103 __isl_take isl_map *map);
5105 #include <isl/union_map.h>
5106 __isl_give isl_union_map *
5107 isl_union_map_remove_redundancies(
5108 __isl_take isl_union_map *umap);
5112 __isl_give isl_basic_set *isl_set_convex_hull(
5113 __isl_take isl_set *set);
5114 __isl_give isl_basic_map *isl_map_convex_hull(
5115 __isl_take isl_map *map);
5117 If the input set or relation has any existentially quantified
5118 variables, then the result of these operations is currently undefined.
5122 #include <isl/set.h>
5123 __isl_give isl_basic_set *
5124 isl_set_unshifted_simple_hull(
5125 __isl_take isl_set *set);
5126 __isl_give isl_basic_set *isl_set_simple_hull(
5127 __isl_take isl_set *set);
5128 __isl_give isl_basic_set *
5129 isl_set_plain_unshifted_simple_hull(
5130 __isl_take isl_set *set);
5131 __isl_give isl_basic_set *
5132 isl_set_unshifted_simple_hull_from_set_list(
5133 __isl_take isl_set *set,
5134 __isl_take isl_set_list *list);
5136 #include <isl/map.h>
5137 __isl_give isl_basic_map *
5138 isl_map_unshifted_simple_hull(
5139 __isl_take isl_map *map);
5140 __isl_give isl_basic_map *isl_map_simple_hull(
5141 __isl_take isl_map *map);
5142 __isl_give isl_basic_map *
5143 isl_map_plain_unshifted_simple_hull(
5144 __isl_take isl_map *map);
5145 __isl_give isl_basic_map *
5146 isl_map_unshifted_simple_hull_from_map_list(
5147 __isl_take isl_map *map,
5148 __isl_take isl_map_list *list);
5150 #include <isl/union_map.h>
5151 __isl_give isl_union_map *isl_union_map_simple_hull(
5152 __isl_take isl_union_map *umap);
5154 These functions compute a single basic set or relation
5155 that contains the whole input set or relation.
5156 In particular, the output is described by translates
5157 of the constraints describing the basic sets or relations in the input.
5158 In case of C<isl_set_unshifted_simple_hull>, only the original
5159 constraints are used, without any translation.
5160 In case of C<isl_set_plain_unshifted_simple_hull> and
5161 C<isl_map_plain_unshifted_simple_hull>, the result is described
5162 by original constraints that are obviously satisfied
5163 by the entire input set or relation.
5164 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5165 C<isl_map_unshifted_simple_hull_from_map_list>, the
5166 constraints are taken from the elements of the second argument.
5170 (See \autoref{s:simple hull}.)
5176 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5177 __isl_take isl_basic_set *bset);
5178 __isl_give isl_basic_set *isl_set_affine_hull(
5179 __isl_take isl_set *set);
5180 __isl_give isl_union_set *isl_union_set_affine_hull(
5181 __isl_take isl_union_set *uset);
5182 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5183 __isl_take isl_basic_map *bmap);
5184 __isl_give isl_basic_map *isl_map_affine_hull(
5185 __isl_take isl_map *map);
5186 __isl_give isl_union_map *isl_union_map_affine_hull(
5187 __isl_take isl_union_map *umap);
5189 In case of union sets and relations, the affine hull is computed
5192 =item * Polyhedral hull
5194 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5195 __isl_take isl_set *set);
5196 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5197 __isl_take isl_map *map);
5198 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5199 __isl_take isl_union_set *uset);
5200 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5201 __isl_take isl_union_map *umap);
5203 These functions compute a single basic set or relation
5204 not involving any existentially quantified variables
5205 that contains the whole input set or relation.
5206 In case of union sets and relations, the polyhedral hull is computed
5209 =item * Other approximations
5211 #include <isl/set.h>
5212 __isl_give isl_basic_set *
5213 isl_basic_set_drop_constraints_involving_dims(
5214 __isl_take isl_basic_set *bset,
5215 enum isl_dim_type type,
5216 unsigned first, unsigned n);
5217 __isl_give isl_basic_set *
5218 isl_basic_set_drop_constraints_not_involving_dims(
5219 __isl_take isl_basic_set *bset,
5220 enum isl_dim_type type,
5221 unsigned first, unsigned n);
5222 __isl_give isl_set *
5223 isl_set_drop_constraints_involving_dims(
5224 __isl_take isl_set *set,
5225 enum isl_dim_type type,
5226 unsigned first, unsigned n);
5227 __isl_give isl_set *
5228 isl_set_drop_constraints_not_involving_dims(
5229 __isl_take isl_set *set,
5230 enum isl_dim_type type,
5231 unsigned first, unsigned n);
5233 #include <isl/map.h>
5234 __isl_give isl_basic_map *
5235 isl_basic_map_drop_constraints_involving_dims(
5236 __isl_take isl_basic_map *bmap,
5237 enum isl_dim_type type,
5238 unsigned first, unsigned n);
5239 __isl_give isl_basic_map *
5240 isl_basic_map_drop_constraints_not_involving_dims(
5241 __isl_take isl_basic_map *bmap,
5242 enum isl_dim_type type,
5243 unsigned first, unsigned n);
5244 __isl_give isl_map *
5245 isl_map_drop_constraints_involving_dims(
5246 __isl_take isl_map *map,
5247 enum isl_dim_type type,
5248 unsigned first, unsigned n);
5249 __isl_give isl_map *
5250 isl_map_drop_constraints_not_involving_dims(
5251 __isl_take isl_map *map,
5252 enum isl_dim_type type,
5253 unsigned first, unsigned n);
5255 These functions drop any constraints (not) involving the specified dimensions.
5256 Note that the result depends on the representation of the input.
5258 #include <isl/polynomial.h>
5259 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5260 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5261 __isl_give isl_union_pw_qpolynomial *
5262 isl_union_pw_qpolynomial_to_polynomial(
5263 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5265 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5266 the polynomial will be an overapproximation. If C<sign> is negative,
5267 it will be an underapproximation. If C<sign> is zero, the approximation
5268 will lie somewhere in between.
5272 __isl_give isl_basic_set *isl_basic_set_sample(
5273 __isl_take isl_basic_set *bset);
5274 __isl_give isl_basic_set *isl_set_sample(
5275 __isl_take isl_set *set);
5276 __isl_give isl_basic_map *isl_basic_map_sample(
5277 __isl_take isl_basic_map *bmap);
5278 __isl_give isl_basic_map *isl_map_sample(
5279 __isl_take isl_map *map);
5281 If the input (basic) set or relation is non-empty, then return
5282 a singleton subset of the input. Otherwise, return an empty set.
5284 =item * Optimization
5286 #include <isl/ilp.h>
5287 __isl_give isl_val *isl_basic_set_max_val(
5288 __isl_keep isl_basic_set *bset,
5289 __isl_keep isl_aff *obj);
5290 __isl_give isl_val *isl_set_min_val(
5291 __isl_keep isl_set *set,
5292 __isl_keep isl_aff *obj);
5293 __isl_give isl_val *isl_set_max_val(
5294 __isl_keep isl_set *set,
5295 __isl_keep isl_aff *obj);
5296 __isl_give isl_multi_val *
5297 isl_union_set_min_multi_union_pw_aff(
5298 __isl_keep isl_union_set *set,
5299 __isl_keep isl_multi_union_pw_aff *obj);
5301 Compute the minimum or maximum of the integer affine expression C<obj>
5302 over the points in C<set>, returning the result in C<opt>.
5303 The result is C<NULL> in case of an error, the optimal value in case
5304 there is one, negative infinity or infinity if the problem is unbounded and
5305 NaN if the problem is empty.
5307 #include <isl/ilp.h>
5308 __isl_give isl_val *isl_basic_set_dim_max_val(
5309 __isl_take isl_basic_set *bset, int pos);
5311 Return the maximal value attained by the given set dimension,
5312 independently of the parameter values and of any other dimensions.
5313 The result is C<NULL> in case of an error, the optimal value in case
5314 there is one, infinity if the problem is unbounded and
5315 NaN if the input is empty.
5317 =item * Parametric optimization
5319 __isl_give isl_pw_aff *isl_set_dim_min(
5320 __isl_take isl_set *set, int pos);
5321 __isl_give isl_pw_aff *isl_set_dim_max(
5322 __isl_take isl_set *set, int pos);
5323 __isl_give isl_pw_aff *isl_map_dim_min(
5324 __isl_take isl_map *map, int pos);
5325 __isl_give isl_pw_aff *isl_map_dim_max(
5326 __isl_take isl_map *map, int pos);
5328 Compute the minimum or maximum of the given set or output dimension
5329 as a function of the parameters (and input dimensions), but independently
5330 of the other set or output dimensions.
5331 For lexicographic optimization, see L<"Lexicographic Optimization">.
5335 The following functions compute either the set of (rational) coefficient
5336 values of valid constraints for the given set or the set of (rational)
5337 values satisfying the constraints with coefficients from the given set.
5338 Internally, these two sets of functions perform essentially the
5339 same operations, except that the set of coefficients is assumed to
5340 be a cone, while the set of values may be any polyhedron.
5341 The current implementation is based on the Farkas lemma and
5342 Fourier-Motzkin elimination, but this may change or be made optional
5343 in future. In particular, future implementations may use different
5344 dualization algorithms or skip the elimination step.
5346 #include <isl/set.h>
5347 __isl_give isl_basic_set *isl_basic_set_coefficients(
5348 __isl_take isl_basic_set *bset);
5349 __isl_give isl_basic_set_list *
5350 isl_basic_set_list_coefficients(
5351 __isl_take isl_basic_set_list *list);
5352 __isl_give isl_basic_set *isl_set_coefficients(
5353 __isl_take isl_set *set);
5354 __isl_give isl_union_set *isl_union_set_coefficients(
5355 __isl_take isl_union_set *bset);
5356 __isl_give isl_basic_set *isl_basic_set_solutions(
5357 __isl_take isl_basic_set *bset);
5358 __isl_give isl_basic_set *isl_set_solutions(
5359 __isl_take isl_set *set);
5360 __isl_give isl_union_set *isl_union_set_solutions(
5361 __isl_take isl_union_set *bset);
5365 __isl_give isl_map *isl_map_fixed_power_val(
5366 __isl_take isl_map *map,
5367 __isl_take isl_val *exp);
5368 __isl_give isl_union_map *
5369 isl_union_map_fixed_power_val(
5370 __isl_take isl_union_map *umap,
5371 __isl_take isl_val *exp);
5373 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5374 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5375 of C<map> is computed.
5377 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5379 __isl_give isl_union_map *isl_union_map_power(
5380 __isl_take isl_union_map *umap, int *exact);
5382 Compute a parametric representation for all positive powers I<k> of C<map>.
5383 The result maps I<k> to a nested relation corresponding to the
5384 I<k>th power of C<map>.
5385 The result may be an overapproximation. If the result is known to be exact,
5386 then C<*exact> is set to C<1>.
5388 =item * Transitive closure
5390 __isl_give isl_map *isl_map_transitive_closure(
5391 __isl_take isl_map *map, int *exact);
5392 __isl_give isl_union_map *isl_union_map_transitive_closure(
5393 __isl_take isl_union_map *umap, int *exact);
5395 Compute the transitive closure of C<map>.
5396 The result may be an overapproximation. If the result is known to be exact,
5397 then C<*exact> is set to C<1>.
5399 =item * Reaching path lengths
5401 __isl_give isl_map *isl_map_reaching_path_lengths(
5402 __isl_take isl_map *map, int *exact);
5404 Compute a relation that maps each element in the range of C<map>
5405 to the lengths of all paths composed of edges in C<map> that
5406 end up in the given element.
5407 The result may be an overapproximation. If the result is known to be exact,
5408 then C<*exact> is set to C<1>.
5409 To compute the I<maximal> path length, the resulting relation
5410 should be postprocessed by C<isl_map_lexmax>.
5411 In particular, if the input relation is a dependence relation
5412 (mapping sources to sinks), then the maximal path length corresponds
5413 to the free schedule.
5414 Note, however, that C<isl_map_lexmax> expects the maximum to be
5415 finite, so if the path lengths are unbounded (possibly due to
5416 the overapproximation), then you will get an error message.
5420 #include <isl/space.h>
5421 __isl_give isl_space *isl_space_wrap(
5422 __isl_take isl_space *space);
5423 __isl_give isl_space *isl_space_unwrap(
5424 __isl_take isl_space *space);
5426 #include <isl/local_space.h>
5427 __isl_give isl_local_space *isl_local_space_wrap(
5428 __isl_take isl_local_space *ls);
5430 #include <isl/set.h>
5431 __isl_give isl_basic_map *isl_basic_set_unwrap(
5432 __isl_take isl_basic_set *bset);
5433 __isl_give isl_map *isl_set_unwrap(
5434 __isl_take isl_set *set);
5436 #include <isl/map.h>
5437 __isl_give isl_basic_set *isl_basic_map_wrap(
5438 __isl_take isl_basic_map *bmap);
5439 __isl_give isl_set *isl_map_wrap(
5440 __isl_take isl_map *map);
5442 #include <isl/union_set.h>
5443 __isl_give isl_union_map *isl_union_set_unwrap(
5444 __isl_take isl_union_set *uset);
5446 #include <isl/union_map.h>
5447 __isl_give isl_union_set *isl_union_map_wrap(
5448 __isl_take isl_union_map *umap);
5450 The input to C<isl_space_unwrap> should
5451 be the space of a set, while that of
5452 C<isl_space_wrap> should be the space of a relation.
5453 Conversely, the output of C<isl_space_unwrap> is the space
5454 of a relation, while that of C<isl_space_wrap> is the space of a set.
5458 Remove any internal structure of domain (and range) of the given
5459 set or relation. If there is any such internal structure in the input,
5460 then the name of the space is also removed.
5462 #include <isl/space.h>
5463 __isl_give isl_space *isl_space_flatten_domain(
5464 __isl_take isl_space *space);
5465 __isl_give isl_space *isl_space_flatten_range(
5466 __isl_take isl_space *space);
5468 #include <isl/local_space.h>
5469 __isl_give isl_local_space *
5470 isl_local_space_flatten_domain(
5471 __isl_take isl_local_space *ls);
5472 __isl_give isl_local_space *
5473 isl_local_space_flatten_range(
5474 __isl_take isl_local_space *ls);
5476 #include <isl/set.h>
5477 __isl_give isl_basic_set *isl_basic_set_flatten(
5478 __isl_take isl_basic_set *bset);
5479 __isl_give isl_set *isl_set_flatten(
5480 __isl_take isl_set *set);
5482 #include <isl/map.h>
5483 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5484 __isl_take isl_basic_map *bmap);
5485 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5486 __isl_take isl_basic_map *bmap);
5487 __isl_give isl_map *isl_map_flatten_range(
5488 __isl_take isl_map *map);
5489 __isl_give isl_map *isl_map_flatten_domain(
5490 __isl_take isl_map *map);
5491 __isl_give isl_basic_map *isl_basic_map_flatten(
5492 __isl_take isl_basic_map *bmap);
5493 __isl_give isl_map *isl_map_flatten(
5494 __isl_take isl_map *map);
5496 #include <isl/val.h>
5497 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5498 __isl_take isl_multi_val *mv);
5500 #include <isl/aff.h>
5501 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5502 __isl_take isl_multi_aff *ma);
5503 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5504 __isl_take isl_multi_aff *ma);
5505 __isl_give isl_multi_pw_aff *
5506 isl_multi_pw_aff_flatten_range(
5507 __isl_take isl_multi_pw_aff *mpa);
5508 __isl_give isl_multi_union_pw_aff *
5509 isl_multi_union_pw_aff_flatten_range(
5510 __isl_take isl_multi_union_pw_aff *mupa);
5512 #include <isl/map.h>
5513 __isl_give isl_map *isl_set_flatten_map(
5514 __isl_take isl_set *set);
5516 The function above constructs a relation
5517 that maps the input set to a flattened version of the set.
5521 Lift the input set to a space with extra dimensions corresponding
5522 to the existentially quantified variables in the input.
5523 In particular, the result lives in a wrapped map where the domain
5524 is the original space and the range corresponds to the original
5525 existentially quantified variables.
5527 #include <isl/set.h>
5528 __isl_give isl_basic_set *isl_basic_set_lift(
5529 __isl_take isl_basic_set *bset);
5530 __isl_give isl_set *isl_set_lift(
5531 __isl_take isl_set *set);
5532 __isl_give isl_union_set *isl_union_set_lift(
5533 __isl_take isl_union_set *uset);
5535 Given a local space that contains the existentially quantified
5536 variables of a set, a basic relation that, when applied to
5537 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5538 can be constructed using the following function.
5540 #include <isl/local_space.h>
5541 __isl_give isl_basic_map *isl_local_space_lifting(
5542 __isl_take isl_local_space *ls);
5544 #include <isl/aff.h>
5545 __isl_give isl_multi_aff *isl_multi_aff_lift(
5546 __isl_take isl_multi_aff *maff,
5547 __isl_give isl_local_space **ls);
5549 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5550 then it is assigned the local space that lies at the basis of
5551 the lifting applied.
5553 =item * Internal Product
5555 #include <isl/space.h>
5556 __isl_give isl_space *isl_space_zip(
5557 __isl_take isl_space *space);
5559 #include <isl/map.h>
5560 __isl_give isl_basic_map *isl_basic_map_zip(
5561 __isl_take isl_basic_map *bmap);
5562 __isl_give isl_map *isl_map_zip(
5563 __isl_take isl_map *map);
5565 #include <isl/union_map.h>
5566 __isl_give isl_union_map *isl_union_map_zip(
5567 __isl_take isl_union_map *umap);
5569 Given a relation with nested relations for domain and range,
5570 interchange the range of the domain with the domain of the range.
5574 #include <isl/space.h>
5575 __isl_give isl_space *isl_space_curry(
5576 __isl_take isl_space *space);
5577 __isl_give isl_space *isl_space_uncurry(
5578 __isl_take isl_space *space);
5580 #include <isl/map.h>
5581 __isl_give isl_basic_map *isl_basic_map_curry(
5582 __isl_take isl_basic_map *bmap);
5583 __isl_give isl_basic_map *isl_basic_map_uncurry(
5584 __isl_take isl_basic_map *bmap);
5585 __isl_give isl_map *isl_map_curry(
5586 __isl_take isl_map *map);
5587 __isl_give isl_map *isl_map_uncurry(
5588 __isl_take isl_map *map);
5590 #include <isl/union_map.h>
5591 __isl_give isl_union_map *isl_union_map_curry(
5592 __isl_take isl_union_map *umap);
5593 __isl_give isl_union_map *isl_union_map_uncurry(
5594 __isl_take isl_union_map *umap);
5596 Given a relation with a nested relation for domain,
5597 the C<curry> functions
5598 move the range of the nested relation out of the domain
5599 and use it as the domain of a nested relation in the range,
5600 with the original range as range of this nested relation.
5601 The C<uncurry> functions perform the inverse operation.
5603 #include <isl/space.h>
5604 __isl_give isl_space *isl_space_range_curry(
5605 __isl_take isl_space *space);
5607 #include <isl/map.h>
5608 __isl_give isl_map *isl_map_range_curry(
5609 __isl_take isl_map *map);
5611 #include <isl/union_map.h>
5612 __isl_give isl_union_map *isl_union_map_range_curry(
5613 __isl_take isl_union_map *umap);
5615 These functions apply the currying to the relation that
5616 is nested inside the range of the input.
5618 =item * Aligning parameters
5620 Change the order of the parameters of the given set, relation
5622 such that the first parameters match those of C<model>.
5623 This may involve the introduction of extra parameters.
5624 All parameters need to be named.
5626 #include <isl/space.h>
5627 __isl_give isl_space *isl_space_align_params(
5628 __isl_take isl_space *space1,
5629 __isl_take isl_space *space2)
5631 #include <isl/set.h>
5632 __isl_give isl_basic_set *isl_basic_set_align_params(
5633 __isl_take isl_basic_set *bset,
5634 __isl_take isl_space *model);
5635 __isl_give isl_set *isl_set_align_params(
5636 __isl_take isl_set *set,
5637 __isl_take isl_space *model);
5639 #include <isl/map.h>
5640 __isl_give isl_basic_map *isl_basic_map_align_params(
5641 __isl_take isl_basic_map *bmap,
5642 __isl_take isl_space *model);
5643 __isl_give isl_map *isl_map_align_params(
5644 __isl_take isl_map *map,
5645 __isl_take isl_space *model);
5647 #include <isl/val.h>
5648 __isl_give isl_multi_val *isl_multi_val_align_params(
5649 __isl_take isl_multi_val *mv,
5650 __isl_take isl_space *model);
5652 #include <isl/aff.h>
5653 __isl_give isl_aff *isl_aff_align_params(
5654 __isl_take isl_aff *aff,
5655 __isl_take isl_space *model);
5656 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5657 __isl_take isl_multi_aff *multi,
5658 __isl_take isl_space *model);
5659 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5660 __isl_take isl_pw_aff *pwaff,
5661 __isl_take isl_space *model);
5662 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5663 __isl_take isl_pw_multi_aff *pma,
5664 __isl_take isl_space *model);
5665 __isl_give isl_union_pw_aff *
5666 isl_union_pw_aff_align_params(
5667 __isl_take isl_union_pw_aff *upa,
5668 __isl_take isl_space *model);
5669 __isl_give isl_union_pw_multi_aff *
5670 isl_union_pw_multi_aff_align_params(
5671 __isl_take isl_union_pw_multi_aff *upma,
5672 __isl_take isl_space *model);
5673 __isl_give isl_multi_union_pw_aff *
5674 isl_multi_union_pw_aff_align_params(
5675 __isl_take isl_multi_union_pw_aff *mupa,
5676 __isl_take isl_space *model);
5678 #include <isl/polynomial.h>
5679 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5680 __isl_take isl_qpolynomial *qp,
5681 __isl_take isl_space *model);
5683 =item * Unary Arithmetic Operations
5685 #include <isl/set.h>
5686 __isl_give isl_set *isl_set_neg(
5687 __isl_take isl_set *set);
5688 #include <isl/map.h>
5689 __isl_give isl_map *isl_map_neg(
5690 __isl_take isl_map *map);
5692 C<isl_set_neg> constructs a set containing the opposites of
5693 the elements in its argument.
5694 The domain of the result of C<isl_map_neg> is the same
5695 as the domain of its argument. The corresponding range
5696 elements are the opposites of the corresponding range
5697 elements in the argument.
5699 #include <isl/val.h>
5700 __isl_give isl_multi_val *isl_multi_val_neg(
5701 __isl_take isl_multi_val *mv);
5703 #include <isl/aff.h>
5704 __isl_give isl_aff *isl_aff_neg(
5705 __isl_take isl_aff *aff);
5706 __isl_give isl_multi_aff *isl_multi_aff_neg(
5707 __isl_take isl_multi_aff *ma);
5708 __isl_give isl_pw_aff *isl_pw_aff_neg(
5709 __isl_take isl_pw_aff *pwaff);
5710 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5711 __isl_take isl_pw_multi_aff *pma);
5712 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5713 __isl_take isl_multi_pw_aff *mpa);
5714 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5715 __isl_take isl_union_pw_aff *upa);
5716 __isl_give isl_union_pw_multi_aff *
5717 isl_union_pw_multi_aff_neg(
5718 __isl_take isl_union_pw_multi_aff *upma);
5719 __isl_give isl_multi_union_pw_aff *
5720 isl_multi_union_pw_aff_neg(
5721 __isl_take isl_multi_union_pw_aff *mupa);
5722 __isl_give isl_aff *isl_aff_ceil(
5723 __isl_take isl_aff *aff);
5724 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5725 __isl_take isl_pw_aff *pwaff);
5726 __isl_give isl_aff *isl_aff_floor(
5727 __isl_take isl_aff *aff);
5728 __isl_give isl_multi_aff *isl_multi_aff_floor(
5729 __isl_take isl_multi_aff *ma);
5730 __isl_give isl_pw_aff *isl_pw_aff_floor(
5731 __isl_take isl_pw_aff *pwaff);
5732 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5733 __isl_take isl_union_pw_aff *upa);
5734 __isl_give isl_multi_union_pw_aff *
5735 isl_multi_union_pw_aff_floor(
5736 __isl_take isl_multi_union_pw_aff *mupa);
5738 #include <isl/aff.h>
5739 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5740 __isl_take isl_pw_aff_list *list);
5741 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5742 __isl_take isl_pw_aff_list *list);
5744 #include <isl/polynomial.h>
5745 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5746 __isl_take isl_qpolynomial *qp);
5747 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5748 __isl_take isl_pw_qpolynomial *pwqp);
5749 __isl_give isl_union_pw_qpolynomial *
5750 isl_union_pw_qpolynomial_neg(
5751 __isl_take isl_union_pw_qpolynomial *upwqp);
5752 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5753 __isl_take isl_qpolynomial *qp,
5755 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5756 __isl_take isl_pw_qpolynomial *pwqp,
5761 The following functions evaluate a function in a point.
5763 #include <isl/aff.h>
5764 __isl_give isl_val *isl_aff_eval(
5765 __isl_take isl_aff *aff,
5766 __isl_take isl_point *pnt);
5767 __isl_give isl_val *isl_pw_aff_eval(
5768 __isl_take isl_pw_aff *pa,
5769 __isl_take isl_point *pnt);
5771 #include <isl/polynomial.h>
5772 __isl_give isl_val *isl_pw_qpolynomial_eval(
5773 __isl_take isl_pw_qpolynomial *pwqp,
5774 __isl_take isl_point *pnt);
5775 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5776 __isl_take isl_pw_qpolynomial_fold *pwf,
5777 __isl_take isl_point *pnt);
5778 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5779 __isl_take isl_union_pw_qpolynomial *upwqp,
5780 __isl_take isl_point *pnt);
5781 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5782 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5783 __isl_take isl_point *pnt);
5785 These functions return NaN when evaluated at a void point.
5786 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
5787 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
5788 when the function is evaluated outside its explicit domain.
5790 =item * Dimension manipulation
5792 It is usually not advisable to directly change the (input or output)
5793 space of a set or a relation as this removes the name and the internal
5794 structure of the space. However, the functions below can be useful
5795 to add new parameters, assuming
5796 C<isl_set_align_params> and C<isl_map_align_params>
5799 #include <isl/space.h>
5800 __isl_give isl_space *isl_space_add_dims(
5801 __isl_take isl_space *space,
5802 enum isl_dim_type type, unsigned n);
5803 __isl_give isl_space *isl_space_insert_dims(
5804 __isl_take isl_space *space,
5805 enum isl_dim_type type, unsigned pos, unsigned n);
5806 __isl_give isl_space *isl_space_drop_dims(
5807 __isl_take isl_space *space,
5808 enum isl_dim_type type, unsigned first, unsigned n);
5809 __isl_give isl_space *isl_space_move_dims(
5810 __isl_take isl_space *space,
5811 enum isl_dim_type dst_type, unsigned dst_pos,
5812 enum isl_dim_type src_type, unsigned src_pos,
5815 #include <isl/local_space.h>
5816 __isl_give isl_local_space *isl_local_space_add_dims(
5817 __isl_take isl_local_space *ls,
5818 enum isl_dim_type type, unsigned n);
5819 __isl_give isl_local_space *isl_local_space_insert_dims(
5820 __isl_take isl_local_space *ls,
5821 enum isl_dim_type type, unsigned first, unsigned n);
5822 __isl_give isl_local_space *isl_local_space_drop_dims(
5823 __isl_take isl_local_space *ls,
5824 enum isl_dim_type type, unsigned first, unsigned n);
5826 #include <isl/set.h>
5827 __isl_give isl_basic_set *isl_basic_set_add_dims(
5828 __isl_take isl_basic_set *bset,
5829 enum isl_dim_type type, unsigned n);
5830 __isl_give isl_set *isl_set_add_dims(
5831 __isl_take isl_set *set,
5832 enum isl_dim_type type, unsigned n);
5833 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5834 __isl_take isl_basic_set *bset,
5835 enum isl_dim_type type, unsigned pos,
5837 __isl_give isl_set *isl_set_insert_dims(
5838 __isl_take isl_set *set,
5839 enum isl_dim_type type, unsigned pos, unsigned n);
5840 __isl_give isl_basic_set *isl_basic_set_move_dims(
5841 __isl_take isl_basic_set *bset,
5842 enum isl_dim_type dst_type, unsigned dst_pos,
5843 enum isl_dim_type src_type, unsigned src_pos,
5845 __isl_give isl_set *isl_set_move_dims(
5846 __isl_take isl_set *set,
5847 enum isl_dim_type dst_type, unsigned dst_pos,
5848 enum isl_dim_type src_type, unsigned src_pos,
5851 #include <isl/map.h>
5852 __isl_give isl_basic_map *isl_basic_map_add_dims(
5853 __isl_take isl_basic_map *bmap,
5854 enum isl_dim_type type, unsigned n);
5855 __isl_give isl_map *isl_map_add_dims(
5856 __isl_take isl_map *map,
5857 enum isl_dim_type type, unsigned n);
5858 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5859 __isl_take isl_basic_map *bmap,
5860 enum isl_dim_type type, unsigned pos,
5862 __isl_give isl_map *isl_map_insert_dims(
5863 __isl_take isl_map *map,
5864 enum isl_dim_type type, unsigned pos, unsigned n);
5865 __isl_give isl_basic_map *isl_basic_map_move_dims(
5866 __isl_take isl_basic_map *bmap,
5867 enum isl_dim_type dst_type, unsigned dst_pos,
5868 enum isl_dim_type src_type, unsigned src_pos,
5870 __isl_give isl_map *isl_map_move_dims(
5871 __isl_take isl_map *map,
5872 enum isl_dim_type dst_type, unsigned dst_pos,
5873 enum isl_dim_type src_type, unsigned src_pos,
5876 #include <isl/val.h>
5877 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5878 __isl_take isl_multi_val *mv,
5879 enum isl_dim_type type, unsigned first, unsigned n);
5880 __isl_give isl_multi_val *isl_multi_val_add_dims(
5881 __isl_take isl_multi_val *mv,
5882 enum isl_dim_type type, unsigned n);
5883 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5884 __isl_take isl_multi_val *mv,
5885 enum isl_dim_type type, unsigned first, unsigned n);
5887 #include <isl/aff.h>
5888 __isl_give isl_aff *isl_aff_insert_dims(
5889 __isl_take isl_aff *aff,
5890 enum isl_dim_type type, unsigned first, unsigned n);
5891 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5892 __isl_take isl_multi_aff *ma,
5893 enum isl_dim_type type, unsigned first, unsigned n);
5894 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5895 __isl_take isl_pw_aff *pwaff,
5896 enum isl_dim_type type, unsigned first, unsigned n);
5897 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5898 __isl_take isl_multi_pw_aff *mpa,
5899 enum isl_dim_type type, unsigned first, unsigned n);
5900 __isl_give isl_aff *isl_aff_add_dims(
5901 __isl_take isl_aff *aff,
5902 enum isl_dim_type type, unsigned n);
5903 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5904 __isl_take isl_multi_aff *ma,
5905 enum isl_dim_type type, unsigned n);
5906 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5907 __isl_take isl_pw_aff *pwaff,
5908 enum isl_dim_type type, unsigned n);
5909 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5910 __isl_take isl_multi_pw_aff *mpa,
5911 enum isl_dim_type type, unsigned n);
5912 __isl_give isl_aff *isl_aff_drop_dims(
5913 __isl_take isl_aff *aff,
5914 enum isl_dim_type type, unsigned first, unsigned n);
5915 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5916 __isl_take isl_multi_aff *maff,
5917 enum isl_dim_type type, unsigned first, unsigned n);
5918 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5919 __isl_take isl_pw_aff *pwaff,
5920 enum isl_dim_type type, unsigned first, unsigned n);
5921 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5922 __isl_take isl_pw_multi_aff *pma,
5923 enum isl_dim_type type, unsigned first, unsigned n);
5924 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5925 __isl_take isl_union_pw_aff *upa,
5926 enum isl_dim_type type, unsigned first, unsigned n);
5927 __isl_give isl_union_pw_multi_aff *
5928 isl_union_pw_multi_aff_drop_dims(
5929 __isl_take isl_union_pw_multi_aff *upma,
5930 enum isl_dim_type type,
5931 unsigned first, unsigned n);
5932 __isl_give isl_multi_union_pw_aff *
5933 isl_multi_union_pw_aff_drop_dims(
5934 __isl_take isl_multi_union_pw_aff *mupa,
5935 enum isl_dim_type type, unsigned first,
5937 __isl_give isl_aff *isl_aff_move_dims(
5938 __isl_take isl_aff *aff,
5939 enum isl_dim_type dst_type, unsigned dst_pos,
5940 enum isl_dim_type src_type, unsigned src_pos,
5942 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5943 __isl_take isl_multi_aff *ma,
5944 enum isl_dim_type dst_type, unsigned dst_pos,
5945 enum isl_dim_type src_type, unsigned src_pos,
5947 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5948 __isl_take isl_pw_aff *pa,
5949 enum isl_dim_type dst_type, unsigned dst_pos,
5950 enum isl_dim_type src_type, unsigned src_pos,
5952 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5953 __isl_take isl_multi_pw_aff *pma,
5954 enum isl_dim_type dst_type, unsigned dst_pos,
5955 enum isl_dim_type src_type, unsigned src_pos,
5958 #include <isl/polynomial.h>
5959 __isl_give isl_union_pw_qpolynomial *
5960 isl_union_pw_qpolynomial_drop_dims(
5961 __isl_take isl_union_pw_qpolynomial *upwqp,
5962 enum isl_dim_type type,
5963 unsigned first, unsigned n);
5964 __isl_give isl_union_pw_qpolynomial_fold *
5965 isl_union_pw_qpolynomial_fold_drop_dims(
5966 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5967 enum isl_dim_type type,
5968 unsigned first, unsigned n);
5970 The operations on union expressions can only manipulate parameters.
5974 =head2 Binary Operations
5976 The two arguments of a binary operation not only need to live
5977 in the same C<isl_ctx>, they currently also need to have
5978 the same (number of) parameters.
5980 =head3 Basic Operations
5984 =item * Intersection
5986 #include <isl/local_space.h>
5987 __isl_give isl_local_space *isl_local_space_intersect(
5988 __isl_take isl_local_space *ls1,
5989 __isl_take isl_local_space *ls2);
5991 #include <isl/set.h>
5992 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5993 __isl_take isl_basic_set *bset1,
5994 __isl_take isl_basic_set *bset2);
5995 __isl_give isl_basic_set *isl_basic_set_intersect(
5996 __isl_take isl_basic_set *bset1,
5997 __isl_take isl_basic_set *bset2);
5998 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5999 __isl_take struct isl_basic_set_list *list);
6000 __isl_give isl_set *isl_set_intersect_params(
6001 __isl_take isl_set *set,
6002 __isl_take isl_set *params);
6003 __isl_give isl_set *isl_set_intersect(
6004 __isl_take isl_set *set1,
6005 __isl_take isl_set *set2);
6007 #include <isl/map.h>
6008 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
6009 __isl_take isl_basic_map *bmap,
6010 __isl_take isl_basic_set *bset);
6011 __isl_give isl_basic_map *isl_basic_map_intersect_range(
6012 __isl_take isl_basic_map *bmap,
6013 __isl_take isl_basic_set *bset);
6014 __isl_give isl_basic_map *isl_basic_map_intersect(
6015 __isl_take isl_basic_map *bmap1,
6016 __isl_take isl_basic_map *bmap2);
6017 __isl_give isl_basic_map *isl_basic_map_list_intersect(
6018 __isl_take isl_basic_map_list *list);
6019 __isl_give isl_map *isl_map_intersect_params(
6020 __isl_take isl_map *map,
6021 __isl_take isl_set *params);
6022 __isl_give isl_map *isl_map_intersect_domain(
6023 __isl_take isl_map *map,
6024 __isl_take isl_set *set);
6025 __isl_give isl_map *isl_map_intersect_range(
6026 __isl_take isl_map *map,
6027 __isl_take isl_set *set);
6028 __isl_give isl_map *isl_map_intersect(
6029 __isl_take isl_map *map1,
6030 __isl_take isl_map *map2);
6031 __isl_give isl_map *
6032 isl_map_intersect_domain_factor_range(
6033 __isl_take isl_map *map,
6034 __isl_take isl_map *factor);
6035 __isl_give isl_map *
6036 isl_map_intersect_range_factor_range(
6037 __isl_take isl_map *map,
6038 __isl_take isl_map *factor);
6040 #include <isl/union_set.h>
6041 __isl_give isl_union_set *isl_union_set_intersect_params(
6042 __isl_take isl_union_set *uset,
6043 __isl_take isl_set *set);
6044 __isl_give isl_union_set *isl_union_set_intersect(
6045 __isl_take isl_union_set *uset1,
6046 __isl_take isl_union_set *uset2);
6048 #include <isl/union_map.h>
6049 __isl_give isl_union_map *isl_union_map_intersect_params(
6050 __isl_take isl_union_map *umap,
6051 __isl_take isl_set *set);
6052 __isl_give isl_union_map *isl_union_map_intersect_domain(
6053 __isl_take isl_union_map *umap,
6054 __isl_take isl_union_set *uset);
6055 __isl_give isl_union_map *isl_union_map_intersect_range(
6056 __isl_take isl_union_map *umap,
6057 __isl_take isl_union_set *uset);
6058 __isl_give isl_union_map *isl_union_map_intersect(
6059 __isl_take isl_union_map *umap1,
6060 __isl_take isl_union_map *umap2);
6061 __isl_give isl_union_map *
6062 isl_union_map_intersect_range_factor_range(
6063 __isl_take isl_union_map *umap,
6064 __isl_take isl_union_map *factor);
6066 #include <isl/aff.h>
6067 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6068 __isl_take isl_pw_aff *pa,
6069 __isl_take isl_set *set);
6070 __isl_give isl_multi_pw_aff *
6071 isl_multi_pw_aff_intersect_domain(
6072 __isl_take isl_multi_pw_aff *mpa,
6073 __isl_take isl_set *domain);
6074 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6075 __isl_take isl_pw_multi_aff *pma,
6076 __isl_take isl_set *set);
6077 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6078 __isl_take isl_union_pw_aff *upa,
6079 __isl_take isl_union_set *uset);
6080 __isl_give isl_union_pw_multi_aff *
6081 isl_union_pw_multi_aff_intersect_domain(
6082 __isl_take isl_union_pw_multi_aff *upma,
6083 __isl_take isl_union_set *uset);
6084 __isl_give isl_multi_union_pw_aff *
6085 isl_multi_union_pw_aff_intersect_domain(
6086 __isl_take isl_multi_union_pw_aff *mupa,
6087 __isl_take isl_union_set *uset);
6088 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6089 __isl_take isl_pw_aff *pa,
6090 __isl_take isl_set *set);
6091 __isl_give isl_multi_pw_aff *
6092 isl_multi_pw_aff_intersect_params(
6093 __isl_take isl_multi_pw_aff *mpa,
6094 __isl_take isl_set *set);
6095 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6096 __isl_take isl_pw_multi_aff *pma,
6097 __isl_take isl_set *set);
6098 __isl_give isl_union_pw_aff *
6099 isl_union_pw_aff_intersect_params(
6100 __isl_take isl_union_pw_aff *upa,
6101 __isl_give isl_union_pw_multi_aff *
6102 isl_union_pw_multi_aff_intersect_params(
6103 __isl_take isl_union_pw_multi_aff *upma,
6104 __isl_take isl_set *set);
6105 __isl_give isl_multi_union_pw_aff *
6106 isl_multi_union_pw_aff_intersect_params(
6107 __isl_take isl_multi_union_pw_aff *mupa,
6108 __isl_take isl_set *params);
6109 isl_multi_union_pw_aff_intersect_range(
6110 __isl_take isl_multi_union_pw_aff *mupa,
6111 __isl_take isl_set *set);
6113 #include <isl/polynomial.h>
6114 __isl_give isl_pw_qpolynomial *
6115 isl_pw_qpolynomial_intersect_domain(
6116 __isl_take isl_pw_qpolynomial *pwpq,
6117 __isl_take isl_set *set);
6118 __isl_give isl_union_pw_qpolynomial *
6119 isl_union_pw_qpolynomial_intersect_domain(
6120 __isl_take isl_union_pw_qpolynomial *upwpq,
6121 __isl_take isl_union_set *uset);
6122 __isl_give isl_union_pw_qpolynomial_fold *
6123 isl_union_pw_qpolynomial_fold_intersect_domain(
6124 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6125 __isl_take isl_union_set *uset);
6126 __isl_give isl_pw_qpolynomial *
6127 isl_pw_qpolynomial_intersect_params(
6128 __isl_take isl_pw_qpolynomial *pwpq,
6129 __isl_take isl_set *set);
6130 __isl_give isl_pw_qpolynomial_fold *
6131 isl_pw_qpolynomial_fold_intersect_params(
6132 __isl_take isl_pw_qpolynomial_fold *pwf,
6133 __isl_take isl_set *set);
6134 __isl_give isl_union_pw_qpolynomial *
6135 isl_union_pw_qpolynomial_intersect_params(
6136 __isl_take isl_union_pw_qpolynomial *upwpq,
6137 __isl_take isl_set *set);
6138 __isl_give isl_union_pw_qpolynomial_fold *
6139 isl_union_pw_qpolynomial_fold_intersect_params(
6140 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6141 __isl_take isl_set *set);
6143 The second argument to the C<_params> functions needs to be
6144 a parametric (basic) set. For the other functions, a parametric set
6145 for either argument is only allowed if the other argument is
6146 a parametric set as well.
6147 The list passed to C<isl_basic_set_list_intersect> needs to have
6148 at least one element and all elements need to live in the same space.
6149 The function C<isl_multi_union_pw_aff_intersect_range>
6150 restricts the input function to those shared domain elements
6151 that map to the specified range.
6155 #include <isl/set.h>
6156 __isl_give isl_set *isl_basic_set_union(
6157 __isl_take isl_basic_set *bset1,
6158 __isl_take isl_basic_set *bset2);
6159 __isl_give isl_set *isl_set_union(
6160 __isl_take isl_set *set1,
6161 __isl_take isl_set *set2);
6162 __isl_give isl_set *isl_set_list_union(
6163 __isl_take isl_set_list *list);
6165 #include <isl/map.h>
6166 __isl_give isl_map *isl_basic_map_union(
6167 __isl_take isl_basic_map *bmap1,
6168 __isl_take isl_basic_map *bmap2);
6169 __isl_give isl_map *isl_map_union(
6170 __isl_take isl_map *map1,
6171 __isl_take isl_map *map2);
6173 #include <isl/union_set.h>
6174 __isl_give isl_union_set *isl_union_set_union(
6175 __isl_take isl_union_set *uset1,
6176 __isl_take isl_union_set *uset2);
6177 __isl_give isl_union_set *isl_union_set_list_union(
6178 __isl_take isl_union_set_list *list);
6180 #include <isl/union_map.h>
6181 __isl_give isl_union_map *isl_union_map_union(
6182 __isl_take isl_union_map *umap1,
6183 __isl_take isl_union_map *umap2);
6185 The list passed to C<isl_set_list_union> needs to have
6186 at least one element and all elements need to live in the same space.
6188 =item * Set difference
6190 #include <isl/set.h>
6191 __isl_give isl_set *isl_set_subtract(
6192 __isl_take isl_set *set1,
6193 __isl_take isl_set *set2);
6195 #include <isl/map.h>
6196 __isl_give isl_map *isl_map_subtract(
6197 __isl_take isl_map *map1,
6198 __isl_take isl_map *map2);
6199 __isl_give isl_map *isl_map_subtract_domain(
6200 __isl_take isl_map *map,
6201 __isl_take isl_set *dom);
6202 __isl_give isl_map *isl_map_subtract_range(
6203 __isl_take isl_map *map,
6204 __isl_take isl_set *dom);
6206 #include <isl/union_set.h>
6207 __isl_give isl_union_set *isl_union_set_subtract(
6208 __isl_take isl_union_set *uset1,
6209 __isl_take isl_union_set *uset2);
6211 #include <isl/union_map.h>
6212 __isl_give isl_union_map *isl_union_map_subtract(
6213 __isl_take isl_union_map *umap1,
6214 __isl_take isl_union_map *umap2);
6215 __isl_give isl_union_map *isl_union_map_subtract_domain(
6216 __isl_take isl_union_map *umap,
6217 __isl_take isl_union_set *dom);
6218 __isl_give isl_union_map *isl_union_map_subtract_range(
6219 __isl_take isl_union_map *umap,
6220 __isl_take isl_union_set *dom);
6222 #include <isl/aff.h>
6223 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6224 __isl_take isl_pw_aff *pa,
6225 __isl_take isl_set *set);
6226 __isl_give isl_pw_multi_aff *
6227 isl_pw_multi_aff_subtract_domain(
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_subtract_domain(
6232 __isl_take isl_union_pw_aff *upa,
6233 __isl_take isl_union_set *uset);
6234 __isl_give isl_union_pw_multi_aff *
6235 isl_union_pw_multi_aff_subtract_domain(
6236 __isl_take isl_union_pw_multi_aff *upma,
6237 __isl_take isl_set *set);
6239 #include <isl/polynomial.h>
6240 __isl_give isl_pw_qpolynomial *
6241 isl_pw_qpolynomial_subtract_domain(
6242 __isl_take isl_pw_qpolynomial *pwpq,
6243 __isl_take isl_set *set);
6244 __isl_give isl_pw_qpolynomial_fold *
6245 isl_pw_qpolynomial_fold_subtract_domain(
6246 __isl_take isl_pw_qpolynomial_fold *pwf,
6247 __isl_take isl_set *set);
6248 __isl_give isl_union_pw_qpolynomial *
6249 isl_union_pw_qpolynomial_subtract_domain(
6250 __isl_take isl_union_pw_qpolynomial *upwpq,
6251 __isl_take isl_union_set *uset);
6252 __isl_give isl_union_pw_qpolynomial_fold *
6253 isl_union_pw_qpolynomial_fold_subtract_domain(
6254 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6255 __isl_take isl_union_set *uset);
6259 #include <isl/space.h>
6260 __isl_give isl_space *isl_space_join(
6261 __isl_take isl_space *left,
6262 __isl_take isl_space *right);
6264 #include <isl/map.h>
6265 __isl_give isl_basic_set *isl_basic_set_apply(
6266 __isl_take isl_basic_set *bset,
6267 __isl_take isl_basic_map *bmap);
6268 __isl_give isl_set *isl_set_apply(
6269 __isl_take isl_set *set,
6270 __isl_take isl_map *map);
6271 __isl_give isl_union_set *isl_union_set_apply(
6272 __isl_take isl_union_set *uset,
6273 __isl_take isl_union_map *umap);
6274 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6275 __isl_take isl_basic_map *bmap1,
6276 __isl_take isl_basic_map *bmap2);
6277 __isl_give isl_basic_map *isl_basic_map_apply_range(
6278 __isl_take isl_basic_map *bmap1,
6279 __isl_take isl_basic_map *bmap2);
6280 __isl_give isl_map *isl_map_apply_domain(
6281 __isl_take isl_map *map1,
6282 __isl_take isl_map *map2);
6283 __isl_give isl_map *isl_map_apply_range(
6284 __isl_take isl_map *map1,
6285 __isl_take isl_map *map2);
6287 #include <isl/union_map.h>
6288 __isl_give isl_union_map *isl_union_map_apply_domain(
6289 __isl_take isl_union_map *umap1,
6290 __isl_take isl_union_map *umap2);
6291 __isl_give isl_union_map *isl_union_map_apply_range(
6292 __isl_take isl_union_map *umap1,
6293 __isl_take isl_union_map *umap2);
6295 #include <isl/aff.h>
6296 __isl_give isl_union_pw_aff *
6297 isl_multi_union_pw_aff_apply_aff(
6298 __isl_take isl_multi_union_pw_aff *mupa,
6299 __isl_take isl_aff *aff);
6300 __isl_give isl_union_pw_aff *
6301 isl_multi_union_pw_aff_apply_pw_aff(
6302 __isl_take isl_multi_union_pw_aff *mupa,
6303 __isl_take isl_pw_aff *pa);
6304 __isl_give isl_multi_union_pw_aff *
6305 isl_multi_union_pw_aff_apply_multi_aff(
6306 __isl_take isl_multi_union_pw_aff *mupa,
6307 __isl_take isl_multi_aff *ma);
6308 __isl_give isl_multi_union_pw_aff *
6309 isl_multi_union_pw_aff_apply_pw_multi_aff(
6310 __isl_take isl_multi_union_pw_aff *mupa,
6311 __isl_take isl_pw_multi_aff *pma);
6313 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6314 over the shared domain of the elements of the input. The dimension is
6315 required to be greater than zero.
6316 The C<isl_multi_union_pw_aff> argument of
6317 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6318 but only if the range of the C<isl_multi_aff> argument
6319 is also zero-dimensional.
6320 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6322 #include <isl/polynomial.h>
6323 __isl_give isl_pw_qpolynomial_fold *
6324 isl_set_apply_pw_qpolynomial_fold(
6325 __isl_take isl_set *set,
6326 __isl_take isl_pw_qpolynomial_fold *pwf,
6328 __isl_give isl_pw_qpolynomial_fold *
6329 isl_map_apply_pw_qpolynomial_fold(
6330 __isl_take isl_map *map,
6331 __isl_take isl_pw_qpolynomial_fold *pwf,
6333 __isl_give isl_union_pw_qpolynomial_fold *
6334 isl_union_set_apply_union_pw_qpolynomial_fold(
6335 __isl_take isl_union_set *uset,
6336 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6338 __isl_give isl_union_pw_qpolynomial_fold *
6339 isl_union_map_apply_union_pw_qpolynomial_fold(
6340 __isl_take isl_union_map *umap,
6341 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6344 The functions taking a map
6345 compose the given map with the given piecewise quasipolynomial reduction.
6346 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6347 over all elements in the intersection of the range of the map
6348 and the domain of the piecewise quasipolynomial reduction
6349 as a function of an element in the domain of the map.
6350 The functions taking a set compute a bound over all elements in the
6351 intersection of the set and the domain of the
6352 piecewise quasipolynomial reduction.
6356 #include <isl/set.h>
6357 __isl_give isl_basic_set *
6358 isl_basic_set_preimage_multi_aff(
6359 __isl_take isl_basic_set *bset,
6360 __isl_take isl_multi_aff *ma);
6361 __isl_give isl_set *isl_set_preimage_multi_aff(
6362 __isl_take isl_set *set,
6363 __isl_take isl_multi_aff *ma);
6364 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6365 __isl_take isl_set *set,
6366 __isl_take isl_pw_multi_aff *pma);
6367 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6368 __isl_take isl_set *set,
6369 __isl_take isl_multi_pw_aff *mpa);
6371 #include <isl/union_set.h>
6372 __isl_give isl_union_set *
6373 isl_union_set_preimage_multi_aff(
6374 __isl_take isl_union_set *uset,
6375 __isl_take isl_multi_aff *ma);
6376 __isl_give isl_union_set *
6377 isl_union_set_preimage_pw_multi_aff(
6378 __isl_take isl_union_set *uset,
6379 __isl_take isl_pw_multi_aff *pma);
6380 __isl_give isl_union_set *
6381 isl_union_set_preimage_union_pw_multi_aff(
6382 __isl_take isl_union_set *uset,
6383 __isl_take isl_union_pw_multi_aff *upma);
6385 #include <isl/map.h>
6386 __isl_give isl_basic_map *
6387 isl_basic_map_preimage_domain_multi_aff(
6388 __isl_take isl_basic_map *bmap,
6389 __isl_take isl_multi_aff *ma);
6390 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6391 __isl_take isl_map *map,
6392 __isl_take isl_multi_aff *ma);
6393 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6394 __isl_take isl_map *map,
6395 __isl_take isl_multi_aff *ma);
6396 __isl_give isl_map *
6397 isl_map_preimage_domain_pw_multi_aff(
6398 __isl_take isl_map *map,
6399 __isl_take isl_pw_multi_aff *pma);
6400 __isl_give isl_map *
6401 isl_map_preimage_range_pw_multi_aff(
6402 __isl_take isl_map *map,
6403 __isl_take isl_pw_multi_aff *pma);
6404 __isl_give isl_map *
6405 isl_map_preimage_domain_multi_pw_aff(
6406 __isl_take isl_map *map,
6407 __isl_take isl_multi_pw_aff *mpa);
6408 __isl_give isl_basic_map *
6409 isl_basic_map_preimage_range_multi_aff(
6410 __isl_take isl_basic_map *bmap,
6411 __isl_take isl_multi_aff *ma);
6413 #include <isl/union_map.h>
6414 __isl_give isl_union_map *
6415 isl_union_map_preimage_domain_multi_aff(
6416 __isl_take isl_union_map *umap,
6417 __isl_take isl_multi_aff *ma);
6418 __isl_give isl_union_map *
6419 isl_union_map_preimage_range_multi_aff(
6420 __isl_take isl_union_map *umap,
6421 __isl_take isl_multi_aff *ma);
6422 __isl_give isl_union_map *
6423 isl_union_map_preimage_domain_pw_multi_aff(
6424 __isl_take isl_union_map *umap,
6425 __isl_take isl_pw_multi_aff *pma);
6426 __isl_give isl_union_map *
6427 isl_union_map_preimage_range_pw_multi_aff(
6428 __isl_take isl_union_map *umap,
6429 __isl_take isl_pw_multi_aff *pma);
6430 __isl_give isl_union_map *
6431 isl_union_map_preimage_domain_union_pw_multi_aff(
6432 __isl_take isl_union_map *umap,
6433 __isl_take isl_union_pw_multi_aff *upma);
6434 __isl_give isl_union_map *
6435 isl_union_map_preimage_range_union_pw_multi_aff(
6436 __isl_take isl_union_map *umap,
6437 __isl_take isl_union_pw_multi_aff *upma);
6439 These functions compute the preimage of the given set or map domain/range under
6440 the given function. In other words, the expression is plugged
6441 into the set description or into the domain/range of the map.
6445 #include <isl/aff.h>
6446 __isl_give isl_aff *isl_aff_pullback_aff(
6447 __isl_take isl_aff *aff1,
6448 __isl_take isl_aff *aff2);
6449 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6450 __isl_take isl_aff *aff,
6451 __isl_take isl_multi_aff *ma);
6452 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6453 __isl_take isl_pw_aff *pa,
6454 __isl_take isl_multi_aff *ma);
6455 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6456 __isl_take isl_pw_aff *pa,
6457 __isl_take isl_pw_multi_aff *pma);
6458 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6459 __isl_take isl_pw_aff *pa,
6460 __isl_take isl_multi_pw_aff *mpa);
6461 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6462 __isl_take isl_multi_aff *ma1,
6463 __isl_take isl_multi_aff *ma2);
6464 __isl_give isl_pw_multi_aff *
6465 isl_pw_multi_aff_pullback_multi_aff(
6466 __isl_take isl_pw_multi_aff *pma,
6467 __isl_take isl_multi_aff *ma);
6468 __isl_give isl_multi_pw_aff *
6469 isl_multi_pw_aff_pullback_multi_aff(
6470 __isl_take isl_multi_pw_aff *mpa,
6471 __isl_take isl_multi_aff *ma);
6472 __isl_give isl_pw_multi_aff *
6473 isl_pw_multi_aff_pullback_pw_multi_aff(
6474 __isl_take isl_pw_multi_aff *pma1,
6475 __isl_take isl_pw_multi_aff *pma2);
6476 __isl_give isl_multi_pw_aff *
6477 isl_multi_pw_aff_pullback_pw_multi_aff(
6478 __isl_take isl_multi_pw_aff *mpa,
6479 __isl_take isl_pw_multi_aff *pma);
6480 __isl_give isl_multi_pw_aff *
6481 isl_multi_pw_aff_pullback_multi_pw_aff(
6482 __isl_take isl_multi_pw_aff *mpa1,
6483 __isl_take isl_multi_pw_aff *mpa2);
6484 __isl_give isl_union_pw_aff *
6485 isl_union_pw_aff_pullback_union_pw_multi_aff(
6486 __isl_take isl_union_pw_aff *upa,
6487 __isl_take isl_union_pw_multi_aff *upma);
6488 __isl_give isl_union_pw_multi_aff *
6489 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6490 __isl_take isl_union_pw_multi_aff *upma1,
6491 __isl_take isl_union_pw_multi_aff *upma2);
6492 __isl_give isl_multi_union_pw_aff *
6493 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6494 __isl_take isl_multi_union_pw_aff *mupa,
6495 __isl_take isl_union_pw_multi_aff *upma);
6497 These functions precompose the first expression by the second function.
6498 In other words, the second function is plugged
6499 into the first expression.
6503 #include <isl/aff.h>
6504 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6505 __isl_take isl_aff *aff1,
6506 __isl_take isl_aff *aff2);
6507 __isl_give isl_set *isl_aff_eq_set(
6508 __isl_take isl_aff *aff1,
6509 __isl_take isl_aff *aff2);
6510 __isl_give isl_set *isl_aff_ne_set(
6511 __isl_take isl_aff *aff1,
6512 __isl_take isl_aff *aff2);
6513 __isl_give isl_basic_set *isl_aff_le_basic_set(
6514 __isl_take isl_aff *aff1,
6515 __isl_take isl_aff *aff2);
6516 __isl_give isl_set *isl_aff_le_set(
6517 __isl_take isl_aff *aff1,
6518 __isl_take isl_aff *aff2);
6519 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6520 __isl_take isl_aff *aff1,
6521 __isl_take isl_aff *aff2);
6522 __isl_give isl_set *isl_aff_lt_set(
6523 __isl_take isl_aff *aff1,
6524 __isl_take isl_aff *aff2);
6525 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6526 __isl_take isl_aff *aff1,
6527 __isl_take isl_aff *aff2);
6528 __isl_give isl_set *isl_aff_ge_set(
6529 __isl_take isl_aff *aff1,
6530 __isl_take isl_aff *aff2);
6531 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6532 __isl_take isl_aff *aff1,
6533 __isl_take isl_aff *aff2);
6534 __isl_give isl_set *isl_aff_gt_set(
6535 __isl_take isl_aff *aff1,
6536 __isl_take isl_aff *aff2);
6537 __isl_give isl_set *isl_pw_aff_eq_set(
6538 __isl_take isl_pw_aff *pwaff1,
6539 __isl_take isl_pw_aff *pwaff2);
6540 __isl_give isl_set *isl_pw_aff_ne_set(
6541 __isl_take isl_pw_aff *pwaff1,
6542 __isl_take isl_pw_aff *pwaff2);
6543 __isl_give isl_set *isl_pw_aff_le_set(
6544 __isl_take isl_pw_aff *pwaff1,
6545 __isl_take isl_pw_aff *pwaff2);
6546 __isl_give isl_set *isl_pw_aff_lt_set(
6547 __isl_take isl_pw_aff *pwaff1,
6548 __isl_take isl_pw_aff *pwaff2);
6549 __isl_give isl_set *isl_pw_aff_ge_set(
6550 __isl_take isl_pw_aff *pwaff1,
6551 __isl_take isl_pw_aff *pwaff2);
6552 __isl_give isl_set *isl_pw_aff_gt_set(
6553 __isl_take isl_pw_aff *pwaff1,
6554 __isl_take isl_pw_aff *pwaff2);
6556 __isl_give isl_set *isl_multi_aff_lex_le_set(
6557 __isl_take isl_multi_aff *ma1,
6558 __isl_take isl_multi_aff *ma2);
6559 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6560 __isl_take isl_multi_aff *ma1,
6561 __isl_take isl_multi_aff *ma2);
6562 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6563 __isl_take isl_multi_aff *ma1,
6564 __isl_take isl_multi_aff *ma2);
6565 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6566 __isl_take isl_multi_aff *ma1,
6567 __isl_take isl_multi_aff *ma2);
6569 __isl_give isl_set *isl_pw_aff_list_eq_set(
6570 __isl_take isl_pw_aff_list *list1,
6571 __isl_take isl_pw_aff_list *list2);
6572 __isl_give isl_set *isl_pw_aff_list_ne_set(
6573 __isl_take isl_pw_aff_list *list1,
6574 __isl_take isl_pw_aff_list *list2);
6575 __isl_give isl_set *isl_pw_aff_list_le_set(
6576 __isl_take isl_pw_aff_list *list1,
6577 __isl_take isl_pw_aff_list *list2);
6578 __isl_give isl_set *isl_pw_aff_list_lt_set(
6579 __isl_take isl_pw_aff_list *list1,
6580 __isl_take isl_pw_aff_list *list2);
6581 __isl_give isl_set *isl_pw_aff_list_ge_set(
6582 __isl_take isl_pw_aff_list *list1,
6583 __isl_take isl_pw_aff_list *list2);
6584 __isl_give isl_set *isl_pw_aff_list_gt_set(
6585 __isl_take isl_pw_aff_list *list1,
6586 __isl_take isl_pw_aff_list *list2);
6588 The function C<isl_aff_ge_basic_set> returns a basic set
6589 containing those elements in the shared space
6590 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6591 The function C<isl_pw_aff_ge_set> returns a set
6592 containing those elements in the shared domain
6593 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6594 greater than or equal to C<pwaff2>.
6595 The function C<isl_multi_aff_lex_le_set> returns a set
6596 containing those elements in the shared domain space
6597 where C<ma1> is lexicographically smaller than or
6599 The functions operating on C<isl_pw_aff_list> apply the corresponding
6600 C<isl_pw_aff> function to each pair of elements in the two lists.
6602 #include <isl/aff.h>
6603 __isl_give isl_map *isl_pw_aff_eq_map(
6604 __isl_take isl_pw_aff *pa1,
6605 __isl_take isl_pw_aff *pa2);
6606 __isl_give isl_map *isl_pw_aff_lt_map(
6607 __isl_take isl_pw_aff *pa1,
6608 __isl_take isl_pw_aff *pa2);
6609 __isl_give isl_map *isl_pw_aff_gt_map(
6610 __isl_take isl_pw_aff *pa1,
6611 __isl_take isl_pw_aff *pa2);
6613 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6614 __isl_take isl_multi_pw_aff *mpa1,
6615 __isl_take isl_multi_pw_aff *mpa2);
6616 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6617 __isl_take isl_multi_pw_aff *mpa1,
6618 __isl_take isl_multi_pw_aff *mpa2);
6619 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6620 __isl_take isl_multi_pw_aff *mpa1,
6621 __isl_take isl_multi_pw_aff *mpa2);
6623 These functions return a map between domain elements of the arguments
6624 where the function values satisfy the given relation.
6626 #include <isl/union_map.h>
6627 __isl_give isl_union_map *
6628 isl_union_map_eq_at_multi_union_pw_aff(
6629 __isl_take isl_union_map *umap,
6630 __isl_take isl_multi_union_pw_aff *mupa);
6631 __isl_give isl_union_map *
6632 isl_union_map_lex_lt_at_multi_union_pw_aff(
6633 __isl_take isl_union_map *umap,
6634 __isl_take isl_multi_union_pw_aff *mupa);
6635 __isl_give isl_union_map *
6636 isl_union_map_lex_gt_at_multi_union_pw_aff(
6637 __isl_take isl_union_map *umap,
6638 __isl_take isl_multi_union_pw_aff *mupa);
6640 These functions select the subset of elements in the union map
6641 that have an equal or lexicographically smaller function value.
6643 =item * Cartesian Product
6645 #include <isl/space.h>
6646 __isl_give isl_space *isl_space_product(
6647 __isl_take isl_space *space1,
6648 __isl_take isl_space *space2);
6649 __isl_give isl_space *isl_space_domain_product(
6650 __isl_take isl_space *space1,
6651 __isl_take isl_space *space2);
6652 __isl_give isl_space *isl_space_range_product(
6653 __isl_take isl_space *space1,
6654 __isl_take isl_space *space2);
6657 C<isl_space_product>, C<isl_space_domain_product>
6658 and C<isl_space_range_product> take pairs or relation spaces and
6659 produce a single relations space, where either the domain, the range
6660 or both domain and range are wrapped spaces of relations between
6661 the domains and/or ranges of the input spaces.
6662 If the product is only constructed over the domain or the range
6663 then the ranges or the domains of the inputs should be the same.
6664 The function C<isl_space_product> also accepts a pair of set spaces,
6665 in which case it returns a wrapped space of a relation between the
6668 #include <isl/set.h>
6669 __isl_give isl_set *isl_set_product(
6670 __isl_take isl_set *set1,
6671 __isl_take isl_set *set2);
6673 #include <isl/map.h>
6674 __isl_give isl_basic_map *isl_basic_map_domain_product(
6675 __isl_take isl_basic_map *bmap1,
6676 __isl_take isl_basic_map *bmap2);
6677 __isl_give isl_basic_map *isl_basic_map_range_product(
6678 __isl_take isl_basic_map *bmap1,
6679 __isl_take isl_basic_map *bmap2);
6680 __isl_give isl_basic_map *isl_basic_map_product(
6681 __isl_take isl_basic_map *bmap1,
6682 __isl_take isl_basic_map *bmap2);
6683 __isl_give isl_map *isl_map_domain_product(
6684 __isl_take isl_map *map1,
6685 __isl_take isl_map *map2);
6686 __isl_give isl_map *isl_map_range_product(
6687 __isl_take isl_map *map1,
6688 __isl_take isl_map *map2);
6689 __isl_give isl_map *isl_map_product(
6690 __isl_take isl_map *map1,
6691 __isl_take isl_map *map2);
6693 #include <isl/union_set.h>
6694 __isl_give isl_union_set *isl_union_set_product(
6695 __isl_take isl_union_set *uset1,
6696 __isl_take isl_union_set *uset2);
6698 #include <isl/union_map.h>
6699 __isl_give isl_union_map *isl_union_map_domain_product(
6700 __isl_take isl_union_map *umap1,
6701 __isl_take isl_union_map *umap2);
6702 __isl_give isl_union_map *isl_union_map_range_product(
6703 __isl_take isl_union_map *umap1,
6704 __isl_take isl_union_map *umap2);
6705 __isl_give isl_union_map *isl_union_map_product(
6706 __isl_take isl_union_map *umap1,
6707 __isl_take isl_union_map *umap2);
6709 #include <isl/val.h>
6710 __isl_give isl_multi_val *isl_multi_val_range_product(
6711 __isl_take isl_multi_val *mv1,
6712 __isl_take isl_multi_val *mv2);
6713 __isl_give isl_multi_val *isl_multi_val_product(
6714 __isl_take isl_multi_val *mv1,
6715 __isl_take isl_multi_val *mv2);
6717 #include <isl/aff.h>
6718 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6719 __isl_take isl_multi_aff *ma1,
6720 __isl_take isl_multi_aff *ma2);
6721 __isl_give isl_multi_aff *isl_multi_aff_product(
6722 __isl_take isl_multi_aff *ma1,
6723 __isl_take isl_multi_aff *ma2);
6724 __isl_give isl_multi_pw_aff *
6725 isl_multi_pw_aff_range_product(
6726 __isl_take isl_multi_pw_aff *mpa1,
6727 __isl_take isl_multi_pw_aff *mpa2);
6728 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6729 __isl_take isl_multi_pw_aff *mpa1,
6730 __isl_take isl_multi_pw_aff *mpa2);
6731 __isl_give isl_pw_multi_aff *
6732 isl_pw_multi_aff_range_product(
6733 __isl_take isl_pw_multi_aff *pma1,
6734 __isl_take isl_pw_multi_aff *pma2);
6735 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6736 __isl_take isl_pw_multi_aff *pma1,
6737 __isl_take isl_pw_multi_aff *pma2);
6738 __isl_give isl_multi_union_pw_aff *
6739 isl_multi_union_pw_aff_range_product(
6740 __isl_take isl_multi_union_pw_aff *mupa1,
6741 __isl_take isl_multi_union_pw_aff *mupa2);
6743 The above functions compute the cross product of the given
6744 sets, relations or functions. The domains and ranges of the results
6745 are wrapped maps between domains and ranges of the inputs.
6746 To obtain a ``flat'' product, use the following functions
6749 #include <isl/set.h>
6750 __isl_give isl_basic_set *isl_basic_set_flat_product(
6751 __isl_take isl_basic_set *bset1,
6752 __isl_take isl_basic_set *bset2);
6753 __isl_give isl_set *isl_set_flat_product(
6754 __isl_take isl_set *set1,
6755 __isl_take isl_set *set2);
6757 #include <isl/map.h>
6758 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6759 __isl_take isl_basic_map *bmap1,
6760 __isl_take isl_basic_map *bmap2);
6761 __isl_give isl_map *isl_map_flat_domain_product(
6762 __isl_take isl_map *map1,
6763 __isl_take isl_map *map2);
6764 __isl_give isl_map *isl_map_flat_range_product(
6765 __isl_take isl_map *map1,
6766 __isl_take isl_map *map2);
6767 __isl_give isl_basic_map *isl_basic_map_flat_product(
6768 __isl_take isl_basic_map *bmap1,
6769 __isl_take isl_basic_map *bmap2);
6770 __isl_give isl_map *isl_map_flat_product(
6771 __isl_take isl_map *map1,
6772 __isl_take isl_map *map2);
6774 #include <isl/union_map.h>
6775 __isl_give isl_union_map *
6776 isl_union_map_flat_domain_product(
6777 __isl_take isl_union_map *umap1,
6778 __isl_take isl_union_map *umap2);
6779 __isl_give isl_union_map *
6780 isl_union_map_flat_range_product(
6781 __isl_take isl_union_map *umap1,
6782 __isl_take isl_union_map *umap2);
6784 #include <isl/val.h>
6785 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6786 __isl_take isl_multi_val *mv1,
6787 __isl_take isl_multi_aff *mv2);
6789 #include <isl/aff.h>
6790 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6791 __isl_take isl_multi_aff *ma1,
6792 __isl_take isl_multi_aff *ma2);
6793 __isl_give isl_pw_multi_aff *
6794 isl_pw_multi_aff_flat_range_product(
6795 __isl_take isl_pw_multi_aff *pma1,
6796 __isl_take isl_pw_multi_aff *pma2);
6797 __isl_give isl_multi_pw_aff *
6798 isl_multi_pw_aff_flat_range_product(
6799 __isl_take isl_multi_pw_aff *mpa1,
6800 __isl_take isl_multi_pw_aff *mpa2);
6801 __isl_give isl_union_pw_multi_aff *
6802 isl_union_pw_multi_aff_flat_range_product(
6803 __isl_take isl_union_pw_multi_aff *upma1,
6804 __isl_take isl_union_pw_multi_aff *upma2);
6805 __isl_give isl_multi_union_pw_aff *
6806 isl_multi_union_pw_aff_flat_range_product(
6807 __isl_take isl_multi_union_pw_aff *mupa1,
6808 __isl_take isl_multi_union_pw_aff *mupa2);
6810 #include <isl/space.h>
6811 __isl_give isl_space *isl_space_factor_domain(
6812 __isl_take isl_space *space);
6813 __isl_give isl_space *isl_space_factor_range(
6814 __isl_take isl_space *space);
6815 __isl_give isl_space *isl_space_domain_factor_domain(
6816 __isl_take isl_space *space);
6817 __isl_give isl_space *isl_space_domain_factor_range(
6818 __isl_take isl_space *space);
6819 __isl_give isl_space *isl_space_range_factor_domain(
6820 __isl_take isl_space *space);
6821 __isl_give isl_space *isl_space_range_factor_range(
6822 __isl_take isl_space *space);
6824 The functions C<isl_space_range_factor_domain> and
6825 C<isl_space_range_factor_range> extract the two arguments from
6826 the result of a call to C<isl_space_range_product>.
6828 The arguments of a call to a product can be extracted
6829 from the result using the following functions.
6831 #include <isl/map.h>
6832 __isl_give isl_map *isl_map_factor_domain(
6833 __isl_take isl_map *map);
6834 __isl_give isl_map *isl_map_factor_range(
6835 __isl_take isl_map *map);
6836 __isl_give isl_map *isl_map_domain_factor_domain(
6837 __isl_take isl_map *map);
6838 __isl_give isl_map *isl_map_domain_factor_range(
6839 __isl_take isl_map *map);
6840 __isl_give isl_map *isl_map_range_factor_domain(
6841 __isl_take isl_map *map);
6842 __isl_give isl_map *isl_map_range_factor_range(
6843 __isl_take isl_map *map);
6845 #include <isl/union_map.h>
6846 __isl_give isl_union_map *isl_union_map_factor_domain(
6847 __isl_take isl_union_map *umap);
6848 __isl_give isl_union_map *isl_union_map_factor_range(
6849 __isl_take isl_union_map *umap);
6850 __isl_give isl_union_map *
6851 isl_union_map_domain_factor_domain(
6852 __isl_take isl_union_map *umap);
6853 __isl_give isl_union_map *
6854 isl_union_map_domain_factor_range(
6855 __isl_take isl_union_map *umap);
6856 __isl_give isl_union_map *
6857 isl_union_map_range_factor_domain(
6858 __isl_take isl_union_map *umap);
6859 __isl_give isl_union_map *
6860 isl_union_map_range_factor_range(
6861 __isl_take isl_union_map *umap);
6863 #include <isl/val.h>
6864 __isl_give isl_multi_val *isl_multi_val_factor_range(
6865 __isl_take isl_multi_val *mv);
6866 __isl_give isl_multi_val *
6867 isl_multi_val_range_factor_domain(
6868 __isl_take isl_multi_val *mv);
6869 __isl_give isl_multi_val *
6870 isl_multi_val_range_factor_range(
6871 __isl_take isl_multi_val *mv);
6873 #include <isl/aff.h>
6874 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6875 __isl_take isl_multi_aff *ma);
6876 __isl_give isl_multi_aff *
6877 isl_multi_aff_range_factor_domain(
6878 __isl_take isl_multi_aff *ma);
6879 __isl_give isl_multi_aff *
6880 isl_multi_aff_range_factor_range(
6881 __isl_take isl_multi_aff *ma);
6882 __isl_give isl_multi_pw_aff *
6883 isl_multi_pw_aff_factor_range(
6884 __isl_take isl_multi_pw_aff *mpa);
6885 __isl_give isl_multi_pw_aff *
6886 isl_multi_pw_aff_range_factor_domain(
6887 __isl_take isl_multi_pw_aff *mpa);
6888 __isl_give isl_multi_pw_aff *
6889 isl_multi_pw_aff_range_factor_range(
6890 __isl_take isl_multi_pw_aff *mpa);
6891 __isl_give isl_multi_union_pw_aff *
6892 isl_multi_union_pw_aff_factor_range(
6893 __isl_take isl_multi_union_pw_aff *mupa);
6894 __isl_give isl_multi_union_pw_aff *
6895 isl_multi_union_pw_aff_range_factor_domain(
6896 __isl_take isl_multi_union_pw_aff *mupa);
6897 __isl_give isl_multi_union_pw_aff *
6898 isl_multi_union_pw_aff_range_factor_range(
6899 __isl_take isl_multi_union_pw_aff *mupa);
6901 The splice functions are a generalization of the flat product functions,
6902 where the second argument may be inserted at any position inside
6903 the first argument rather than being placed at the end.
6904 The functions C<isl_multi_val_factor_range>,
6905 C<isl_multi_aff_factor_range>,
6906 C<isl_multi_pw_aff_factor_range> and
6907 C<isl_multi_union_pw_aff_factor_range>
6908 take functions that live in a set space.
6910 #include <isl/val.h>
6911 __isl_give isl_multi_val *isl_multi_val_range_splice(
6912 __isl_take isl_multi_val *mv1, unsigned pos,
6913 __isl_take isl_multi_val *mv2);
6915 #include <isl/aff.h>
6916 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6917 __isl_take isl_multi_aff *ma1, unsigned pos,
6918 __isl_take isl_multi_aff *ma2);
6919 __isl_give isl_multi_aff *isl_multi_aff_splice(
6920 __isl_take isl_multi_aff *ma1,
6921 unsigned in_pos, unsigned out_pos,
6922 __isl_take isl_multi_aff *ma2);
6923 __isl_give isl_multi_pw_aff *
6924 isl_multi_pw_aff_range_splice(
6925 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6926 __isl_take isl_multi_pw_aff *mpa2);
6927 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6928 __isl_take isl_multi_pw_aff *mpa1,
6929 unsigned in_pos, unsigned out_pos,
6930 __isl_take isl_multi_pw_aff *mpa2);
6931 __isl_give isl_multi_union_pw_aff *
6932 isl_multi_union_pw_aff_range_splice(
6933 __isl_take isl_multi_union_pw_aff *mupa1,
6935 __isl_take isl_multi_union_pw_aff *mupa2);
6937 =item * Simplification
6939 When applied to a set or relation,
6940 the gist operation returns a set or relation that has the
6941 same intersection with the context as the input set or relation.
6942 Any implicit equality in the intersection is made explicit in the result,
6943 while all inequalities that are redundant with respect to the intersection
6945 In case of union sets and relations, the gist operation is performed
6948 When applied to a function,
6949 the gist operation applies the set gist operation to each of
6950 the cells in the domain of the input piecewise expression.
6951 The context is also exploited
6952 to simplify the expression associated to each cell.
6954 #include <isl/set.h>
6955 __isl_give isl_basic_set *isl_basic_set_gist(
6956 __isl_take isl_basic_set *bset,
6957 __isl_take isl_basic_set *context);
6958 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6959 __isl_take isl_set *context);
6960 __isl_give isl_set *isl_set_gist_params(
6961 __isl_take isl_set *set,
6962 __isl_take isl_set *context);
6964 #include <isl/map.h>
6965 __isl_give isl_basic_map *isl_basic_map_gist(
6966 __isl_take isl_basic_map *bmap,
6967 __isl_take isl_basic_map *context);
6968 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6969 __isl_take isl_basic_map *bmap,
6970 __isl_take isl_basic_set *context);
6971 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6972 __isl_take isl_map *context);
6973 __isl_give isl_map *isl_map_gist_params(
6974 __isl_take isl_map *map,
6975 __isl_take isl_set *context);
6976 __isl_give isl_map *isl_map_gist_domain(
6977 __isl_take isl_map *map,
6978 __isl_take isl_set *context);
6979 __isl_give isl_map *isl_map_gist_range(
6980 __isl_take isl_map *map,
6981 __isl_take isl_set *context);
6983 #include <isl/union_set.h>
6984 __isl_give isl_union_set *isl_union_set_gist(
6985 __isl_take isl_union_set *uset,
6986 __isl_take isl_union_set *context);
6987 __isl_give isl_union_set *isl_union_set_gist_params(
6988 __isl_take isl_union_set *uset,
6989 __isl_take isl_set *set);
6991 #include <isl/union_map.h>
6992 __isl_give isl_union_map *isl_union_map_gist(
6993 __isl_take isl_union_map *umap,
6994 __isl_take isl_union_map *context);
6995 __isl_give isl_union_map *isl_union_map_gist_params(
6996 __isl_take isl_union_map *umap,
6997 __isl_take isl_set *set);
6998 __isl_give isl_union_map *isl_union_map_gist_domain(
6999 __isl_take isl_union_map *umap,
7000 __isl_take isl_union_set *uset);
7001 __isl_give isl_union_map *isl_union_map_gist_range(
7002 __isl_take isl_union_map *umap,
7003 __isl_take isl_union_set *uset);
7005 #include <isl/aff.h>
7006 __isl_give isl_aff *isl_aff_gist_params(
7007 __isl_take isl_aff *aff,
7008 __isl_take isl_set *context);
7009 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
7010 __isl_take isl_set *context);
7011 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
7012 __isl_take isl_multi_aff *maff,
7013 __isl_take isl_set *context);
7014 __isl_give isl_multi_aff *isl_multi_aff_gist(
7015 __isl_take isl_multi_aff *maff,
7016 __isl_take isl_set *context);
7017 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
7018 __isl_take isl_pw_aff *pwaff,
7019 __isl_take isl_set *context);
7020 __isl_give isl_pw_aff *isl_pw_aff_gist(
7021 __isl_take isl_pw_aff *pwaff,
7022 __isl_take isl_set *context);
7023 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
7024 __isl_take isl_pw_multi_aff *pma,
7025 __isl_take isl_set *set);
7026 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
7027 __isl_take isl_pw_multi_aff *pma,
7028 __isl_take isl_set *set);
7029 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
7030 __isl_take isl_multi_pw_aff *mpa,
7031 __isl_take isl_set *set);
7032 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
7033 __isl_take isl_multi_pw_aff *mpa,
7034 __isl_take isl_set *set);
7035 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
7036 __isl_take isl_union_pw_aff *upa,
7037 __isl_take isl_union_set *context);
7038 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
7039 __isl_take isl_union_pw_aff *upa,
7040 __isl_take isl_set *context);
7041 __isl_give isl_union_pw_multi_aff *
7042 isl_union_pw_multi_aff_gist_params(
7043 __isl_take isl_union_pw_multi_aff *upma,
7044 __isl_take isl_set *context);
7045 __isl_give isl_union_pw_multi_aff *
7046 isl_union_pw_multi_aff_gist(
7047 __isl_take isl_union_pw_multi_aff *upma,
7048 __isl_take isl_union_set *context);
7049 __isl_give isl_multi_union_pw_aff *
7050 isl_multi_union_pw_aff_gist_params(
7051 __isl_take isl_multi_union_pw_aff *aff,
7052 __isl_take isl_set *context);
7053 __isl_give isl_multi_union_pw_aff *
7054 isl_multi_union_pw_aff_gist(
7055 __isl_take isl_multi_union_pw_aff *aff,
7056 __isl_take isl_union_set *context);
7058 #include <isl/polynomial.h>
7059 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
7060 __isl_take isl_qpolynomial *qp,
7061 __isl_take isl_set *context);
7062 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
7063 __isl_take isl_qpolynomial *qp,
7064 __isl_take isl_set *context);
7065 __isl_give isl_qpolynomial_fold *
7066 isl_qpolynomial_fold_gist_params(
7067 __isl_take isl_qpolynomial_fold *fold,
7068 __isl_take isl_set *context);
7069 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7070 __isl_take isl_qpolynomial_fold *fold,
7071 __isl_take isl_set *context);
7072 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7073 __isl_take isl_pw_qpolynomial *pwqp,
7074 __isl_take isl_set *context);
7075 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7076 __isl_take isl_pw_qpolynomial *pwqp,
7077 __isl_take isl_set *context);
7078 __isl_give isl_pw_qpolynomial_fold *
7079 isl_pw_qpolynomial_fold_gist(
7080 __isl_take isl_pw_qpolynomial_fold *pwf,
7081 __isl_take isl_set *context);
7082 __isl_give isl_pw_qpolynomial_fold *
7083 isl_pw_qpolynomial_fold_gist_params(
7084 __isl_take isl_pw_qpolynomial_fold *pwf,
7085 __isl_take isl_set *context);
7086 __isl_give isl_union_pw_qpolynomial *
7087 isl_union_pw_qpolynomial_gist_params(
7088 __isl_take isl_union_pw_qpolynomial *upwqp,
7089 __isl_take isl_set *context);
7090 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7091 __isl_take isl_union_pw_qpolynomial *upwqp,
7092 __isl_take isl_union_set *context);
7093 __isl_give isl_union_pw_qpolynomial_fold *
7094 isl_union_pw_qpolynomial_fold_gist(
7095 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7096 __isl_take isl_union_set *context);
7097 __isl_give isl_union_pw_qpolynomial_fold *
7098 isl_union_pw_qpolynomial_fold_gist_params(
7099 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7100 __isl_take isl_set *context);
7102 =item * Binary Arithmetic Operations
7104 #include <isl/set.h>
7105 __isl_give isl_set *isl_set_sum(
7106 __isl_take isl_set *set1,
7107 __isl_take isl_set *set2);
7108 #include <isl/map.h>
7109 __isl_give isl_map *isl_map_sum(
7110 __isl_take isl_map *map1,
7111 __isl_take isl_map *map2);
7113 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7114 i.e., the set containing the sums of pairs of elements from
7115 C<set1> and C<set2>.
7116 The domain of the result of C<isl_map_sum> is the intersection
7117 of the domains of its two arguments. The corresponding range
7118 elements are the sums of the corresponding range elements
7119 in the two arguments.
7121 #include <isl/val.h>
7122 __isl_give isl_multi_val *isl_multi_val_add(
7123 __isl_take isl_multi_val *mv1,
7124 __isl_take isl_multi_val *mv2);
7125 __isl_give isl_multi_val *isl_multi_val_sub(
7126 __isl_take isl_multi_val *mv1,
7127 __isl_take isl_multi_val *mv2);
7129 #include <isl/aff.h>
7130 __isl_give isl_aff *isl_aff_add(
7131 __isl_take isl_aff *aff1,
7132 __isl_take isl_aff *aff2);
7133 __isl_give isl_multi_aff *isl_multi_aff_add(
7134 __isl_take isl_multi_aff *maff1,
7135 __isl_take isl_multi_aff *maff2);
7136 __isl_give isl_pw_aff *isl_pw_aff_add(
7137 __isl_take isl_pw_aff *pwaff1,
7138 __isl_take isl_pw_aff *pwaff2);
7139 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7140 __isl_take isl_multi_pw_aff *mpa1,
7141 __isl_take isl_multi_pw_aff *mpa2);
7142 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7143 __isl_take isl_pw_multi_aff *pma1,
7144 __isl_take isl_pw_multi_aff *pma2);
7145 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7146 __isl_take isl_union_pw_aff *upa1,
7147 __isl_take isl_union_pw_aff *upa2);
7148 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7149 __isl_take isl_union_pw_multi_aff *upma1,
7150 __isl_take isl_union_pw_multi_aff *upma2);
7151 __isl_give isl_multi_union_pw_aff *
7152 isl_multi_union_pw_aff_add(
7153 __isl_take isl_multi_union_pw_aff *mupa1,
7154 __isl_take isl_multi_union_pw_aff *mupa2);
7155 __isl_give isl_pw_aff *isl_pw_aff_min(
7156 __isl_take isl_pw_aff *pwaff1,
7157 __isl_take isl_pw_aff *pwaff2);
7158 __isl_give isl_pw_aff *isl_pw_aff_max(
7159 __isl_take isl_pw_aff *pwaff1,
7160 __isl_take isl_pw_aff *pwaff2);
7161 __isl_give isl_aff *isl_aff_sub(
7162 __isl_take isl_aff *aff1,
7163 __isl_take isl_aff *aff2);
7164 __isl_give isl_multi_aff *isl_multi_aff_sub(
7165 __isl_take isl_multi_aff *ma1,
7166 __isl_take isl_multi_aff *ma2);
7167 __isl_give isl_pw_aff *isl_pw_aff_sub(
7168 __isl_take isl_pw_aff *pwaff1,
7169 __isl_take isl_pw_aff *pwaff2);
7170 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7171 __isl_take isl_multi_pw_aff *mpa1,
7172 __isl_take isl_multi_pw_aff *mpa2);
7173 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7174 __isl_take isl_pw_multi_aff *pma1,
7175 __isl_take isl_pw_multi_aff *pma2);
7176 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7177 __isl_take isl_union_pw_aff *upa1,
7178 __isl_take isl_union_pw_aff *upa2);
7179 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7180 __isl_take isl_union_pw_multi_aff *upma1,
7181 __isl_take isl_union_pw_multi_aff *upma2);
7182 __isl_give isl_multi_union_pw_aff *
7183 isl_multi_union_pw_aff_sub(
7184 __isl_take isl_multi_union_pw_aff *mupa1,
7185 __isl_take isl_multi_union_pw_aff *mupa2);
7187 C<isl_aff_sub> subtracts the second argument from the first.
7189 #include <isl/polynomial.h>
7190 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7191 __isl_take isl_qpolynomial *qp1,
7192 __isl_take isl_qpolynomial *qp2);
7193 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7194 __isl_take isl_pw_qpolynomial *pwqp1,
7195 __isl_take isl_pw_qpolynomial *pwqp2);
7196 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7197 __isl_take isl_pw_qpolynomial *pwqp1,
7198 __isl_take isl_pw_qpolynomial *pwqp2);
7199 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7200 __isl_take isl_pw_qpolynomial_fold *pwf1,
7201 __isl_take isl_pw_qpolynomial_fold *pwf2);
7202 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7203 __isl_take isl_union_pw_qpolynomial *upwqp1,
7204 __isl_take isl_union_pw_qpolynomial *upwqp2);
7205 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7206 __isl_take isl_qpolynomial *qp1,
7207 __isl_take isl_qpolynomial *qp2);
7208 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7209 __isl_take isl_pw_qpolynomial *pwqp1,
7210 __isl_take isl_pw_qpolynomial *pwqp2);
7211 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7212 __isl_take isl_union_pw_qpolynomial *upwqp1,
7213 __isl_take isl_union_pw_qpolynomial *upwqp2);
7214 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7215 __isl_take isl_pw_qpolynomial_fold *pwf1,
7216 __isl_take isl_pw_qpolynomial_fold *pwf2);
7217 __isl_give isl_union_pw_qpolynomial_fold *
7218 isl_union_pw_qpolynomial_fold_fold(
7219 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7220 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7222 #include <isl/aff.h>
7223 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7224 __isl_take isl_pw_aff *pwaff1,
7225 __isl_take isl_pw_aff *pwaff2);
7226 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7227 __isl_take isl_pw_multi_aff *pma1,
7228 __isl_take isl_pw_multi_aff *pma2);
7229 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7230 __isl_take isl_union_pw_aff *upa1,
7231 __isl_take isl_union_pw_aff *upa2);
7232 __isl_give isl_union_pw_multi_aff *
7233 isl_union_pw_multi_aff_union_add(
7234 __isl_take isl_union_pw_multi_aff *upma1,
7235 __isl_take isl_union_pw_multi_aff *upma2);
7236 __isl_give isl_multi_union_pw_aff *
7237 isl_multi_union_pw_aff_union_add(
7238 __isl_take isl_multi_union_pw_aff *mupa1,
7239 __isl_take isl_multi_union_pw_aff *mupa2);
7240 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7241 __isl_take isl_pw_aff *pwaff1,
7242 __isl_take isl_pw_aff *pwaff2);
7243 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7244 __isl_take isl_pw_aff *pwaff1,
7245 __isl_take isl_pw_aff *pwaff2);
7247 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7248 expression with a domain that is the union of those of C<pwaff1> and
7249 C<pwaff2> and such that on each cell, the quasi-affine expression is
7250 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7251 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7252 associated expression is the defined one.
7253 This in contrast to the C<isl_pw_aff_max> function, which is
7254 only defined on the shared definition domain of the arguments.
7256 #include <isl/val.h>
7257 __isl_give isl_multi_val *isl_multi_val_add_val(
7258 __isl_take isl_multi_val *mv,
7259 __isl_take isl_val *v);
7260 __isl_give isl_multi_val *isl_multi_val_mod_val(
7261 __isl_take isl_multi_val *mv,
7262 __isl_take isl_val *v);
7263 __isl_give isl_multi_val *isl_multi_val_scale_val(
7264 __isl_take isl_multi_val *mv,
7265 __isl_take isl_val *v);
7266 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7267 __isl_take isl_multi_val *mv,
7268 __isl_take isl_val *v);
7270 #include <isl/aff.h>
7271 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7272 __isl_take isl_val *mod);
7273 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7274 __isl_take isl_pw_aff *pa,
7275 __isl_take isl_val *mod);
7276 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7277 __isl_take isl_union_pw_aff *upa,
7278 __isl_take isl_val *f);
7279 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7280 __isl_take isl_val *v);
7281 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7282 __isl_take isl_multi_aff *ma,
7283 __isl_take isl_val *v);
7284 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7285 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7286 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7287 __isl_take isl_multi_pw_aff *mpa,
7288 __isl_take isl_val *v);
7289 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7290 __isl_take isl_pw_multi_aff *pma,
7291 __isl_take isl_val *v);
7292 __isl_give isl_union_pw_multi_aff *
7293 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7294 __isl_take isl_union_pw_aff *upa,
7295 __isl_take isl_val *f);
7296 isl_union_pw_multi_aff_scale_val(
7297 __isl_take isl_union_pw_multi_aff *upma,
7298 __isl_take isl_val *val);
7299 __isl_give isl_multi_union_pw_aff *
7300 isl_multi_union_pw_aff_scale_val(
7301 __isl_take isl_multi_union_pw_aff *mupa,
7302 __isl_take isl_val *v);
7303 __isl_give isl_aff *isl_aff_scale_down_ui(
7304 __isl_take isl_aff *aff, unsigned f);
7305 __isl_give isl_aff *isl_aff_scale_down_val(
7306 __isl_take isl_aff *aff, __isl_take isl_val *v);
7307 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7308 __isl_take isl_multi_aff *ma,
7309 __isl_take isl_val *v);
7310 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7311 __isl_take isl_pw_aff *pa,
7312 __isl_take isl_val *f);
7313 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7314 __isl_take isl_multi_pw_aff *mpa,
7315 __isl_take isl_val *v);
7316 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7317 __isl_take isl_pw_multi_aff *pma,
7318 __isl_take isl_val *v);
7319 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7320 __isl_take isl_union_pw_aff *upa,
7321 __isl_take isl_val *v);
7322 __isl_give isl_union_pw_multi_aff *
7323 isl_union_pw_multi_aff_scale_down_val(
7324 __isl_take isl_union_pw_multi_aff *upma,
7325 __isl_take isl_val *val);
7326 __isl_give isl_multi_union_pw_aff *
7327 isl_multi_union_pw_aff_scale_down_val(
7328 __isl_take isl_multi_union_pw_aff *mupa,
7329 __isl_take isl_val *v);
7331 #include <isl/polynomial.h>
7332 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7333 __isl_take isl_qpolynomial *qp,
7334 __isl_take isl_val *v);
7335 __isl_give isl_qpolynomial_fold *
7336 isl_qpolynomial_fold_scale_val(
7337 __isl_take isl_qpolynomial_fold *fold,
7338 __isl_take isl_val *v);
7339 __isl_give isl_pw_qpolynomial *
7340 isl_pw_qpolynomial_scale_val(
7341 __isl_take isl_pw_qpolynomial *pwqp,
7342 __isl_take isl_val *v);
7343 __isl_give isl_pw_qpolynomial_fold *
7344 isl_pw_qpolynomial_fold_scale_val(
7345 __isl_take isl_pw_qpolynomial_fold *pwf,
7346 __isl_take isl_val *v);
7347 __isl_give isl_union_pw_qpolynomial *
7348 isl_union_pw_qpolynomial_scale_val(
7349 __isl_take isl_union_pw_qpolynomial *upwqp,
7350 __isl_take isl_val *v);
7351 __isl_give isl_union_pw_qpolynomial_fold *
7352 isl_union_pw_qpolynomial_fold_scale_val(
7353 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7354 __isl_take isl_val *v);
7355 __isl_give isl_qpolynomial *
7356 isl_qpolynomial_scale_down_val(
7357 __isl_take isl_qpolynomial *qp,
7358 __isl_take isl_val *v);
7359 __isl_give isl_qpolynomial_fold *
7360 isl_qpolynomial_fold_scale_down_val(
7361 __isl_take isl_qpolynomial_fold *fold,
7362 __isl_take isl_val *v);
7363 __isl_give isl_pw_qpolynomial *
7364 isl_pw_qpolynomial_scale_down_val(
7365 __isl_take isl_pw_qpolynomial *pwqp,
7366 __isl_take isl_val *v);
7367 __isl_give isl_pw_qpolynomial_fold *
7368 isl_pw_qpolynomial_fold_scale_down_val(
7369 __isl_take isl_pw_qpolynomial_fold *pwf,
7370 __isl_take isl_val *v);
7371 __isl_give isl_union_pw_qpolynomial *
7372 isl_union_pw_qpolynomial_scale_down_val(
7373 __isl_take isl_union_pw_qpolynomial *upwqp,
7374 __isl_take isl_val *v);
7375 __isl_give isl_union_pw_qpolynomial_fold *
7376 isl_union_pw_qpolynomial_fold_scale_down_val(
7377 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7378 __isl_take isl_val *v);
7380 #include <isl/val.h>
7381 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7382 __isl_take isl_multi_val *mv1,
7383 __isl_take isl_multi_val *mv2);
7384 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7385 __isl_take isl_multi_val *mv1,
7386 __isl_take isl_multi_val *mv2);
7387 __isl_give isl_multi_val *
7388 isl_multi_val_scale_down_multi_val(
7389 __isl_take isl_multi_val *mv1,
7390 __isl_take isl_multi_val *mv2);
7392 #include <isl/aff.h>
7393 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7394 __isl_take isl_multi_aff *ma,
7395 __isl_take isl_multi_val *mv);
7396 __isl_give isl_multi_union_pw_aff *
7397 isl_multi_union_pw_aff_mod_multi_val(
7398 __isl_take isl_multi_union_pw_aff *upma,
7399 __isl_take isl_multi_val *mv);
7400 __isl_give isl_multi_pw_aff *
7401 isl_multi_pw_aff_mod_multi_val(
7402 __isl_take isl_multi_pw_aff *mpa,
7403 __isl_take isl_multi_val *mv);
7404 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7405 __isl_take isl_multi_aff *ma,
7406 __isl_take isl_multi_val *mv);
7407 __isl_give isl_pw_multi_aff *
7408 isl_pw_multi_aff_scale_multi_val(
7409 __isl_take isl_pw_multi_aff *pma,
7410 __isl_take isl_multi_val *mv);
7411 __isl_give isl_multi_pw_aff *
7412 isl_multi_pw_aff_scale_multi_val(
7413 __isl_take isl_multi_pw_aff *mpa,
7414 __isl_take isl_multi_val *mv);
7415 __isl_give isl_multi_union_pw_aff *
7416 isl_multi_union_pw_aff_scale_multi_val(
7417 __isl_take isl_multi_union_pw_aff *mupa,
7418 __isl_take isl_multi_val *mv);
7419 __isl_give isl_union_pw_multi_aff *
7420 isl_union_pw_multi_aff_scale_multi_val(
7421 __isl_take isl_union_pw_multi_aff *upma,
7422 __isl_take isl_multi_val *mv);
7423 __isl_give isl_multi_aff *
7424 isl_multi_aff_scale_down_multi_val(
7425 __isl_take isl_multi_aff *ma,
7426 __isl_take isl_multi_val *mv);
7427 __isl_give isl_multi_pw_aff *
7428 isl_multi_pw_aff_scale_down_multi_val(
7429 __isl_take isl_multi_pw_aff *mpa,
7430 __isl_take isl_multi_val *mv);
7431 __isl_give isl_multi_union_pw_aff *
7432 isl_multi_union_pw_aff_scale_down_multi_val(
7433 __isl_take isl_multi_union_pw_aff *mupa,
7434 __isl_take isl_multi_val *mv);
7436 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7437 by the corresponding elements of C<mv>.
7439 #include <isl/aff.h>
7440 __isl_give isl_aff *isl_aff_mul(
7441 __isl_take isl_aff *aff1,
7442 __isl_take isl_aff *aff2);
7443 __isl_give isl_aff *isl_aff_div(
7444 __isl_take isl_aff *aff1,
7445 __isl_take isl_aff *aff2);
7446 __isl_give isl_pw_aff *isl_pw_aff_mul(
7447 __isl_take isl_pw_aff *pwaff1,
7448 __isl_take isl_pw_aff *pwaff2);
7449 __isl_give isl_pw_aff *isl_pw_aff_div(
7450 __isl_take isl_pw_aff *pa1,
7451 __isl_take isl_pw_aff *pa2);
7452 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7453 __isl_take isl_pw_aff *pa1,
7454 __isl_take isl_pw_aff *pa2);
7455 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7456 __isl_take isl_pw_aff *pa1,
7457 __isl_take isl_pw_aff *pa2);
7459 When multiplying two affine expressions, at least one of the two needs
7460 to be a constant. Similarly, when dividing an affine expression by another,
7461 the second expression needs to be a constant.
7462 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7463 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7466 #include <isl/polynomial.h>
7467 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7468 __isl_take isl_qpolynomial *qp1,
7469 __isl_take isl_qpolynomial *qp2);
7470 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7471 __isl_take isl_pw_qpolynomial *pwqp1,
7472 __isl_take isl_pw_qpolynomial *pwqp2);
7473 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7474 __isl_take isl_union_pw_qpolynomial *upwqp1,
7475 __isl_take isl_union_pw_qpolynomial *upwqp2);
7479 =head3 Lexicographic Optimization
7481 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7482 the following functions
7483 compute a set that contains the lexicographic minimum or maximum
7484 of the elements in C<set> (or C<bset>) for those values of the parameters
7485 that satisfy C<dom>.
7486 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7487 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7489 In other words, the union of the parameter values
7490 for which the result is non-empty and of C<*empty>
7493 #include <isl/set.h>
7494 __isl_give isl_set *isl_basic_set_partial_lexmin(
7495 __isl_take isl_basic_set *bset,
7496 __isl_take isl_basic_set *dom,
7497 __isl_give isl_set **empty);
7498 __isl_give isl_set *isl_basic_set_partial_lexmax(
7499 __isl_take isl_basic_set *bset,
7500 __isl_take isl_basic_set *dom,
7501 __isl_give isl_set **empty);
7502 __isl_give isl_set *isl_set_partial_lexmin(
7503 __isl_take isl_set *set, __isl_take isl_set *dom,
7504 __isl_give isl_set **empty);
7505 __isl_give isl_set *isl_set_partial_lexmax(
7506 __isl_take isl_set *set, __isl_take isl_set *dom,
7507 __isl_give isl_set **empty);
7509 Given a (basic) set C<set> (or C<bset>), the following functions simply
7510 return a set containing the lexicographic minimum or maximum
7511 of the elements in C<set> (or C<bset>).
7512 In case of union sets, the optimum is computed per space.
7514 #include <isl/set.h>
7515 __isl_give isl_set *isl_basic_set_lexmin(
7516 __isl_take isl_basic_set *bset);
7517 __isl_give isl_set *isl_basic_set_lexmax(
7518 __isl_take isl_basic_set *bset);
7519 __isl_give isl_set *isl_set_lexmin(
7520 __isl_take isl_set *set);
7521 __isl_give isl_set *isl_set_lexmax(
7522 __isl_take isl_set *set);
7523 __isl_give isl_union_set *isl_union_set_lexmin(
7524 __isl_take isl_union_set *uset);
7525 __isl_give isl_union_set *isl_union_set_lexmax(
7526 __isl_take isl_union_set *uset);
7528 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7529 the following functions
7530 compute a relation that maps each element of C<dom>
7531 to the single lexicographic minimum or maximum
7532 of the elements that are associated to that same
7533 element in C<map> (or C<bmap>).
7534 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7535 that contains the elements in C<dom> that do not map
7536 to any elements in C<map> (or C<bmap>).
7537 In other words, the union of the domain of the result and of C<*empty>
7540 #include <isl/map.h>
7541 __isl_give isl_map *isl_basic_map_partial_lexmax(
7542 __isl_take isl_basic_map *bmap,
7543 __isl_take isl_basic_set *dom,
7544 __isl_give isl_set **empty);
7545 __isl_give isl_map *isl_basic_map_partial_lexmin(
7546 __isl_take isl_basic_map *bmap,
7547 __isl_take isl_basic_set *dom,
7548 __isl_give isl_set **empty);
7549 __isl_give isl_map *isl_map_partial_lexmax(
7550 __isl_take isl_map *map, __isl_take isl_set *dom,
7551 __isl_give isl_set **empty);
7552 __isl_give isl_map *isl_map_partial_lexmin(
7553 __isl_take isl_map *map, __isl_take isl_set *dom,
7554 __isl_give isl_set **empty);
7556 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7557 return a map mapping each element in the domain of
7558 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7559 of all elements associated to that element.
7560 In case of union relations, the optimum is computed per space.
7562 #include <isl/map.h>
7563 __isl_give isl_map *isl_basic_map_lexmin(
7564 __isl_take isl_basic_map *bmap);
7565 __isl_give isl_map *isl_basic_map_lexmax(
7566 __isl_take isl_basic_map *bmap);
7567 __isl_give isl_map *isl_map_lexmin(
7568 __isl_take isl_map *map);
7569 __isl_give isl_map *isl_map_lexmax(
7570 __isl_take isl_map *map);
7571 __isl_give isl_union_map *isl_union_map_lexmin(
7572 __isl_take isl_union_map *umap);
7573 __isl_give isl_union_map *isl_union_map_lexmax(
7574 __isl_take isl_union_map *umap);
7576 The following functions return their result in the form of
7577 a piecewise multi-affine expression,
7578 but are otherwise equivalent to the corresponding functions
7579 returning a basic set or relation.
7581 #include <isl/set.h>
7582 __isl_give isl_pw_multi_aff *
7583 isl_basic_set_partial_lexmin_pw_multi_aff(
7584 __isl_take isl_basic_set *bset,
7585 __isl_take isl_basic_set *dom,
7586 __isl_give isl_set **empty);
7587 __isl_give isl_pw_multi_aff *
7588 isl_basic_set_partial_lexmax_pw_multi_aff(
7589 __isl_take isl_basic_set *bset,
7590 __isl_take isl_basic_set *dom,
7591 __isl_give isl_set **empty);
7592 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7593 __isl_take isl_set *set);
7594 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7595 __isl_take isl_set *set);
7597 #include <isl/map.h>
7598 __isl_give isl_pw_multi_aff *
7599 isl_basic_map_lexmin_pw_multi_aff(
7600 __isl_take isl_basic_map *bmap);
7601 __isl_give isl_pw_multi_aff *
7602 isl_basic_map_partial_lexmin_pw_multi_aff(
7603 __isl_take isl_basic_map *bmap,
7604 __isl_take isl_basic_set *dom,
7605 __isl_give isl_set **empty);
7606 __isl_give isl_pw_multi_aff *
7607 isl_basic_map_partial_lexmax_pw_multi_aff(
7608 __isl_take isl_basic_map *bmap,
7609 __isl_take isl_basic_set *dom,
7610 __isl_give isl_set **empty);
7611 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7612 __isl_take isl_map *map);
7613 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7614 __isl_take isl_map *map);
7616 The following functions return the lexicographic minimum or maximum
7617 on the shared domain of the inputs and the single defined function
7618 on those parts of the domain where only a single function is defined.
7620 #include <isl/aff.h>
7621 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7622 __isl_take isl_pw_multi_aff *pma1,
7623 __isl_take isl_pw_multi_aff *pma2);
7624 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7625 __isl_take isl_pw_multi_aff *pma1,
7626 __isl_take isl_pw_multi_aff *pma2);
7628 If the input to a lexicographic optimization problem has
7629 multiple constraints with the same coefficients for the optimized
7630 variables, then, by default, this symmetry is exploited by
7631 replacing those constraints by a single constraint with
7632 an abstract bound, which is in turn bounded by the corresponding terms
7633 in the original constraints.
7634 Without this optimization, the solver would typically consider
7635 all possible orderings of those original bounds, resulting in a needless
7636 decomposition of the domain.
7637 However, the optimization can also result in slowdowns since
7638 an extra parameter is introduced that may get used in additional
7640 The following option determines whether symmetry detection is applied
7641 during lexicographic optimization.
7643 #include <isl/options.h>
7644 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7646 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7650 See also \autoref{s:offline}.
7654 =head2 Ternary Operations
7656 #include <isl/aff.h>
7657 __isl_give isl_pw_aff *isl_pw_aff_cond(
7658 __isl_take isl_pw_aff *cond,
7659 __isl_take isl_pw_aff *pwaff_true,
7660 __isl_take isl_pw_aff *pwaff_false);
7662 The function C<isl_pw_aff_cond> performs a conditional operator
7663 and returns an expression that is equal to C<pwaff_true>
7664 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7665 where C<cond> is zero.
7669 Lists are defined over several element types, including
7670 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7671 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7672 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7673 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7674 Here we take lists of C<isl_set>s as an example.
7675 Lists can be created, copied, modified and freed using the following functions.
7677 #include <isl/set.h>
7678 __isl_give isl_set_list *isl_set_list_from_set(
7679 __isl_take isl_set *el);
7680 __isl_give isl_set_list *isl_set_list_alloc(
7681 isl_ctx *ctx, int n);
7682 __isl_give isl_set_list *isl_set_list_copy(
7683 __isl_keep isl_set_list *list);
7684 __isl_give isl_set_list *isl_set_list_insert(
7685 __isl_take isl_set_list *list, unsigned pos,
7686 __isl_take isl_set *el);
7687 __isl_give isl_set_list *isl_set_list_add(
7688 __isl_take isl_set_list *list,
7689 __isl_take isl_set *el);
7690 __isl_give isl_set_list *isl_set_list_drop(
7691 __isl_take isl_set_list *list,
7692 unsigned first, unsigned n);
7693 __isl_give isl_set_list *isl_set_list_set_set(
7694 __isl_take isl_set_list *list, int index,
7695 __isl_take isl_set *set);
7696 __isl_give isl_set_list *isl_set_list_concat(
7697 __isl_take isl_set_list *list1,
7698 __isl_take isl_set_list *list2);
7699 __isl_give isl_set_list *isl_set_list_map(
7700 __isl_take isl_set_list *list,
7701 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7704 __isl_give isl_set_list *isl_set_list_sort(
7705 __isl_take isl_set_list *list,
7706 int (*cmp)(__isl_keep isl_set *a,
7707 __isl_keep isl_set *b, void *user),
7709 __isl_null isl_set_list *isl_set_list_free(
7710 __isl_take isl_set_list *list);
7712 C<isl_set_list_alloc> creates an empty list with an initial capacity
7713 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7714 add elements to a list, increasing its capacity as needed.
7715 C<isl_set_list_from_set> creates a list with a single element.
7717 Lists can be inspected using the following functions.
7719 #include <isl/set.h>
7720 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7721 __isl_give isl_set *isl_set_list_get_set(
7722 __isl_keep isl_set_list *list, int index);
7723 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7724 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7726 isl_stat isl_set_list_foreach_scc(
7727 __isl_keep isl_set_list *list,
7728 isl_bool (*follows)(__isl_keep isl_set *a,
7729 __isl_keep isl_set *b, void *user),
7731 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7734 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7735 strongly connected components of the graph with as vertices the elements
7736 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7737 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7738 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7740 Lists can be printed using
7742 #include <isl/set.h>
7743 __isl_give isl_printer *isl_printer_print_set_list(
7744 __isl_take isl_printer *p,
7745 __isl_keep isl_set_list *list);
7747 =head2 Associative arrays
7749 Associative arrays map isl objects of a specific type to isl objects
7750 of some (other) specific type. They are defined for several pairs
7751 of types, including (C<isl_map>, C<isl_basic_set>),
7752 (C<isl_id>, C<isl_ast_expr>),
7753 (C<isl_id>, C<isl_id>) and
7754 (C<isl_id>, C<isl_pw_aff>).
7755 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7758 Associative arrays can be created, copied and freed using
7759 the following functions.
7761 #include <isl/id_to_ast_expr.h>
7762 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7763 isl_ctx *ctx, int min_size);
7764 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7765 __isl_keep isl_id_to_ast_expr *id2expr);
7766 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7767 __isl_take isl_id_to_ast_expr *id2expr);
7769 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7770 to specify the expected size of the associative array.
7771 The associative array will be grown automatically as needed.
7773 Associative arrays can be inspected using the following functions.
7775 #include <isl/id_to_ast_expr.h>
7776 __isl_give isl_maybe_isl_ast_expr
7777 isl_id_to_ast_expr_try_get(
7778 __isl_keep isl_id_to_ast_expr *id2expr,
7779 __isl_keep isl_id *key);
7780 isl_bool isl_id_to_ast_expr_has(
7781 __isl_keep isl_id_to_ast_expr *id2expr,
7782 __isl_keep isl_id *key);
7783 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7784 __isl_keep isl_id_to_ast_expr *id2expr,
7785 __isl_take isl_id *key);
7786 isl_stat isl_id_to_ast_expr_foreach(
7787 __isl_keep isl_id_to_ast_expr *id2expr,
7788 isl_stat (*fn)(__isl_take isl_id *key,
7789 __isl_take isl_ast_expr *val, void *user),
7792 The function C<isl_id_to_ast_expr_try_get> returns a structure
7793 containing two elements, C<valid> and C<value>.
7794 If there is a value associated to the key, then C<valid>
7795 is set to C<isl_bool_true> and C<value> contains a copy of
7796 the associated value. Otherwise C<value> is C<NULL> and
7797 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7798 on whether some error has occurred or there simply is no associated value.
7799 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7800 in the structure and
7801 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7803 Associative arrays can be modified using the following functions.
7805 #include <isl/id_to_ast_expr.h>
7806 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7807 __isl_take isl_id_to_ast_expr *id2expr,
7808 __isl_take isl_id *key,
7809 __isl_take isl_ast_expr *val);
7810 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7811 __isl_take isl_id_to_ast_expr *id2expr,
7812 __isl_take isl_id *key);
7814 Associative arrays can be printed using the following function.
7816 #include <isl/id_to_ast_expr.h>
7817 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7818 __isl_take isl_printer *p,
7819 __isl_keep isl_id_to_ast_expr *id2expr);
7823 Vectors can be created, copied and freed using the following functions.
7825 #include <isl/vec.h>
7826 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7828 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
7830 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7831 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7833 Note that the elements of a vector created by C<isl_vec_alloc>
7834 may have arbitrary values.
7835 A vector created by C<isl_vec_zero> has elements with value zero.
7836 The elements can be changed and inspected using the following functions.
7838 int isl_vec_size(__isl_keep isl_vec *vec);
7839 __isl_give isl_val *isl_vec_get_element_val(
7840 __isl_keep isl_vec *vec, int pos);
7841 __isl_give isl_vec *isl_vec_set_element_si(
7842 __isl_take isl_vec *vec, int pos, int v);
7843 __isl_give isl_vec *isl_vec_set_element_val(
7844 __isl_take isl_vec *vec, int pos,
7845 __isl_take isl_val *v);
7846 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7848 __isl_give isl_vec *isl_vec_set_val(
7849 __isl_take isl_vec *vec, __isl_take isl_val *v);
7850 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7851 __isl_keep isl_vec *vec2, int pos);
7853 C<isl_vec_get_element> will return a negative value if anything went wrong.
7854 In that case, the value of C<*v> is undefined.
7856 The following function can be used to concatenate two vectors.
7858 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7859 __isl_take isl_vec *vec2);
7863 Matrices can be created, copied and freed using the following functions.
7865 #include <isl/mat.h>
7866 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7867 unsigned n_row, unsigned n_col);
7868 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7869 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7871 Note that the elements of a newly created matrix may have arbitrary values.
7872 The elements can be changed and inspected using the following functions.
7874 int isl_mat_rows(__isl_keep isl_mat *mat);
7875 int isl_mat_cols(__isl_keep isl_mat *mat);
7876 __isl_give isl_val *isl_mat_get_element_val(
7877 __isl_keep isl_mat *mat, int row, int col);
7878 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7879 int row, int col, int v);
7880 __isl_give isl_mat *isl_mat_set_element_val(
7881 __isl_take isl_mat *mat, int row, int col,
7882 __isl_take isl_val *v);
7884 The following function computes the rank of a matrix.
7885 The return value may be -1 if some error occurred.
7887 #include <isl/mat.h>
7888 int isl_mat_rank(__isl_keep isl_mat *mat);
7890 The following function can be used to compute the (right) inverse
7891 of a matrix, i.e., a matrix such that the product of the original
7892 and the inverse (in that order) is a multiple of the identity matrix.
7893 The input matrix is assumed to be of full row-rank.
7895 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7897 The following function can be used to compute the (right) kernel
7898 (or null space) of a matrix, i.e., a matrix such that the product of
7899 the original and the kernel (in that order) is the zero matrix.
7901 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7903 The following function computes a basis for the space spanned
7904 by the rows of a matrix.
7906 __isl_give isl_mat *isl_mat_row_basis(
7907 __isl_take isl_mat *mat);
7909 The following function computes rows that extend a basis of C<mat1>
7910 to a basis that also covers C<mat2>.
7912 __isl_give isl_mat *isl_mat_row_basis_extension(
7913 __isl_take isl_mat *mat1,
7914 __isl_take isl_mat *mat2);
7916 The following function checks whether there is no linear dependence
7917 among the combined rows of "mat1" and "mat2" that is not already present
7918 in "mat1" or "mat2" individually.
7919 If "mat1" and "mat2" have linearly independent rows by themselves,
7920 then this means that there is no linear dependence among all rows together.
7922 isl_bool isl_mat_has_linearly_independent_rows(
7923 __isl_keep isl_mat *mat1,
7924 __isl_keep isl_mat *mat2);
7926 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7928 The following functions determine
7929 an upper or lower bound on a quasipolynomial over its domain.
7931 __isl_give isl_pw_qpolynomial_fold *
7932 isl_pw_qpolynomial_bound(
7933 __isl_take isl_pw_qpolynomial *pwqp,
7934 enum isl_fold type, int *tight);
7936 __isl_give isl_union_pw_qpolynomial_fold *
7937 isl_union_pw_qpolynomial_bound(
7938 __isl_take isl_union_pw_qpolynomial *upwqp,
7939 enum isl_fold type, int *tight);
7941 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7942 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7943 is the returned bound is known be tight, i.e., for each value
7944 of the parameters there is at least
7945 one element in the domain that reaches the bound.
7946 If the domain of C<pwqp> is not wrapping, then the bound is computed
7947 over all elements in that domain and the result has a purely parametric
7948 domain. If the domain of C<pwqp> is wrapping, then the bound is
7949 computed over the range of the wrapped relation. The domain of the
7950 wrapped relation becomes the domain of the result.
7952 =head2 Parametric Vertex Enumeration
7954 The parametric vertex enumeration described in this section
7955 is mainly intended to be used internally and by the C<barvinok>
7958 #include <isl/vertices.h>
7959 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7960 __isl_keep isl_basic_set *bset);
7962 The function C<isl_basic_set_compute_vertices> performs the
7963 actual computation of the parametric vertices and the chamber
7964 decomposition and stores the result in an C<isl_vertices> object.
7965 This information can be queried by either iterating over all
7966 the vertices or iterating over all the chambers or cells
7967 and then iterating over all vertices that are active on the chamber.
7969 isl_stat isl_vertices_foreach_vertex(
7970 __isl_keep isl_vertices *vertices,
7971 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7972 void *user), void *user);
7974 isl_stat isl_vertices_foreach_cell(
7975 __isl_keep isl_vertices *vertices,
7976 isl_stat (*fn)(__isl_take isl_cell *cell,
7977 void *user), void *user);
7978 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7979 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7980 void *user), void *user);
7982 Other operations that can be performed on an C<isl_vertices> object are
7985 int isl_vertices_get_n_vertices(
7986 __isl_keep isl_vertices *vertices);
7987 __isl_null isl_vertices *isl_vertices_free(
7988 __isl_take isl_vertices *vertices);
7990 Vertices can be inspected and destroyed using the following functions.
7992 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7993 __isl_give isl_basic_set *isl_vertex_get_domain(
7994 __isl_keep isl_vertex *vertex);
7995 __isl_give isl_multi_aff *isl_vertex_get_expr(
7996 __isl_keep isl_vertex *vertex);
7997 void isl_vertex_free(__isl_take isl_vertex *vertex);
7999 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
8000 describing the vertex in terms of the parameters,
8001 while C<isl_vertex_get_domain> returns the activity domain
8004 Chambers can be inspected and destroyed using the following functions.
8006 __isl_give isl_basic_set *isl_cell_get_domain(
8007 __isl_keep isl_cell *cell);
8008 void isl_cell_free(__isl_take isl_cell *cell);
8010 =head1 Polyhedral Compilation Library
8012 This section collects functionality in C<isl> that has been specifically
8013 designed for use during polyhedral compilation.
8015 =head2 Schedule Trees
8017 A schedule tree is a structured representation of a schedule,
8018 assigning a relative order to a set of domain elements.
8019 The relative order expressed by the schedule tree is
8020 defined recursively. In particular, the order between
8021 two domain elements is determined by the node that is closest
8022 to the root that refers to both elements and that orders them apart.
8023 Each node in the tree is of one of several types.
8024 The root node is always of type C<isl_schedule_node_domain>
8025 (or C<isl_schedule_node_extension>)
8026 and it describes the (extra) domain elements to which the schedule applies.
8027 The other types of nodes are as follows.
8031 =item C<isl_schedule_node_band>
8033 A band of schedule dimensions. Each schedule dimension is represented
8034 by a union piecewise quasi-affine expression. If this expression
8035 assigns a different value to two domain elements, while all previous
8036 schedule dimensions in the same band assign them the same value,
8037 then the two domain elements are ordered according to these two
8039 Each expression is required to be total in the domain elements
8040 that reach the band node.
8042 =item C<isl_schedule_node_expansion>
8044 An expansion node maps each of the domain elements that reach the node
8045 to one or more domain elements. The image of this mapping forms
8046 the set of domain elements that reach the child of the expansion node.
8047 The function that maps each of the expanded domain elements
8048 to the original domain element from which it was expanded
8049 is called the contraction.
8051 =item C<isl_schedule_node_filter>
8053 A filter node does not impose any ordering, but rather intersects
8054 the set of domain elements that the current subtree refers to
8055 with a given union set. The subtree of the filter node only
8056 refers to domain elements in the intersection.
8057 A filter node is typically only used as a child of a sequence or
8060 =item C<isl_schedule_node_leaf>
8062 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
8064 =item C<isl_schedule_node_mark>
8066 A mark node can be used to attach any kind of information to a subtree
8067 of the schedule tree.
8069 =item C<isl_schedule_node_sequence>
8071 A sequence node has one or more children, each of which is a filter node.
8072 The filters on these filter nodes form a partition of
8073 the domain elements that the current subtree refers to.
8074 If two domain elements appear in distinct filters then the sequence
8075 node orders them according to the child positions of the corresponding
8078 =item C<isl_schedule_node_set>
8080 A set node is similar to a sequence node, except that
8081 it expresses that domain elements appearing in distinct filters
8082 may have any order. The order of the children of a set node
8083 is therefore also immaterial.
8087 The following node types are only supported by the AST generator.
8091 =item C<isl_schedule_node_context>
8093 The context describes constraints on the parameters and
8094 the schedule dimensions of outer
8095 bands that the AST generator may assume to hold. It is also the only
8096 kind of node that may introduce additional parameters.
8097 The space of the context is that of the flat product of the outer
8098 band nodes. In particular, if there are no outer band nodes, then
8099 this space is the unnamed zero-dimensional space.
8100 Since a context node references the outer band nodes, any tree
8101 containing a context node is considered to be anchored.
8103 =item C<isl_schedule_node_extension>
8105 An extension node instructs the AST generator to add additional
8106 domain elements that need to be scheduled.
8107 The additional domain elements are described by the range of
8108 the extension map in terms of the outer schedule dimensions,
8109 i.e., the flat product of the outer band nodes.
8110 Note that domain elements are added whenever the AST generator
8111 reaches the extension node, meaning that there are still some
8112 active domain elements for which an AST needs to be generated.
8113 The conditions under which some domain elements are still active
8114 may however not be completely described by the outer AST nodes
8115 generated at that point.
8116 Since an extension node references the outer band nodes, any tree
8117 containing an extension node is considered to be anchored.
8119 An extension node may also appear as the root of a schedule tree,
8120 when it is intended to be inserted into another tree
8121 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8122 In this case, the domain of the extension node should
8123 correspond to the flat product of the outer band nodes
8124 in this other schedule tree at the point where the extension tree
8127 =item C<isl_schedule_node_guard>
8129 The guard describes constraints on the parameters and
8130 the schedule dimensions of outer
8131 bands that need to be enforced by the outer nodes
8132 in the generated AST.
8133 That is, the part of the AST that is generated from descendants
8134 of the guard node can assume that these constraints are satisfied.
8135 The space of the guard is that of the flat product of the outer
8136 band nodes. In particular, if there are no outer band nodes, then
8137 this space is the unnamed zero-dimensional space.
8138 Since a guard node references the outer band nodes, any tree
8139 containing a guard node is considered to be anchored.
8143 Except for the C<isl_schedule_node_context> nodes,
8144 none of the nodes may introduce any parameters that were not
8145 already present in the root domain node.
8147 A schedule tree is encapsulated in an C<isl_schedule> object.
8148 The simplest such objects, those with a tree consisting of single domain node,
8149 can be created using the following functions with either an empty
8150 domain or a given domain.
8152 #include <isl/schedule.h>
8153 __isl_give isl_schedule *isl_schedule_empty(
8154 __isl_take isl_space *space);
8155 __isl_give isl_schedule *isl_schedule_from_domain(
8156 __isl_take isl_union_set *domain);
8158 The function C<isl_schedule_constraints_compute_schedule> described
8159 in L</"Scheduling"> can also be used to construct schedules.
8161 C<isl_schedule> objects may be copied and freed using the following functions.
8163 #include <isl/schedule.h>
8164 __isl_give isl_schedule *isl_schedule_copy(
8165 __isl_keep isl_schedule *sched);
8166 __isl_null isl_schedule *isl_schedule_free(
8167 __isl_take isl_schedule *sched);
8169 The following functions checks whether two C<isl_schedule> objects
8170 are obviously the same.
8172 #include <isl/schedule.h>
8173 isl_bool isl_schedule_plain_is_equal(
8174 __isl_keep isl_schedule *schedule1,
8175 __isl_keep isl_schedule *schedule2);
8177 The domain of the schedule, i.e., the domain described by the root node,
8178 can be obtained using the following function.
8180 #include <isl/schedule.h>
8181 __isl_give isl_union_set *isl_schedule_get_domain(
8182 __isl_keep isl_schedule *schedule);
8184 An extra top-level band node (right underneath the domain node) can
8185 be introduced into the schedule using the following function.
8186 The schedule tree is assumed not to have any anchored nodes.
8188 #include <isl/schedule.h>
8189 __isl_give isl_schedule *
8190 isl_schedule_insert_partial_schedule(
8191 __isl_take isl_schedule *schedule,
8192 __isl_take isl_multi_union_pw_aff *partial);
8194 A top-level context node (right underneath the domain node) can
8195 be introduced into the schedule using the following function.
8197 #include <isl/schedule.h>
8198 __isl_give isl_schedule *isl_schedule_insert_context(
8199 __isl_take isl_schedule *schedule,
8200 __isl_take isl_set *context)
8202 A top-level guard node (right underneath the domain node) can
8203 be introduced into the schedule using the following function.
8205 #include <isl/schedule.h>
8206 __isl_give isl_schedule *isl_schedule_insert_guard(
8207 __isl_take isl_schedule *schedule,
8208 __isl_take isl_set *guard)
8210 A schedule that combines two schedules either in the given
8211 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8212 or an C<isl_schedule_node_set> node,
8213 can be created using the following functions.
8215 #include <isl/schedule.h>
8216 __isl_give isl_schedule *isl_schedule_sequence(
8217 __isl_take isl_schedule *schedule1,
8218 __isl_take isl_schedule *schedule2);
8219 __isl_give isl_schedule *isl_schedule_set(
8220 __isl_take isl_schedule *schedule1,
8221 __isl_take isl_schedule *schedule2);
8223 The domains of the two input schedules need to be disjoint.
8225 The following function can be used to restrict the domain
8226 of a schedule with a domain node as root to be a subset of the given union set.
8227 This operation may remove nodes in the tree that have become
8230 #include <isl/schedule.h>
8231 __isl_give isl_schedule *isl_schedule_intersect_domain(
8232 __isl_take isl_schedule *schedule,
8233 __isl_take isl_union_set *domain);
8235 The following function can be used to simplify the domain
8236 of a schedule with a domain node as root with respect to the given
8239 #include <isl/schedule.h>
8240 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8241 __isl_take isl_schedule *schedule,
8242 __isl_take isl_set *context);
8244 The following function resets the user pointers on all parameter
8245 and tuple identifiers referenced by the nodes of the given schedule.
8247 #include <isl/schedule.h>
8248 __isl_give isl_schedule *isl_schedule_reset_user(
8249 __isl_take isl_schedule *schedule);
8251 The following function aligns the parameters of all nodes
8252 in the given schedule to the given space.
8254 #include <isl/schedule.h>
8255 __isl_give isl_schedule *isl_schedule_align_params(
8256 __isl_take isl_schedule *schedule,
8257 __isl_take isl_space *space);
8259 The following function allows the user to plug in a given function
8260 in the iteration domains. The input schedule is not allowed to contain
8261 any expansion nodes.
8263 #include <isl/schedule.h>
8264 __isl_give isl_schedule *
8265 isl_schedule_pullback_union_pw_multi_aff(
8266 __isl_take isl_schedule *schedule,
8267 __isl_take isl_union_pw_multi_aff *upma);
8269 The following function can be used to plug in the schedule C<expansion>
8270 in the leaves of C<schedule>, where C<contraction> describes how
8271 the domain elements of C<expansion> map to the domain elements
8272 at the original leaves of C<schedule>.
8273 The resulting schedule will contain expansion nodes, unless
8274 C<contraction> is an identity function.
8276 #include <isl/schedule.h>
8277 __isl_give isl_schedule *isl_schedule_expand(
8278 __isl_take isl_schedule *schedule,
8279 __isl_take isl_union_pw_multi_aff *contraction,
8280 __isl_take isl_schedule *expansion);
8282 An C<isl_union_map> representation of the schedule can be obtained
8283 from an C<isl_schedule> using the following function.
8285 #include <isl/schedule.h>
8286 __isl_give isl_union_map *isl_schedule_get_map(
8287 __isl_keep isl_schedule *sched);
8289 The resulting relation encodes the same relative ordering as
8290 the schedule by mapping the domain elements to a common schedule space.
8291 If the schedule_separate_components option is set, then the order
8292 of the children of a set node is explicitly encoded in the result.
8293 If the tree contains any expansion nodes, then the relation
8294 is formulated in terms of the expanded domain elements.
8296 Schedules can be read from input using the following functions.
8298 #include <isl/schedule.h>
8299 __isl_give isl_schedule *isl_schedule_read_from_file(
8300 isl_ctx *ctx, FILE *input);
8301 __isl_give isl_schedule *isl_schedule_read_from_str(
8302 isl_ctx *ctx, const char *str);
8304 A representation of the schedule can be printed using
8306 #include <isl/schedule.h>
8307 __isl_give isl_printer *isl_printer_print_schedule(
8308 __isl_take isl_printer *p,
8309 __isl_keep isl_schedule *schedule);
8310 __isl_give char *isl_schedule_to_str(
8311 __isl_keep isl_schedule *schedule);
8313 C<isl_schedule_to_str> prints the schedule in flow format.
8315 The schedule tree can be traversed through the use of
8316 C<isl_schedule_node> objects that point to a particular
8317 position in the schedule tree. Whenever a C<isl_schedule_node>
8318 is used to modify a node in the schedule tree, the original schedule
8319 tree is left untouched and the modifications are performed to a copy
8320 of the tree. The returned C<isl_schedule_node> then points to
8321 this modified copy of the tree.
8323 The root of the schedule tree can be obtained using the following function.
8325 #include <isl/schedule.h>
8326 __isl_give isl_schedule_node *isl_schedule_get_root(
8327 __isl_keep isl_schedule *schedule);
8329 A pointer to a newly created schedule tree with a single domain
8330 node can be created using the following functions.
8332 #include <isl/schedule_node.h>
8333 __isl_give isl_schedule_node *
8334 isl_schedule_node_from_domain(
8335 __isl_take isl_union_set *domain);
8336 __isl_give isl_schedule_node *
8337 isl_schedule_node_from_extension(
8338 __isl_take isl_union_map *extension);
8340 C<isl_schedule_node_from_extension> creates a tree with an extension
8343 Schedule nodes can be copied and freed using the following functions.
8345 #include <isl/schedule_node.h>
8346 __isl_give isl_schedule_node *isl_schedule_node_copy(
8347 __isl_keep isl_schedule_node *node);
8348 __isl_null isl_schedule_node *isl_schedule_node_free(
8349 __isl_take isl_schedule_node *node);
8351 The following functions can be used to check if two schedule
8352 nodes point to the same position in the same schedule.
8354 #include <isl/schedule_node.h>
8355 isl_bool isl_schedule_node_is_equal(
8356 __isl_keep isl_schedule_node *node1,
8357 __isl_keep isl_schedule_node *node2);
8359 The following properties can be obtained from a schedule node.
8361 #include <isl/schedule_node.h>
8362 enum isl_schedule_node_type isl_schedule_node_get_type(
8363 __isl_keep isl_schedule_node *node);
8364 enum isl_schedule_node_type
8365 isl_schedule_node_get_parent_type(
8366 __isl_keep isl_schedule_node *node);
8367 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8368 __isl_keep isl_schedule_node *node);
8370 The function C<isl_schedule_node_get_type> returns the type of
8371 the node, while C<isl_schedule_node_get_parent_type> returns
8372 type of the parent of the node, which is required to exist.
8373 The function C<isl_schedule_node_get_schedule> returns a copy
8374 to the schedule to which the node belongs.
8376 The following functions can be used to move the schedule node
8377 to a different position in the tree or to check if such a position
8380 #include <isl/schedule_node.h>
8381 isl_bool isl_schedule_node_has_parent(
8382 __isl_keep isl_schedule_node *node);
8383 __isl_give isl_schedule_node *isl_schedule_node_parent(
8384 __isl_take isl_schedule_node *node);
8385 __isl_give isl_schedule_node *isl_schedule_node_root(
8386 __isl_take isl_schedule_node *node);
8387 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8388 __isl_take isl_schedule_node *node,
8390 int isl_schedule_node_n_children(
8391 __isl_keep isl_schedule_node *node);
8392 __isl_give isl_schedule_node *isl_schedule_node_child(
8393 __isl_take isl_schedule_node *node, int pos);
8394 isl_bool isl_schedule_node_has_children(
8395 __isl_keep isl_schedule_node *node);
8396 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8397 __isl_take isl_schedule_node *node);
8398 isl_bool isl_schedule_node_has_previous_sibling(
8399 __isl_keep isl_schedule_node *node);
8400 __isl_give isl_schedule_node *
8401 isl_schedule_node_previous_sibling(
8402 __isl_take isl_schedule_node *node);
8403 isl_bool isl_schedule_node_has_next_sibling(
8404 __isl_keep isl_schedule_node *node);
8405 __isl_give isl_schedule_node *
8406 isl_schedule_node_next_sibling(
8407 __isl_take isl_schedule_node *node);
8409 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8410 is the node itself, the ancestor of generation 1 is its parent and so on.
8412 It is also possible to query the number of ancestors of a node,
8413 the position of the current node
8414 within the children of its parent, the position of the subtree
8415 containing a node within the children of an ancestor
8416 or to obtain a copy of a given
8417 child without destroying the current node.
8418 Given two nodes that point to the same schedule, their closest
8419 shared ancestor can be obtained using
8420 C<isl_schedule_node_get_shared_ancestor>.
8422 #include <isl/schedule_node.h>
8423 int isl_schedule_node_get_tree_depth(
8424 __isl_keep isl_schedule_node *node);
8425 int isl_schedule_node_get_child_position(
8426 __isl_keep isl_schedule_node *node);
8427 int isl_schedule_node_get_ancestor_child_position(
8428 __isl_keep isl_schedule_node *node,
8429 __isl_keep isl_schedule_node *ancestor);
8430 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8431 __isl_keep isl_schedule_node *node, int pos);
8432 __isl_give isl_schedule_node *
8433 isl_schedule_node_get_shared_ancestor(
8434 __isl_keep isl_schedule_node *node1,
8435 __isl_keep isl_schedule_node *node2);
8437 All nodes in a schedule tree or
8438 all descendants of a specific node (including the node) can be visited
8439 in depth-first pre-order using the following functions.
8441 #include <isl/schedule.h>
8442 isl_stat isl_schedule_foreach_schedule_node_top_down(
8443 __isl_keep isl_schedule *sched,
8444 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8445 void *user), void *user);
8447 #include <isl/schedule_node.h>
8448 isl_stat isl_schedule_node_foreach_descendant_top_down(
8449 __isl_keep isl_schedule_node *node,
8450 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8451 void *user), void *user);
8453 The callback function is slightly different from the usual
8454 callbacks in that it not only indicates success (non-negative result)
8455 or failure (negative result), but also indicates whether the children
8456 of the given node should be visited. In particular, if the callback
8457 returns a positive value, then the children are visited, but if
8458 the callback returns zero, then the children are not visited.
8460 The following functions checks whether
8461 all descendants of a specific node (including the node itself)
8462 satisfy a user-specified test.
8464 #include <isl/schedule_node.h>
8465 isl_bool isl_schedule_node_every_descendant(
8466 __isl_keep isl_schedule_node *node,
8467 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8468 void *user), void *user)
8470 The ancestors of a node in a schedule tree can be visited from
8471 the root down to and including the parent of the node using
8472 the following function.
8474 #include <isl/schedule_node.h>
8475 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8476 __isl_keep isl_schedule_node *node,
8477 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8478 void *user), void *user);
8480 The following functions allows for a depth-first post-order
8481 traversal of the nodes in a schedule tree or
8482 of the descendants of a specific node (including the node
8483 itself), where the user callback is allowed to modify the
8486 #include <isl/schedule.h>
8487 __isl_give isl_schedule *
8488 isl_schedule_map_schedule_node_bottom_up(
8489 __isl_take isl_schedule *schedule,
8490 __isl_give isl_schedule_node *(*fn)(
8491 __isl_take isl_schedule_node *node,
8492 void *user), void *user);
8494 #include <isl/schedule_node.h>
8495 __isl_give isl_schedule_node *
8496 isl_schedule_node_map_descendant_bottom_up(
8497 __isl_take isl_schedule_node *node,
8498 __isl_give isl_schedule_node *(*fn)(
8499 __isl_take isl_schedule_node *node,
8500 void *user), void *user);
8502 The traversal continues from the node returned by the callback function.
8503 It is the responsibility of the user to ensure that this does not
8504 lead to an infinite loop. It is safest to always return a pointer
8505 to the same position (same ancestors and child positions) as the input node.
8507 The following function removes a node (along with its descendants)
8508 from a schedule tree and returns a pointer to the leaf at the
8509 same position in the updated tree.
8510 It is not allowed to remove the root of a schedule tree or
8511 a child of a set or sequence node.
8513 #include <isl/schedule_node.h>
8514 __isl_give isl_schedule_node *isl_schedule_node_cut(
8515 __isl_take isl_schedule_node *node);
8517 The following function removes a single node
8518 from a schedule tree and returns a pointer to the child
8519 of the node, now located at the position of the original node
8520 or to a leaf node at that position if there was no child.
8521 It is not allowed to remove the root of a schedule tree,
8522 a set or sequence node, a child of a set or sequence node or
8523 a band node with an anchored subtree.
8525 #include <isl/schedule_node.h>
8526 __isl_give isl_schedule_node *isl_schedule_node_delete(
8527 __isl_take isl_schedule_node *node);
8529 Most nodes in a schedule tree only contain local information.
8530 In some cases, however, a node may also refer to the schedule dimensions
8531 of its outer band nodes.
8532 This means that the position of the node within the tree should
8533 not be changed, or at least that no changes are performed to the
8534 outer band nodes. The following function can be used to test
8535 whether the subtree rooted at a given node contains any such nodes.
8537 #include <isl/schedule_node.h>
8538 isl_bool isl_schedule_node_is_subtree_anchored(
8539 __isl_keep isl_schedule_node *node);
8541 The following function resets the user pointers on all parameter
8542 and tuple identifiers referenced by the given schedule node.
8544 #include <isl/schedule_node.h>
8545 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8546 __isl_take isl_schedule_node *node);
8548 The following function aligns the parameters of the given schedule
8549 node to the given space.
8551 #include <isl/schedule_node.h>
8552 __isl_give isl_schedule_node *
8553 isl_schedule_node_align_params(
8554 __isl_take isl_schedule_node *node,
8555 __isl_take isl_space *space);
8557 Several node types have their own functions for querying
8558 (and in some cases setting) some node type specific properties.
8560 #include <isl/schedule_node.h>
8561 __isl_give isl_space *isl_schedule_node_band_get_space(
8562 __isl_keep isl_schedule_node *node);
8563 __isl_give isl_multi_union_pw_aff *
8564 isl_schedule_node_band_get_partial_schedule(
8565 __isl_keep isl_schedule_node *node);
8566 __isl_give isl_union_map *
8567 isl_schedule_node_band_get_partial_schedule_union_map(
8568 __isl_keep isl_schedule_node *node);
8569 unsigned isl_schedule_node_band_n_member(
8570 __isl_keep isl_schedule_node *node);
8571 isl_bool isl_schedule_node_band_member_get_coincident(
8572 __isl_keep isl_schedule_node *node, int pos);
8573 __isl_give isl_schedule_node *
8574 isl_schedule_node_band_member_set_coincident(
8575 __isl_take isl_schedule_node *node, int pos,
8577 isl_bool isl_schedule_node_band_get_permutable(
8578 __isl_keep isl_schedule_node *node);
8579 __isl_give isl_schedule_node *
8580 isl_schedule_node_band_set_permutable(
8581 __isl_take isl_schedule_node *node, int permutable);
8582 enum isl_ast_loop_type
8583 isl_schedule_node_band_member_get_ast_loop_type(
8584 __isl_keep isl_schedule_node *node, int pos);
8585 __isl_give isl_schedule_node *
8586 isl_schedule_node_band_member_set_ast_loop_type(
8587 __isl_take isl_schedule_node *node, int pos,
8588 enum isl_ast_loop_type type);
8589 __isl_give isl_union_set *
8590 enum isl_ast_loop_type
8591 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8592 __isl_keep isl_schedule_node *node, int pos);
8593 __isl_give isl_schedule_node *
8594 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8595 __isl_take isl_schedule_node *node, int pos,
8596 enum isl_ast_loop_type type);
8597 isl_schedule_node_band_get_ast_build_options(
8598 __isl_keep isl_schedule_node *node);
8599 __isl_give isl_schedule_node *
8600 isl_schedule_node_band_set_ast_build_options(
8601 __isl_take isl_schedule_node *node,
8602 __isl_take isl_union_set *options);
8603 __isl_give isl_set *
8604 isl_schedule_node_band_get_ast_isolate_option(
8605 __isl_keep isl_schedule_node *node);
8607 The function C<isl_schedule_node_band_get_space> returns the space
8608 of the partial schedule of the band.
8609 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8610 returns a representation of the partial schedule of the band node
8611 in the form of an C<isl_union_map>.
8612 The coincident and permutable properties are set by
8613 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8615 A scheduling dimension is considered to be ``coincident''
8616 if it satisfies the coincidence constraints within its band.
8617 That is, if the dependence distances of the coincidence
8618 constraints are all zero in that direction (for fixed
8619 iterations of outer bands).
8620 A band is marked permutable if it was produced using the Pluto-like scheduler.
8621 Note that the scheduler may have to resort to a Feautrier style scheduling
8622 step even if the default scheduler is used.
8623 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8624 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8625 For the meaning of these loop AST generation types and the difference
8626 between the regular loop AST generation type and the isolate
8627 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8628 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8629 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8630 may return C<isl_ast_loop_error> if an error occurs.
8631 The AST build options govern how an AST is generated for
8632 the individual schedule dimensions during AST generation.
8633 See L</"AST Generation Options (Schedule Tree)">.
8634 The isolate option for the given node can be extracted from these
8635 AST build options using the function
8636 C<isl_schedule_node_band_get_ast_isolate_option>.
8638 #include <isl/schedule_node.h>
8639 __isl_give isl_set *
8640 isl_schedule_node_context_get_context(
8641 __isl_keep isl_schedule_node *node);
8643 #include <isl/schedule_node.h>
8644 __isl_give isl_union_set *
8645 isl_schedule_node_domain_get_domain(
8646 __isl_keep isl_schedule_node *node);
8648 #include <isl/schedule_node.h>
8649 __isl_give isl_union_map *
8650 isl_schedule_node_expansion_get_expansion(
8651 __isl_keep isl_schedule_node *node);
8652 __isl_give isl_union_pw_multi_aff *
8653 isl_schedule_node_expansion_get_contraction(
8654 __isl_keep isl_schedule_node *node);
8656 #include <isl/schedule_node.h>
8657 __isl_give isl_union_map *
8658 isl_schedule_node_extension_get_extension(
8659 __isl_keep isl_schedule_node *node);
8661 #include <isl/schedule_node.h>
8662 __isl_give isl_union_set *
8663 isl_schedule_node_filter_get_filter(
8664 __isl_keep isl_schedule_node *node);
8666 #include <isl/schedule_node.h>
8667 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8668 __isl_keep isl_schedule_node *node);
8670 #include <isl/schedule_node.h>
8671 __isl_give isl_id *isl_schedule_node_mark_get_id(
8672 __isl_keep isl_schedule_node *node);
8674 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8675 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8676 partial schedules related to the node.
8678 #include <isl/schedule_node.h>
8679 __isl_give isl_multi_union_pw_aff *
8680 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8681 __isl_keep isl_schedule_node *node);
8682 __isl_give isl_union_pw_multi_aff *
8683 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8684 __isl_keep isl_schedule_node *node);
8685 __isl_give isl_union_map *
8686 isl_schedule_node_get_prefix_schedule_union_map(
8687 __isl_keep isl_schedule_node *node);
8688 __isl_give isl_union_map *
8689 isl_schedule_node_get_prefix_schedule_relation(
8690 __isl_keep isl_schedule_node *node);
8691 __isl_give isl_union_map *
8692 isl_schedule_node_get_subtree_schedule_union_map(
8693 __isl_keep isl_schedule_node *node);
8695 In particular, the functions
8696 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8697 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8698 and C<isl_schedule_node_get_prefix_schedule_union_map>
8699 return a relative ordering on the domain elements that reach the given
8700 node determined by its ancestors.
8701 The function C<isl_schedule_node_get_prefix_schedule_relation>
8702 additionally includes the domain constraints in the result.
8703 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8704 returns a representation of the partial schedule defined by the
8705 subtree rooted at the given node.
8706 If the tree contains any expansion nodes, then the subtree schedule
8707 is formulated in terms of the expanded domain elements.
8708 The tree passed to functions returning a prefix schedule
8709 may only contain extension nodes if these would not affect
8710 the result of these functions. That is, if one of the ancestors
8711 is an extension node, then all of the domain elements that were
8712 added by the extension node need to have been filtered out
8713 by filter nodes between the extension node and the input node.
8714 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8715 may not contain in extension nodes in the selected subtree.
8717 The expansion/contraction defined by an entire subtree, combining
8718 the expansions/contractions
8719 on the expansion nodes in the subtree, can be obtained using
8720 the following functions.
8722 #include <isl/schedule_node.h>
8723 __isl_give isl_union_map *
8724 isl_schedule_node_get_subtree_expansion(
8725 __isl_keep isl_schedule_node *node);
8726 __isl_give isl_union_pw_multi_aff *
8727 isl_schedule_node_get_subtree_contraction(
8728 __isl_keep isl_schedule_node *node);
8730 The total number of outer band members of given node, i.e.,
8731 the shared output dimension of the maps in the result
8732 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8733 using the following function.
8735 #include <isl/schedule_node.h>
8736 int isl_schedule_node_get_schedule_depth(
8737 __isl_keep isl_schedule_node *node);
8739 The following functions return the elements that reach the given node
8740 or the union of universes in the spaces that contain these elements.
8742 #include <isl/schedule_node.h>
8743 __isl_give isl_union_set *
8744 isl_schedule_node_get_domain(
8745 __isl_keep isl_schedule_node *node);
8746 __isl_give isl_union_set *
8747 isl_schedule_node_get_universe_domain(
8748 __isl_keep isl_schedule_node *node);
8750 The input tree of C<isl_schedule_node_get_domain>
8751 may only contain extension nodes if these would not affect
8752 the result of this function. That is, if one of the ancestors
8753 is an extension node, then all of the domain elements that were
8754 added by the extension node need to have been filtered out
8755 by filter nodes between the extension node and the input node.
8757 The following functions can be used to introduce additional nodes
8758 in the schedule tree. The new node is introduced at the point
8759 in the tree where the C<isl_schedule_node> points to and
8760 the results points to the new node.
8762 #include <isl/schedule_node.h>
8763 __isl_give isl_schedule_node *
8764 isl_schedule_node_insert_partial_schedule(
8765 __isl_take isl_schedule_node *node,
8766 __isl_take isl_multi_union_pw_aff *schedule);
8768 This function inserts a new band node with (the greatest integer
8769 part of) the given partial schedule.
8770 The subtree rooted at the given node is assumed not to have
8773 #include <isl/schedule_node.h>
8774 __isl_give isl_schedule_node *
8775 isl_schedule_node_insert_context(
8776 __isl_take isl_schedule_node *node,
8777 __isl_take isl_set *context);
8779 This function inserts a new context node with the given context constraints.
8781 #include <isl/schedule_node.h>
8782 __isl_give isl_schedule_node *
8783 isl_schedule_node_insert_filter(
8784 __isl_take isl_schedule_node *node,
8785 __isl_take isl_union_set *filter);
8787 This function inserts a new filter node with the given filter.
8788 If the original node already pointed to a filter node, then the
8789 two filter nodes are merged into one.
8791 #include <isl/schedule_node.h>
8792 __isl_give isl_schedule_node *
8793 isl_schedule_node_insert_guard(
8794 __isl_take isl_schedule_node *node,
8795 __isl_take isl_set *guard);
8797 This function inserts a new guard node with the given guard constraints.
8799 #include <isl/schedule_node.h>
8800 __isl_give isl_schedule_node *
8801 isl_schedule_node_insert_mark(
8802 __isl_take isl_schedule_node *node,
8803 __isl_take isl_id *mark);
8805 This function inserts a new mark node with the give mark identifier.
8807 #include <isl/schedule_node.h>
8808 __isl_give isl_schedule_node *
8809 isl_schedule_node_insert_sequence(
8810 __isl_take isl_schedule_node *node,
8811 __isl_take isl_union_set_list *filters);
8812 __isl_give isl_schedule_node *
8813 isl_schedule_node_insert_set(
8814 __isl_take isl_schedule_node *node,
8815 __isl_take isl_union_set_list *filters);
8817 These functions insert a new sequence or set node with the given
8818 filters as children.
8820 #include <isl/schedule_node.h>
8821 __isl_give isl_schedule_node *isl_schedule_node_group(
8822 __isl_take isl_schedule_node *node,
8823 __isl_take isl_id *group_id);
8825 This function introduces an expansion node in between the current
8826 node and its parent that expands instances of a space with tuple
8827 identifier C<group_id> to the original domain elements that reach
8828 the node. The group instances are identified by the prefix schedule
8829 of those domain elements. The ancestors of the node are adjusted
8830 to refer to the group instances instead of the original domain
8831 elements. The return value points to the same node in the updated
8832 schedule tree as the input node, i.e., to the child of the newly
8833 introduced expansion node. Grouping instances of different statements
8834 ensures that they will be treated as a single statement by the
8835 AST generator up to the point of the expansion node.
8837 The following function can be used to flatten a nested
8840 #include <isl/schedule_node.h>
8841 __isl_give isl_schedule_node *
8842 isl_schedule_node_sequence_splice_child(
8843 __isl_take isl_schedule_node *node, int pos);
8845 That is, given a sequence node C<node> that has another sequence node
8846 in its child at position C<pos> (in particular, the child of that filter
8847 node is a sequence node), attach the children of that other sequence
8848 node as children of C<node>, replacing the original child at position
8851 The partial schedule of a band node can be scaled (down) or reduced using
8852 the following functions.
8854 #include <isl/schedule_node.h>
8855 __isl_give isl_schedule_node *
8856 isl_schedule_node_band_scale(
8857 __isl_take isl_schedule_node *node,
8858 __isl_take isl_multi_val *mv);
8859 __isl_give isl_schedule_node *
8860 isl_schedule_node_band_scale_down(
8861 __isl_take isl_schedule_node *node,
8862 __isl_take isl_multi_val *mv);
8863 __isl_give isl_schedule_node *
8864 isl_schedule_node_band_mod(
8865 __isl_take isl_schedule_node *node,
8866 __isl_take isl_multi_val *mv);
8868 The spaces of the two arguments need to match.
8869 After scaling, the partial schedule is replaced by its greatest
8870 integer part to ensure that the schedule remains integral.
8872 The partial schedule of a band node can be shifted by an
8873 C<isl_multi_union_pw_aff> with a domain that is a superset
8874 of the domain of the partial schedule using
8875 the following function.
8877 #include <isl/schedule_node.h>
8878 __isl_give isl_schedule_node *
8879 isl_schedule_node_band_shift(
8880 __isl_take isl_schedule_node *node,
8881 __isl_take isl_multi_union_pw_aff *shift);
8883 A band node can be tiled using the following function.
8885 #include <isl/schedule_node.h>
8886 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8887 __isl_take isl_schedule_node *node,
8888 __isl_take isl_multi_val *sizes);
8890 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8892 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8893 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8895 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8897 The C<isl_schedule_node_band_tile> function tiles
8898 the band using the given tile sizes inside its schedule.
8899 A new child band node is created to represent the point loops and it is
8900 inserted between the modified band and its children.
8901 The subtree rooted at the given node is assumed not to have
8903 The C<tile_scale_tile_loops> option specifies whether the tile
8904 loops iterators should be scaled by the tile sizes.
8905 If the C<tile_shift_point_loops> option is set, then the point loops
8906 are shifted to start at zero.
8908 A band node can be split into two nested band nodes
8909 using the following function.
8911 #include <isl/schedule_node.h>
8912 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8913 __isl_take isl_schedule_node *node, int pos);
8915 The resulting outer band node contains the first C<pos> dimensions of
8916 the schedule of C<node> while the inner band contains the remaining dimensions.
8917 The schedules of the two band nodes live in anonymous spaces.
8918 The loop AST generation type options and the isolate option
8919 are split over the two band nodes.
8921 A band node can be moved down to the leaves of the subtree rooted
8922 at the band node using the following function.
8924 #include <isl/schedule_node.h>
8925 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8926 __isl_take isl_schedule_node *node);
8928 The subtree rooted at the given node is assumed not to have
8930 The result points to the node in the resulting tree that is in the same
8931 position as the node pointed to by C<node> in the original tree.
8933 #include <isl/schedule_node.h>
8934 __isl_give isl_schedule_node *
8935 isl_schedule_node_order_before(
8936 __isl_take isl_schedule_node *node,
8937 __isl_take isl_union_set *filter);
8938 __isl_give isl_schedule_node *
8939 isl_schedule_node_order_after(
8940 __isl_take isl_schedule_node *node,
8941 __isl_take isl_union_set *filter);
8943 These functions split the domain elements that reach C<node>
8944 into those that satisfy C<filter> and those that do not and
8945 arranges for the elements that do satisfy the filter to be
8946 executed before (in case of C<isl_schedule_node_order_before>)
8947 or after (in case of C<isl_schedule_node_order_after>)
8948 those that do not. The order is imposed by
8949 a sequence node, possibly reusing the grandparent of C<node>
8950 on two copies of the subtree attached to the original C<node>.
8951 Both copies are simplified with respect to their filter.
8953 Return a pointer to the copy of the subtree that does not
8954 satisfy C<filter>. If there is no such copy (because all
8955 reaching domain elements satisfy the filter), then return
8956 the original pointer.
8958 #include <isl/schedule_node.h>
8959 __isl_give isl_schedule_node *
8960 isl_schedule_node_graft_before(
8961 __isl_take isl_schedule_node *node,
8962 __isl_take isl_schedule_node *graft);
8963 __isl_give isl_schedule_node *
8964 isl_schedule_node_graft_after(
8965 __isl_take isl_schedule_node *node,
8966 __isl_take isl_schedule_node *graft);
8968 This function inserts the C<graft> tree into the tree containing C<node>
8969 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8970 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8971 The root node of C<graft>
8972 should be an extension node where the domain of the extension
8973 is the flat product of all outer band nodes of C<node>.
8974 The root node may also be a domain node.
8975 The elements of the domain or the range of the extension may not
8976 intersect with the domain elements that reach "node".
8977 The schedule tree of C<graft> may not be anchored.
8979 The schedule tree of C<node> is modified to include an extension node
8980 corresponding to the root node of C<graft> as a child of the original
8981 parent of C<node>. The original node that C<node> points to and the
8982 child of the root node of C<graft> are attached to this extension node
8983 through a sequence, with appropriate filters and with the child
8984 of C<graft> appearing before or after the original C<node>.
8986 If C<node> already appears inside a sequence that is the child of
8987 an extension node and if the spaces of the new domain elements
8988 do not overlap with those of the original domain elements,
8989 then that extension node is extended with the new extension
8990 rather than introducing a new segment of extension and sequence nodes.
8992 Return a pointer to the same node in the modified tree that
8993 C<node> pointed to in the original tree.
8995 A representation of the schedule node can be printed using
8997 #include <isl/schedule_node.h>
8998 __isl_give isl_printer *isl_printer_print_schedule_node(
8999 __isl_take isl_printer *p,
9000 __isl_keep isl_schedule_node *node);
9001 __isl_give char *isl_schedule_node_to_str(
9002 __isl_keep isl_schedule_node *node);
9004 C<isl_schedule_node_to_str> prints the schedule node in block format.
9006 =head2 Dependence Analysis
9008 C<isl> contains specialized functionality for performing
9009 array dataflow analysis. That is, given a I<sink> access relation,
9010 a collection of possible I<source> accesses and
9011 a collection of I<kill> accesses,
9012 C<isl> can compute relations that describe
9013 for each iteration of the sink access, which iterations
9014 of which of the source access relations may have
9015 accessed the same data element before the given iteration
9016 of the sink access without any intermediate kill of that data element.
9017 The resulting dependence relations map source iterations
9018 to either the corresponding sink iterations or
9019 pairs of corresponding sink iterations and accessed data elements.
9020 To compute standard flow dependences, the sink should be
9021 a read, while the sources should be writes.
9022 If no kills are specified,
9023 then memory based dependence analysis is performed.
9024 If, on the other hand, all sources are also kills,
9025 then value based dependence analysis is performed.
9026 If any of the source accesses are marked as being I<must>
9027 accesses, then they are also treated as kills.
9028 Furthermore, the specification of must-sources results
9029 in the computation of must-dependences.
9030 Only dependences originating in a must access not coscheduled
9031 with any other access to the same element and without
9032 any may accesses between the must access and the sink access
9033 are considered to be must dependences.
9035 =head3 High-level Interface
9037 A high-level interface to dependence analysis is provided
9038 by the following function.
9040 #include <isl/flow.h>
9041 __isl_give isl_union_flow *
9042 isl_union_access_info_compute_flow(
9043 __isl_take isl_union_access_info *access);
9045 The input C<isl_union_access_info> object describes the sink
9046 access relations, the source access relations and a schedule,
9047 while the output C<isl_union_flow> object describes
9048 the resulting dependence relations and the subsets of the
9049 sink relations for which no source was found.
9051 An C<isl_union_access_info> is created, modified, copied and freed using
9052 the following functions.
9054 #include <isl/flow.h>
9055 __isl_give isl_union_access_info *
9056 isl_union_access_info_from_sink(
9057 __isl_take isl_union_map *sink);
9058 __isl_give isl_union_access_info *
9059 isl_union_access_info_set_kill(
9060 __isl_take isl_union_access_info *access,
9061 __isl_take isl_union_map *kill);
9062 __isl_give isl_union_access_info *
9063 isl_union_access_info_set_may_source(
9064 __isl_take isl_union_access_info *access,
9065 __isl_take isl_union_map *may_source);
9066 __isl_give isl_union_access_info *
9067 isl_union_access_info_set_must_source(
9068 __isl_take isl_union_access_info *access,
9069 __isl_take isl_union_map *must_source);
9070 __isl_give isl_union_access_info *
9071 isl_union_access_info_set_schedule(
9072 __isl_take isl_union_access_info *access,
9073 __isl_take isl_schedule *schedule);
9074 __isl_give isl_union_access_info *
9075 isl_union_access_info_set_schedule_map(
9076 __isl_take isl_union_access_info *access,
9077 __isl_take isl_union_map *schedule_map);
9078 __isl_give isl_union_access_info *
9079 isl_union_access_info_copy(
9080 __isl_keep isl_union_access_info *access);
9081 __isl_null isl_union_access_info *
9082 isl_union_access_info_free(
9083 __isl_take isl_union_access_info *access);
9085 The may sources set by C<isl_union_access_info_set_may_source>
9086 do not need to include the must sources set by
9087 C<isl_union_access_info_set_must_source> as a subset.
9088 The kills set by C<isl_union_access_info_set_kill> may overlap
9089 with the may-sources and/or must-sources.
9090 The user is free not to call one (or more) of these functions,
9091 in which case the corresponding set is kept to its empty default.
9092 Similarly, the default schedule initialized by
9093 C<isl_union_access_info_from_sink> is empty.
9094 The current schedule is determined by the last call to either
9095 C<isl_union_access_info_set_schedule> or
9096 C<isl_union_access_info_set_schedule_map>.
9097 The domain of the schedule corresponds to the domains of
9098 the access relations. In particular, the domains of the access
9099 relations are effectively intersected with the domain of the schedule
9100 and only the resulting accesses are considered by the dependence analysis.
9102 An C<isl_union_access_info> object can be read from input
9103 using the following function.
9105 #include <isl/flow.h>
9106 __isl_give isl_union_access_info *
9107 isl_union_access_info_read_from_file(isl_ctx *ctx,
9110 A representation of the information contained in an object
9111 of type C<isl_union_access_info> can be obtained using
9113 #include <isl/flow.h>
9114 __isl_give isl_printer *
9115 isl_printer_print_union_access_info(
9116 __isl_take isl_printer *p,
9117 __isl_keep isl_union_access_info *access);
9118 __isl_give char *isl_union_access_info_to_str(
9119 __isl_keep isl_union_access_info *access);
9121 C<isl_union_access_info_to_str> prints the information in flow format.
9123 The output of C<isl_union_access_info_compute_flow> can be examined,
9124 copied, and freed using the following functions.
9126 #include <isl/flow.h>
9127 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9128 __isl_keep isl_union_flow *flow);
9129 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9130 __isl_keep isl_union_flow *flow);
9131 __isl_give isl_union_map *
9132 isl_union_flow_get_full_must_dependence(
9133 __isl_keep isl_union_flow *flow);
9134 __isl_give isl_union_map *
9135 isl_union_flow_get_full_may_dependence(
9136 __isl_keep isl_union_flow *flow);
9137 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9138 __isl_keep isl_union_flow *flow);
9139 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9140 __isl_keep isl_union_flow *flow);
9141 __isl_give isl_union_flow *isl_union_flow_copy(
9142 __isl_keep isl_union_flow *flow);
9143 __isl_null isl_union_flow *isl_union_flow_free(
9144 __isl_take isl_union_flow *flow);
9146 The relation returned by C<isl_union_flow_get_must_dependence>
9147 relates domain elements of must sources to domain elements of the sink.
9148 The relation returned by C<isl_union_flow_get_may_dependence>
9149 relates domain elements of must or may sources to domain elements of the sink
9150 and includes the previous relation as a subset.
9151 The relation returned by C<isl_union_flow_get_full_must_dependence>
9152 relates domain elements of must sources to pairs of domain elements of the sink
9153 and accessed data elements.
9154 The relation returned by C<isl_union_flow_get_full_may_dependence>
9155 relates domain elements of must or may sources to pairs of
9156 domain elements of the sink and accessed data elements.
9157 This relation includes the previous relation as a subset.
9158 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9159 of the sink relation for which no dependences have been found.
9160 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9161 of the sink relation for which no definite dependences have been found.
9162 That is, it contains those sink access that do not contribute to any
9163 of the elements in the relation returned
9164 by C<isl_union_flow_get_must_dependence>.
9166 A representation of the information contained in an object
9167 of type C<isl_union_flow> can be obtained using
9169 #include <isl/flow.h>
9170 __isl_give isl_printer *isl_printer_print_union_flow(
9171 __isl_take isl_printer *p,
9172 __isl_keep isl_union_flow *flow);
9173 __isl_give char *isl_union_flow_to_str(
9174 __isl_keep isl_union_flow *flow);
9176 C<isl_union_flow_to_str> prints the information in flow format.
9178 =head3 Low-level Interface
9180 A lower-level interface is provided by the following functions.
9182 #include <isl/flow.h>
9184 typedef int (*isl_access_level_before)(void *first, void *second);
9186 __isl_give isl_access_info *isl_access_info_alloc(
9187 __isl_take isl_map *sink,
9188 void *sink_user, isl_access_level_before fn,
9190 __isl_give isl_access_info *isl_access_info_add_source(
9191 __isl_take isl_access_info *acc,
9192 __isl_take isl_map *source, int must,
9194 __isl_null isl_access_info *isl_access_info_free(
9195 __isl_take isl_access_info *acc);
9197 __isl_give isl_flow *isl_access_info_compute_flow(
9198 __isl_take isl_access_info *acc);
9200 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9201 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9202 void *dep_user, void *user),
9204 __isl_give isl_map *isl_flow_get_no_source(
9205 __isl_keep isl_flow *deps, int must);
9206 void isl_flow_free(__isl_take isl_flow *deps);
9208 The function C<isl_access_info_compute_flow> performs the actual
9209 dependence analysis. The other functions are used to construct
9210 the input for this function or to read off the output.
9212 The input is collected in an C<isl_access_info>, which can
9213 be created through a call to C<isl_access_info_alloc>.
9214 The arguments to this functions are the sink access relation
9215 C<sink>, a token C<sink_user> used to identify the sink
9216 access to the user, a callback function for specifying the
9217 relative order of source and sink accesses, and the number
9218 of source access relations that will be added.
9220 The callback function has type C<int (*)(void *first, void *second)>.
9221 The function is called with two user supplied tokens identifying
9222 either a source or the sink and it should return the shared nesting
9223 level and the relative order of the two accesses.
9224 In particular, let I<n> be the number of loops shared by
9225 the two accesses. If C<first> precedes C<second> textually,
9226 then the function should return I<2 * n + 1>; otherwise,
9227 it should return I<2 * n>.
9228 The low-level interface assumes that no sources are coscheduled.
9229 If the information returned by the callback does not allow
9230 the relative order to be determined, then one of the sources
9231 is arbitrarily taken to be executed after the other(s).
9233 The sources can be added to the C<isl_access_info> object by performing
9234 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9235 C<must> indicates whether the source is a I<must> access
9236 or a I<may> access. Note that a multi-valued access relation
9237 should only be marked I<must> if every iteration in the domain
9238 of the relation accesses I<all> elements in its image.
9239 The C<source_user> token is again used to identify
9240 the source access. The range of the source access relation
9241 C<source> should have the same dimension as the range
9242 of the sink access relation.
9243 The C<isl_access_info_free> function should usually not be
9244 called explicitly, because it is already called implicitly by
9245 C<isl_access_info_compute_flow>.
9247 The result of the dependence analysis is collected in an
9248 C<isl_flow>. There may be elements of
9249 the sink access for which no preceding source access could be
9250 found or for which all preceding sources are I<may> accesses.
9251 The relations containing these elements can be obtained through
9252 calls to C<isl_flow_get_no_source>, the first with C<must> set
9253 and the second with C<must> unset.
9254 In the case of standard flow dependence analysis,
9255 with the sink a read and the sources I<must> writes,
9256 the first relation corresponds to the reads from uninitialized
9257 array elements and the second relation is empty.
9258 The actual flow dependences can be extracted using
9259 C<isl_flow_foreach>. This function will call the user-specified
9260 callback function C<fn> for each B<non-empty> dependence between
9261 a source and the sink. The callback function is called
9262 with four arguments, the actual flow dependence relation
9263 mapping source iterations to sink iterations, a boolean that
9264 indicates whether it is a I<must> or I<may> dependence, a token
9265 identifying the source and an additional C<void *> with value
9266 equal to the third argument of the C<isl_flow_foreach> call.
9267 A dependence is marked I<must> if it originates from a I<must>
9268 source and if it is not followed by any I<may> sources.
9270 After finishing with an C<isl_flow>, the user should call
9271 C<isl_flow_free> to free all associated memory.
9273 =head3 Interaction with the Low-level Interface
9275 During the dependence analysis, we frequently need to perform
9276 the following operation. Given a relation between sink iterations
9277 and potential source iterations from a particular source domain,
9278 what is the last potential source iteration corresponding to each
9279 sink iteration. It can sometimes be convenient to adjust
9280 the set of potential source iterations before or after each such operation.
9281 The prototypical example is fuzzy array dataflow analysis,
9282 where we need to analyze if, based on data-dependent constraints,
9283 the sink iteration can ever be executed without one or more of
9284 the corresponding potential source iterations being executed.
9285 If so, we can introduce extra parameters and select an unknown
9286 but fixed source iteration from the potential source iterations.
9287 To be able to perform such manipulations, C<isl> provides the following
9290 #include <isl/flow.h>
9292 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9293 __isl_keep isl_map *source_map,
9294 __isl_keep isl_set *sink, void *source_user,
9296 __isl_give isl_access_info *isl_access_info_set_restrict(
9297 __isl_take isl_access_info *acc,
9298 isl_access_restrict fn, void *user);
9300 The function C<isl_access_info_set_restrict> should be called
9301 before calling C<isl_access_info_compute_flow> and registers a callback function
9302 that will be called any time C<isl> is about to compute the last
9303 potential source. The first argument is the (reverse) proto-dependence,
9304 mapping sink iterations to potential source iterations.
9305 The second argument represents the sink iterations for which
9306 we want to compute the last source iteration.
9307 The third argument is the token corresponding to the source
9308 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9309 The callback is expected to return a restriction on either the input or
9310 the output of the operation computing the last potential source.
9311 If the input needs to be restricted then restrictions are needed
9312 for both the source and the sink iterations. The sink iterations
9313 and the potential source iterations will be intersected with these sets.
9314 If the output needs to be restricted then only a restriction on the source
9315 iterations is required.
9316 If any error occurs, the callback should return C<NULL>.
9317 An C<isl_restriction> object can be created, freed and inspected
9318 using the following functions.
9320 #include <isl/flow.h>
9322 __isl_give isl_restriction *isl_restriction_input(
9323 __isl_take isl_set *source_restr,
9324 __isl_take isl_set *sink_restr);
9325 __isl_give isl_restriction *isl_restriction_output(
9326 __isl_take isl_set *source_restr);
9327 __isl_give isl_restriction *isl_restriction_none(
9328 __isl_take isl_map *source_map);
9329 __isl_give isl_restriction *isl_restriction_empty(
9330 __isl_take isl_map *source_map);
9331 __isl_null isl_restriction *isl_restriction_free(
9332 __isl_take isl_restriction *restr);
9334 C<isl_restriction_none> and C<isl_restriction_empty> are special
9335 cases of C<isl_restriction_input>. C<isl_restriction_none>
9336 is essentially equivalent to
9338 isl_restriction_input(isl_set_universe(
9339 isl_space_range(isl_map_get_space(source_map))),
9341 isl_space_domain(isl_map_get_space(source_map))));
9343 whereas C<isl_restriction_empty> is essentially equivalent to
9345 isl_restriction_input(isl_set_empty(
9346 isl_space_range(isl_map_get_space(source_map))),
9348 isl_space_domain(isl_map_get_space(source_map))));
9352 #include <isl/schedule.h>
9353 __isl_give isl_schedule *
9354 isl_schedule_constraints_compute_schedule(
9355 __isl_take isl_schedule_constraints *sc);
9357 The function C<isl_schedule_constraints_compute_schedule> can be
9358 used to compute a schedule that satisfies the given schedule constraints.
9359 These schedule constraints include the iteration domain for which
9360 a schedule should be computed and dependences between pairs of
9361 iterations. In particular, these dependences include
9362 I<validity> dependences and I<proximity> dependences.
9363 By default, the algorithm used to construct the schedule is similar
9364 to that of C<Pluto>.
9365 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9367 The generated schedule respects all validity dependences.
9368 That is, all dependence distances over these dependences in the
9369 scheduled space are lexicographically positive.
9371 The default algorithm tries to ensure that the dependence distances
9372 over coincidence constraints are zero and to minimize the
9373 dependence distances over proximity dependences.
9374 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9375 for groups of domains where the dependence distances over validity
9376 dependences have only non-negative values.
9377 Note that when minimizing the maximal dependence distance
9378 over proximity dependences, a single affine expression in the parameters
9379 is constructed that bounds all dependence distances. If no such expression
9380 exists, then the algorithm will fail and resort to an alternative
9381 scheduling algorithm. In particular, this means that adding proximity
9382 dependences may eliminate valid solutions. A typical example where this
9383 phenomenon may occur is when some subset of the proximity dependences
9384 has no restriction on some parameter, forcing the coefficient of that
9385 parameter to be zero, while some other subset forces the dependence
9386 distance to depend on that parameter, requiring the same coefficient
9388 When using Feautrier's algorithm, the coincidence and proximity constraints
9389 are only taken into account during the extension to a
9390 full-dimensional schedule.
9392 An C<isl_schedule_constraints> object can be constructed
9393 and manipulated using the following functions.
9395 #include <isl/schedule.h>
9396 __isl_give isl_schedule_constraints *
9397 isl_schedule_constraints_copy(
9398 __isl_keep isl_schedule_constraints *sc);
9399 __isl_give isl_schedule_constraints *
9400 isl_schedule_constraints_on_domain(
9401 __isl_take isl_union_set *domain);
9402 __isl_give isl_schedule_constraints *
9403 isl_schedule_constraints_set_context(
9404 __isl_take isl_schedule_constraints *sc,
9405 __isl_take isl_set *context);
9406 __isl_give isl_schedule_constraints *
9407 isl_schedule_constraints_set_validity(
9408 __isl_take isl_schedule_constraints *sc,
9409 __isl_take isl_union_map *validity);
9410 __isl_give isl_schedule_constraints *
9411 isl_schedule_constraints_set_coincidence(
9412 __isl_take isl_schedule_constraints *sc,
9413 __isl_take isl_union_map *coincidence);
9414 __isl_give isl_schedule_constraints *
9415 isl_schedule_constraints_set_proximity(
9416 __isl_take isl_schedule_constraints *sc,
9417 __isl_take isl_union_map *proximity);
9418 __isl_give isl_schedule_constraints *
9419 isl_schedule_constraints_set_conditional_validity(
9420 __isl_take isl_schedule_constraints *sc,
9421 __isl_take isl_union_map *condition,
9422 __isl_take isl_union_map *validity);
9423 __isl_give isl_schedule_constraints *
9424 isl_schedule_constraints_apply(
9425 __isl_take isl_schedule_constraints *sc,
9426 __isl_take isl_union_map *umap);
9427 __isl_null isl_schedule_constraints *
9428 isl_schedule_constraints_free(
9429 __isl_take isl_schedule_constraints *sc);
9431 The initial C<isl_schedule_constraints> object created by
9432 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9433 That is, it has an empty set of dependences.
9434 The function C<isl_schedule_constraints_set_context> allows the user
9435 to specify additional constraints on the parameters that may
9436 be assumed to hold during the construction of the schedule.
9437 The function C<isl_schedule_constraints_set_validity> replaces the
9438 validity dependences, mapping domain elements I<i> to domain
9439 elements that should be scheduled after I<i>.
9440 The function C<isl_schedule_constraints_set_coincidence> replaces the
9441 coincidence dependences, mapping domain elements I<i> to domain
9442 elements that should be scheduled together with I<I>, if possible.
9443 The function C<isl_schedule_constraints_set_proximity> replaces the
9444 proximity dependences, mapping domain elements I<i> to domain
9445 elements that should be scheduled either before I<I>
9446 or as early as possible after I<i>.
9448 The function C<isl_schedule_constraints_set_conditional_validity>
9449 replaces the conditional validity constraints.
9450 A conditional validity constraint is only imposed when any of the corresponding
9451 conditions is satisfied, i.e., when any of them is non-zero.
9452 That is, the scheduler ensures that within each band if the dependence
9453 distances over the condition constraints are not all zero
9454 then all corresponding conditional validity constraints are respected.
9455 A conditional validity constraint corresponds to a condition
9456 if the two are adjacent, i.e., if the domain of one relation intersect
9457 the range of the other relation.
9458 The typical use case of conditional validity constraints is
9459 to allow order constraints between live ranges to be violated
9460 as long as the live ranges themselves are local to the band.
9461 To allow more fine-grained control over which conditions correspond
9462 to which conditional validity constraints, the domains and ranges
9463 of these relations may include I<tags>. That is, the domains and
9464 ranges of those relation may themselves be wrapped relations
9465 where the iteration domain appears in the domain of those wrapped relations
9466 and the range of the wrapped relations can be arbitrarily chosen
9467 by the user. Conditions and conditional validity constraints are only
9468 considered adjacent to each other if the entire wrapped relation matches.
9469 In particular, a relation with a tag will never be considered adjacent
9470 to a relation without a tag.
9472 The function C<isl_schedule_constraints_apply> takes
9473 schedule constraints that are defined on some set of domain elements
9474 and transforms them to schedule constraints on the elements
9475 to which these domain elements are mapped by the given transformation.
9477 An C<isl_schedule_constraints> object can be inspected
9478 using the following functions.
9480 #include <isl/schedule.h>
9481 __isl_give isl_union_set *
9482 isl_schedule_constraints_get_domain(
9483 __isl_keep isl_schedule_constraints *sc);
9484 __isl_give isl_set *isl_schedule_constraints_get_context(
9485 __isl_keep isl_schedule_constraints *sc);
9486 __isl_give isl_union_map *
9487 isl_schedule_constraints_get_validity(
9488 __isl_keep isl_schedule_constraints *sc);
9489 __isl_give isl_union_map *
9490 isl_schedule_constraints_get_coincidence(
9491 __isl_keep isl_schedule_constraints *sc);
9492 __isl_give isl_union_map *
9493 isl_schedule_constraints_get_proximity(
9494 __isl_keep isl_schedule_constraints *sc);
9495 __isl_give isl_union_map *
9496 isl_schedule_constraints_get_conditional_validity(
9497 __isl_keep isl_schedule_constraints *sc);
9498 __isl_give isl_union_map *
9499 isl_schedule_constraints_get_conditional_validity_condition(
9500 __isl_keep isl_schedule_constraints *sc);
9502 An C<isl_schedule_constraints> object can be read from input
9503 using the following functions.
9505 #include <isl/schedule.h>
9506 __isl_give isl_schedule_constraints *
9507 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9509 __isl_give isl_schedule_constraints *
9510 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9513 The contents of an C<isl_schedule_constraints> object can be printed
9514 using the following functions.
9516 #include <isl/schedule.h>
9517 __isl_give isl_printer *
9518 isl_printer_print_schedule_constraints(
9519 __isl_take isl_printer *p,
9520 __isl_keep isl_schedule_constraints *sc);
9521 __isl_give char *isl_schedule_constraints_to_str(
9522 __isl_keep isl_schedule_constraints *sc);
9524 The following function computes a schedule directly from
9525 an iteration domain and validity and proximity dependences
9526 and is implemented in terms of the functions described above.
9527 The use of C<isl_union_set_compute_schedule> is discouraged.
9529 #include <isl/schedule.h>
9530 __isl_give isl_schedule *isl_union_set_compute_schedule(
9531 __isl_take isl_union_set *domain,
9532 __isl_take isl_union_map *validity,
9533 __isl_take isl_union_map *proximity);
9535 The generated schedule represents a schedule tree.
9536 For more information on schedule trees, see
9537 L</"Schedule Trees">.
9541 #include <isl/schedule.h>
9542 isl_stat isl_options_set_schedule_max_coefficient(
9543 isl_ctx *ctx, int val);
9544 int isl_options_get_schedule_max_coefficient(
9546 isl_stat isl_options_set_schedule_max_constant_term(
9547 isl_ctx *ctx, int val);
9548 int isl_options_get_schedule_max_constant_term(
9550 isl_stat isl_options_set_schedule_serialize_sccs(
9551 isl_ctx *ctx, int val);
9552 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9553 isl_stat isl_options_set_schedule_whole_component(
9554 isl_ctx *ctx, int val);
9555 int isl_options_get_schedule_whole_component(
9557 isl_stat isl_options_set_schedule_maximize_band_depth(
9558 isl_ctx *ctx, int val);
9559 int isl_options_get_schedule_maximize_band_depth(
9561 isl_stat isl_options_set_schedule_maximize_coincidence(
9562 isl_ctx *ctx, int val);
9563 int isl_options_get_schedule_maximize_coincidence(
9565 isl_stat isl_options_set_schedule_outer_coincidence(
9566 isl_ctx *ctx, int val);
9567 int isl_options_get_schedule_outer_coincidence(
9569 isl_stat isl_options_set_schedule_split_scaled(
9570 isl_ctx *ctx, int val);
9571 int isl_options_get_schedule_split_scaled(
9573 isl_stat isl_options_set_schedule_treat_coalescing(
9574 isl_ctx *ctx, int val);
9575 int isl_options_get_schedule_treat_coalescing(
9577 isl_stat isl_options_set_schedule_algorithm(
9578 isl_ctx *ctx, int val);
9579 int isl_options_get_schedule_algorithm(
9581 isl_stat isl_options_set_schedule_carry_self_first(
9582 isl_ctx *ctx, int val);
9583 int isl_options_get_schedule_carry_self_first(
9585 isl_stat isl_options_set_schedule_separate_components(
9586 isl_ctx *ctx, int val);
9587 int isl_options_get_schedule_separate_components(
9592 =item * schedule_max_coefficient
9594 This option enforces that the coefficients for variable and parameter
9595 dimensions in the calculated schedule are not larger than the specified value.
9596 This option can significantly increase the speed of the scheduling calculation
9597 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9598 this option does not introduce bounds on the variable or parameter
9601 =item * schedule_max_constant_term
9603 This option enforces that the constant coefficients in the calculated schedule
9604 are not larger than the maximal constant term. This option can significantly
9605 increase the speed of the scheduling calculation and may also prevent fusing of
9606 unrelated dimensions. A value of -1 means that this option does not introduce
9607 bounds on the constant coefficients.
9609 =item * schedule_serialize_sccs
9611 If this option is set, then all strongly connected components
9612 in the dependence graph are serialized as soon as they are detected.
9613 This means in particular that instances of statements will only
9614 appear in the same band node if these statements belong
9615 to the same strongly connected component at the point where
9616 the band node is constructed.
9618 =item * schedule_whole_component
9620 If this option is set, then entire (weakly) connected
9621 components in the dependence graph are scheduled together
9623 Otherwise, each strongly connected component within
9624 such a weakly connected component is first scheduled separately
9625 and then combined with other strongly connected components.
9626 This option has no effect if C<schedule_serialize_sccs> is set.
9628 =item * schedule_maximize_band_depth
9630 If this option is set, then the scheduler tries to maximize
9631 the width of the bands. Wider bands give more possibilities for tiling.
9632 In particular, if the C<schedule_whole_component> option is set,
9633 then bands are split if this might result in wider bands.
9634 Otherwise, the effect of this option is to only allow
9635 strongly connected components to be combined if this does
9636 not reduce the width of the bands.
9637 Note that if the C<schedule_serialize_sccs> options is set, then
9638 the C<schedule_maximize_band_depth> option therefore has no effect.
9640 =item * schedule_maximize_coincidence
9642 This option is only effective if the C<schedule_whole_component>
9643 option is turned off.
9644 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9645 strongly connected components are only combined with each other
9646 if this does not reduce the number of coincident band members.
9648 =item * schedule_outer_coincidence
9650 If this option is set, then we try to construct schedules
9651 where the outermost scheduling dimension in each band
9652 satisfies the coincidence constraints.
9654 =item * schedule_algorithm
9656 Selects the scheduling algorithm to be used.
9657 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9658 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9660 =item * schedule_split_scaled
9662 If this option is set, then we try to construct schedules in which the
9663 constant term is split off from the linear part if the linear parts of
9664 the scheduling rows for all nodes in the graph have a common non-trivial
9666 The constant term is then dropped and the linear
9668 This option is only effective when the Feautrier style scheduler is
9669 being used, either as the main scheduler or as a fallback for the
9670 Pluto-like scheduler.
9672 =item * schedule_treat_coalescing
9674 If this option is set, then the scheduler will try and avoid
9675 producing schedules that perform loop coalescing.
9676 In particular, for the Pluto-like scheduler, this option places
9677 bounds on the schedule coefficients based on the sizes of the instance sets.
9678 For the Feautrier style scheduler, this option detects potentially
9679 coalescing schedules and then tries to adjust the schedule to avoid
9682 =item * schedule_carry_self_first
9684 If this option is set, then the Feautrier style scheduler
9685 (when used as a fallback for the Pluto-like scheduler) will
9686 first try to only carry self-dependences.
9688 =item * schedule_separate_components
9690 If this option is set then the function C<isl_schedule_get_map>
9691 will treat set nodes in the same way as sequence nodes.
9695 =head2 AST Generation
9697 This section describes the C<isl> functionality for generating
9698 ASTs that visit all the elements
9699 in a domain in an order specified by a schedule tree or
9701 In case the schedule given as a C<isl_union_map>, an AST is generated
9702 that visits all the elements in the domain of the C<isl_union_map>
9703 according to the lexicographic order of the corresponding image
9704 element(s). If the range of the C<isl_union_map> consists of
9705 elements in more than one space, then each of these spaces is handled
9706 separately in an arbitrary order.
9707 It should be noted that the schedule tree or the image elements
9708 in a schedule map only specify the I<order>
9709 in which the corresponding domain elements should be visited.
9710 No direct relation between the partial schedule values
9711 or the image elements on the one hand and the loop iterators
9712 in the generated AST on the other hand should be assumed.
9714 Each AST is generated within a build. The initial build
9715 simply specifies the constraints on the parameters (if any)
9716 and can be created, inspected, copied and freed using the following functions.
9718 #include <isl/ast_build.h>
9719 __isl_give isl_ast_build *isl_ast_build_alloc(
9721 __isl_give isl_ast_build *isl_ast_build_from_context(
9722 __isl_take isl_set *set);
9723 __isl_give isl_ast_build *isl_ast_build_copy(
9724 __isl_keep isl_ast_build *build);
9725 __isl_null isl_ast_build *isl_ast_build_free(
9726 __isl_take isl_ast_build *build);
9728 The C<set> argument is usually a parameter set with zero or more parameters.
9729 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9730 this set is required to be a parameter set.
9731 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9732 specify any parameter constraints.
9733 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9734 and L</"Fine-grained Control over AST Generation">.
9735 Finally, the AST itself can be constructed using one of the following
9738 #include <isl/ast_build.h>
9739 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9740 __isl_keep isl_ast_build *build,
9741 __isl_take isl_schedule *schedule);
9742 __isl_give isl_ast_node *
9743 isl_ast_build_node_from_schedule_map(
9744 __isl_keep isl_ast_build *build,
9745 __isl_take isl_union_map *schedule);
9747 =head3 Inspecting the AST
9749 The basic properties of an AST node can be obtained as follows.
9751 #include <isl/ast.h>
9752 enum isl_ast_node_type isl_ast_node_get_type(
9753 __isl_keep isl_ast_node *node);
9755 The type of an AST node is one of
9756 C<isl_ast_node_for>,
9758 C<isl_ast_node_block>,
9759 C<isl_ast_node_mark> or
9760 C<isl_ast_node_user>.
9761 An C<isl_ast_node_for> represents a for node.
9762 An C<isl_ast_node_if> represents an if node.
9763 An C<isl_ast_node_block> represents a compound node.
9764 An C<isl_ast_node_mark> introduces a mark in the AST.
9765 An C<isl_ast_node_user> represents an expression statement.
9766 An expression statement typically corresponds to a domain element, i.e.,
9767 one of the elements that is visited by the AST.
9769 Each type of node has its own additional properties.
9771 #include <isl/ast.h>
9772 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9773 __isl_keep isl_ast_node *node);
9774 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9775 __isl_keep isl_ast_node *node);
9776 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9777 __isl_keep isl_ast_node *node);
9778 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9779 __isl_keep isl_ast_node *node);
9780 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9781 __isl_keep isl_ast_node *node);
9782 isl_bool isl_ast_node_for_is_degenerate(
9783 __isl_keep isl_ast_node *node);
9785 An C<isl_ast_for> is considered degenerate if it is known to execute
9788 #include <isl/ast.h>
9789 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9790 __isl_keep isl_ast_node *node);
9791 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9792 __isl_keep isl_ast_node *node);
9793 isl_bool isl_ast_node_if_has_else(
9794 __isl_keep isl_ast_node *node);
9795 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9796 __isl_keep isl_ast_node *node);
9798 __isl_give isl_ast_node_list *
9799 isl_ast_node_block_get_children(
9800 __isl_keep isl_ast_node *node);
9802 __isl_give isl_id *isl_ast_node_mark_get_id(
9803 __isl_keep isl_ast_node *node);
9804 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9805 __isl_keep isl_ast_node *node);
9807 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9808 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9810 #include <isl/ast.h>
9811 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9812 __isl_keep isl_ast_node *node);
9814 All descendants of a specific node in the AST (including the node itself)
9816 in depth-first pre-order using the following function.
9818 #include <isl/ast.h>
9819 isl_stat isl_ast_node_foreach_descendant_top_down(
9820 __isl_keep isl_ast_node *node,
9821 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9822 void *user), void *user);
9824 The callback function should return C<isl_bool_true> if the children
9825 of the given node should be visited and C<isl_bool_false> if they should not.
9826 It should return C<isl_bool_error> in case of failure, in which case
9827 the entire traversal is aborted.
9829 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9830 the following functions.
9832 #include <isl/ast.h>
9833 enum isl_ast_expr_type isl_ast_expr_get_type(
9834 __isl_keep isl_ast_expr *expr);
9836 The type of an AST expression is one of
9838 C<isl_ast_expr_id> or
9839 C<isl_ast_expr_int>.
9840 An C<isl_ast_expr_op> represents the result of an operation.
9841 An C<isl_ast_expr_id> represents an identifier.
9842 An C<isl_ast_expr_int> represents an integer value.
9844 Each type of expression has its own additional properties.
9846 #include <isl/ast.h>
9847 enum isl_ast_op_type isl_ast_expr_get_op_type(
9848 __isl_keep isl_ast_expr *expr);
9849 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9850 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9851 __isl_keep isl_ast_expr *expr, int pos);
9852 isl_stat isl_ast_expr_foreach_ast_op_type(
9853 __isl_keep isl_ast_expr *expr,
9854 isl_stat (*fn)(enum isl_ast_op_type type,
9855 void *user), void *user);
9856 isl_stat isl_ast_node_foreach_ast_op_type(
9857 __isl_keep isl_ast_node *node,
9858 isl_stat (*fn)(enum isl_ast_op_type type,
9859 void *user), void *user);
9861 C<isl_ast_expr_get_op_type> returns the type of the operation
9862 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9863 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9865 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9866 C<isl_ast_op_type> that appears in C<expr>.
9867 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9868 C<isl_ast_op_type> that appears in C<node>.
9869 The operation type is one of the following.
9873 =item C<isl_ast_op_and>
9875 Logical I<and> of two arguments.
9876 Both arguments can be evaluated.
9878 =item C<isl_ast_op_and_then>
9880 Logical I<and> of two arguments.
9881 The second argument can only be evaluated if the first evaluates to true.
9883 =item C<isl_ast_op_or>
9885 Logical I<or> of two arguments.
9886 Both arguments can be evaluated.
9888 =item C<isl_ast_op_or_else>
9890 Logical I<or> of two arguments.
9891 The second argument can only be evaluated if the first evaluates to false.
9893 =item C<isl_ast_op_max>
9895 Maximum of two or more arguments.
9897 =item C<isl_ast_op_min>
9899 Minimum of two or more arguments.
9901 =item C<isl_ast_op_minus>
9905 =item C<isl_ast_op_add>
9907 Sum of two arguments.
9909 =item C<isl_ast_op_sub>
9911 Difference of two arguments.
9913 =item C<isl_ast_op_mul>
9915 Product of two arguments.
9917 =item C<isl_ast_op_div>
9919 Exact division. That is, the result is known to be an integer.
9921 =item C<isl_ast_op_fdiv_q>
9923 Result of integer division, rounded towards negative
9926 =item C<isl_ast_op_pdiv_q>
9928 Result of integer division, where dividend is known to be non-negative.
9930 =item C<isl_ast_op_pdiv_r>
9932 Remainder of integer division, where dividend is known to be non-negative.
9934 =item C<isl_ast_op_zdiv_r>
9936 Equal to zero iff the remainder on integer division is zero.
9938 =item C<isl_ast_op_cond>
9940 Conditional operator defined on three arguments.
9941 If the first argument evaluates to true, then the result
9942 is equal to the second argument. Otherwise, the result
9943 is equal to the third argument.
9944 The second and third argument may only be evaluated if
9945 the first argument evaluates to true and false, respectively.
9946 Corresponds to C<a ? b : c> in C.
9948 =item C<isl_ast_op_select>
9950 Conditional operator defined on three arguments.
9951 If the first argument evaluates to true, then the result
9952 is equal to the second argument. Otherwise, the result
9953 is equal to the third argument.
9954 The second and third argument may be evaluated independently
9955 of the value of the first argument.
9956 Corresponds to C<a * b + (1 - a) * c> in C.
9958 =item C<isl_ast_op_eq>
9962 =item C<isl_ast_op_le>
9964 Less than or equal relation.
9966 =item C<isl_ast_op_lt>
9970 =item C<isl_ast_op_ge>
9972 Greater than or equal relation.
9974 =item C<isl_ast_op_gt>
9976 Greater than relation.
9978 =item C<isl_ast_op_call>
9981 The number of arguments of the C<isl_ast_expr> is one more than
9982 the number of arguments in the function call, the first argument
9983 representing the function being called.
9985 =item C<isl_ast_op_access>
9988 The number of arguments of the C<isl_ast_expr> is one more than
9989 the number of index expressions in the array access, the first argument
9990 representing the array being accessed.
9992 =item C<isl_ast_op_member>
9995 This operation has two arguments, a structure and the name of
9996 the member of the structure being accessed.
10000 #include <isl/ast.h>
10001 __isl_give isl_id *isl_ast_expr_get_id(
10002 __isl_keep isl_ast_expr *expr);
10004 Return the identifier represented by the AST expression.
10006 #include <isl/ast.h>
10007 __isl_give isl_val *isl_ast_expr_get_val(
10008 __isl_keep isl_ast_expr *expr);
10010 Return the integer represented by the AST expression.
10012 =head3 Properties of ASTs
10014 #include <isl/ast.h>
10015 isl_bool isl_ast_expr_is_equal(
10016 __isl_keep isl_ast_expr *expr1,
10017 __isl_keep isl_ast_expr *expr2);
10019 Check if two C<isl_ast_expr>s are equal to each other.
10021 =head3 Manipulating and printing the AST
10023 AST nodes can be copied and freed using the following functions.
10025 #include <isl/ast.h>
10026 __isl_give isl_ast_node *isl_ast_node_copy(
10027 __isl_keep isl_ast_node *node);
10028 __isl_null isl_ast_node *isl_ast_node_free(
10029 __isl_take isl_ast_node *node);
10031 AST expressions can be copied and freed using the following functions.
10033 #include <isl/ast.h>
10034 __isl_give isl_ast_expr *isl_ast_expr_copy(
10035 __isl_keep isl_ast_expr *expr);
10036 __isl_null isl_ast_expr *isl_ast_expr_free(
10037 __isl_take isl_ast_expr *expr);
10039 New AST expressions can be created either directly or within
10040 the context of an C<isl_ast_build>.
10042 #include <isl/ast.h>
10043 __isl_give isl_ast_expr *isl_ast_expr_from_val(
10044 __isl_take isl_val *v);
10045 __isl_give isl_ast_expr *isl_ast_expr_from_id(
10046 __isl_take isl_id *id);
10047 __isl_give isl_ast_expr *isl_ast_expr_neg(
10048 __isl_take isl_ast_expr *expr);
10049 __isl_give isl_ast_expr *isl_ast_expr_address_of(
10050 __isl_take isl_ast_expr *expr);
10051 __isl_give isl_ast_expr *isl_ast_expr_add(
10052 __isl_take isl_ast_expr *expr1,
10053 __isl_take isl_ast_expr *expr2);
10054 __isl_give isl_ast_expr *isl_ast_expr_sub(
10055 __isl_take isl_ast_expr *expr1,
10056 __isl_take isl_ast_expr *expr2);
10057 __isl_give isl_ast_expr *isl_ast_expr_mul(
10058 __isl_take isl_ast_expr *expr1,
10059 __isl_take isl_ast_expr *expr2);
10060 __isl_give isl_ast_expr *isl_ast_expr_div(
10061 __isl_take isl_ast_expr *expr1,
10062 __isl_take isl_ast_expr *expr2);
10063 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
10064 __isl_take isl_ast_expr *expr1,
10065 __isl_take isl_ast_expr *expr2);
10066 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
10067 __isl_take isl_ast_expr *expr1,
10068 __isl_take isl_ast_expr *expr2);
10069 __isl_give isl_ast_expr *isl_ast_expr_and(
10070 __isl_take isl_ast_expr *expr1,
10071 __isl_take isl_ast_expr *expr2)
10072 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10073 __isl_take isl_ast_expr *expr1,
10074 __isl_take isl_ast_expr *expr2)
10075 __isl_give isl_ast_expr *isl_ast_expr_or(
10076 __isl_take isl_ast_expr *expr1,
10077 __isl_take isl_ast_expr *expr2)
10078 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10079 __isl_take isl_ast_expr *expr1,
10080 __isl_take isl_ast_expr *expr2)
10081 __isl_give isl_ast_expr *isl_ast_expr_eq(
10082 __isl_take isl_ast_expr *expr1,
10083 __isl_take isl_ast_expr *expr2);
10084 __isl_give isl_ast_expr *isl_ast_expr_le(
10085 __isl_take isl_ast_expr *expr1,
10086 __isl_take isl_ast_expr *expr2);
10087 __isl_give isl_ast_expr *isl_ast_expr_lt(
10088 __isl_take isl_ast_expr *expr1,
10089 __isl_take isl_ast_expr *expr2);
10090 __isl_give isl_ast_expr *isl_ast_expr_ge(
10091 __isl_take isl_ast_expr *expr1,
10092 __isl_take isl_ast_expr *expr2);
10093 __isl_give isl_ast_expr *isl_ast_expr_gt(
10094 __isl_take isl_ast_expr *expr1,
10095 __isl_take isl_ast_expr *expr2);
10096 __isl_give isl_ast_expr *isl_ast_expr_access(
10097 __isl_take isl_ast_expr *array,
10098 __isl_take isl_ast_expr_list *indices);
10099 __isl_give isl_ast_expr *isl_ast_expr_call(
10100 __isl_take isl_ast_expr *function,
10101 __isl_take isl_ast_expr_list *arguments);
10103 The function C<isl_ast_expr_address_of> can be applied to an
10104 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10105 to represent the address of the C<isl_ast_expr_access>. The function
10106 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10107 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10109 #include <isl/ast_build.h>
10110 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10111 __isl_keep isl_ast_build *build,
10112 __isl_take isl_set *set);
10113 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10114 __isl_keep isl_ast_build *build,
10115 __isl_take isl_pw_aff *pa);
10116 __isl_give isl_ast_expr *
10117 isl_ast_build_access_from_pw_multi_aff(
10118 __isl_keep isl_ast_build *build,
10119 __isl_take isl_pw_multi_aff *pma);
10120 __isl_give isl_ast_expr *
10121 isl_ast_build_access_from_multi_pw_aff(
10122 __isl_keep isl_ast_build *build,
10123 __isl_take isl_multi_pw_aff *mpa);
10124 __isl_give isl_ast_expr *
10125 isl_ast_build_call_from_pw_multi_aff(
10126 __isl_keep isl_ast_build *build,
10127 __isl_take isl_pw_multi_aff *pma);
10128 __isl_give isl_ast_expr *
10129 isl_ast_build_call_from_multi_pw_aff(
10130 __isl_keep isl_ast_build *build,
10131 __isl_take isl_multi_pw_aff *mpa);
10134 the domains of C<pa>, C<mpa> and C<pma> should correspond
10135 to the schedule space of C<build>.
10136 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10137 the function being called.
10138 If the accessed space is a nested relation, then it is taken
10139 to represent an access of the member specified by the range
10140 of this nested relation of the structure specified by the domain
10141 of the nested relation.
10143 The following functions can be used to modify an C<isl_ast_expr>.
10145 #include <isl/ast.h>
10146 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10147 __isl_take isl_ast_expr *expr, int pos,
10148 __isl_take isl_ast_expr *arg);
10150 Replace the argument of C<expr> at position C<pos> by C<arg>.
10152 #include <isl/ast.h>
10153 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10154 __isl_take isl_ast_expr *expr,
10155 __isl_take isl_id_to_ast_expr *id2expr);
10157 The function C<isl_ast_expr_substitute_ids> replaces the
10158 subexpressions of C<expr> of type C<isl_ast_expr_id>
10159 by the corresponding expression in C<id2expr>, if there is any.
10162 User specified data can be attached to an C<isl_ast_node> and obtained
10163 from the same C<isl_ast_node> using the following functions.
10165 #include <isl/ast.h>
10166 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10167 __isl_take isl_ast_node *node,
10168 __isl_take isl_id *annotation);
10169 __isl_give isl_id *isl_ast_node_get_annotation(
10170 __isl_keep isl_ast_node *node);
10172 Basic printing can be performed using the following functions.
10174 #include <isl/ast.h>
10175 __isl_give isl_printer *isl_printer_print_ast_expr(
10176 __isl_take isl_printer *p,
10177 __isl_keep isl_ast_expr *expr);
10178 __isl_give isl_printer *isl_printer_print_ast_node(
10179 __isl_take isl_printer *p,
10180 __isl_keep isl_ast_node *node);
10181 __isl_give char *isl_ast_expr_to_str(
10182 __isl_keep isl_ast_expr *expr);
10183 __isl_give char *isl_ast_node_to_str(
10184 __isl_keep isl_ast_node *node);
10185 __isl_give char *isl_ast_expr_to_C_str(
10186 __isl_keep isl_ast_expr *expr);
10187 __isl_give char *isl_ast_node_to_C_str(
10188 __isl_keep isl_ast_node *node);
10190 The functions C<isl_ast_expr_to_C_str> and
10191 C<isl_ast_node_to_C_str> are convenience functions
10192 that return a string representation of the input in C format.
10194 More advanced printing can be performed using the following functions.
10196 #include <isl/ast.h>
10197 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10198 __isl_take isl_printer *p,
10199 enum isl_ast_op_type type,
10200 __isl_keep const char *name);
10201 isl_stat isl_options_set_ast_print_macro_once(
10202 isl_ctx *ctx, int val);
10203 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10204 __isl_give isl_printer *isl_ast_op_type_print_macro(
10205 enum isl_ast_op_type type,
10206 __isl_take isl_printer *p);
10207 __isl_give isl_printer *isl_ast_expr_print_macros(
10208 __isl_keep isl_ast_expr *expr,
10209 __isl_take isl_printer *p);
10210 __isl_give isl_printer *isl_ast_node_print_macros(
10211 __isl_keep isl_ast_node *node,
10212 __isl_take isl_printer *p);
10213 __isl_give isl_printer *isl_ast_node_print(
10214 __isl_keep isl_ast_node *node,
10215 __isl_take isl_printer *p,
10216 __isl_take isl_ast_print_options *options);
10217 __isl_give isl_printer *isl_ast_node_for_print(
10218 __isl_keep isl_ast_node *node,
10219 __isl_take isl_printer *p,
10220 __isl_take isl_ast_print_options *options);
10221 __isl_give isl_printer *isl_ast_node_if_print(
10222 __isl_keep isl_ast_node *node,
10223 __isl_take isl_printer *p,
10224 __isl_take isl_ast_print_options *options);
10226 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10227 C<isl> may print out an AST that makes use of macros such
10228 as C<floord>, C<min> and C<max>.
10229 The names of these macros may be modified by a call
10230 to C<isl_ast_op_type_set_print_name>. The user-specified
10231 names are associated to the printer object.
10232 C<isl_ast_op_type_print_macro> prints out the macro
10233 corresponding to a specific C<isl_ast_op_type>.
10234 If the print-macro-once option is set, then a given macro definition
10235 is only printed once to any given printer object.
10236 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10237 for subexpressions where these macros would be used and prints
10238 out the required macro definitions.
10239 Essentially, C<isl_ast_expr_print_macros> calls
10240 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10241 as function argument.
10242 C<isl_ast_node_print_macros> does the same
10243 for expressions in its C<isl_ast_node> argument.
10244 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10245 C<isl_ast_node_if_print> print an C<isl_ast_node>
10246 in C<ISL_FORMAT_C>, but allow for some extra control
10247 through an C<isl_ast_print_options> object.
10248 This object can be created using the following functions.
10250 #include <isl/ast.h>
10251 __isl_give isl_ast_print_options *
10252 isl_ast_print_options_alloc(isl_ctx *ctx);
10253 __isl_give isl_ast_print_options *
10254 isl_ast_print_options_copy(
10255 __isl_keep isl_ast_print_options *options);
10256 __isl_null isl_ast_print_options *
10257 isl_ast_print_options_free(
10258 __isl_take isl_ast_print_options *options);
10260 __isl_give isl_ast_print_options *
10261 isl_ast_print_options_set_print_user(
10262 __isl_take isl_ast_print_options *options,
10263 __isl_give isl_printer *(*print_user)(
10264 __isl_take isl_printer *p,
10265 __isl_take isl_ast_print_options *options,
10266 __isl_keep isl_ast_node *node, void *user),
10268 __isl_give isl_ast_print_options *
10269 isl_ast_print_options_set_print_for(
10270 __isl_take isl_ast_print_options *options,
10271 __isl_give isl_printer *(*print_for)(
10272 __isl_take isl_printer *p,
10273 __isl_take isl_ast_print_options *options,
10274 __isl_keep isl_ast_node *node, void *user),
10277 The callback set by C<isl_ast_print_options_set_print_user>
10278 is called whenever a node of type C<isl_ast_node_user> needs to
10280 The callback set by C<isl_ast_print_options_set_print_for>
10281 is called whenever a node of type C<isl_ast_node_for> needs to
10283 Note that C<isl_ast_node_for_print> will I<not> call the
10284 callback set by C<isl_ast_print_options_set_print_for> on the node
10285 on which C<isl_ast_node_for_print> is called, but only on nested
10286 nodes of type C<isl_ast_node_for>. It is therefore safe to
10287 call C<isl_ast_node_for_print> from within the callback set by
10288 C<isl_ast_print_options_set_print_for>.
10290 The following option determines the type to be used for iterators
10291 while printing the AST.
10293 isl_stat isl_options_set_ast_iterator_type(
10294 isl_ctx *ctx, const char *val);
10295 const char *isl_options_get_ast_iterator_type(
10298 The AST printer only prints body nodes as blocks if these
10299 blocks cannot be safely omitted.
10300 For example, a C<for> node with one body node will not be
10301 surrounded with braces in C<ISL_FORMAT_C>.
10302 A block will always be printed by setting the following option.
10304 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10306 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10310 #include <isl/ast_build.h>
10311 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10312 isl_ctx *ctx, int val);
10313 int isl_options_get_ast_build_atomic_upper_bound(
10315 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10317 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10318 isl_stat isl_options_set_ast_build_detect_min_max(
10319 isl_ctx *ctx, int val);
10320 int isl_options_get_ast_build_detect_min_max(
10322 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10323 isl_ctx *ctx, int val);
10324 int isl_options_get_ast_build_exploit_nested_bounds(
10326 isl_stat isl_options_set_ast_build_group_coscheduled(
10327 isl_ctx *ctx, int val);
10328 int isl_options_get_ast_build_group_coscheduled(
10330 isl_stat isl_options_set_ast_build_scale_strides(
10331 isl_ctx *ctx, int val);
10332 int isl_options_get_ast_build_scale_strides(
10334 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10336 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10337 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10339 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10343 =item * ast_build_atomic_upper_bound
10345 Generate loop upper bounds that consist of the current loop iterator,
10346 an operator and an expression not involving the iterator.
10347 If this option is not set, then the current loop iterator may appear
10348 several times in the upper bound.
10349 For example, when this option is turned off, AST generation
10352 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10356 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10359 When the option is turned on, the following AST is generated
10361 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10364 =item * ast_build_prefer_pdiv
10366 If this option is turned off, then the AST generation will
10367 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10368 operators, but no C<isl_ast_op_pdiv_q> or
10369 C<isl_ast_op_pdiv_r> operators.
10370 If this option is turned on, then C<isl> will try to convert
10371 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10372 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10374 =item * ast_build_detect_min_max
10376 If this option is turned on, then C<isl> will try and detect
10377 min or max-expressions when building AST expressions from
10378 piecewise affine expressions.
10380 =item * ast_build_exploit_nested_bounds
10382 Simplify conditions based on bounds of nested for loops.
10383 In particular, remove conditions that are implied by the fact
10384 that one or more nested loops have at least one iteration,
10385 meaning that the upper bound is at least as large as the lower bound.
10386 For example, when this option is turned off, AST generation
10389 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10395 for (int c0 = 0; c0 <= N; c0 += 1)
10396 for (int c1 = 0; c1 <= M; c1 += 1)
10399 When the option is turned on, the following AST is generated
10401 for (int c0 = 0; c0 <= N; c0 += 1)
10402 for (int c1 = 0; c1 <= M; c1 += 1)
10405 =item * ast_build_group_coscheduled
10407 If two domain elements are assigned the same schedule point, then
10408 they may be executed in any order and they may even appear in different
10409 loops. If this options is set, then the AST generator will make
10410 sure that coscheduled domain elements do not appear in separate parts
10411 of the AST. This is useful in case of nested AST generation
10412 if the outer AST generation is given only part of a schedule
10413 and the inner AST generation should handle the domains that are
10414 coscheduled by this initial part of the schedule together.
10415 For example if an AST is generated for a schedule
10417 { A[i] -> [0]; B[i] -> [0] }
10419 then the C<isl_ast_build_set_create_leaf> callback described
10420 below may get called twice, once for each domain.
10421 Setting this option ensures that the callback is only called once
10422 on both domains together.
10424 =item * ast_build_separation_bounds
10426 This option specifies which bounds to use during separation.
10427 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10428 then all (possibly implicit) bounds on the current dimension will
10429 be used during separation.
10430 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10431 then only those bounds that are explicitly available will
10432 be used during separation.
10434 =item * ast_build_scale_strides
10436 This option specifies whether the AST generator is allowed
10437 to scale down iterators of strided loops.
10439 =item * ast_build_allow_else
10441 This option specifies whether the AST generator is allowed
10442 to construct if statements with else branches.
10444 =item * ast_build_allow_or
10446 This option specifies whether the AST generator is allowed
10447 to construct if conditions with disjunctions.
10451 =head3 AST Generation Options (Schedule Tree)
10453 In case of AST construction from a schedule tree, the options
10454 that control how an AST is created from the individual schedule
10455 dimensions are stored in the band nodes of the tree
10456 (see L</"Schedule Trees">).
10458 In particular, a schedule dimension can be handled in four
10459 different ways, atomic, separate, unroll or the default.
10460 This loop AST generation type can be set using
10461 C<isl_schedule_node_band_member_set_ast_loop_type>.
10463 the first three can be selected by including a one-dimensional
10464 element with as value the position of the schedule dimension
10465 within the band and as name one of C<atomic>, C<separate>
10466 or C<unroll> in the options
10467 set by C<isl_schedule_node_band_set_ast_build_options>.
10468 Only one of these three may be specified for
10469 any given schedule dimension within a band node.
10470 If none of these is specified, then the default
10471 is used. The meaning of the options is as follows.
10477 When this option is specified, the AST generator will make
10478 sure that a given domains space only appears in a single
10479 loop at the specified level.
10481 For example, for the schedule tree
10483 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10485 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10486 options: "{ atomic[x] }"
10488 the following AST will be generated
10490 for (int c0 = 0; c0 <= 10; c0 += 1) {
10497 On the other hand, for the schedule tree
10499 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10501 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10502 options: "{ separate[x] }"
10504 the following AST will be generated
10508 for (int c0 = 1; c0 <= 9; c0 += 1) {
10515 If neither C<atomic> nor C<separate> is specified, then the AST generator
10516 may produce either of these two results or some intermediate form.
10520 When this option is specified, the AST generator will
10521 split the domain of the specified schedule dimension
10522 into pieces with a fixed set of statements for which
10523 instances need to be executed by the iterations in
10524 the schedule domain part. This option tends to avoid
10525 the generation of guards inside the corresponding loops.
10526 See also the C<atomic> option.
10530 When this option is specified, the AST generator will
10531 I<completely> unroll the corresponding schedule dimension.
10532 It is the responsibility of the user to ensure that such
10533 unrolling is possible.
10534 To obtain a partial unrolling, the user should apply an additional
10535 strip-mining to the schedule and fully unroll the inner schedule
10540 The C<isolate> option is a bit more involved. It allows the user
10541 to isolate a range of schedule dimension values from smaller and
10542 greater values. Additionally, the user may specify a different
10543 atomic/separate/unroll choice for the isolated part and the remaining
10544 parts. The typical use case of the C<isolate> option is to isolate
10545 full tiles from partial tiles.
10546 The part that needs to be isolated may depend on outer schedule dimensions.
10547 The option therefore needs to be able to reference those outer schedule
10548 dimensions. In particular, the space of the C<isolate> option is that
10549 of a wrapped map with as domain the flat product of all outer band nodes
10550 and as range the space of the current band node.
10551 The atomic/separate/unroll choice for the isolated part is determined
10552 by an option that lives in an unnamed wrapped space with as domain
10553 a zero-dimensional C<isolate> space and as range the regular
10554 C<atomic>, C<separate> or C<unroll> space.
10555 This option may also be set directly using
10556 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10557 The atomic/separate/unroll choice for the remaining part is determined
10558 by the regular C<atomic>, C<separate> or C<unroll> option.
10559 Since the C<isolate> option references outer schedule dimensions,
10560 its use in a band node causes any tree containing the node
10561 to be considered anchored.
10563 As an example, consider the isolation of full tiles from partial tiles
10564 in a tiling of a triangular domain. The original schedule is as follows.
10566 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10568 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10569 { A[i,j] -> [floor(j/10)] }, \
10570 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10574 for (int c0 = 0; c0 <= 10; c0 += 1)
10575 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10576 for (int c2 = 10 * c0;
10577 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10578 for (int c3 = 10 * c1;
10579 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10582 Isolating the full tiles, we have the following input
10584 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10586 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10587 { A[i,j] -> [floor(j/10)] }, \
10588 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10589 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10590 10a+9+10b+9 <= 100 }"
10595 for (int c0 = 0; c0 <= 8; c0 += 1) {
10596 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10597 for (int c2 = 10 * c0;
10598 c2 <= 10 * c0 + 9; c2 += 1)
10599 for (int c3 = 10 * c1;
10600 c3 <= 10 * c1 + 9; c3 += 1)
10602 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10603 for (int c2 = 10 * c0;
10604 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10605 for (int c3 = 10 * c1;
10606 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10609 for (int c0 = 9; c0 <= 10; c0 += 1)
10610 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10611 for (int c2 = 10 * c0;
10612 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10613 for (int c3 = 10 * c1;
10614 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10618 We may then additionally unroll the innermost loop of the isolated part
10620 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10622 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10623 { A[i,j] -> [floor(j/10)] }, \
10624 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10625 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10626 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10631 for (int c0 = 0; c0 <= 8; c0 += 1) {
10632 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10633 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10635 A(c2, 10 * c1 + 1);
10636 A(c2, 10 * c1 + 2);
10637 A(c2, 10 * c1 + 3);
10638 A(c2, 10 * c1 + 4);
10639 A(c2, 10 * c1 + 5);
10640 A(c2, 10 * c1 + 6);
10641 A(c2, 10 * c1 + 7);
10642 A(c2, 10 * c1 + 8);
10643 A(c2, 10 * c1 + 9);
10645 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10646 for (int c2 = 10 * c0;
10647 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10648 for (int c3 = 10 * c1;
10649 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10652 for (int c0 = 9; c0 <= 10; c0 += 1)
10653 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10654 for (int c2 = 10 * c0;
10655 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10656 for (int c3 = 10 * c1;
10657 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10662 =head3 AST Generation Options (Schedule Map)
10664 In case of AST construction using
10665 C<isl_ast_build_node_from_schedule_map>, the options
10666 that control how an AST is created from the individual schedule
10667 dimensions are stored in the C<isl_ast_build>.
10668 They can be set using the following function.
10670 #include <isl/ast_build.h>
10671 __isl_give isl_ast_build *
10672 isl_ast_build_set_options(
10673 __isl_take isl_ast_build *build,
10674 __isl_take isl_union_map *options);
10676 The options are encoded in an C<isl_union_map>.
10677 The domain of this union relation refers to the schedule domain,
10678 i.e., the range of the schedule passed
10679 to C<isl_ast_build_node_from_schedule_map>.
10680 In the case of nested AST generation (see L</"Nested AST Generation">),
10681 the domain of C<options> should refer to the extra piece of the schedule.
10682 That is, it should be equal to the range of the wrapped relation in the
10683 range of the schedule.
10684 The range of the options can consist of elements in one or more spaces,
10685 the names of which determine the effect of the option.
10686 The values of the range typically also refer to the schedule dimension
10687 to which the option applies, with value C<0> representing
10688 the outermost schedule dimension. In case of nested AST generation
10689 (see L</"Nested AST Generation">), these values refer to the position
10690 of the schedule dimension within the innermost AST generation.
10691 The constraints on the domain elements of
10692 the option should only refer to this dimension and earlier dimensions.
10693 We consider the following spaces.
10697 =item C<separation_class>
10699 B<This option has been deprecated. Use the isolate option on
10700 schedule trees instead.>
10702 This space is a wrapped relation between two one dimensional spaces.
10703 The input space represents the schedule dimension to which the option
10704 applies and the output space represents the separation class.
10705 While constructing a loop corresponding to the specified schedule
10706 dimension(s), the AST generator will try to generate separate loops
10707 for domain elements that are assigned different classes.
10708 If only some of the elements are assigned a class, then those elements
10709 that are not assigned any class will be treated as belonging to a class
10710 that is separate from the explicitly assigned classes.
10711 The typical use case for this option is to separate full tiles from
10713 The other options, described below, are applied after the separation
10716 As an example, consider the separation into full and partial tiles
10717 of a tiling of a triangular domain.
10718 Take, for example, the domain
10720 { A[i,j] : 0 <= i,j and i + j <= 100 }
10722 and a tiling into tiles of 10 by 10. The input to the AST generator
10723 is then the schedule
10725 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10728 Without any options, the following AST is generated
10730 for (int c0 = 0; c0 <= 10; c0 += 1)
10731 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10732 for (int c2 = 10 * c0;
10733 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10735 for (int c3 = 10 * c1;
10736 c3 <= min(10 * c1 + 9, -c2 + 100);
10740 Separation into full and partial tiles can be obtained by assigning
10741 a class, say C<0>, to the full tiles. The full tiles are represented by those
10742 values of the first and second schedule dimensions for which there are
10743 values of the third and fourth dimensions to cover an entire tile.
10744 That is, we need to specify the following option
10746 { [a,b,c,d] -> separation_class[[0]->[0]] :
10747 exists b': 0 <= 10a,10b' and
10748 10a+9+10b'+9 <= 100;
10749 [a,b,c,d] -> separation_class[[1]->[0]] :
10750 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10752 which simplifies to
10754 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10755 a >= 0 and b >= 0 and b <= 8 - a;
10756 [a, b, c, d] -> separation_class[[0] -> [0]] :
10757 a >= 0 and a <= 8 }
10759 With this option, the generated AST is as follows
10762 for (int c0 = 0; c0 <= 8; c0 += 1) {
10763 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10764 for (int c2 = 10 * c0;
10765 c2 <= 10 * c0 + 9; c2 += 1)
10766 for (int c3 = 10 * c1;
10767 c3 <= 10 * c1 + 9; c3 += 1)
10769 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10770 for (int c2 = 10 * c0;
10771 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10773 for (int c3 = 10 * c1;
10774 c3 <= min(-c2 + 100, 10 * c1 + 9);
10778 for (int c0 = 9; c0 <= 10; c0 += 1)
10779 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10780 for (int c2 = 10 * c0;
10781 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10783 for (int c3 = 10 * c1;
10784 c3 <= min(10 * c1 + 9, -c2 + 100);
10791 This is a single-dimensional space representing the schedule dimension(s)
10792 to which ``separation'' should be applied. Separation tries to split
10793 a loop into several pieces if this can avoid the generation of guards
10795 See also the C<atomic> option.
10799 This is a single-dimensional space representing the schedule dimension(s)
10800 for which the domains should be considered ``atomic''. That is, the
10801 AST generator will make sure that any given domain space will only appear
10802 in a single loop at the specified level.
10804 Consider the following schedule
10806 { a[i] -> [i] : 0 <= i < 10;
10807 b[i] -> [i+1] : 0 <= i < 10 }
10809 If the following option is specified
10811 { [i] -> separate[x] }
10813 then the following AST will be generated
10817 for (int c0 = 1; c0 <= 9; c0 += 1) {
10824 If, on the other hand, the following option is specified
10826 { [i] -> atomic[x] }
10828 then the following AST will be generated
10830 for (int c0 = 0; c0 <= 10; c0 += 1) {
10837 If neither C<atomic> nor C<separate> is specified, then the AST generator
10838 may produce either of these two results or some intermediate form.
10842 This is a single-dimensional space representing the schedule dimension(s)
10843 that should be I<completely> unrolled.
10844 To obtain a partial unrolling, the user should apply an additional
10845 strip-mining to the schedule and fully unroll the inner loop.
10849 =head3 Fine-grained Control over AST Generation
10851 Besides specifying the constraints on the parameters,
10852 an C<isl_ast_build> object can be used to control
10853 various aspects of the AST generation process.
10854 In case of AST construction using
10855 C<isl_ast_build_node_from_schedule_map>,
10856 the most prominent way of control is through ``options'',
10857 as explained above.
10859 Additional control is available through the following functions.
10861 #include <isl/ast_build.h>
10862 __isl_give isl_ast_build *
10863 isl_ast_build_set_iterators(
10864 __isl_take isl_ast_build *build,
10865 __isl_take isl_id_list *iterators);
10867 The function C<isl_ast_build_set_iterators> allows the user to
10868 specify a list of iterator C<isl_id>s to be used as iterators.
10869 If the input schedule is injective, then
10870 the number of elements in this list should be as large as the dimension
10871 of the schedule space, but no direct correspondence should be assumed
10872 between dimensions and elements.
10873 If the input schedule is not injective, then an additional number
10874 of C<isl_id>s equal to the largest dimension of the input domains
10876 If the number of provided C<isl_id>s is insufficient, then additional
10877 names are automatically generated.
10879 #include <isl/ast_build.h>
10880 __isl_give isl_ast_build *
10881 isl_ast_build_set_create_leaf(
10882 __isl_take isl_ast_build *build,
10883 __isl_give isl_ast_node *(*fn)(
10884 __isl_take isl_ast_build *build,
10885 void *user), void *user);
10888 C<isl_ast_build_set_create_leaf> function allows for the
10889 specification of a callback that should be called whenever the AST
10890 generator arrives at an element of the schedule domain.
10891 The callback should return an AST node that should be inserted
10892 at the corresponding position of the AST. The default action (when
10893 the callback is not set) is to continue generating parts of the AST to scan
10894 all the domain elements associated to the schedule domain element
10895 and to insert user nodes, ``calling'' the domain element, for each of them.
10896 The C<build> argument contains the current state of the C<isl_ast_build>.
10897 To ease nested AST generation (see L</"Nested AST Generation">),
10898 all control information that is
10899 specific to the current AST generation such as the options and
10900 the callbacks has been removed from this C<isl_ast_build>.
10901 The callback would typically return the result of a nested
10902 AST generation or a
10903 user defined node created using the following function.
10905 #include <isl/ast.h>
10906 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10907 __isl_take isl_ast_expr *expr);
10909 #include <isl/ast_build.h>
10910 __isl_give isl_ast_build *
10911 isl_ast_build_set_at_each_domain(
10912 __isl_take isl_ast_build *build,
10913 __isl_give isl_ast_node *(*fn)(
10914 __isl_take isl_ast_node *node,
10915 __isl_keep isl_ast_build *build,
10916 void *user), void *user);
10917 __isl_give isl_ast_build *
10918 isl_ast_build_set_before_each_for(
10919 __isl_take isl_ast_build *build,
10920 __isl_give isl_id *(*fn)(
10921 __isl_keep isl_ast_build *build,
10922 void *user), void *user);
10923 __isl_give isl_ast_build *
10924 isl_ast_build_set_after_each_for(
10925 __isl_take isl_ast_build *build,
10926 __isl_give isl_ast_node *(*fn)(
10927 __isl_take isl_ast_node *node,
10928 __isl_keep isl_ast_build *build,
10929 void *user), void *user);
10930 __isl_give isl_ast_build *
10931 isl_ast_build_set_before_each_mark(
10932 __isl_take isl_ast_build *build,
10933 isl_stat (*fn)(__isl_keep isl_id *mark,
10934 __isl_keep isl_ast_build *build,
10935 void *user), void *user);
10936 __isl_give isl_ast_build *
10937 isl_ast_build_set_after_each_mark(
10938 __isl_take isl_ast_build *build,
10939 __isl_give isl_ast_node *(*fn)(
10940 __isl_take isl_ast_node *node,
10941 __isl_keep isl_ast_build *build,
10942 void *user), void *user);
10944 The callback set by C<isl_ast_build_set_at_each_domain> will
10945 be called for each domain AST node.
10946 The callbacks set by C<isl_ast_build_set_before_each_for>
10947 and C<isl_ast_build_set_after_each_for> will be called
10948 for each for AST node. The first will be called in depth-first
10949 pre-order, while the second will be called in depth-first post-order.
10950 Since C<isl_ast_build_set_before_each_for> is called before the for
10951 node is actually constructed, it is only passed an C<isl_ast_build>.
10952 The returned C<isl_id> will be added as an annotation (using
10953 C<isl_ast_node_set_annotation>) to the constructed for node.
10954 In particular, if the user has also specified an C<after_each_for>
10955 callback, then the annotation can be retrieved from the node passed to
10956 that callback using C<isl_ast_node_get_annotation>.
10957 The callbacks set by C<isl_ast_build_set_before_each_mark>
10958 and C<isl_ast_build_set_after_each_mark> will be called for each
10959 mark AST node that is created, i.e., for each mark schedule node
10960 in the input schedule tree. The first will be called in depth-first
10961 pre-order, while the second will be called in depth-first post-order.
10962 Since the callback set by C<isl_ast_build_set_before_each_mark>
10963 is called before the mark AST node is actually constructed, it is passed
10964 the identifier of the mark node.
10965 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
10966 The given C<isl_ast_build> can be used to create new
10967 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10968 or C<isl_ast_build_call_from_pw_multi_aff>.
10970 =head3 Nested AST Generation
10972 C<isl> allows the user to create an AST within the context
10973 of another AST. These nested ASTs are created using the
10974 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10975 the outer AST. The C<build> argument should be an C<isl_ast_build>
10976 passed to a callback set by
10977 C<isl_ast_build_set_create_leaf>.
10978 The space of the range of the C<schedule> argument should refer
10979 to this build. In particular, the space should be a wrapped
10980 relation and the domain of this wrapped relation should be the
10981 same as that of the range of the schedule returned by
10982 C<isl_ast_build_get_schedule> below.
10983 In practice, the new schedule is typically
10984 created by calling C<isl_union_map_range_product> on the old schedule
10985 and some extra piece of the schedule.
10986 The space of the schedule domain is also available from
10987 the C<isl_ast_build>.
10989 #include <isl/ast_build.h>
10990 __isl_give isl_union_map *isl_ast_build_get_schedule(
10991 __isl_keep isl_ast_build *build);
10992 __isl_give isl_space *isl_ast_build_get_schedule_space(
10993 __isl_keep isl_ast_build *build);
10994 __isl_give isl_ast_build *isl_ast_build_restrict(
10995 __isl_take isl_ast_build *build,
10996 __isl_take isl_set *set);
10998 The C<isl_ast_build_get_schedule> function returns a (partial)
10999 schedule for the domains elements for which part of the AST still needs to
11000 be generated in the current build.
11001 In particular, the domain elements are mapped to those iterations of the loops
11002 enclosing the current point of the AST generation inside which
11003 the domain elements are executed.
11004 No direct correspondence between
11005 the input schedule and this schedule should be assumed.
11006 The space obtained from C<isl_ast_build_get_schedule_space> can be used
11007 to create a set for C<isl_ast_build_restrict> to intersect
11008 with the current build. In particular, the set passed to
11009 C<isl_ast_build_restrict> can have additional parameters.
11010 The ids of the set dimensions in the space returned by
11011 C<isl_ast_build_get_schedule_space> correspond to the
11012 iterators of the already generated loops.
11013 The user should not rely on the ids of the output dimensions
11014 of the relations in the union relation returned by
11015 C<isl_ast_build_get_schedule> having any particular value.
11017 =head1 Applications
11019 Although C<isl> is mainly meant to be used as a library,
11020 it also contains some basic applications that use some
11021 of the functionality of C<isl>.
11022 For applications that take one or more polytopes or polyhedra
11023 as input, this input may be specified in either the L<isl format>
11024 or the L<PolyLib format>.
11026 =head2 C<isl_polyhedron_sample>
11028 C<isl_polyhedron_sample> takes a polyhedron as input and prints
11029 an integer element of the polyhedron, if there is any.
11030 The first column in the output is the denominator and is always
11031 equal to 1. If the polyhedron contains no integer points,
11032 then a vector of length zero is printed.
11036 C<isl_pip> takes the same input as the C<example> program
11037 from the C<piplib> distribution, i.e., a set of constraints
11038 on the parameters, a line containing only -1 and finally a set
11039 of constraints on a parametric polyhedron.
11040 The coefficients of the parameters appear in the last columns
11041 (but before the final constant column).
11042 The output is the lexicographic minimum of the parametric polyhedron.
11043 As C<isl> currently does not have its own output format, the output
11044 is just a dump of the internal state.
11046 =head2 C<isl_polyhedron_minimize>
11048 C<isl_polyhedron_minimize> computes the minimum of some linear
11049 or affine objective function over the integer points in a polyhedron.
11050 If an affine objective function
11051 is given, then the constant should appear in the last column.
11053 =head2 C<isl_polytope_scan>
11055 Given a polytope, C<isl_polytope_scan> prints
11056 all integer points in the polytope.
11060 Given an C<isl_union_access_info> object as input,
11061 C<isl_flow> prints out the corresponding dependences,
11062 as computed by C<isl_union_access_info_compute_flow>.
11064 =head2 C<isl_codegen>
11066 Given either a schedule tree or a sequence consisting of
11067 a schedule map, a context set and an options relation,
11068 C<isl_codegen> prints out an AST that scans the domain elements
11069 of the schedule in the order of their image(s) taking into account
11070 the constraints in the context set.
11072 =head2 C<isl_schedule>
11074 Given an C<isl_schedule_constraints> object as input,
11075 C<isl_schedule> prints out a schedule that satisfies the given