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 function. The result is undefined for NaN.
750 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
752 The following unary operations are available on C<isl_val>s.
755 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
756 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
757 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
758 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
759 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
760 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
761 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
763 The following binary operations are available on C<isl_val>s.
766 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
767 __isl_take isl_val *v2);
768 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
769 __isl_take isl_val *v2);
770 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
771 __isl_take isl_val *v2);
772 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
774 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
775 __isl_take isl_val *v2);
776 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
778 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
779 __isl_take isl_val *v2);
780 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
782 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
783 __isl_take isl_val *v2);
784 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
787 On integer values, we additionally have the following operations.
790 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
791 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
792 __isl_take isl_val *v2);
793 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
794 __isl_take isl_val *v2);
795 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
796 __isl_take isl_val *v2, __isl_give isl_val **x,
797 __isl_give isl_val **y);
799 The function C<isl_val_gcdext> returns the greatest common divisor g
800 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
801 that C<*x> * C<v1> + C<*y> * C<v2> = g.
803 =head3 GMP specific functions
805 These functions are only available if C<isl> has been compiled with C<GMP>
808 Specific integer and rational values can be created from C<GMP> values using
809 the following functions.
811 #include <isl/val_gmp.h>
812 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
814 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
815 const mpz_t n, const mpz_t d);
817 The numerator and denominator of a rational value can be extracted as
818 C<GMP> values using the following functions.
820 #include <isl/val_gmp.h>
821 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
822 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
824 =head2 Sets and Relations
826 C<isl> uses six types of objects for representing sets and relations,
827 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
828 C<isl_union_set> and C<isl_union_map>.
829 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
830 can be described as a conjunction of affine constraints, while
831 C<isl_set> and C<isl_map> represent unions of
832 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
833 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
834 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
835 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
836 where spaces are considered different if they have a different number
837 of dimensions and/or different names (see L<"Spaces">).
838 The difference between sets and relations (maps) is that sets have
839 one set of variables, while relations have two sets of variables,
840 input variables and output variables.
842 =head2 Error Handling
844 C<isl> supports different ways to react in case a runtime error is triggered.
845 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
846 with two maps that have incompatible spaces. There are three possible ways
847 to react on error: to warn, to continue or to abort.
849 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
850 the last error in the corresponding C<isl_ctx> and the function in which the
851 error was triggered returns a value indicating that some error has
852 occurred. In case of functions returning a pointer, this value is
853 C<NULL>. In case of functions returning an C<isl_bool> or an
854 C<isl_stat>, this value is C<isl_bool_error> or C<isl_stat_error>.
855 An error does not corrupt internal state,
856 such that isl can continue to be used. C<isl> also provides functions to
857 read the last error, including the specific error message,
858 the isl source file where the error occurred and the line number,
859 and to reset all information about the last error. The
860 last error is only stored for information purposes. Its presence does not
861 change the behavior of C<isl>. Hence, resetting an error is not required to
862 continue to use isl, but only to observe new errors.
865 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
866 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
867 const char *isl_ctx_last_error_file(isl_ctx *ctx);
868 int isl_ctx_last_error_line(isl_ctx *ctx);
869 void isl_ctx_reset_error(isl_ctx *ctx);
871 If no error has occurred since the last call to C<isl_ctx_reset_error>,
872 then the functions C<isl_ctx_last_error_msg> and
873 C<isl_ctx_last_error_file> return C<NULL>.
875 Another option is to continue on error. This is similar to warn on error mode,
876 except that C<isl> does not print any warning. This allows a program to
877 implement its own error reporting.
879 The last option is to directly abort the execution of the program from within
880 the isl library. This makes it obviously impossible to recover from an error,
881 but it allows to directly spot the error location. By aborting on error,
882 debuggers break at the location the error occurred and can provide a stack
883 trace. Other tools that automatically provide stack traces on abort or that do
884 not want to continue execution after an error was triggered may also prefer to
887 The on error behavior of isl can be specified by calling
888 C<isl_options_set_on_error> or by setting the command line option
889 C<--isl-on-error>. Valid arguments for the function call are
890 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
891 choices for the command line option are C<warn>, C<continue> and C<abort>.
892 It is also possible to query the current error mode.
894 #include <isl/options.h>
895 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
896 int isl_options_get_on_error(isl_ctx *ctx);
900 Identifiers are used to identify both individual dimensions
901 and tuples of dimensions. They consist of an optional name and an optional
902 user pointer. The name and the user pointer cannot both be C<NULL>, however.
903 Identifiers with the same name but different pointer values
904 are considered to be distinct.
905 Similarly, identifiers with different names but the same pointer value
906 are also considered to be distinct.
907 Equal identifiers are represented using the same object.
908 Pairs of identifiers can therefore be tested for equality using the
910 Identifiers can be constructed, copied, freed, inspected and printed
911 using the following functions.
914 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
915 __isl_keep const char *name, void *user);
916 __isl_give isl_id *isl_id_set_free_user(
917 __isl_take isl_id *id,
918 void (*free_user)(void *user));
919 __isl_give isl_id *isl_id_copy(isl_id *id);
920 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
922 void *isl_id_get_user(__isl_keep isl_id *id);
923 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
925 __isl_give isl_printer *isl_printer_print_id(
926 __isl_take isl_printer *p, __isl_keep isl_id *id);
928 The callback set by C<isl_id_set_free_user> is called on the user
929 pointer when the last reference to the C<isl_id> is freed.
930 Note that C<isl_id_get_name> returns a pointer to some internal
931 data structure, so the result can only be used while the
932 corresponding C<isl_id> is alive.
936 Whenever a new set, relation or similar object is created from scratch,
937 the space in which it lives needs to be specified using an C<isl_space>.
938 Each space involves zero or more parameters and zero, one or two
939 tuples of set or input/output dimensions. The parameters and dimensions
940 are identified by an C<isl_dim_type> and a position.
941 The type C<isl_dim_param> refers to parameters,
942 the type C<isl_dim_set> refers to set dimensions (for spaces
943 with a single tuple of dimensions) and the types C<isl_dim_in>
944 and C<isl_dim_out> refer to input and output dimensions
945 (for spaces with two tuples of dimensions).
946 Local spaces (see L</"Local Spaces">) also contain dimensions
947 of type C<isl_dim_div>.
948 Note that parameters are only identified by their position within
949 a given object. Across different objects, parameters are (usually)
950 identified by their names or identifiers. Only unnamed parameters
951 are identified by their positions across objects. The use of unnamed
952 parameters is discouraged.
954 #include <isl/space.h>
955 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
956 unsigned nparam, unsigned n_in, unsigned n_out);
957 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
959 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
960 unsigned nparam, unsigned dim);
961 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
962 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
964 The space used for creating a parameter domain
965 needs to be created using C<isl_space_params_alloc>.
966 For other sets, the space
967 needs to be created using C<isl_space_set_alloc>, while
968 for a relation, the space
969 needs to be created using C<isl_space_alloc>.
971 To check whether a given space is that of a set or a map
972 or whether it is a parameter space, use these functions:
974 #include <isl/space.h>
975 isl_bool isl_space_is_params(__isl_keep isl_space *space);
976 isl_bool isl_space_is_set(__isl_keep isl_space *space);
977 isl_bool isl_space_is_map(__isl_keep isl_space *space);
979 Spaces can be compared using the following functions:
981 #include <isl/space.h>
982 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
983 __isl_keep isl_space *space2);
984 isl_bool isl_space_has_equal_params(
985 __isl_keep isl_space *space1,
986 __isl_keep isl_space *space2);
987 isl_bool isl_space_has_equal_tuples(
988 __isl_keep isl_space *space1,
989 __isl_keep isl_space *space2);
990 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
991 __isl_keep isl_space *space2);
992 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
993 __isl_keep isl_space *space2);
994 isl_bool isl_space_tuple_is_equal(
995 __isl_keep isl_space *space1,
996 enum isl_dim_type type1,
997 __isl_keep isl_space *space2,
998 enum isl_dim_type type2);
1000 C<isl_space_is_domain> checks whether the first argument is equal
1001 to the domain of the second argument. This requires in particular that
1002 the first argument is a set space and that the second argument
1003 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1004 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1005 spaces are the same. That is, it checks if they have the same
1006 identifier (if any), the same dimension and the same internal structure
1009 C<isl_space_has_equal_params> checks whether two spaces
1010 have the same parameters in the same order.
1011 C<isl_space_has_equal_tuples> check whether two spaces have
1012 the same tuples. In contrast to C<isl_space_is_equal> below,
1013 it does not check the
1014 parameters. This is useful because many C<isl> functions align the
1015 parameters before they perform their operations, such that equivalence
1017 C<isl_space_is_equal> checks whether two spaces are identical,
1018 meaning that they have the same parameters and the same tuples.
1019 That is, it checks whether both C<isl_space_has_equal_params> and
1020 C<isl_space_has_equal_tuples> hold.
1022 It is often useful to create objects that live in the
1023 same space as some other object. This can be accomplished
1024 by creating the new objects
1025 (see L</"Creating New Sets and Relations"> or
1026 L</"Functions">) based on the space
1027 of the original object.
1029 #include <isl/set.h>
1030 __isl_give isl_space *isl_basic_set_get_space(
1031 __isl_keep isl_basic_set *bset);
1032 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1034 #include <isl/union_set.h>
1035 __isl_give isl_space *isl_union_set_get_space(
1036 __isl_keep isl_union_set *uset);
1038 #include <isl/map.h>
1039 __isl_give isl_space *isl_basic_map_get_space(
1040 __isl_keep isl_basic_map *bmap);
1041 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1043 #include <isl/union_map.h>
1044 __isl_give isl_space *isl_union_map_get_space(
1045 __isl_keep isl_union_map *umap);
1047 #include <isl/constraint.h>
1048 __isl_give isl_space *isl_constraint_get_space(
1049 __isl_keep isl_constraint *constraint);
1051 #include <isl/polynomial.h>
1052 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1053 __isl_keep isl_qpolynomial *qp);
1054 __isl_give isl_space *isl_qpolynomial_get_space(
1055 __isl_keep isl_qpolynomial *qp);
1056 __isl_give isl_space *
1057 isl_qpolynomial_fold_get_domain_space(
1058 __isl_keep isl_qpolynomial_fold *fold);
1059 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1060 __isl_keep isl_qpolynomial_fold *fold);
1061 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1062 __isl_keep isl_pw_qpolynomial *pwqp);
1063 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1064 __isl_keep isl_pw_qpolynomial *pwqp);
1065 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1066 __isl_keep isl_pw_qpolynomial_fold *pwf);
1067 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1068 __isl_keep isl_pw_qpolynomial_fold *pwf);
1069 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1070 __isl_keep isl_union_pw_qpolynomial *upwqp);
1071 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1072 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1074 #include <isl/val.h>
1075 __isl_give isl_space *isl_multi_val_get_space(
1076 __isl_keep isl_multi_val *mv);
1078 #include <isl/aff.h>
1079 __isl_give isl_space *isl_aff_get_domain_space(
1080 __isl_keep isl_aff *aff);
1081 __isl_give isl_space *isl_aff_get_space(
1082 __isl_keep isl_aff *aff);
1083 __isl_give isl_space *isl_pw_aff_get_domain_space(
1084 __isl_keep isl_pw_aff *pwaff);
1085 __isl_give isl_space *isl_pw_aff_get_space(
1086 __isl_keep isl_pw_aff *pwaff);
1087 __isl_give isl_space *isl_multi_aff_get_domain_space(
1088 __isl_keep isl_multi_aff *maff);
1089 __isl_give isl_space *isl_multi_aff_get_space(
1090 __isl_keep isl_multi_aff *maff);
1091 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1092 __isl_keep isl_pw_multi_aff *pma);
1093 __isl_give isl_space *isl_pw_multi_aff_get_space(
1094 __isl_keep isl_pw_multi_aff *pma);
1095 __isl_give isl_space *isl_union_pw_aff_get_space(
1096 __isl_keep isl_union_pw_aff *upa);
1097 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1098 __isl_keep isl_union_pw_multi_aff *upma);
1099 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1100 __isl_keep isl_multi_pw_aff *mpa);
1101 __isl_give isl_space *isl_multi_pw_aff_get_space(
1102 __isl_keep isl_multi_pw_aff *mpa);
1103 __isl_give isl_space *
1104 isl_multi_union_pw_aff_get_domain_space(
1105 __isl_keep isl_multi_union_pw_aff *mupa);
1106 __isl_give isl_space *
1107 isl_multi_union_pw_aff_get_space(
1108 __isl_keep isl_multi_union_pw_aff *mupa);
1110 #include <isl/point.h>
1111 __isl_give isl_space *isl_point_get_space(
1112 __isl_keep isl_point *pnt);
1114 The number of dimensions of a given type of space
1115 may be read off from a space or an object that lives
1116 in a space using the following functions.
1117 In case of C<isl_space_dim>, type may be
1118 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1119 C<isl_dim_out> (only for relations), C<isl_dim_set>
1120 (only for sets) or C<isl_dim_all>.
1122 #include <isl/space.h>
1123 unsigned isl_space_dim(__isl_keep isl_space *space,
1124 enum isl_dim_type type);
1126 #include <isl/local_space.h>
1127 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1128 enum isl_dim_type type);
1130 #include <isl/set.h>
1131 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1132 enum isl_dim_type type);
1133 unsigned isl_set_dim(__isl_keep isl_set *set,
1134 enum isl_dim_type type);
1136 #include <isl/union_set.h>
1137 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1138 enum isl_dim_type type);
1140 #include <isl/map.h>
1141 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1142 enum isl_dim_type type);
1143 unsigned isl_map_dim(__isl_keep isl_map *map,
1144 enum isl_dim_type type);
1146 #include <isl/union_map.h>
1147 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1148 enum isl_dim_type type);
1150 #include <isl/val.h>
1151 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1152 enum isl_dim_type type);
1154 #include <isl/aff.h>
1155 int isl_aff_dim(__isl_keep isl_aff *aff,
1156 enum isl_dim_type type);
1157 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1158 enum isl_dim_type type);
1159 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1160 enum isl_dim_type type);
1161 unsigned isl_pw_multi_aff_dim(
1162 __isl_keep isl_pw_multi_aff *pma,
1163 enum isl_dim_type type);
1164 unsigned isl_multi_pw_aff_dim(
1165 __isl_keep isl_multi_pw_aff *mpa,
1166 enum isl_dim_type type);
1167 unsigned isl_union_pw_aff_dim(
1168 __isl_keep isl_union_pw_aff *upa,
1169 enum isl_dim_type type);
1170 unsigned isl_union_pw_multi_aff_dim(
1171 __isl_keep isl_union_pw_multi_aff *upma,
1172 enum isl_dim_type type);
1173 unsigned isl_multi_union_pw_aff_dim(
1174 __isl_keep isl_multi_union_pw_aff *mupa,
1175 enum isl_dim_type type);
1177 #include <isl/polynomial.h>
1178 unsigned isl_union_pw_qpolynomial_dim(
1179 __isl_keep isl_union_pw_qpolynomial *upwqp,
1180 enum isl_dim_type type);
1181 unsigned isl_union_pw_qpolynomial_fold_dim(
1182 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1183 enum isl_dim_type type);
1185 Note that an C<isl_union_set>, an C<isl_union_map>,
1186 an C<isl_union_pw_multi_aff>,
1187 an C<isl_union_pw_qpolynomial> and
1188 an C<isl_union_pw_qpolynomial_fold>
1189 only have parameters.
1191 Additional parameters can be added to a space using the following function.
1193 #include <isl/space.h>
1194 __isl_give isl_space *isl_space_add_param_id(
1195 __isl_take isl_space *space,
1196 __isl_take isl_id *id);
1198 If a parameter with the given identifier already appears in the space,
1199 then it is not added again.
1201 The identifiers or names of the individual dimensions of spaces
1202 may be set or read off using the following functions on spaces
1203 or objects that live in spaces.
1204 These functions are mostly useful to obtain the identifiers, positions
1205 or names of the parameters. Identifiers of individual dimensions are
1206 essentially only useful for printing. They are ignored by all other
1207 operations and may not be preserved across those operations.
1209 #include <isl/space.h>
1210 __isl_give isl_space *isl_space_set_dim_id(
1211 __isl_take isl_space *space,
1212 enum isl_dim_type type, unsigned pos,
1213 __isl_take isl_id *id);
1214 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1215 enum isl_dim_type type, unsigned pos);
1216 __isl_give isl_id *isl_space_get_dim_id(
1217 __isl_keep isl_space *space,
1218 enum isl_dim_type type, unsigned pos);
1219 __isl_give isl_space *isl_space_set_dim_name(
1220 __isl_take isl_space *space,
1221 enum isl_dim_type type, unsigned pos,
1222 __isl_keep const char *name);
1223 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1224 enum isl_dim_type type, unsigned pos);
1225 __isl_keep const char *isl_space_get_dim_name(
1226 __isl_keep isl_space *space,
1227 enum isl_dim_type type, unsigned pos);
1229 #include <isl/local_space.h>
1230 __isl_give isl_local_space *isl_local_space_set_dim_id(
1231 __isl_take isl_local_space *ls,
1232 enum isl_dim_type type, unsigned pos,
1233 __isl_take isl_id *id);
1234 isl_bool isl_local_space_has_dim_id(
1235 __isl_keep isl_local_space *ls,
1236 enum isl_dim_type type, unsigned pos);
1237 __isl_give isl_id *isl_local_space_get_dim_id(
1238 __isl_keep isl_local_space *ls,
1239 enum isl_dim_type type, unsigned pos);
1240 __isl_give isl_local_space *isl_local_space_set_dim_name(
1241 __isl_take isl_local_space *ls,
1242 enum isl_dim_type type, unsigned pos, const char *s);
1243 isl_bool isl_local_space_has_dim_name(
1244 __isl_keep isl_local_space *ls,
1245 enum isl_dim_type type, unsigned pos)
1246 const char *isl_local_space_get_dim_name(
1247 __isl_keep isl_local_space *ls,
1248 enum isl_dim_type type, unsigned pos);
1250 #include <isl/constraint.h>
1251 const char *isl_constraint_get_dim_name(
1252 __isl_keep isl_constraint *constraint,
1253 enum isl_dim_type type, unsigned pos);
1255 #include <isl/set.h>
1256 __isl_give isl_id *isl_basic_set_get_dim_id(
1257 __isl_keep isl_basic_set *bset,
1258 enum isl_dim_type type, unsigned pos);
1259 __isl_give isl_set *isl_set_set_dim_id(
1260 __isl_take isl_set *set, enum isl_dim_type type,
1261 unsigned pos, __isl_take isl_id *id);
1262 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1263 enum isl_dim_type type, unsigned pos);
1264 __isl_give isl_id *isl_set_get_dim_id(
1265 __isl_keep isl_set *set, enum isl_dim_type type,
1267 const char *isl_basic_set_get_dim_name(
1268 __isl_keep isl_basic_set *bset,
1269 enum isl_dim_type type, unsigned pos);
1270 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1271 enum isl_dim_type type, unsigned pos);
1272 const char *isl_set_get_dim_name(
1273 __isl_keep isl_set *set,
1274 enum isl_dim_type type, unsigned pos);
1276 #include <isl/map.h>
1277 __isl_give isl_map *isl_map_set_dim_id(
1278 __isl_take isl_map *map, enum isl_dim_type type,
1279 unsigned pos, __isl_take isl_id *id);
1280 isl_bool isl_basic_map_has_dim_id(
1281 __isl_keep isl_basic_map *bmap,
1282 enum isl_dim_type type, unsigned pos);
1283 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1284 enum isl_dim_type type, unsigned pos);
1285 __isl_give isl_id *isl_map_get_dim_id(
1286 __isl_keep isl_map *map, enum isl_dim_type type,
1288 __isl_give isl_id *isl_union_map_get_dim_id(
1289 __isl_keep isl_union_map *umap,
1290 enum isl_dim_type type, unsigned pos);
1291 const char *isl_basic_map_get_dim_name(
1292 __isl_keep isl_basic_map *bmap,
1293 enum isl_dim_type type, unsigned pos);
1294 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1295 enum isl_dim_type type, unsigned pos);
1296 const char *isl_map_get_dim_name(
1297 __isl_keep isl_map *map,
1298 enum isl_dim_type type, unsigned pos);
1300 #include <isl/val.h>
1301 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1302 __isl_take isl_multi_val *mv,
1303 enum isl_dim_type type, unsigned pos,
1304 __isl_take isl_id *id);
1305 __isl_give isl_id *isl_multi_val_get_dim_id(
1306 __isl_keep isl_multi_val *mv,
1307 enum isl_dim_type type, unsigned pos);
1308 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1309 __isl_take isl_multi_val *mv,
1310 enum isl_dim_type type, unsigned pos, const char *s);
1312 #include <isl/aff.h>
1313 __isl_give isl_aff *isl_aff_set_dim_id(
1314 __isl_take isl_aff *aff, enum isl_dim_type type,
1315 unsigned pos, __isl_take isl_id *id);
1316 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1317 __isl_take isl_multi_aff *maff,
1318 enum isl_dim_type type, unsigned pos,
1319 __isl_take isl_id *id);
1320 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1321 __isl_take isl_pw_aff *pma,
1322 enum isl_dim_type type, unsigned pos,
1323 __isl_take isl_id *id);
1324 __isl_give isl_multi_pw_aff *
1325 isl_multi_pw_aff_set_dim_id(
1326 __isl_take isl_multi_pw_aff *mpa,
1327 enum isl_dim_type type, unsigned pos,
1328 __isl_take isl_id *id);
1329 __isl_give isl_multi_union_pw_aff *
1330 isl_multi_union_pw_aff_set_dim_id(
1331 __isl_take isl_multi_union_pw_aff *mupa,
1332 enum isl_dim_type type, unsigned pos,
1333 __isl_take isl_id *id);
1334 __isl_give isl_id *isl_multi_aff_get_dim_id(
1335 __isl_keep isl_multi_aff *ma,
1336 enum isl_dim_type type, unsigned pos);
1337 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1338 enum isl_dim_type type, unsigned pos);
1339 __isl_give isl_id *isl_pw_aff_get_dim_id(
1340 __isl_keep isl_pw_aff *pa,
1341 enum isl_dim_type type, unsigned pos);
1342 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1343 __isl_keep isl_pw_multi_aff *pma,
1344 enum isl_dim_type type, unsigned pos);
1345 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1346 __isl_keep isl_multi_pw_aff *mpa,
1347 enum isl_dim_type type, unsigned pos);
1348 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1349 __isl_keep isl_multi_union_pw_aff *mupa,
1350 enum isl_dim_type type, unsigned pos);
1351 __isl_give isl_aff *isl_aff_set_dim_name(
1352 __isl_take isl_aff *aff, enum isl_dim_type type,
1353 unsigned pos, const char *s);
1354 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1355 __isl_take isl_multi_aff *maff,
1356 enum isl_dim_type type, unsigned pos, const char *s);
1357 __isl_give isl_multi_pw_aff *
1358 isl_multi_pw_aff_set_dim_name(
1359 __isl_take isl_multi_pw_aff *mpa,
1360 enum isl_dim_type type, unsigned pos, const char *s);
1361 __isl_give isl_union_pw_aff *
1362 isl_union_pw_aff_set_dim_name(
1363 __isl_take isl_union_pw_aff *upa,
1364 enum isl_dim_type type, unsigned pos,
1366 __isl_give isl_union_pw_multi_aff *
1367 isl_union_pw_multi_aff_set_dim_name(
1368 __isl_take isl_union_pw_multi_aff *upma,
1369 enum isl_dim_type type, unsigned pos,
1371 __isl_give isl_multi_union_pw_aff *
1372 isl_multi_union_pw_aff_set_dim_name(
1373 __isl_take isl_multi_union_pw_aff *mupa,
1374 enum isl_dim_type type, unsigned pos,
1375 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1376 enum isl_dim_type type, unsigned pos);
1377 const char *isl_pw_aff_get_dim_name(
1378 __isl_keep isl_pw_aff *pa,
1379 enum isl_dim_type type, unsigned pos);
1380 const char *isl_pw_multi_aff_get_dim_name(
1381 __isl_keep isl_pw_multi_aff *pma,
1382 enum isl_dim_type type, unsigned pos);
1384 #include <isl/polynomial.h>
1385 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1386 __isl_take isl_qpolynomial *qp,
1387 enum isl_dim_type type, unsigned pos,
1389 __isl_give isl_pw_qpolynomial *
1390 isl_pw_qpolynomial_set_dim_name(
1391 __isl_take isl_pw_qpolynomial *pwqp,
1392 enum isl_dim_type type, unsigned pos,
1394 __isl_give isl_pw_qpolynomial_fold *
1395 isl_pw_qpolynomial_fold_set_dim_name(
1396 __isl_take isl_pw_qpolynomial_fold *pwf,
1397 enum isl_dim_type type, unsigned pos,
1399 __isl_give isl_union_pw_qpolynomial *
1400 isl_union_pw_qpolynomial_set_dim_name(
1401 __isl_take isl_union_pw_qpolynomial *upwqp,
1402 enum isl_dim_type type, unsigned pos,
1404 __isl_give isl_union_pw_qpolynomial_fold *
1405 isl_union_pw_qpolynomial_fold_set_dim_name(
1406 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1407 enum isl_dim_type type, unsigned pos,
1410 Note that C<isl_space_get_name> returns a pointer to some internal
1411 data structure, so the result can only be used while the
1412 corresponding C<isl_space> is alive.
1413 Also note that every function that operates on two sets or relations
1414 requires that both arguments have the same parameters. This also
1415 means that if one of the arguments has named parameters, then the
1416 other needs to have named parameters too and the names need to match.
1417 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1418 arguments may have different parameters (as long as they are named),
1419 in which case the result will have as parameters the union of the parameters of
1422 Given the identifier or name of a dimension (typically a parameter),
1423 its position can be obtained from the following functions.
1425 #include <isl/space.h>
1426 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1427 enum isl_dim_type type, __isl_keep isl_id *id);
1428 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1429 enum isl_dim_type type, const char *name);
1431 #include <isl/local_space.h>
1432 int isl_local_space_find_dim_by_name(
1433 __isl_keep isl_local_space *ls,
1434 enum isl_dim_type type, const char *name);
1436 #include <isl/val.h>
1437 int isl_multi_val_find_dim_by_id(
1438 __isl_keep isl_multi_val *mv,
1439 enum isl_dim_type type, __isl_keep isl_id *id);
1440 int isl_multi_val_find_dim_by_name(
1441 __isl_keep isl_multi_val *mv,
1442 enum isl_dim_type type, const char *name);
1444 #include <isl/set.h>
1445 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1446 enum isl_dim_type type, __isl_keep isl_id *id);
1447 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1448 enum isl_dim_type type, const char *name);
1450 #include <isl/map.h>
1451 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1452 enum isl_dim_type type, __isl_keep isl_id *id);
1453 int isl_basic_map_find_dim_by_name(
1454 __isl_keep isl_basic_map *bmap,
1455 enum isl_dim_type type, const char *name);
1456 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1457 enum isl_dim_type type, const char *name);
1458 int isl_union_map_find_dim_by_name(
1459 __isl_keep isl_union_map *umap,
1460 enum isl_dim_type type, const char *name);
1462 #include <isl/aff.h>
1463 int isl_multi_aff_find_dim_by_id(
1464 __isl_keep isl_multi_aff *ma,
1465 enum isl_dim_type type, __isl_keep isl_id *id);
1466 int isl_multi_pw_aff_find_dim_by_id(
1467 __isl_keep isl_multi_pw_aff *mpa,
1468 enum isl_dim_type type, __isl_keep isl_id *id);
1469 int isl_multi_union_pw_aff_find_dim_by_id(
1470 __isl_keep isl_union_multi_pw_aff *mupa,
1471 enum isl_dim_type type, __isl_keep isl_id *id);
1472 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1473 enum isl_dim_type type, const char *name);
1474 int isl_multi_aff_find_dim_by_name(
1475 __isl_keep isl_multi_aff *ma,
1476 enum isl_dim_type type, const char *name);
1477 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1478 enum isl_dim_type type, const char *name);
1479 int isl_multi_pw_aff_find_dim_by_name(
1480 __isl_keep isl_multi_pw_aff *mpa,
1481 enum isl_dim_type type, const char *name);
1482 int isl_pw_multi_aff_find_dim_by_name(
1483 __isl_keep isl_pw_multi_aff *pma,
1484 enum isl_dim_type type, const char *name);
1485 int isl_union_pw_aff_find_dim_by_name(
1486 __isl_keep isl_union_pw_aff *upa,
1487 enum isl_dim_type type, const char *name);
1488 int isl_union_pw_multi_aff_find_dim_by_name(
1489 __isl_keep isl_union_pw_multi_aff *upma,
1490 enum isl_dim_type type, const char *name);
1491 int isl_multi_union_pw_aff_find_dim_by_name(
1492 __isl_keep isl_multi_union_pw_aff *mupa,
1493 enum isl_dim_type type, const char *name);
1495 #include <isl/polynomial.h>
1496 int isl_pw_qpolynomial_find_dim_by_name(
1497 __isl_keep isl_pw_qpolynomial *pwqp,
1498 enum isl_dim_type type, const char *name);
1499 int isl_pw_qpolynomial_fold_find_dim_by_name(
1500 __isl_keep isl_pw_qpolynomial_fold *pwf,
1501 enum isl_dim_type type, const char *name);
1502 int isl_union_pw_qpolynomial_find_dim_by_name(
1503 __isl_keep isl_union_pw_qpolynomial *upwqp,
1504 enum isl_dim_type type, const char *name);
1505 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1506 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1507 enum isl_dim_type type, const char *name);
1509 The identifiers or names of entire spaces may be set or read off
1510 using the following functions.
1512 #include <isl/space.h>
1513 __isl_give isl_space *isl_space_set_tuple_id(
1514 __isl_take isl_space *space,
1515 enum isl_dim_type type, __isl_take isl_id *id);
1516 __isl_give isl_space *isl_space_reset_tuple_id(
1517 __isl_take isl_space *space, enum isl_dim_type type);
1518 isl_bool isl_space_has_tuple_id(
1519 __isl_keep isl_space *space,
1520 enum isl_dim_type type);
1521 __isl_give isl_id *isl_space_get_tuple_id(
1522 __isl_keep isl_space *space, enum isl_dim_type type);
1523 __isl_give isl_space *isl_space_set_tuple_name(
1524 __isl_take isl_space *space,
1525 enum isl_dim_type type, const char *s);
1526 isl_bool isl_space_has_tuple_name(
1527 __isl_keep isl_space *space,
1528 enum isl_dim_type type);
1529 __isl_keep const char *isl_space_get_tuple_name(
1530 __isl_keep isl_space *space,
1531 enum isl_dim_type type);
1533 #include <isl/local_space.h>
1534 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1535 __isl_take isl_local_space *ls,
1536 enum isl_dim_type type, __isl_take isl_id *id);
1538 #include <isl/set.h>
1539 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1540 __isl_take isl_basic_set *bset,
1541 __isl_take isl_id *id);
1542 __isl_give isl_set *isl_set_set_tuple_id(
1543 __isl_take isl_set *set, __isl_take isl_id *id);
1544 __isl_give isl_set *isl_set_reset_tuple_id(
1545 __isl_take isl_set *set);
1546 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1547 __isl_give isl_id *isl_set_get_tuple_id(
1548 __isl_keep isl_set *set);
1549 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1550 __isl_take isl_basic_set *set, const char *s);
1551 __isl_give isl_set *isl_set_set_tuple_name(
1552 __isl_take isl_set *set, const char *s);
1553 const char *isl_basic_set_get_tuple_name(
1554 __isl_keep isl_basic_set *bset);
1555 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1556 const char *isl_set_get_tuple_name(
1557 __isl_keep isl_set *set);
1559 #include <isl/map.h>
1560 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1561 __isl_take isl_basic_map *bmap,
1562 enum isl_dim_type type, __isl_take isl_id *id);
1563 __isl_give isl_map *isl_map_set_tuple_id(
1564 __isl_take isl_map *map, enum isl_dim_type type,
1565 __isl_take isl_id *id);
1566 __isl_give isl_map *isl_map_reset_tuple_id(
1567 __isl_take isl_map *map, enum isl_dim_type type);
1568 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1569 enum isl_dim_type type);
1570 __isl_give isl_id *isl_map_get_tuple_id(
1571 __isl_keep isl_map *map, enum isl_dim_type type);
1572 __isl_give isl_map *isl_map_set_tuple_name(
1573 __isl_take isl_map *map,
1574 enum isl_dim_type type, const char *s);
1575 const char *isl_basic_map_get_tuple_name(
1576 __isl_keep isl_basic_map *bmap,
1577 enum isl_dim_type type);
1578 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1579 __isl_take isl_basic_map *bmap,
1580 enum isl_dim_type type, const char *s);
1581 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1582 enum isl_dim_type type);
1583 const char *isl_map_get_tuple_name(
1584 __isl_keep isl_map *map,
1585 enum isl_dim_type type);
1587 #include <isl/val.h>
1588 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1589 __isl_take isl_multi_val *mv,
1590 enum isl_dim_type type, __isl_take isl_id *id);
1591 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1592 __isl_take isl_multi_val *mv,
1593 enum isl_dim_type type);
1594 isl_bool isl_multi_val_has_tuple_id(
1595 __isl_keep isl_multi_val *mv,
1596 enum isl_dim_type type);
1597 __isl_give isl_id *isl_multi_val_get_tuple_id(
1598 __isl_keep isl_multi_val *mv,
1599 enum isl_dim_type type);
1600 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1601 __isl_take isl_multi_val *mv,
1602 enum isl_dim_type type, const char *s);
1603 const char *isl_multi_val_get_tuple_name(
1604 __isl_keep isl_multi_val *mv,
1605 enum isl_dim_type type);
1607 #include <isl/aff.h>
1608 __isl_give isl_aff *isl_aff_set_tuple_id(
1609 __isl_take isl_aff *aff,
1610 enum isl_dim_type type, __isl_take isl_id *id);
1611 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1612 __isl_take isl_multi_aff *maff,
1613 enum isl_dim_type type, __isl_take isl_id *id);
1614 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1615 __isl_take isl_pw_aff *pwaff,
1616 enum isl_dim_type type, __isl_take isl_id *id);
1617 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1618 __isl_take isl_pw_multi_aff *pma,
1619 enum isl_dim_type type, __isl_take isl_id *id);
1620 __isl_give isl_multi_union_pw_aff *
1621 isl_multi_union_pw_aff_set_tuple_id(
1622 __isl_take isl_multi_union_pw_aff *mupa,
1623 enum isl_dim_type type, __isl_take isl_id *id);
1624 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1625 __isl_take isl_multi_aff *ma,
1626 enum isl_dim_type type);
1627 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1628 __isl_take isl_pw_aff *pa,
1629 enum isl_dim_type type);
1630 __isl_give isl_multi_pw_aff *
1631 isl_multi_pw_aff_reset_tuple_id(
1632 __isl_take isl_multi_pw_aff *mpa,
1633 enum isl_dim_type type);
1634 __isl_give isl_pw_multi_aff *
1635 isl_pw_multi_aff_reset_tuple_id(
1636 __isl_take isl_pw_multi_aff *pma,
1637 enum isl_dim_type type);
1638 __isl_give isl_multi_union_pw_aff *
1639 isl_multi_union_pw_aff_reset_tuple_id(
1640 __isl_take isl_multi_union_pw_aff *mupa,
1641 enum isl_dim_type type);
1642 isl_bool isl_multi_aff_has_tuple_id(
1643 __isl_keep isl_multi_aff *ma,
1644 enum isl_dim_type type);
1645 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1646 __isl_keep isl_multi_aff *ma,
1647 enum isl_dim_type type);
1648 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1649 enum isl_dim_type type);
1650 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1651 __isl_keep isl_pw_aff *pa,
1652 enum isl_dim_type type);
1653 isl_bool isl_pw_multi_aff_has_tuple_id(
1654 __isl_keep isl_pw_multi_aff *pma,
1655 enum isl_dim_type type);
1656 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1657 __isl_keep isl_pw_multi_aff *pma,
1658 enum isl_dim_type type);
1659 isl_bool isl_multi_pw_aff_has_tuple_id(
1660 __isl_keep isl_multi_pw_aff *mpa,
1661 enum isl_dim_type type);
1662 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1663 __isl_keep isl_multi_pw_aff *mpa,
1664 enum isl_dim_type type);
1665 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1666 __isl_keep isl_multi_union_pw_aff *mupa,
1667 enum isl_dim_type type);
1668 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1669 __isl_keep isl_multi_union_pw_aff *mupa,
1670 enum isl_dim_type type);
1671 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1672 __isl_take isl_multi_aff *maff,
1673 enum isl_dim_type type, const char *s);
1674 __isl_give isl_multi_pw_aff *
1675 isl_multi_pw_aff_set_tuple_name(
1676 __isl_take isl_multi_pw_aff *mpa,
1677 enum isl_dim_type type, const char *s);
1678 __isl_give isl_multi_union_pw_aff *
1679 isl_multi_union_pw_aff_set_tuple_name(
1680 __isl_take isl_multi_union_pw_aff *mupa,
1681 enum isl_dim_type type, const char *s);
1682 const char *isl_multi_aff_get_tuple_name(
1683 __isl_keep isl_multi_aff *multi,
1684 enum isl_dim_type type);
1685 isl_bool isl_pw_multi_aff_has_tuple_name(
1686 __isl_keep isl_pw_multi_aff *pma,
1687 enum isl_dim_type type);
1688 const char *isl_pw_multi_aff_get_tuple_name(
1689 __isl_keep isl_pw_multi_aff *pma,
1690 enum isl_dim_type type);
1691 const char *isl_multi_union_pw_aff_get_tuple_name(
1692 __isl_keep isl_multi_union_pw_aff *mupa,
1693 enum isl_dim_type type);
1695 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1696 or C<isl_dim_set>. As with C<isl_space_get_name>,
1697 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1699 Binary operations require the corresponding spaces of their arguments
1700 to have the same name.
1702 To keep the names of all parameters and tuples, but reset the user pointers
1703 of all the corresponding identifiers, use the following function.
1705 #include <isl/space.h>
1706 __isl_give isl_space *isl_space_reset_user(
1707 __isl_take isl_space *space);
1709 #include <isl/set.h>
1710 __isl_give isl_set *isl_set_reset_user(
1711 __isl_take isl_set *set);
1713 #include <isl/map.h>
1714 __isl_give isl_map *isl_map_reset_user(
1715 __isl_take isl_map *map);
1717 #include <isl/union_set.h>
1718 __isl_give isl_union_set *isl_union_set_reset_user(
1719 __isl_take isl_union_set *uset);
1721 #include <isl/union_map.h>
1722 __isl_give isl_union_map *isl_union_map_reset_user(
1723 __isl_take isl_union_map *umap);
1725 #include <isl/val.h>
1726 __isl_give isl_multi_val *isl_multi_val_reset_user(
1727 __isl_take isl_multi_val *mv);
1729 #include <isl/aff.h>
1730 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1731 __isl_take isl_multi_aff *ma);
1732 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1733 __isl_take isl_pw_aff *pa);
1734 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1735 __isl_take isl_multi_pw_aff *mpa);
1736 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1737 __isl_take isl_pw_multi_aff *pma);
1738 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1739 __isl_take isl_union_pw_aff *upa);
1740 __isl_give isl_multi_union_pw_aff *
1741 isl_multi_union_pw_aff_reset_user(
1742 __isl_take isl_multi_union_pw_aff *mupa);
1743 __isl_give isl_union_pw_multi_aff *
1744 isl_union_pw_multi_aff_reset_user(
1745 __isl_take isl_union_pw_multi_aff *upma);
1747 #include <isl/polynomial.h>
1748 __isl_give isl_pw_qpolynomial *
1749 isl_pw_qpolynomial_reset_user(
1750 __isl_take isl_pw_qpolynomial *pwqp);
1751 __isl_give isl_union_pw_qpolynomial *
1752 isl_union_pw_qpolynomial_reset_user(
1753 __isl_take isl_union_pw_qpolynomial *upwqp);
1754 __isl_give isl_pw_qpolynomial_fold *
1755 isl_pw_qpolynomial_fold_reset_user(
1756 __isl_take isl_pw_qpolynomial_fold *pwf);
1757 __isl_give isl_union_pw_qpolynomial_fold *
1758 isl_union_pw_qpolynomial_fold_reset_user(
1759 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1761 Spaces can be nested. In particular, the domain of a set or
1762 the domain or range of a relation can be a nested relation.
1763 This process is also called I<wrapping>.
1764 The functions for detecting, constructing and deconstructing
1765 such nested spaces can be found in the wrapping properties
1766 of L</"Unary Properties">, the wrapping operations
1767 of L</"Unary Operations"> and the Cartesian product operations
1768 of L</"Basic Operations">.
1770 Spaces can be created from other spaces
1771 using the functions described in L</"Unary Operations">
1772 and L</"Binary Operations">.
1776 A local space is essentially a space with
1777 zero or more existentially quantified variables.
1778 The local space of various objects can be obtained
1779 using the following functions.
1781 #include <isl/constraint.h>
1782 __isl_give isl_local_space *isl_constraint_get_local_space(
1783 __isl_keep isl_constraint *constraint);
1785 #include <isl/set.h>
1786 __isl_give isl_local_space *isl_basic_set_get_local_space(
1787 __isl_keep isl_basic_set *bset);
1789 #include <isl/map.h>
1790 __isl_give isl_local_space *isl_basic_map_get_local_space(
1791 __isl_keep isl_basic_map *bmap);
1793 #include <isl/aff.h>
1794 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1795 __isl_keep isl_aff *aff);
1796 __isl_give isl_local_space *isl_aff_get_local_space(
1797 __isl_keep isl_aff *aff);
1799 A new local space can be created from a space using
1801 #include <isl/local_space.h>
1802 __isl_give isl_local_space *isl_local_space_from_space(
1803 __isl_take isl_space *space);
1805 They can be inspected, modified, copied and freed using the following functions.
1807 #include <isl/local_space.h>
1808 isl_bool isl_local_space_is_params(
1809 __isl_keep isl_local_space *ls);
1810 isl_bool isl_local_space_is_set(
1811 __isl_keep isl_local_space *ls);
1812 __isl_give isl_space *isl_local_space_get_space(
1813 __isl_keep isl_local_space *ls);
1814 __isl_give isl_aff *isl_local_space_get_div(
1815 __isl_keep isl_local_space *ls, int pos);
1816 __isl_give isl_local_space *isl_local_space_copy(
1817 __isl_keep isl_local_space *ls);
1818 __isl_null isl_local_space *isl_local_space_free(
1819 __isl_take isl_local_space *ls);
1821 Note that C<isl_local_space_get_div> can only be used on local spaces
1824 Two local spaces can be compared using
1826 isl_bool isl_local_space_is_equal(
1827 __isl_keep isl_local_space *ls1,
1828 __isl_keep isl_local_space *ls2);
1830 Local spaces can be created from other local spaces
1831 using the functions described in L</"Unary Operations">
1832 and L</"Binary Operations">.
1834 =head2 Creating New Sets and Relations
1836 C<isl> has functions for creating some standard sets and relations.
1840 =item * Empty sets and relations
1842 __isl_give isl_basic_set *isl_basic_set_empty(
1843 __isl_take isl_space *space);
1844 __isl_give isl_basic_map *isl_basic_map_empty(
1845 __isl_take isl_space *space);
1846 __isl_give isl_set *isl_set_empty(
1847 __isl_take isl_space *space);
1848 __isl_give isl_map *isl_map_empty(
1849 __isl_take isl_space *space);
1850 __isl_give isl_union_set *isl_union_set_empty(
1851 __isl_take isl_space *space);
1852 __isl_give isl_union_map *isl_union_map_empty(
1853 __isl_take isl_space *space);
1855 For C<isl_union_set>s and C<isl_union_map>s, the space
1856 is only used to specify the parameters.
1858 =item * Universe sets and relations
1860 __isl_give isl_basic_set *isl_basic_set_universe(
1861 __isl_take isl_space *space);
1862 __isl_give isl_basic_map *isl_basic_map_universe(
1863 __isl_take isl_space *space);
1864 __isl_give isl_set *isl_set_universe(
1865 __isl_take isl_space *space);
1866 __isl_give isl_map *isl_map_universe(
1867 __isl_take isl_space *space);
1868 __isl_give isl_union_set *isl_union_set_universe(
1869 __isl_take isl_union_set *uset);
1870 __isl_give isl_union_map *isl_union_map_universe(
1871 __isl_take isl_union_map *umap);
1873 The sets and relations constructed by the functions above
1874 contain all integer values, while those constructed by the
1875 functions below only contain non-negative values.
1877 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1878 __isl_take isl_space *space);
1879 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1880 __isl_take isl_space *space);
1881 __isl_give isl_set *isl_set_nat_universe(
1882 __isl_take isl_space *space);
1883 __isl_give isl_map *isl_map_nat_universe(
1884 __isl_take isl_space *space);
1886 =item * Identity relations
1888 __isl_give isl_basic_map *isl_basic_map_identity(
1889 __isl_take isl_space *space);
1890 __isl_give isl_map *isl_map_identity(
1891 __isl_take isl_space *space);
1893 The number of input and output dimensions in C<space> needs
1896 =item * Lexicographic order
1898 __isl_give isl_map *isl_map_lex_lt(
1899 __isl_take isl_space *set_space);
1900 __isl_give isl_map *isl_map_lex_le(
1901 __isl_take isl_space *set_space);
1902 __isl_give isl_map *isl_map_lex_gt(
1903 __isl_take isl_space *set_space);
1904 __isl_give isl_map *isl_map_lex_ge(
1905 __isl_take isl_space *set_space);
1906 __isl_give isl_map *isl_map_lex_lt_first(
1907 __isl_take isl_space *space, unsigned n);
1908 __isl_give isl_map *isl_map_lex_le_first(
1909 __isl_take isl_space *space, unsigned n);
1910 __isl_give isl_map *isl_map_lex_gt_first(
1911 __isl_take isl_space *space, unsigned n);
1912 __isl_give isl_map *isl_map_lex_ge_first(
1913 __isl_take isl_space *space, unsigned n);
1915 The first four functions take a space for a B<set>
1916 and return relations that express that the elements in the domain
1917 are lexicographically less
1918 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1919 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1920 than the elements in the range.
1921 The last four functions take a space for a map
1922 and return relations that express that the first C<n> dimensions
1923 in the domain are lexicographically less
1924 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1925 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1926 than the first C<n> dimensions in the range.
1930 A basic set or relation can be converted to a set or relation
1931 using the following functions.
1933 __isl_give isl_set *isl_set_from_basic_set(
1934 __isl_take isl_basic_set *bset);
1935 __isl_give isl_map *isl_map_from_basic_map(
1936 __isl_take isl_basic_map *bmap);
1938 Sets and relations can be converted to union sets and relations
1939 using the following functions.
1941 __isl_give isl_union_set *isl_union_set_from_basic_set(
1942 __isl_take isl_basic_set *bset);
1943 __isl_give isl_union_map *isl_union_map_from_basic_map(
1944 __isl_take isl_basic_map *bmap);
1945 __isl_give isl_union_set *isl_union_set_from_set(
1946 __isl_take isl_set *set);
1947 __isl_give isl_union_map *isl_union_map_from_map(
1948 __isl_take isl_map *map);
1950 The inverse conversions below can only be used if the input
1951 union set or relation is known to contain elements in exactly one
1954 __isl_give isl_set *isl_set_from_union_set(
1955 __isl_take isl_union_set *uset);
1956 __isl_give isl_map *isl_map_from_union_map(
1957 __isl_take isl_union_map *umap);
1959 Sets and relations can be copied and freed again using the following
1962 __isl_give isl_basic_set *isl_basic_set_copy(
1963 __isl_keep isl_basic_set *bset);
1964 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1965 __isl_give isl_union_set *isl_union_set_copy(
1966 __isl_keep isl_union_set *uset);
1967 __isl_give isl_basic_map *isl_basic_map_copy(
1968 __isl_keep isl_basic_map *bmap);
1969 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1970 __isl_give isl_union_map *isl_union_map_copy(
1971 __isl_keep isl_union_map *umap);
1972 __isl_null isl_basic_set *isl_basic_set_free(
1973 __isl_take isl_basic_set *bset);
1974 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1975 __isl_null isl_union_set *isl_union_set_free(
1976 __isl_take isl_union_set *uset);
1977 __isl_null isl_basic_map *isl_basic_map_free(
1978 __isl_take isl_basic_map *bmap);
1979 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1980 __isl_null isl_union_map *isl_union_map_free(
1981 __isl_take isl_union_map *umap);
1983 Other sets and relations can be constructed by starting
1984 from a universe set or relation, adding equality and/or
1985 inequality constraints and then projecting out the
1986 existentially quantified variables, if any.
1987 Constraints can be constructed, manipulated and
1988 added to (or removed from) (basic) sets and relations
1989 using the following functions.
1991 #include <isl/constraint.h>
1992 __isl_give isl_constraint *isl_constraint_alloc_equality(
1993 __isl_take isl_local_space *ls);
1994 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1995 __isl_take isl_local_space *ls);
1996 __isl_give isl_constraint *isl_constraint_set_constant_si(
1997 __isl_take isl_constraint *constraint, int v);
1998 __isl_give isl_constraint *isl_constraint_set_constant_val(
1999 __isl_take isl_constraint *constraint,
2000 __isl_take isl_val *v);
2001 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2002 __isl_take isl_constraint *constraint,
2003 enum isl_dim_type type, int pos, int v);
2004 __isl_give isl_constraint *
2005 isl_constraint_set_coefficient_val(
2006 __isl_take isl_constraint *constraint,
2007 enum isl_dim_type type, int pos,
2008 __isl_take isl_val *v);
2009 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2010 __isl_take isl_basic_map *bmap,
2011 __isl_take isl_constraint *constraint);
2012 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2013 __isl_take isl_basic_set *bset,
2014 __isl_take isl_constraint *constraint);
2015 __isl_give isl_map *isl_map_add_constraint(
2016 __isl_take isl_map *map,
2017 __isl_take isl_constraint *constraint);
2018 __isl_give isl_set *isl_set_add_constraint(
2019 __isl_take isl_set *set,
2020 __isl_take isl_constraint *constraint);
2022 For example, to create a set containing the even integers
2023 between 10 and 42, you would use the following code.
2026 isl_local_space *ls;
2028 isl_basic_set *bset;
2030 space = isl_space_set_alloc(ctx, 0, 2);
2031 bset = isl_basic_set_universe(isl_space_copy(space));
2032 ls = isl_local_space_from_space(space);
2034 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2035 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2036 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2037 bset = isl_basic_set_add_constraint(bset, c);
2039 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2040 c = isl_constraint_set_constant_si(c, -10);
2041 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2042 bset = isl_basic_set_add_constraint(bset, c);
2044 c = isl_constraint_alloc_inequality(ls);
2045 c = isl_constraint_set_constant_si(c, 42);
2046 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2047 bset = isl_basic_set_add_constraint(bset, c);
2049 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2053 isl_basic_set *bset;
2054 bset = isl_basic_set_read_from_str(ctx,
2055 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2057 A basic set or relation can also be constructed from two matrices
2058 describing the equalities and the inequalities.
2060 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2061 __isl_take isl_space *space,
2062 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2063 enum isl_dim_type c1,
2064 enum isl_dim_type c2, enum isl_dim_type c3,
2065 enum isl_dim_type c4);
2066 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2067 __isl_take isl_space *space,
2068 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2069 enum isl_dim_type c1,
2070 enum isl_dim_type c2, enum isl_dim_type c3,
2071 enum isl_dim_type c4, enum isl_dim_type c5);
2073 The C<isl_dim_type> arguments indicate the order in which
2074 different kinds of variables appear in the input matrices
2075 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2076 C<isl_dim_set> and C<isl_dim_div> for sets and
2077 of C<isl_dim_cst>, C<isl_dim_param>,
2078 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2080 A (basic or union) set or relation can also be constructed from a
2081 (union) (piecewise) (multiple) affine expression
2082 or a list of affine expressions
2083 (See L</"Functions">), provided these affine expressions do not
2086 __isl_give isl_basic_map *isl_basic_map_from_aff(
2087 __isl_take isl_aff *aff);
2088 __isl_give isl_map *isl_map_from_aff(
2089 __isl_take isl_aff *aff);
2090 __isl_give isl_set *isl_set_from_pw_aff(
2091 __isl_take isl_pw_aff *pwaff);
2092 __isl_give isl_map *isl_map_from_pw_aff(
2093 __isl_take isl_pw_aff *pwaff);
2094 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2095 __isl_take isl_space *domain_space,
2096 __isl_take isl_aff_list *list);
2097 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2098 __isl_take isl_multi_aff *maff)
2099 __isl_give isl_map *isl_map_from_multi_aff(
2100 __isl_take isl_multi_aff *maff)
2101 __isl_give isl_set *isl_set_from_pw_multi_aff(
2102 __isl_take isl_pw_multi_aff *pma);
2103 __isl_give isl_map *isl_map_from_pw_multi_aff(
2104 __isl_take isl_pw_multi_aff *pma);
2105 __isl_give isl_set *isl_set_from_multi_pw_aff(
2106 __isl_take isl_multi_pw_aff *mpa);
2107 __isl_give isl_map *isl_map_from_multi_pw_aff(
2108 __isl_take isl_multi_pw_aff *mpa);
2109 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2110 __isl_take isl_union_pw_aff *upa);
2111 __isl_give isl_union_map *
2112 isl_union_map_from_union_pw_multi_aff(
2113 __isl_take isl_union_pw_multi_aff *upma);
2114 __isl_give isl_union_map *
2115 isl_union_map_from_multi_union_pw_aff(
2116 __isl_take isl_multi_union_pw_aff *mupa);
2118 The C<domain_space> argument describes the domain of the resulting
2119 basic relation. It is required because the C<list> may consist
2120 of zero affine expressions.
2121 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2122 is not allowed to be zero-dimensional. The domain of the result
2123 is the shared domain of the union piecewise affine elements.
2125 =head2 Inspecting Sets and Relations
2127 Usually, the user should not have to care about the actual constraints
2128 of the sets and maps, but should instead apply the abstract operations
2129 explained in the following sections.
2130 Occasionally, however, it may be required to inspect the individual
2131 coefficients of the constraints. This section explains how to do so.
2132 In these cases, it may also be useful to have C<isl> compute
2133 an explicit representation of the existentially quantified variables.
2135 __isl_give isl_set *isl_set_compute_divs(
2136 __isl_take isl_set *set);
2137 __isl_give isl_map *isl_map_compute_divs(
2138 __isl_take isl_map *map);
2139 __isl_give isl_union_set *isl_union_set_compute_divs(
2140 __isl_take isl_union_set *uset);
2141 __isl_give isl_union_map *isl_union_map_compute_divs(
2142 __isl_take isl_union_map *umap);
2144 This explicit representation defines the existentially quantified
2145 variables as integer divisions of the other variables, possibly
2146 including earlier existentially quantified variables.
2147 An explicitly represented existentially quantified variable therefore
2148 has a unique value when the values of the other variables are known.
2150 Alternatively, the existentially quantified variables can be removed
2151 using the following functions, which compute an overapproximation.
2153 #include <isl/set.h>
2154 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2155 __isl_take isl_basic_set *bset);
2156 __isl_give isl_set *isl_set_remove_divs(
2157 __isl_take isl_set *set);
2159 #include <isl/map.h>
2160 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2161 __isl_take isl_basic_map *bmap);
2162 __isl_give isl_map *isl_map_remove_divs(
2163 __isl_take isl_map *map);
2165 #include <isl/union_set.h>
2166 __isl_give isl_union_set *isl_union_set_remove_divs(
2167 __isl_take isl_union_set *bset);
2169 #include <isl/union_map.h>
2170 __isl_give isl_union_map *isl_union_map_remove_divs(
2171 __isl_take isl_union_map *bmap);
2173 It is also possible to only remove those divs that are defined
2174 in terms of a given range of dimensions or only those for which
2175 no explicit representation is known.
2177 __isl_give isl_basic_set *
2178 isl_basic_set_remove_divs_involving_dims(
2179 __isl_take isl_basic_set *bset,
2180 enum isl_dim_type type,
2181 unsigned first, unsigned n);
2182 __isl_give isl_basic_map *
2183 isl_basic_map_remove_divs_involving_dims(
2184 __isl_take isl_basic_map *bmap,
2185 enum isl_dim_type type,
2186 unsigned first, unsigned n);
2187 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2188 __isl_take isl_set *set, enum isl_dim_type type,
2189 unsigned first, unsigned n);
2190 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2191 __isl_take isl_map *map, enum isl_dim_type type,
2192 unsigned first, unsigned n);
2194 __isl_give isl_basic_set *
2195 isl_basic_set_remove_unknown_divs(
2196 __isl_take isl_basic_set *bset);
2197 __isl_give isl_set *isl_set_remove_unknown_divs(
2198 __isl_take isl_set *set);
2199 __isl_give isl_map *isl_map_remove_unknown_divs(
2200 __isl_take isl_map *map);
2202 To iterate over all the sets or maps in a union set or map, use
2204 #include <isl/union_set.h>
2205 isl_stat isl_union_set_foreach_set(
2206 __isl_keep isl_union_set *uset,
2207 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2210 #include <isl/union_map.h>
2211 isl_stat isl_union_map_foreach_map(
2212 __isl_keep isl_union_map *umap,
2213 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2215 isl_bool isl_union_map_every_map(
2216 __isl_keep isl_union_map *umap,
2217 isl_bool (*test)(__isl_keep isl_map *map,
2221 These functions call the callback function once for each
2222 (pair of) space(s) for which there are elements in the input.
2223 The argument to the callback contains all elements in the input
2224 with that (pair of) space(s).
2225 The C<isl_union_map_every_map> variant check whether each
2226 call to the callback returns true and stops checking as soon as one
2227 of these calls returns false.
2229 The number of sets or maps in a union set or map can be obtained
2232 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2233 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2235 To extract the set or map in a given space from a union, use
2237 __isl_give isl_set *isl_union_set_extract_set(
2238 __isl_keep isl_union_set *uset,
2239 __isl_take isl_space *space);
2240 __isl_give isl_map *isl_union_map_extract_map(
2241 __isl_keep isl_union_map *umap,
2242 __isl_take isl_space *space);
2244 To iterate over all the basic sets or maps in a set or map, use
2246 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2247 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2250 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2251 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2255 The callback function C<fn> should return C<isl_stat_ok> if successful and
2256 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2257 occurs, the above functions will return C<isl_stat_error>.
2259 It should be noted that C<isl> does not guarantee that
2260 the basic sets or maps passed to C<fn> are disjoint.
2261 If this is required, then the user should call one of
2262 the following functions first.
2264 __isl_give isl_set *isl_set_make_disjoint(
2265 __isl_take isl_set *set);
2266 __isl_give isl_map *isl_map_make_disjoint(
2267 __isl_take isl_map *map);
2269 The number of basic sets in a set can be obtained
2270 or the number of basic maps in a map can be obtained
2273 #include <isl/set.h>
2274 int isl_set_n_basic_set(__isl_keep isl_set *set);
2276 #include <isl/map.h>
2277 int isl_map_n_basic_map(__isl_keep isl_map *map);
2279 It is also possible to obtain a list of basic sets from a set
2282 #include <isl/set.h>
2283 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2284 __isl_keep isl_set *set);
2286 #include <isl/union_set.h>
2287 __isl_give isl_basic_set_list *
2288 isl_union_set_get_basic_set_list(
2289 __isl_keep isl_union_set *uset);
2291 The returned list can be manipulated using the functions in L<"Lists">.
2293 To iterate over the constraints of a basic set or map, use
2295 #include <isl/constraint.h>
2297 int isl_basic_set_n_constraint(
2298 __isl_keep isl_basic_set *bset);
2299 isl_stat isl_basic_set_foreach_constraint(
2300 __isl_keep isl_basic_set *bset,
2301 isl_stat (*fn)(__isl_take isl_constraint *c,
2304 int isl_basic_map_n_constraint(
2305 __isl_keep isl_basic_map *bmap);
2306 isl_stat isl_basic_map_foreach_constraint(
2307 __isl_keep isl_basic_map *bmap,
2308 isl_stat (*fn)(__isl_take isl_constraint *c,
2311 __isl_null isl_constraint *isl_constraint_free(
2312 __isl_take isl_constraint *c);
2314 Again, the callback function C<fn> should return C<isl_stat_ok>
2316 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2317 occurs, the above functions will return C<isl_stat_error>.
2318 The constraint C<c> represents either an equality or an inequality.
2319 Use the following function to find out whether a constraint
2320 represents an equality. If not, it represents an inequality.
2322 isl_bool isl_constraint_is_equality(
2323 __isl_keep isl_constraint *constraint);
2325 It is also possible to obtain a list of constraints from a basic
2328 #include <isl/constraint.h>
2329 __isl_give isl_constraint_list *
2330 isl_basic_map_get_constraint_list(
2331 __isl_keep isl_basic_map *bmap);
2332 __isl_give isl_constraint_list *
2333 isl_basic_set_get_constraint_list(
2334 __isl_keep isl_basic_set *bset);
2336 These functions require that all existentially quantified variables
2337 have an explicit representation.
2338 The returned list can be manipulated using the functions in L<"Lists">.
2340 The coefficients of the constraints can be inspected using
2341 the following functions.
2343 isl_bool isl_constraint_is_lower_bound(
2344 __isl_keep isl_constraint *constraint,
2345 enum isl_dim_type type, unsigned pos);
2346 isl_bool isl_constraint_is_upper_bound(
2347 __isl_keep isl_constraint *constraint,
2348 enum isl_dim_type type, unsigned pos);
2349 __isl_give isl_val *isl_constraint_get_constant_val(
2350 __isl_keep isl_constraint *constraint);
2351 __isl_give isl_val *isl_constraint_get_coefficient_val(
2352 __isl_keep isl_constraint *constraint,
2353 enum isl_dim_type type, int pos);
2355 The explicit representations of the existentially quantified
2356 variables can be inspected using the following function.
2357 Note that the user is only allowed to use this function
2358 if the inspected set or map is the result of a call
2359 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2360 The existentially quantified variable is equal to the floor
2361 of the returned affine expression. The affine expression
2362 itself can be inspected using the functions in
2365 __isl_give isl_aff *isl_constraint_get_div(
2366 __isl_keep isl_constraint *constraint, int pos);
2368 To obtain the constraints of a basic set or map in matrix
2369 form, use the following functions.
2371 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2372 __isl_keep isl_basic_set *bset,
2373 enum isl_dim_type c1, enum isl_dim_type c2,
2374 enum isl_dim_type c3, enum isl_dim_type c4);
2375 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2376 __isl_keep isl_basic_set *bset,
2377 enum isl_dim_type c1, enum isl_dim_type c2,
2378 enum isl_dim_type c3, enum isl_dim_type c4);
2379 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2380 __isl_keep isl_basic_map *bmap,
2381 enum isl_dim_type c1,
2382 enum isl_dim_type c2, enum isl_dim_type c3,
2383 enum isl_dim_type c4, enum isl_dim_type c5);
2384 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2385 __isl_keep isl_basic_map *bmap,
2386 enum isl_dim_type c1,
2387 enum isl_dim_type c2, enum isl_dim_type c3,
2388 enum isl_dim_type c4, enum isl_dim_type c5);
2390 The C<isl_dim_type> arguments dictate the order in which
2391 different kinds of variables appear in the resulting matrix.
2392 For set inputs, they should be a permutation of
2393 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2394 For map inputs, they should be a permutation of
2395 C<isl_dim_cst>, C<isl_dim_param>,
2396 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2400 Points are elements of a set. They can be used to construct
2401 simple sets (boxes) or they can be used to represent the
2402 individual elements of a set.
2403 The zero point (the origin) can be created using
2405 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2407 The coordinates of a point can be inspected, set and changed
2410 __isl_give isl_val *isl_point_get_coordinate_val(
2411 __isl_keep isl_point *pnt,
2412 enum isl_dim_type type, int pos);
2413 __isl_give isl_point *isl_point_set_coordinate_val(
2414 __isl_take isl_point *pnt,
2415 enum isl_dim_type type, int pos,
2416 __isl_take isl_val *v);
2418 __isl_give isl_point *isl_point_add_ui(
2419 __isl_take isl_point *pnt,
2420 enum isl_dim_type type, int pos, unsigned val);
2421 __isl_give isl_point *isl_point_sub_ui(
2422 __isl_take isl_point *pnt,
2423 enum isl_dim_type type, int pos, unsigned val);
2425 Points can be copied or freed using
2427 __isl_give isl_point *isl_point_copy(
2428 __isl_keep isl_point *pnt);
2429 __isl_null isl_point *isl_point_free(
2430 __isl_take isl_point *pnt);
2432 A singleton set can be created from a point using
2434 __isl_give isl_basic_set *isl_basic_set_from_point(
2435 __isl_take isl_point *pnt);
2436 __isl_give isl_set *isl_set_from_point(
2437 __isl_take isl_point *pnt);
2438 __isl_give isl_union_set *isl_union_set_from_point(
2439 __isl_take isl_point *pnt);
2441 and a box can be created from two opposite extremal points using
2443 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2444 __isl_take isl_point *pnt1,
2445 __isl_take isl_point *pnt2);
2446 __isl_give isl_set *isl_set_box_from_points(
2447 __isl_take isl_point *pnt1,
2448 __isl_take isl_point *pnt2);
2450 All elements of a B<bounded> (union) set can be enumerated using
2451 the following functions.
2453 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2454 isl_stat (*fn)(__isl_take isl_point *pnt,
2457 isl_stat isl_union_set_foreach_point(
2458 __isl_keep isl_union_set *uset,
2459 isl_stat (*fn)(__isl_take isl_point *pnt,
2463 The function C<fn> is called for each integer point in
2464 C<set> with as second argument the last argument of
2465 the C<isl_set_foreach_point> call. The function C<fn>
2466 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2467 In the latter case, C<isl_set_foreach_point> will stop
2468 enumerating and return C<isl_stat_error> as well.
2469 If the enumeration is performed successfully and to completion,
2470 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2472 To obtain a single point of a (basic or union) set, use
2474 __isl_give isl_point *isl_basic_set_sample_point(
2475 __isl_take isl_basic_set *bset);
2476 __isl_give isl_point *isl_set_sample_point(
2477 __isl_take isl_set *set);
2478 __isl_give isl_point *isl_union_set_sample_point(
2479 __isl_take isl_union_set *uset);
2481 If C<set> does not contain any (integer) points, then the
2482 resulting point will be ``void'', a property that can be
2485 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2489 Besides sets and relation, C<isl> also supports various types of functions.
2490 Each of these types is derived from the value type (see L</"Values">)
2491 or from one of two primitive function types
2492 through the application of zero or more type constructors.
2493 We first describe the primitive type and then we describe
2494 the types derived from these primitive types.
2496 =head3 Primitive Functions
2498 C<isl> support two primitive function types, quasi-affine
2499 expressions and quasipolynomials.
2500 A quasi-affine expression is defined either over a parameter
2501 space or over a set and is composed of integer constants,
2502 parameters and set variables, addition, subtraction and
2503 integer division by an integer constant.
2504 For example, the quasi-affine expression
2506 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2508 maps C<x> to C<2*floor((4 n + x)/9>.
2509 A quasipolynomial is a polynomial expression in quasi-affine
2510 expression. That is, it additionally allows for multiplication.
2511 Note, though, that it is not allowed to construct an integer
2512 division of an expression involving multiplications.
2513 Here is an example of a quasipolynomial that is not
2514 quasi-affine expression
2516 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2518 Note that the external representations of quasi-affine expressions
2519 and quasipolynomials are different. Quasi-affine expressions
2520 use a notation with square brackets just like binary relations,
2521 while quasipolynomials do not. This might change at some point.
2523 If a primitive function is defined over a parameter space,
2524 then the space of the function itself is that of a set.
2525 If it is defined over a set, then the space of the function
2526 is that of a relation. In both cases, the set space (or
2527 the output space) is single-dimensional, anonymous and unstructured.
2528 To create functions with multiple dimensions or with other kinds
2529 of set or output spaces, use multiple expressions
2530 (see L</"Multiple Expressions">).
2534 =item * Quasi-affine Expressions
2536 Besides the expressions described above, a quasi-affine
2537 expression can also be set to NaN. Such expressions
2538 typically represent a failure to represent a result
2539 as a quasi-affine expression.
2541 The zero quasi affine expression or the quasi affine expression
2542 that is equal to a given value, parameter or
2543 a specified dimension on a given domain can be created using
2545 #include <isl/aff.h>
2546 __isl_give isl_aff *isl_aff_zero_on_domain(
2547 __isl_take isl_local_space *ls);
2548 __isl_give isl_aff *isl_aff_val_on_domain(
2549 __isl_take isl_local_space *ls,
2550 __isl_take isl_val *val);
2551 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2552 __isl_take isl_space *space,
2553 __isl_take isl_id *id);
2554 __isl_give isl_aff *isl_aff_var_on_domain(
2555 __isl_take isl_local_space *ls,
2556 enum isl_dim_type type, unsigned pos);
2557 __isl_give isl_aff *isl_aff_nan_on_domain(
2558 __isl_take isl_local_space *ls);
2560 The space passed to C<isl_aff_param_on_domain_space_id>
2561 is required to have a parameter with the given identifier.
2563 Quasi affine expressions can be copied and freed using
2565 #include <isl/aff.h>
2566 __isl_give isl_aff *isl_aff_copy(
2567 __isl_keep isl_aff *aff);
2568 __isl_null isl_aff *isl_aff_free(
2569 __isl_take isl_aff *aff);
2571 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2572 using the following function. The constraint is required to have
2573 a non-zero coefficient for the specified dimension.
2575 #include <isl/constraint.h>
2576 __isl_give isl_aff *isl_constraint_get_bound(
2577 __isl_keep isl_constraint *constraint,
2578 enum isl_dim_type type, int pos);
2580 The entire affine expression of the constraint can also be extracted
2581 using the following function.
2583 #include <isl/constraint.h>
2584 __isl_give isl_aff *isl_constraint_get_aff(
2585 __isl_keep isl_constraint *constraint);
2587 Conversely, an equality constraint equating
2588 the affine expression to zero or an inequality constraint enforcing
2589 the affine expression to be non-negative, can be constructed using
2591 __isl_give isl_constraint *isl_equality_from_aff(
2592 __isl_take isl_aff *aff);
2593 __isl_give isl_constraint *isl_inequality_from_aff(
2594 __isl_take isl_aff *aff);
2596 The coefficients and the integer divisions of an affine expression
2597 can be inspected using the following functions.
2599 #include <isl/aff.h>
2600 __isl_give isl_val *isl_aff_get_constant_val(
2601 __isl_keep isl_aff *aff);
2602 __isl_give isl_val *isl_aff_get_coefficient_val(
2603 __isl_keep isl_aff *aff,
2604 enum isl_dim_type type, int pos);
2605 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2606 enum isl_dim_type type, int pos);
2607 __isl_give isl_val *isl_aff_get_denominator_val(
2608 __isl_keep isl_aff *aff);
2609 __isl_give isl_aff *isl_aff_get_div(
2610 __isl_keep isl_aff *aff, int pos);
2612 They can be modified using the following functions.
2614 #include <isl/aff.h>
2615 __isl_give isl_aff *isl_aff_set_constant_si(
2616 __isl_take isl_aff *aff, int v);
2617 __isl_give isl_aff *isl_aff_set_constant_val(
2618 __isl_take isl_aff *aff, __isl_take isl_val *v);
2619 __isl_give isl_aff *isl_aff_set_coefficient_si(
2620 __isl_take isl_aff *aff,
2621 enum isl_dim_type type, int pos, int v);
2622 __isl_give isl_aff *isl_aff_set_coefficient_val(
2623 __isl_take isl_aff *aff,
2624 enum isl_dim_type type, int pos,
2625 __isl_take isl_val *v);
2627 __isl_give isl_aff *isl_aff_add_constant_si(
2628 __isl_take isl_aff *aff, int v);
2629 __isl_give isl_aff *isl_aff_add_constant_val(
2630 __isl_take isl_aff *aff, __isl_take isl_val *v);
2631 __isl_give isl_aff *isl_aff_add_constant_num_si(
2632 __isl_take isl_aff *aff, int v);
2633 __isl_give isl_aff *isl_aff_add_coefficient_si(
2634 __isl_take isl_aff *aff,
2635 enum isl_dim_type type, int pos, int v);
2636 __isl_give isl_aff *isl_aff_add_coefficient_val(
2637 __isl_take isl_aff *aff,
2638 enum isl_dim_type type, int pos,
2639 __isl_take isl_val *v);
2641 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2642 set the I<numerator> of the constant or coefficient, while
2643 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2644 the constant or coefficient as a whole.
2645 The C<add_constant> and C<add_coefficient> functions add an integer
2646 or rational value to
2647 the possibly rational constant or coefficient.
2648 The C<add_constant_num> functions add an integer value to
2651 =item * Quasipolynomials
2653 Some simple quasipolynomials can be created using the following functions.
2655 #include <isl/polynomial.h>
2656 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2657 __isl_take isl_space *domain);
2658 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2659 __isl_take isl_space *domain);
2660 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2661 __isl_take isl_space *domain);
2662 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2663 __isl_take isl_space *domain);
2664 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2665 __isl_take isl_space *domain);
2666 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2667 __isl_take isl_space *domain,
2668 __isl_take isl_val *val);
2669 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2670 __isl_take isl_space *domain,
2671 enum isl_dim_type type, unsigned pos);
2672 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2673 __isl_take isl_aff *aff);
2675 Recall that the space in which a quasipolynomial lives is a map space
2676 with a one-dimensional range. The C<domain> argument in some of
2677 the functions above corresponds to the domain of this map space.
2679 Quasipolynomials can be copied and freed again using the following
2682 #include <isl/polynomial.h>
2683 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2684 __isl_keep isl_qpolynomial *qp);
2685 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2686 __isl_take isl_qpolynomial *qp);
2688 The constant term of a quasipolynomial can be extracted using
2690 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2691 __isl_keep isl_qpolynomial *qp);
2693 To iterate over all terms in a quasipolynomial,
2696 isl_stat isl_qpolynomial_foreach_term(
2697 __isl_keep isl_qpolynomial *qp,
2698 isl_stat (*fn)(__isl_take isl_term *term,
2699 void *user), void *user);
2701 The terms themselves can be inspected and freed using
2704 unsigned isl_term_dim(__isl_keep isl_term *term,
2705 enum isl_dim_type type);
2706 __isl_give isl_val *isl_term_get_coefficient_val(
2707 __isl_keep isl_term *term);
2708 int isl_term_get_exp(__isl_keep isl_term *term,
2709 enum isl_dim_type type, unsigned pos);
2710 __isl_give isl_aff *isl_term_get_div(
2711 __isl_keep isl_term *term, unsigned pos);
2712 void isl_term_free(__isl_take isl_term *term);
2714 Each term is a product of parameters, set variables and
2715 integer divisions. The function C<isl_term_get_exp>
2716 returns the exponent of a given dimensions in the given term.
2722 A reduction represents a maximum or a minimum of its
2724 The only reduction type defined by C<isl> is
2725 C<isl_qpolynomial_fold>.
2727 There are currently no functions to directly create such
2728 objects, but they do appear in the piecewise quasipolynomial
2729 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2731 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2733 Reductions can be copied and freed using
2734 the following functions.
2736 #include <isl/polynomial.h>
2737 __isl_give isl_qpolynomial_fold *
2738 isl_qpolynomial_fold_copy(
2739 __isl_keep isl_qpolynomial_fold *fold);
2740 void isl_qpolynomial_fold_free(
2741 __isl_take isl_qpolynomial_fold *fold);
2743 To iterate over all quasipolynomials in a reduction, use
2745 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2746 __isl_keep isl_qpolynomial_fold *fold,
2747 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2748 void *user), void *user);
2750 =head3 Multiple Expressions
2752 A multiple expression represents a sequence of zero or
2753 more base expressions, all defined on the same domain space.
2754 The domain space of the multiple expression is the same
2755 as that of the base expressions, but the range space
2756 can be any space. In case the base expressions have
2757 a set space, the corresponding multiple expression
2758 also has a set space.
2759 Objects of the value type do not have an associated space.
2760 The space of a multiple value is therefore always a set space.
2761 Similarly, the space of a multiple union piecewise
2762 affine expression is always a set space.
2763 If the base expressions are not total, then
2764 a corresponding zero-dimensional multiple expression may
2765 have an explicit domain that keeps track of the domain
2766 outside of any base expressions.
2768 The multiple expression types defined by C<isl>
2769 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2770 C<isl_multi_union_pw_aff>.
2772 A multiple expression with the value zero for
2773 each output (or set) dimension can be created
2774 using the following functions.
2776 #include <isl/val.h>
2777 __isl_give isl_multi_val *isl_multi_val_zero(
2778 __isl_take isl_space *space);
2780 #include <isl/aff.h>
2781 __isl_give isl_multi_aff *isl_multi_aff_zero(
2782 __isl_take isl_space *space);
2783 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2784 __isl_take isl_space *space);
2785 __isl_give isl_multi_union_pw_aff *
2786 isl_multi_union_pw_aff_zero(
2787 __isl_take isl_space *space);
2789 Since there is no canonical way of representing a zero
2790 value of type C<isl_union_pw_aff>, the space passed
2791 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2793 An identity function can be created using the following
2794 functions. The space needs to be that of a relation
2795 with the same number of input and output dimensions.
2797 #include <isl/aff.h>
2798 __isl_give isl_multi_aff *isl_multi_aff_identity(
2799 __isl_take isl_space *space);
2800 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2801 __isl_take isl_space *space);
2803 A function that performs a projection on a universe
2804 relation or set can be created using the following functions.
2805 See also the corresponding
2806 projection operations in L</"Unary Operations">.
2808 #include <isl/aff.h>
2809 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2810 __isl_take isl_space *space);
2811 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2812 __isl_take isl_space *space);
2813 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2814 __isl_take isl_space *space,
2815 enum isl_dim_type type,
2816 unsigned first, unsigned n);
2818 A multiple expression can be created from a single
2819 base expression using the following functions.
2820 The space of the created multiple expression is the same
2821 as that of the base expression, except for
2822 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2823 lives in a parameter space and the output lives
2824 in a single-dimensional set space.
2826 #include <isl/aff.h>
2827 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2828 __isl_take isl_aff *aff);
2829 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2830 __isl_take isl_pw_aff *pa);
2831 __isl_give isl_multi_union_pw_aff *
2832 isl_multi_union_pw_aff_from_union_pw_aff(
2833 __isl_take isl_union_pw_aff *upa);
2835 A multiple expression can be created from a list
2836 of base expression in a specified space.
2837 The domain of this space needs to be the same
2838 as the domains of the base expressions in the list.
2839 If the base expressions have a set space (or no associated space),
2840 then this space also needs to be a set space.
2842 #include <isl/val.h>
2843 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2844 __isl_take isl_space *space,
2845 __isl_take isl_val_list *list);
2847 #include <isl/aff.h>
2848 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2849 __isl_take isl_space *space,
2850 __isl_take isl_aff_list *list);
2851 __isl_give isl_multi_pw_aff *
2852 isl_multi_pw_aff_from_pw_aff_list(
2853 __isl_take isl_space *space,
2854 __isl_take isl_pw_aff_list *list);
2855 __isl_give isl_multi_union_pw_aff *
2856 isl_multi_union_pw_aff_from_union_pw_aff_list(
2857 __isl_take isl_space *space,
2858 __isl_take isl_union_pw_aff_list *list);
2860 As a convenience, a multiple piecewise expression can
2861 also be created from a multiple expression.
2862 Each piecewise expression in the result has a single
2865 #include <isl/aff.h>
2866 __isl_give isl_multi_pw_aff *
2867 isl_multi_pw_aff_from_multi_aff(
2868 __isl_take isl_multi_aff *ma);
2870 Similarly, a multiple union expression can be
2871 created from a multiple expression.
2873 #include <isl/aff.h>
2874 __isl_give isl_multi_union_pw_aff *
2875 isl_multi_union_pw_aff_from_multi_aff(
2876 __isl_take isl_multi_aff *ma);
2877 __isl_give isl_multi_union_pw_aff *
2878 isl_multi_union_pw_aff_from_multi_pw_aff(
2879 __isl_take isl_multi_pw_aff *mpa);
2881 A multiple quasi-affine expression can be created from
2882 a multiple value with a given domain space using the following
2885 #include <isl/aff.h>
2886 __isl_give isl_multi_aff *
2887 isl_multi_aff_multi_val_on_space(
2888 __isl_take isl_space *space,
2889 __isl_take isl_multi_val *mv);
2892 a multiple union piecewise affine expression can be created from
2893 a multiple value with a given domain or
2894 a (piecewise) multiple affine expression with a given domain
2895 using the following functions.
2897 #include <isl/aff.h>
2898 __isl_give isl_multi_union_pw_aff *
2899 isl_multi_union_pw_aff_multi_val_on_domain(
2900 __isl_take isl_union_set *domain,
2901 __isl_take isl_multi_val *mv);
2902 __isl_give isl_multi_union_pw_aff *
2903 isl_multi_union_pw_aff_multi_aff_on_domain(
2904 __isl_take isl_union_set *domain,
2905 __isl_take isl_multi_aff *ma);
2906 __isl_give isl_multi_union_pw_aff *
2907 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2908 __isl_take isl_union_set *domain,
2909 __isl_take isl_pw_multi_aff *pma);
2911 Multiple expressions can be copied and freed using
2912 the following functions.
2914 #include <isl/val.h>
2915 __isl_give isl_multi_val *isl_multi_val_copy(
2916 __isl_keep isl_multi_val *mv);
2917 __isl_null isl_multi_val *isl_multi_val_free(
2918 __isl_take isl_multi_val *mv);
2920 #include <isl/aff.h>
2921 __isl_give isl_multi_aff *isl_multi_aff_copy(
2922 __isl_keep isl_multi_aff *maff);
2923 __isl_null isl_multi_aff *isl_multi_aff_free(
2924 __isl_take isl_multi_aff *maff);
2925 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2926 __isl_keep isl_multi_pw_aff *mpa);
2927 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2928 __isl_take isl_multi_pw_aff *mpa);
2929 __isl_give isl_multi_union_pw_aff *
2930 isl_multi_union_pw_aff_copy(
2931 __isl_keep isl_multi_union_pw_aff *mupa);
2932 __isl_null isl_multi_union_pw_aff *
2933 isl_multi_union_pw_aff_free(
2934 __isl_take isl_multi_union_pw_aff *mupa);
2936 The base expression at a given position of a multiple
2937 expression can be extracted using the following functions.
2939 #include <isl/val.h>
2940 __isl_give isl_val *isl_multi_val_get_val(
2941 __isl_keep isl_multi_val *mv, int pos);
2943 #include <isl/aff.h>
2944 __isl_give isl_aff *isl_multi_aff_get_aff(
2945 __isl_keep isl_multi_aff *multi, int pos);
2946 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2947 __isl_keep isl_multi_pw_aff *mpa, int pos);
2948 __isl_give isl_union_pw_aff *
2949 isl_multi_union_pw_aff_get_union_pw_aff(
2950 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2952 It can be replaced using the following functions.
2954 #include <isl/val.h>
2955 __isl_give isl_multi_val *isl_multi_val_set_val(
2956 __isl_take isl_multi_val *mv, int pos,
2957 __isl_take isl_val *val);
2959 #include <isl/aff.h>
2960 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2961 __isl_take isl_multi_aff *multi, int pos,
2962 __isl_take isl_aff *aff);
2963 __isl_give isl_multi_union_pw_aff *
2964 isl_multi_union_pw_aff_set_union_pw_aff(
2965 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2966 __isl_take isl_union_pw_aff *upa);
2968 As a convenience, a sequence of base expressions that have
2969 their domains in a given space can be extracted from a sequence
2970 of union expressions using the following function.
2972 #include <isl/aff.h>
2973 __isl_give isl_multi_pw_aff *
2974 isl_multi_union_pw_aff_extract_multi_pw_aff(
2975 __isl_keep isl_multi_union_pw_aff *mupa,
2976 __isl_take isl_space *space);
2978 Note that there is a difference between C<isl_multi_union_pw_aff>
2979 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2980 of unions of piecewise expressions, while the second is a union
2981 of piecewise sequences. In particular, multiple affine expressions
2982 in an C<isl_union_pw_multi_aff> may live in different spaces,
2983 while there is only a single multiple expression in
2984 an C<isl_multi_union_pw_aff>, which can therefore only live
2985 in a single space. This means that not every
2986 C<isl_union_pw_multi_aff> can be converted to
2987 an C<isl_multi_union_pw_aff>. Conversely, the elements
2988 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2989 while each multiple expression inside an C<isl_union_pw_multi_aff>
2990 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2991 of dimension greater than one may therefore not be exact.
2992 The following functions can
2993 be used to perform these conversions when they are possible.
2995 #include <isl/aff.h>
2996 __isl_give isl_multi_union_pw_aff *
2997 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2998 __isl_take isl_union_pw_multi_aff *upma);
2999 __isl_give isl_union_pw_multi_aff *
3000 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3001 __isl_take isl_multi_union_pw_aff *mupa);
3003 =head3 Piecewise Expressions
3005 A piecewise expression is an expression that is described
3006 using zero or more base expression defined over the same
3007 number of cells in the domain space of the base expressions.
3008 All base expressions are defined over the same
3009 domain space and the cells are disjoint.
3010 The space of a piecewise expression is the same as
3011 that of the base expressions.
3012 If the union of the cells is a strict subset of the domain
3013 space, then the value of the piecewise expression outside
3014 this union is different for types derived from quasi-affine
3015 expressions and those derived from quasipolynomials.
3016 Piecewise expressions derived from quasi-affine expressions
3017 are considered to be undefined outside the union of their cells.
3018 Piecewise expressions derived from quasipolynomials
3019 are considered to be zero outside the union of their cells.
3021 Piecewise quasipolynomials are mainly used by the C<barvinok>
3022 library for representing the number of elements in a parametric set or map.
3023 For example, the piecewise quasipolynomial
3025 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3027 represents the number of points in the map
3029 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3031 The piecewise expression types defined by C<isl>
3032 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3033 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3035 A piecewise expression with no cells can be created using
3036 the following functions.
3038 #include <isl/aff.h>
3039 __isl_give isl_pw_aff *isl_pw_aff_empty(
3040 __isl_take isl_space *space);
3041 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3042 __isl_take isl_space *space);
3044 A piecewise expression with a single universe cell can be
3045 created using the following functions.
3047 #include <isl/aff.h>
3048 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3049 __isl_take isl_aff *aff);
3050 __isl_give isl_pw_multi_aff *
3051 isl_pw_multi_aff_from_multi_aff(
3052 __isl_take isl_multi_aff *ma);
3054 #include <isl/polynomial.h>
3055 __isl_give isl_pw_qpolynomial *
3056 isl_pw_qpolynomial_from_qpolynomial(
3057 __isl_take isl_qpolynomial *qp);
3059 A piecewise expression with a single specified cell can be
3060 created using the following functions.
3062 #include <isl/aff.h>
3063 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3064 __isl_take isl_set *set, __isl_take isl_aff *aff);
3065 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3066 __isl_take isl_set *set,
3067 __isl_take isl_multi_aff *maff);
3069 #include <isl/polynomial.h>
3070 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3071 __isl_take isl_set *set,
3072 __isl_take isl_qpolynomial *qp);
3074 The following convenience functions first create a base expression and
3075 then create a piecewise expression over a universe domain.
3077 #include <isl/aff.h>
3078 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3079 __isl_take isl_local_space *ls);
3080 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3081 __isl_take isl_local_space *ls,
3082 enum isl_dim_type type, unsigned pos);
3083 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3084 __isl_take isl_local_space *ls);
3085 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3086 __isl_take isl_space *space);
3087 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3088 __isl_take isl_space *space);
3089 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3090 __isl_take isl_space *space);
3091 __isl_give isl_pw_multi_aff *
3092 isl_pw_multi_aff_project_out_map(
3093 __isl_take isl_space *space,
3094 enum isl_dim_type type,
3095 unsigned first, unsigned n);
3097 #include <isl/polynomial.h>
3098 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3099 __isl_take isl_space *space);
3101 The following convenience functions first create a base expression and
3102 then create a piecewise expression over a given domain.
3104 #include <isl/aff.h>
3105 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3106 __isl_take isl_set *domain,
3107 __isl_take isl_val *v);
3108 __isl_give isl_pw_multi_aff *
3109 isl_pw_multi_aff_multi_val_on_domain(
3110 __isl_take isl_set *domain,
3111 __isl_take isl_multi_val *mv);
3113 As a convenience, a piecewise multiple expression can
3114 also be created from a piecewise expression.
3115 Each multiple expression in the result is derived
3116 from the corresponding base expression.
3118 #include <isl/aff.h>
3119 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3120 __isl_take isl_pw_aff *pa);
3122 Similarly, a piecewise quasipolynomial can be
3123 created from a piecewise quasi-affine expression using
3124 the following function.
3126 #include <isl/polynomial.h>
3127 __isl_give isl_pw_qpolynomial *
3128 isl_pw_qpolynomial_from_pw_aff(
3129 __isl_take isl_pw_aff *pwaff);
3131 Piecewise expressions can be copied and freed using the following functions.
3133 #include <isl/aff.h>
3134 __isl_give isl_pw_aff *isl_pw_aff_copy(
3135 __isl_keep isl_pw_aff *pwaff);
3136 __isl_null isl_pw_aff *isl_pw_aff_free(
3137 __isl_take isl_pw_aff *pwaff);
3138 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3139 __isl_keep isl_pw_multi_aff *pma);
3140 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3141 __isl_take isl_pw_multi_aff *pma);
3143 #include <isl/polynomial.h>
3144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3145 __isl_keep isl_pw_qpolynomial *pwqp);
3146 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3147 __isl_take isl_pw_qpolynomial *pwqp);
3148 __isl_give isl_pw_qpolynomial_fold *
3149 isl_pw_qpolynomial_fold_copy(
3150 __isl_keep isl_pw_qpolynomial_fold *pwf);
3151 __isl_null isl_pw_qpolynomial_fold *
3152 isl_pw_qpolynomial_fold_free(
3153 __isl_take isl_pw_qpolynomial_fold *pwf);
3155 To iterate over the different cells of a piecewise expression,
3156 use the following functions.
3158 #include <isl/aff.h>
3159 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3160 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3161 isl_stat isl_pw_aff_foreach_piece(
3162 __isl_keep isl_pw_aff *pwaff,
3163 isl_stat (*fn)(__isl_take isl_set *set,
3164 __isl_take isl_aff *aff,
3165 void *user), void *user);
3166 int isl_pw_multi_aff_n_piece(
3167 __isl_keep isl_pw_multi_aff *pma);
3168 isl_stat isl_pw_multi_aff_foreach_piece(
3169 __isl_keep isl_pw_multi_aff *pma,
3170 isl_stat (*fn)(__isl_take isl_set *set,
3171 __isl_take isl_multi_aff *maff,
3172 void *user), void *user);
3174 #include <isl/polynomial.h>
3175 int isl_pw_qpolynomial_n_piece(
3176 __isl_keep isl_pw_qpolynomial *pwqp);
3177 isl_stat isl_pw_qpolynomial_foreach_piece(
3178 __isl_keep isl_pw_qpolynomial *pwqp,
3179 isl_stat (*fn)(__isl_take isl_set *set,
3180 __isl_take isl_qpolynomial *qp,
3181 void *user), void *user);
3182 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3183 __isl_keep isl_pw_qpolynomial *pwqp,
3184 isl_stat (*fn)(__isl_take isl_set *set,
3185 __isl_take isl_qpolynomial *qp,
3186 void *user), void *user);
3187 int isl_pw_qpolynomial_fold_n_piece(
3188 __isl_keep isl_pw_qpolynomial_fold *pwf);
3189 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3190 __isl_keep isl_pw_qpolynomial_fold *pwf,
3191 isl_stat (*fn)(__isl_take isl_set *set,
3192 __isl_take isl_qpolynomial_fold *fold,
3193 void *user), void *user);
3194 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3195 __isl_keep isl_pw_qpolynomial_fold *pwf,
3196 isl_stat (*fn)(__isl_take isl_set *set,
3197 __isl_take isl_qpolynomial_fold *fold,
3198 void *user), void *user);
3200 As usual, the function C<fn> should return C<isl_stat_ok> on success
3201 and C<isl_stat_error> on failure. The difference between
3202 C<isl_pw_qpolynomial_foreach_piece> and
3203 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3204 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3205 compute unique representations for all existentially quantified
3206 variables and then turn these existentially quantified variables
3207 into extra set variables, adapting the associated quasipolynomial
3208 accordingly. This means that the C<set> passed to C<fn>
3209 will not have any existentially quantified variables, but that
3210 the dimensions of the sets may be different for different
3211 invocations of C<fn>.
3212 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3213 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3215 A piecewise expression consisting of the expressions at a given
3216 position of a piecewise multiple expression can be extracted
3217 using the following function.
3219 #include <isl/aff.h>
3220 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3221 __isl_keep isl_pw_multi_aff *pma, int pos);
3223 These expressions can be replaced using the following function.
3225 #include <isl/aff.h>
3226 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3227 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3228 __isl_take isl_pw_aff *pa);
3230 Note that there is a difference between C<isl_multi_pw_aff> and
3231 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3232 affine expressions, while the second is a piecewise sequence
3233 of affine expressions. In particular, each of the piecewise
3234 affine expressions in an C<isl_multi_pw_aff> may have a different
3235 domain, while all multiple expressions associated to a cell
3236 in an C<isl_pw_multi_aff> have the same domain.
3237 It is possible to convert between the two, but when converting
3238 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3239 of the result is the intersection of the domains of the input.
3240 The reverse conversion is exact.
3242 #include <isl/aff.h>
3243 __isl_give isl_pw_multi_aff *
3244 isl_pw_multi_aff_from_multi_pw_aff(
3245 __isl_take isl_multi_pw_aff *mpa);
3246 __isl_give isl_multi_pw_aff *
3247 isl_multi_pw_aff_from_pw_multi_aff(
3248 __isl_take isl_pw_multi_aff *pma);
3250 =head3 Union Expressions
3252 A union expression collects base expressions defined
3253 over different domains. The space of a union expression
3254 is that of the shared parameter space.
3256 The union expression types defined by C<isl>
3257 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3258 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3260 C<isl_union_pw_aff>,
3261 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3262 there can be at most one base expression for a given domain space.
3264 C<isl_union_pw_multi_aff>,
3265 there can be multiple such expressions for a given domain space,
3266 but the domains of these expressions need to be disjoint.
3268 An empty union expression can be created using the following functions.
3270 #include <isl/aff.h>
3271 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3272 __isl_take isl_space *space);
3273 __isl_give isl_union_pw_multi_aff *
3274 isl_union_pw_multi_aff_empty(
3275 __isl_take isl_space *space);
3277 #include <isl/polynomial.h>
3278 __isl_give isl_union_pw_qpolynomial *
3279 isl_union_pw_qpolynomial_zero(
3280 __isl_take isl_space *space);
3282 A union expression containing a single base expression
3283 can be created using the following functions.
3285 #include <isl/aff.h>
3286 __isl_give isl_union_pw_aff *
3287 isl_union_pw_aff_from_pw_aff(
3288 __isl_take isl_pw_aff *pa);
3289 __isl_give isl_union_pw_multi_aff *
3290 isl_union_pw_multi_aff_from_aff(
3291 __isl_take isl_aff *aff);
3292 __isl_give isl_union_pw_multi_aff *
3293 isl_union_pw_multi_aff_from_pw_multi_aff(
3294 __isl_take isl_pw_multi_aff *pma);
3296 #include <isl/polynomial.h>
3297 __isl_give isl_union_pw_qpolynomial *
3298 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3299 __isl_take isl_pw_qpolynomial *pwqp);
3301 The following functions create a base expression on each
3302 of the sets in the union set and collect the results.
3304 #include <isl/aff.h>
3305 __isl_give isl_union_pw_multi_aff *
3306 isl_union_pw_multi_aff_from_union_pw_aff(
3307 __isl_take isl_union_pw_aff *upa);
3308 __isl_give isl_union_pw_aff *
3309 isl_union_pw_multi_aff_get_union_pw_aff(
3310 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3311 __isl_give isl_union_pw_aff *
3312 isl_union_pw_aff_val_on_domain(
3313 __isl_take isl_union_set *domain,
3314 __isl_take isl_val *v);
3315 __isl_give isl_union_pw_multi_aff *
3316 isl_union_pw_multi_aff_multi_val_on_domain(
3317 __isl_take isl_union_set *domain,
3318 __isl_take isl_multi_val *mv);
3319 __isl_give isl_union_pw_aff *
3320 isl_union_pw_aff_param_on_domain_id(
3321 __isl_take isl_union_set *domain,
3322 __isl_take isl_id *id);
3324 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3325 is the identifier of a parameter that may or may not already
3326 be present in C<domain>.
3328 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3330 expression on a given domain can be created using the following
3333 #include <isl/aff.h>
3334 __isl_give isl_union_pw_aff *
3335 isl_union_pw_aff_aff_on_domain(
3336 __isl_take isl_union_set *domain,
3337 __isl_take isl_aff *aff);
3338 __isl_give isl_union_pw_aff *
3339 isl_union_pw_aff_pw_aff_on_domain(
3340 __isl_take isl_union_set *domain,
3341 __isl_take isl_pw_aff *pa);
3343 A base expression can be added to a union expression using
3344 the following functions.
3346 #include <isl/aff.h>
3347 __isl_give isl_union_pw_aff *
3348 isl_union_pw_aff_add_pw_aff(
3349 __isl_take isl_union_pw_aff *upa,
3350 __isl_take isl_pw_aff *pa);
3351 __isl_give isl_union_pw_multi_aff *
3352 isl_union_pw_multi_aff_add_pw_multi_aff(
3353 __isl_take isl_union_pw_multi_aff *upma,
3354 __isl_take isl_pw_multi_aff *pma);
3356 #include <isl/polynomial.h>
3357 __isl_give isl_union_pw_qpolynomial *
3358 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3359 __isl_take isl_union_pw_qpolynomial *upwqp,
3360 __isl_take isl_pw_qpolynomial *pwqp);
3362 Union expressions can be copied and freed using
3363 the following functions.
3365 #include <isl/aff.h>
3366 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3367 __isl_keep isl_union_pw_aff *upa);
3368 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3369 __isl_take isl_union_pw_aff *upa);
3370 __isl_give isl_union_pw_multi_aff *
3371 isl_union_pw_multi_aff_copy(
3372 __isl_keep isl_union_pw_multi_aff *upma);
3373 __isl_null isl_union_pw_multi_aff *
3374 isl_union_pw_multi_aff_free(
3375 __isl_take isl_union_pw_multi_aff *upma);
3377 #include <isl/polynomial.h>
3378 __isl_give isl_union_pw_qpolynomial *
3379 isl_union_pw_qpolynomial_copy(
3380 __isl_keep isl_union_pw_qpolynomial *upwqp);
3381 __isl_null isl_union_pw_qpolynomial *
3382 isl_union_pw_qpolynomial_free(
3383 __isl_take isl_union_pw_qpolynomial *upwqp);
3384 __isl_give isl_union_pw_qpolynomial_fold *
3385 isl_union_pw_qpolynomial_fold_copy(
3386 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3387 __isl_null isl_union_pw_qpolynomial_fold *
3388 isl_union_pw_qpolynomial_fold_free(
3389 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3391 To iterate over the base expressions in a union expression,
3392 use the following functions.
3394 #include <isl/aff.h>
3395 int isl_union_pw_aff_n_pw_aff(
3396 __isl_keep isl_union_pw_aff *upa);
3397 isl_stat isl_union_pw_aff_foreach_pw_aff(
3398 __isl_keep isl_union_pw_aff *upa,
3399 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3400 void *user), void *user);
3401 int isl_union_pw_multi_aff_n_pw_multi_aff(
3402 __isl_keep isl_union_pw_multi_aff *upma);
3403 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3404 __isl_keep isl_union_pw_multi_aff *upma,
3405 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3406 void *user), void *user);
3408 #include <isl/polynomial.h>
3409 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3410 __isl_keep isl_union_pw_qpolynomial *upwqp);
3411 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3412 __isl_keep isl_union_pw_qpolynomial *upwqp,
3413 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3414 void *user), void *user);
3415 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3416 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3417 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3418 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3419 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3420 void *user), void *user);
3422 To extract the base expression in a given space from a union, use
3423 the following functions.
3425 #include <isl/aff.h>
3426 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3427 __isl_keep isl_union_pw_aff *upa,
3428 __isl_take isl_space *space);
3429 __isl_give isl_pw_multi_aff *
3430 isl_union_pw_multi_aff_extract_pw_multi_aff(
3431 __isl_keep isl_union_pw_multi_aff *upma,
3432 __isl_take isl_space *space);
3434 #include <isl/polynomial.h>
3435 __isl_give isl_pw_qpolynomial *
3436 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3437 __isl_keep isl_union_pw_qpolynomial *upwqp,
3438 __isl_take isl_space *space);
3440 =head2 Input and Output
3442 For set and relation,
3443 C<isl> supports its own input/output format, which is similar
3444 to the C<Omega> format, but also supports the C<PolyLib> format
3446 For other object types, typically only an C<isl> format is supported.
3448 =head3 C<isl> format
3450 The C<isl> format is similar to that of C<Omega>, but has a different
3451 syntax for describing the parameters and allows for the definition
3452 of an existentially quantified variable as the integer division
3453 of an affine expression.
3454 For example, the set of integers C<i> between C<0> and C<n>
3455 such that C<i % 10 <= 6> can be described as
3457 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3460 A set or relation can have several disjuncts, separated
3461 by the keyword C<or>. Each disjunct is either a conjunction
3462 of constraints or a projection (C<exists>) of a conjunction
3463 of constraints. The constraints are separated by the keyword
3466 =head3 C<PolyLib> format
3468 If the represented set is a union, then the first line
3469 contains a single number representing the number of disjuncts.
3470 Otherwise, a line containing the number C<1> is optional.
3472 Each disjunct is represented by a matrix of constraints.
3473 The first line contains two numbers representing
3474 the number of rows and columns,
3475 where the number of rows is equal to the number of constraints
3476 and the number of columns is equal to two plus the number of variables.
3477 The following lines contain the actual rows of the constraint matrix.
3478 In each row, the first column indicates whether the constraint
3479 is an equality (C<0>) or inequality (C<1>). The final column
3480 corresponds to the constant term.
3482 If the set is parametric, then the coefficients of the parameters
3483 appear in the last columns before the constant column.
3484 The coefficients of any existentially quantified variables appear
3485 between those of the set variables and those of the parameters.
3487 =head3 Extended C<PolyLib> format
3489 The extended C<PolyLib> format is nearly identical to the
3490 C<PolyLib> format. The only difference is that the line
3491 containing the number of rows and columns of a constraint matrix
3492 also contains four additional numbers:
3493 the number of output dimensions, the number of input dimensions,
3494 the number of local dimensions (i.e., the number of existentially
3495 quantified variables) and the number of parameters.
3496 For sets, the number of ``output'' dimensions is equal
3497 to the number of set dimensions, while the number of ``input''
3502 Objects can be read from input using the following functions.
3504 #include <isl/val.h>
3505 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3507 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3508 isl_ctx *ctx, const char *str);
3510 #include <isl/set.h>
3511 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3512 isl_ctx *ctx, FILE *input);
3513 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3514 isl_ctx *ctx, const char *str);
3515 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3517 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3520 #include <isl/map.h>
3521 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3522 isl_ctx *ctx, FILE *input);
3523 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3524 isl_ctx *ctx, const char *str);
3525 __isl_give isl_map *isl_map_read_from_file(
3526 isl_ctx *ctx, FILE *input);
3527 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3530 #include <isl/union_set.h>
3531 __isl_give isl_union_set *isl_union_set_read_from_file(
3532 isl_ctx *ctx, FILE *input);
3533 __isl_give isl_union_set *isl_union_set_read_from_str(
3534 isl_ctx *ctx, const char *str);
3536 #include <isl/union_map.h>
3537 __isl_give isl_union_map *isl_union_map_read_from_file(
3538 isl_ctx *ctx, FILE *input);
3539 __isl_give isl_union_map *isl_union_map_read_from_str(
3540 isl_ctx *ctx, const char *str);
3542 #include <isl/aff.h>
3543 __isl_give isl_aff *isl_aff_read_from_str(
3544 isl_ctx *ctx, const char *str);
3545 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3546 isl_ctx *ctx, const char *str);
3547 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3548 isl_ctx *ctx, const char *str);
3549 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3550 isl_ctx *ctx, const char *str);
3551 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3552 isl_ctx *ctx, const char *str);
3553 __isl_give isl_union_pw_aff *
3554 isl_union_pw_aff_read_from_str(
3555 isl_ctx *ctx, const char *str);
3556 __isl_give isl_union_pw_multi_aff *
3557 isl_union_pw_multi_aff_read_from_str(
3558 isl_ctx *ctx, const char *str);
3559 __isl_give isl_multi_union_pw_aff *
3560 isl_multi_union_pw_aff_read_from_str(
3561 isl_ctx *ctx, const char *str);
3563 #include <isl/polynomial.h>
3564 __isl_give isl_union_pw_qpolynomial *
3565 isl_union_pw_qpolynomial_read_from_str(
3566 isl_ctx *ctx, const char *str);
3568 For sets and relations,
3569 the input format is autodetected and may be either the C<PolyLib> format
3570 or the C<isl> format.
3574 Before anything can be printed, an C<isl_printer> needs to
3577 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3579 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3580 __isl_null isl_printer *isl_printer_free(
3581 __isl_take isl_printer *printer);
3583 C<isl_printer_to_file> prints to the given file, while
3584 C<isl_printer_to_str> prints to a string that can be extracted
3585 using the following function.
3587 #include <isl/printer.h>
3588 __isl_give char *isl_printer_get_str(
3589 __isl_keep isl_printer *printer);
3591 The printer can be inspected using the following functions.
3593 FILE *isl_printer_get_file(
3594 __isl_keep isl_printer *printer);
3595 int isl_printer_get_output_format(
3596 __isl_keep isl_printer *p);
3597 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3599 The behavior of the printer can be modified in various ways
3601 __isl_give isl_printer *isl_printer_set_output_format(
3602 __isl_take isl_printer *p, int output_format);
3603 __isl_give isl_printer *isl_printer_set_indent(
3604 __isl_take isl_printer *p, int indent);
3605 __isl_give isl_printer *isl_printer_set_indent_prefix(
3606 __isl_take isl_printer *p, const char *prefix);
3607 __isl_give isl_printer *isl_printer_indent(
3608 __isl_take isl_printer *p, int indent);
3609 __isl_give isl_printer *isl_printer_set_prefix(
3610 __isl_take isl_printer *p, const char *prefix);
3611 __isl_give isl_printer *isl_printer_set_suffix(
3612 __isl_take isl_printer *p, const char *suffix);
3613 __isl_give isl_printer *isl_printer_set_yaml_style(
3614 __isl_take isl_printer *p, int yaml_style);
3616 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3617 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3618 and defaults to C<ISL_FORMAT_ISL>.
3619 Each line in the output is prefixed by C<indent_prefix>,
3620 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3621 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3622 In the C<PolyLib> format output,
3623 the coefficients of the existentially quantified variables
3624 appear between those of the set variables and those
3626 The function C<isl_printer_indent> increases the indentation
3627 by the specified amount (which may be negative).
3628 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3629 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3632 To actually print something, use
3634 #include <isl/printer.h>
3635 __isl_give isl_printer *isl_printer_print_double(
3636 __isl_take isl_printer *p, double d);
3638 #include <isl/val.h>
3639 __isl_give isl_printer *isl_printer_print_val(
3640 __isl_take isl_printer *p, __isl_keep isl_val *v);
3642 #include <isl/set.h>
3643 __isl_give isl_printer *isl_printer_print_basic_set(
3644 __isl_take isl_printer *printer,
3645 __isl_keep isl_basic_set *bset);
3646 __isl_give isl_printer *isl_printer_print_set(
3647 __isl_take isl_printer *printer,
3648 __isl_keep isl_set *set);
3650 #include <isl/map.h>
3651 __isl_give isl_printer *isl_printer_print_basic_map(
3652 __isl_take isl_printer *printer,
3653 __isl_keep isl_basic_map *bmap);
3654 __isl_give isl_printer *isl_printer_print_map(
3655 __isl_take isl_printer *printer,
3656 __isl_keep isl_map *map);
3658 #include <isl/union_set.h>
3659 __isl_give isl_printer *isl_printer_print_union_set(
3660 __isl_take isl_printer *p,
3661 __isl_keep isl_union_set *uset);
3663 #include <isl/union_map.h>
3664 __isl_give isl_printer *isl_printer_print_union_map(
3665 __isl_take isl_printer *p,
3666 __isl_keep isl_union_map *umap);
3668 #include <isl/val.h>
3669 __isl_give isl_printer *isl_printer_print_multi_val(
3670 __isl_take isl_printer *p,
3671 __isl_keep isl_multi_val *mv);
3673 #include <isl/aff.h>
3674 __isl_give isl_printer *isl_printer_print_aff(
3675 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3676 __isl_give isl_printer *isl_printer_print_multi_aff(
3677 __isl_take isl_printer *p,
3678 __isl_keep isl_multi_aff *maff);
3679 __isl_give isl_printer *isl_printer_print_pw_aff(
3680 __isl_take isl_printer *p,
3681 __isl_keep isl_pw_aff *pwaff);
3682 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3683 __isl_take isl_printer *p,
3684 __isl_keep isl_pw_multi_aff *pma);
3685 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3686 __isl_take isl_printer *p,
3687 __isl_keep isl_multi_pw_aff *mpa);
3688 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3689 __isl_take isl_printer *p,
3690 __isl_keep isl_union_pw_aff *upa);
3691 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3692 __isl_take isl_printer *p,
3693 __isl_keep isl_union_pw_multi_aff *upma);
3694 __isl_give isl_printer *
3695 isl_printer_print_multi_union_pw_aff(
3696 __isl_take isl_printer *p,
3697 __isl_keep isl_multi_union_pw_aff *mupa);
3699 #include <isl/polynomial.h>
3700 __isl_give isl_printer *isl_printer_print_qpolynomial(
3701 __isl_take isl_printer *p,
3702 __isl_keep isl_qpolynomial *qp);
3703 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3704 __isl_take isl_printer *p,
3705 __isl_keep isl_pw_qpolynomial *pwqp);
3706 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3707 __isl_take isl_printer *p,
3708 __isl_keep isl_union_pw_qpolynomial *upwqp);
3710 __isl_give isl_printer *
3711 isl_printer_print_pw_qpolynomial_fold(
3712 __isl_take isl_printer *p,
3713 __isl_keep isl_pw_qpolynomial_fold *pwf);
3714 __isl_give isl_printer *
3715 isl_printer_print_union_pw_qpolynomial_fold(
3716 __isl_take isl_printer *p,
3717 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3719 For C<isl_printer_print_qpolynomial>,
3720 C<isl_printer_print_pw_qpolynomial> and
3721 C<isl_printer_print_pw_qpolynomial_fold>,
3722 the output format of the printer
3723 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3724 For C<isl_printer_print_union_pw_qpolynomial> and
3725 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3727 In case of printing in C<ISL_FORMAT_C>, the user may want
3728 to set the names of all dimensions first.
3730 C<isl> also provides limited support for printing YAML documents,
3731 just enough for the internal use for printing such documents.
3733 #include <isl/printer.h>
3734 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3735 __isl_take isl_printer *p);
3736 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3737 __isl_take isl_printer *p);
3738 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3739 __isl_take isl_printer *p);
3740 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3741 __isl_take isl_printer *p);
3742 __isl_give isl_printer *isl_printer_yaml_next(
3743 __isl_take isl_printer *p);
3745 A document is started by a call to either
3746 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3747 Anything printed to the printer after such a call belong to the
3748 first key of the mapping or the first element in the sequence.
3749 The function C<isl_printer_yaml_next> moves to the value if
3750 we are currently printing a mapping key, the next key if we
3751 are printing a value or the next element if we are printing
3752 an element in a sequence.
3753 Nested mappings and sequences are initiated by the same
3754 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3755 Each call to these functions needs to have a corresponding call to
3756 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3758 When called on a file printer, the following function flushes
3759 the file. When called on a string printer, the buffer is cleared.
3761 __isl_give isl_printer *isl_printer_flush(
3762 __isl_take isl_printer *p);
3764 The following functions allow the user to attach
3765 notes to a printer in order to keep track of additional state.
3767 #include <isl/printer.h>
3768 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3769 __isl_keep isl_id *id);
3770 __isl_give isl_id *isl_printer_get_note(
3771 __isl_keep isl_printer *p, __isl_take isl_id *id);
3772 __isl_give isl_printer *isl_printer_set_note(
3773 __isl_take isl_printer *p,
3774 __isl_take isl_id *id, __isl_take isl_id *note);
3776 C<isl_printer_set_note> associates the given note to the given
3777 identifier in the printer.
3778 C<isl_printer_get_note> retrieves a note associated to an
3780 C<isl_printer_has_note> checks if there is such a note.
3781 C<isl_printer_get_note> fails if the requested note does not exist.
3783 Alternatively, a string representation can be obtained
3784 directly using the following functions, which always print
3788 __isl_give char *isl_id_to_str(
3789 __isl_keep isl_id *id);
3791 #include <isl/space.h>
3792 __isl_give char *isl_space_to_str(
3793 __isl_keep isl_space *space);
3795 #include <isl/val.h>
3796 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3797 __isl_give char *isl_multi_val_to_str(
3798 __isl_keep isl_multi_val *mv);
3800 #include <isl/set.h>
3801 __isl_give char *isl_basic_set_to_str(
3802 __isl_keep isl_basic_set *bset);
3803 __isl_give char *isl_set_to_str(
3804 __isl_keep isl_set *set);
3806 #include <isl/union_set.h>
3807 __isl_give char *isl_union_set_to_str(
3808 __isl_keep isl_union_set *uset);
3810 #include <isl/map.h>
3811 __isl_give char *isl_basic_map_to_str(
3812 __isl_keep isl_basic_map *bmap);
3813 __isl_give char *isl_map_to_str(
3814 __isl_keep isl_map *map);
3816 #include <isl/union_map.h>
3817 __isl_give char *isl_union_map_to_str(
3818 __isl_keep isl_union_map *umap);
3820 #include <isl/aff.h>
3821 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3822 __isl_give char *isl_pw_aff_to_str(
3823 __isl_keep isl_pw_aff *pa);
3824 __isl_give char *isl_multi_aff_to_str(
3825 __isl_keep isl_multi_aff *ma);
3826 __isl_give char *isl_pw_multi_aff_to_str(
3827 __isl_keep isl_pw_multi_aff *pma);
3828 __isl_give char *isl_multi_pw_aff_to_str(
3829 __isl_keep isl_multi_pw_aff *mpa);
3830 __isl_give char *isl_union_pw_aff_to_str(
3831 __isl_keep isl_union_pw_aff *upa);
3832 __isl_give char *isl_union_pw_multi_aff_to_str(
3833 __isl_keep isl_union_pw_multi_aff *upma);
3834 __isl_give char *isl_multi_union_pw_aff_to_str(
3835 __isl_keep isl_multi_union_pw_aff *mupa);
3837 #include <isl/point.h>
3838 __isl_give char *isl_point_to_str(
3839 __isl_keep isl_point *pnt);
3841 #include <isl/polynomial.h>
3842 __isl_give char *isl_pw_qpolynomial_to_str(
3843 __isl_keep isl_pw_qpolynomial *pwqp);
3844 __isl_give char *isl_union_pw_qpolynomial_to_str(
3845 __isl_keep isl_union_pw_qpolynomial *upwqp);
3849 =head3 Unary Properties
3855 The following functions test whether the given set or relation
3856 contains any integer points. The ``plain'' variants do not perform
3857 any computations, but simply check if the given set or relation
3858 is already known to be empty.
3860 #include <isl/set.h>
3861 isl_bool isl_basic_set_plain_is_empty(
3862 __isl_keep isl_basic_set *bset);
3863 isl_bool isl_basic_set_is_empty(
3864 __isl_keep isl_basic_set *bset);
3865 isl_bool isl_set_plain_is_empty(
3866 __isl_keep isl_set *set);
3867 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3869 #include <isl/union_set.h>
3870 isl_bool isl_union_set_is_empty(
3871 __isl_keep isl_union_set *uset);
3873 #include <isl/map.h>
3874 isl_bool isl_basic_map_plain_is_empty(
3875 __isl_keep isl_basic_map *bmap);
3876 isl_bool isl_basic_map_is_empty(
3877 __isl_keep isl_basic_map *bmap);
3878 isl_bool isl_map_plain_is_empty(
3879 __isl_keep isl_map *map);
3880 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3882 #include <isl/union_map.h>
3883 isl_bool isl_union_map_plain_is_empty(
3884 __isl_keep isl_union_map *umap);
3885 isl_bool isl_union_map_is_empty(
3886 __isl_keep isl_union_map *umap);
3888 =item * Universality
3890 isl_bool isl_basic_set_plain_is_universe(
3891 __isl_keep isl_basic_set *bset);
3892 isl_bool isl_basic_set_is_universe(
3893 __isl_keep isl_basic_set *bset);
3894 isl_bool isl_basic_map_plain_is_universe(
3895 __isl_keep isl_basic_map *bmap);
3896 isl_bool isl_basic_map_is_universe(
3897 __isl_keep isl_basic_map *bmap);
3898 isl_bool isl_set_plain_is_universe(
3899 __isl_keep isl_set *set);
3900 isl_bool isl_map_plain_is_universe(
3901 __isl_keep isl_map *map);
3903 =item * Single-valuedness
3905 #include <isl/set.h>
3906 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3908 #include <isl/map.h>
3909 isl_bool isl_basic_map_is_single_valued(
3910 __isl_keep isl_basic_map *bmap);
3911 isl_bool isl_map_plain_is_single_valued(
3912 __isl_keep isl_map *map);
3913 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3915 #include <isl/union_map.h>
3916 isl_bool isl_union_map_is_single_valued(
3917 __isl_keep isl_union_map *umap);
3921 isl_bool isl_map_plain_is_injective(
3922 __isl_keep isl_map *map);
3923 isl_bool isl_map_is_injective(
3924 __isl_keep isl_map *map);
3925 isl_bool isl_union_map_plain_is_injective(
3926 __isl_keep isl_union_map *umap);
3927 isl_bool isl_union_map_is_injective(
3928 __isl_keep isl_union_map *umap);
3932 isl_bool isl_map_is_bijective(
3933 __isl_keep isl_map *map);
3934 isl_bool isl_union_map_is_bijective(
3935 __isl_keep isl_union_map *umap);
3939 The following functions test whether the given relation
3940 only maps elements to themselves.
3942 #include <isl/map.h>
3943 isl_bool isl_map_is_identity(
3944 __isl_keep isl_map *map);
3946 #include <isl/union_map.h>
3947 isl_bool isl_union_map_is_identity(
3948 __isl_keep isl_union_map *umap);
3952 __isl_give isl_val *
3953 isl_basic_map_plain_get_val_if_fixed(
3954 __isl_keep isl_basic_map *bmap,
3955 enum isl_dim_type type, unsigned pos);
3956 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3957 __isl_keep isl_set *set,
3958 enum isl_dim_type type, unsigned pos);
3959 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3960 __isl_keep isl_map *map,
3961 enum isl_dim_type type, unsigned pos);
3963 If the set or relation obviously lies on a hyperplane where the given dimension
3964 has a fixed value, then return that value.
3965 Otherwise return NaN.
3969 isl_stat isl_set_dim_residue_class_val(
3970 __isl_keep isl_set *set,
3971 int pos, __isl_give isl_val **modulo,
3972 __isl_give isl_val **residue);
3974 Check if the values of the given set dimension are equal to a fixed
3975 value modulo some integer value. If so, assign the modulo to C<*modulo>
3976 and the fixed value to C<*residue>. If the given dimension attains only
3977 a single value, then assign C<0> to C<*modulo> and the fixed value to
3979 If the dimension does not attain only a single value and if no modulo
3980 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3982 #include <isl/set.h>
3983 __isl_give isl_stride_info *isl_set_get_stride_info(
3984 __isl_keep isl_set *set, int pos);
3985 __isl_give isl_val *isl_set_get_stride(
3986 __isl_keep isl_set *set, int pos);
3988 Check if the values of the given set dimension are equal to
3989 some affine expression of the other dimensions (the offset)
3990 modulo some integer stride.
3991 If no more specific information can be found, then the stride
3992 is taken to be one and the offset is taken to be the zero expression.
3993 The function C<isl_set_get_stride_info> performs the same
3994 computation but only returns the stride.
3996 the stride and offset can be extracted from the returned object
3997 using the following functions.
3999 #include <isl/set.h>
4000 __isl_give isl_val *isl_stride_info_get_stride(
4001 __isl_keep isl_stride_info *si);
4002 __isl_give isl_aff *isl_stride_info_get_offset(
4003 __isl_keep isl_stride_info *si);
4005 The stride info object can be released using the following function.
4007 #include <isl/set.h>
4008 __isl_null isl_stride_info *isl_stride_info_free(
4009 __isl_take isl_stride_info *si);
4013 To check whether the description of a set, relation or function depends
4014 on one or more given dimensions,
4015 the following functions can be used.
4017 #include <isl/constraint.h>
4018 isl_bool isl_constraint_involves_dims(
4019 __isl_keep isl_constraint *constraint,
4020 enum isl_dim_type type, unsigned first, unsigned n);
4022 #include <isl/set.h>
4023 isl_bool isl_basic_set_involves_dims(
4024 __isl_keep isl_basic_set *bset,
4025 enum isl_dim_type type, unsigned first, unsigned n);
4026 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4027 enum isl_dim_type type, unsigned first, unsigned n);
4029 #include <isl/map.h>
4030 isl_bool isl_basic_map_involves_dims(
4031 __isl_keep isl_basic_map *bmap,
4032 enum isl_dim_type type, unsigned first, unsigned n);
4033 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4034 enum isl_dim_type type, unsigned first, unsigned n);
4036 #include <isl/union_map.h>
4037 isl_bool isl_union_map_involves_dims(
4038 __isl_keep isl_union_map *umap,
4039 enum isl_dim_type type, unsigned first, unsigned n);
4041 #include <isl/aff.h>
4042 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4043 enum isl_dim_type type, unsigned first, unsigned n);
4044 isl_bool isl_pw_aff_involves_dims(
4045 __isl_keep isl_pw_aff *pwaff,
4046 enum isl_dim_type type, unsigned first, unsigned n);
4047 isl_bool isl_multi_aff_involves_dims(
4048 __isl_keep isl_multi_aff *ma,
4049 enum isl_dim_type type, unsigned first, unsigned n);
4050 isl_bool isl_multi_pw_aff_involves_dims(
4051 __isl_keep isl_multi_pw_aff *mpa,
4052 enum isl_dim_type type, unsigned first, unsigned n);
4054 #include <isl/polynomial.h>
4055 isl_bool isl_qpolynomial_involves_dims(
4056 __isl_keep isl_qpolynomial *qp,
4057 enum isl_dim_type type, unsigned first, unsigned n);
4059 Similarly, the following functions can be used to check whether
4060 a given dimension is involved in any lower or upper bound.
4062 #include <isl/set.h>
4063 isl_bool isl_set_dim_has_any_lower_bound(
4064 __isl_keep isl_set *set,
4065 enum isl_dim_type type, unsigned pos);
4066 isl_bool isl_set_dim_has_any_upper_bound(
4067 __isl_keep isl_set *set,
4068 enum isl_dim_type type, unsigned pos);
4070 Note that these functions return true even if there is a bound on
4071 the dimension on only some of the basic sets of C<set>.
4072 To check if they have a bound for all of the basic sets in C<set>,
4073 use the following functions instead.
4075 #include <isl/set.h>
4076 isl_bool isl_set_dim_has_lower_bound(
4077 __isl_keep isl_set *set,
4078 enum isl_dim_type type, unsigned pos);
4079 isl_bool isl_set_dim_has_upper_bound(
4080 __isl_keep isl_set *set,
4081 enum isl_dim_type type, unsigned pos);
4085 To check whether a set is a parameter domain, use this function:
4087 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4088 isl_bool isl_union_set_is_params(
4089 __isl_keep isl_union_set *uset);
4093 The following functions check whether the space of the given
4094 (basic) set or relation domain and/or range is a wrapped relation.
4096 #include <isl/space.h>
4097 isl_bool isl_space_is_wrapping(
4098 __isl_keep isl_space *space);
4099 isl_bool isl_space_domain_is_wrapping(
4100 __isl_keep isl_space *space);
4101 isl_bool isl_space_range_is_wrapping(
4102 __isl_keep isl_space *space);
4103 isl_bool isl_space_is_product(
4104 __isl_keep isl_space *space);
4106 #include <isl/set.h>
4107 isl_bool isl_basic_set_is_wrapping(
4108 __isl_keep isl_basic_set *bset);
4109 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4111 #include <isl/map.h>
4112 isl_bool isl_map_domain_is_wrapping(
4113 __isl_keep isl_map *map);
4114 isl_bool isl_map_range_is_wrapping(
4115 __isl_keep isl_map *map);
4116 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4118 #include <isl/val.h>
4119 isl_bool isl_multi_val_range_is_wrapping(
4120 __isl_keep isl_multi_val *mv);
4122 #include <isl/aff.h>
4123 isl_bool isl_multi_aff_range_is_wrapping(
4124 __isl_keep isl_multi_aff *ma);
4125 isl_bool isl_multi_pw_aff_range_is_wrapping(
4126 __isl_keep isl_multi_pw_aff *mpa);
4127 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4128 __isl_keep isl_multi_union_pw_aff *mupa);
4130 The input to C<isl_space_is_wrapping> should
4131 be the space of a set, while that of
4132 C<isl_space_domain_is_wrapping> and
4133 C<isl_space_range_is_wrapping> should be the space of a relation.
4134 The input to C<isl_space_is_product> can be either the space
4135 of a set or that of a binary relation.
4136 In case the input is the space of a binary relation, it checks
4137 whether both domain and range are wrapping.
4139 =item * Internal Product
4141 isl_bool isl_basic_map_can_zip(
4142 __isl_keep isl_basic_map *bmap);
4143 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4145 Check whether the product of domain and range of the given relation
4147 i.e., whether both domain and range are nested relations.
4151 #include <isl/space.h>
4152 isl_bool isl_space_can_curry(
4153 __isl_keep isl_space *space);
4155 #include <isl/map.h>
4156 isl_bool isl_basic_map_can_curry(
4157 __isl_keep isl_basic_map *bmap);
4158 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4160 Check whether the domain of the (basic) relation is a wrapped relation.
4162 #include <isl/space.h>
4163 __isl_give isl_space *isl_space_uncurry(
4164 __isl_take isl_space *space);
4166 #include <isl/map.h>
4167 isl_bool isl_basic_map_can_uncurry(
4168 __isl_keep isl_basic_map *bmap);
4169 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4171 Check whether the range of the (basic) relation is a wrapped relation.
4173 #include <isl/space.h>
4174 isl_bool isl_space_can_range_curry(
4175 __isl_keep isl_space *space);
4177 #include <isl/map.h>
4178 isl_bool isl_map_can_range_curry(
4179 __isl_keep isl_map *map);
4181 Check whether the domain of the relation wrapped in the range of
4182 the input is itself a wrapped relation.
4184 =item * Special Values
4186 #include <isl/aff.h>
4187 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4188 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4189 isl_bool isl_multi_pw_aff_is_cst(
4190 __isl_keep isl_multi_pw_aff *mpa);
4192 Check whether the given expression is a constant.
4194 #include <isl/val.h>
4195 isl_bool isl_multi_val_involves_nan(
4196 __isl_keep isl_multi_val *mv);
4198 #include <isl/aff.h>
4199 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4200 isl_bool isl_multi_aff_involves_nan(
4201 __isl_keep isl_multi_aff *ma);
4202 isl_bool isl_pw_aff_involves_nan(
4203 __isl_keep isl_pw_aff *pa);
4204 isl_bool isl_pw_multi_aff_involves_nan(
4205 __isl_keep isl_pw_multi_aff *pma);
4206 isl_bool isl_multi_pw_aff_involves_nan(
4207 __isl_keep isl_multi_pw_aff *mpa);
4208 isl_bool isl_union_pw_aff_involves_nan(
4209 __isl_keep isl_union_pw_aff *upa);
4210 isl_bool isl_union_pw_multi_aff_involves_nan(
4211 __isl_keep isl_union_pw_multi_aff *upma);
4212 isl_bool isl_multi_union_pw_aff_involves_nan(
4213 __isl_keep isl_multi_union_pw_aff *mupa);
4215 #include <isl/polynomial.h>
4216 isl_bool isl_qpolynomial_is_nan(
4217 __isl_keep isl_qpolynomial *qp);
4218 isl_bool isl_qpolynomial_fold_is_nan(
4219 __isl_keep isl_qpolynomial_fold *fold);
4220 isl_bool isl_pw_qpolynomial_involves_nan(
4221 __isl_keep isl_pw_qpolynomial *pwqp);
4222 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4223 __isl_keep isl_pw_qpolynomial_fold *pwf);
4224 isl_bool isl_union_pw_qpolynomial_involves_nan(
4225 __isl_keep isl_union_pw_qpolynomial *upwqp);
4226 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4227 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4229 Check whether the given expression is equal to or involves NaN.
4231 #include <isl/aff.h>
4232 isl_bool isl_aff_plain_is_zero(
4233 __isl_keep isl_aff *aff);
4235 Check whether the affine expression is obviously zero.
4239 =head3 Binary Properties
4245 The following functions check whether two objects
4246 represent the same set, relation or function.
4247 The C<plain> variants only return true if the objects
4248 are obviously the same. That is, they may return false
4249 even if the objects are the same, but they will never
4250 return true if the objects are not the same.
4252 #include <isl/set.h>
4253 isl_bool isl_basic_set_plain_is_equal(
4254 __isl_keep isl_basic_set *bset1,
4255 __isl_keep isl_basic_set *bset2);
4256 isl_bool isl_basic_set_is_equal(
4257 __isl_keep isl_basic_set *bset1,
4258 __isl_keep isl_basic_set *bset2);
4259 isl_bool isl_set_plain_is_equal(
4260 __isl_keep isl_set *set1,
4261 __isl_keep isl_set *set2);
4262 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4263 __isl_keep isl_set *set2);
4265 #include <isl/map.h>
4266 isl_bool isl_basic_map_is_equal(
4267 __isl_keep isl_basic_map *bmap1,
4268 __isl_keep isl_basic_map *bmap2);
4269 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4270 __isl_keep isl_map *map2);
4271 isl_bool isl_map_plain_is_equal(
4272 __isl_keep isl_map *map1,
4273 __isl_keep isl_map *map2);
4275 #include <isl/union_set.h>
4276 isl_bool isl_union_set_is_equal(
4277 __isl_keep isl_union_set *uset1,
4278 __isl_keep isl_union_set *uset2);
4280 #include <isl/union_map.h>
4281 isl_bool isl_union_map_is_equal(
4282 __isl_keep isl_union_map *umap1,
4283 __isl_keep isl_union_map *umap2);
4285 #include <isl/aff.h>
4286 isl_bool isl_aff_plain_is_equal(
4287 __isl_keep isl_aff *aff1,
4288 __isl_keep isl_aff *aff2);
4289 isl_bool isl_multi_aff_plain_is_equal(
4290 __isl_keep isl_multi_aff *maff1,
4291 __isl_keep isl_multi_aff *maff2);
4292 isl_bool isl_pw_aff_plain_is_equal(
4293 __isl_keep isl_pw_aff *pwaff1,
4294 __isl_keep isl_pw_aff *pwaff2);
4295 isl_bool isl_pw_aff_is_equal(
4296 __isl_keep isl_pw_aff *pa1,
4297 __isl_keep isl_pw_aff *pa2);
4298 isl_bool isl_pw_multi_aff_plain_is_equal(
4299 __isl_keep isl_pw_multi_aff *pma1,
4300 __isl_keep isl_pw_multi_aff *pma2);
4301 isl_bool isl_pw_multi_aff_is_equal(
4302 __isl_keep isl_pw_multi_aff *pma1,
4303 __isl_keep isl_pw_multi_aff *pma2);
4304 isl_bool isl_multi_pw_aff_plain_is_equal(
4305 __isl_keep isl_multi_pw_aff *mpa1,
4306 __isl_keep isl_multi_pw_aff *mpa2);
4307 isl_bool isl_multi_pw_aff_is_equal(
4308 __isl_keep isl_multi_pw_aff *mpa1,
4309 __isl_keep isl_multi_pw_aff *mpa2);
4310 isl_bool isl_union_pw_aff_plain_is_equal(
4311 __isl_keep isl_union_pw_aff *upa1,
4312 __isl_keep isl_union_pw_aff *upa2);
4313 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4314 __isl_keep isl_union_pw_multi_aff *upma1,
4315 __isl_keep isl_union_pw_multi_aff *upma2);
4316 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4317 __isl_keep isl_multi_union_pw_aff *mupa1,
4318 __isl_keep isl_multi_union_pw_aff *mupa2);
4320 #include <isl/polynomial.h>
4321 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4322 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4323 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4324 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4325 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4326 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4328 =item * Disjointness
4330 #include <isl/set.h>
4331 isl_bool isl_basic_set_is_disjoint(
4332 __isl_keep isl_basic_set *bset1,
4333 __isl_keep isl_basic_set *bset2);
4334 isl_bool isl_set_plain_is_disjoint(
4335 __isl_keep isl_set *set1,
4336 __isl_keep isl_set *set2);
4337 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4338 __isl_keep isl_set *set2);
4340 #include <isl/map.h>
4341 isl_bool isl_basic_map_is_disjoint(
4342 __isl_keep isl_basic_map *bmap1,
4343 __isl_keep isl_basic_map *bmap2);
4344 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4345 __isl_keep isl_map *map2);
4347 #include <isl/union_set.h>
4348 isl_bool isl_union_set_is_disjoint(
4349 __isl_keep isl_union_set *uset1,
4350 __isl_keep isl_union_set *uset2);
4352 #include <isl/union_map.h>
4353 isl_bool isl_union_map_is_disjoint(
4354 __isl_keep isl_union_map *umap1,
4355 __isl_keep isl_union_map *umap2);
4359 isl_bool isl_basic_set_is_subset(
4360 __isl_keep isl_basic_set *bset1,
4361 __isl_keep isl_basic_set *bset2);
4362 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4363 __isl_keep isl_set *set2);
4364 isl_bool isl_set_is_strict_subset(
4365 __isl_keep isl_set *set1,
4366 __isl_keep isl_set *set2);
4367 isl_bool isl_union_set_is_subset(
4368 __isl_keep isl_union_set *uset1,
4369 __isl_keep isl_union_set *uset2);
4370 isl_bool isl_union_set_is_strict_subset(
4371 __isl_keep isl_union_set *uset1,
4372 __isl_keep isl_union_set *uset2);
4373 isl_bool isl_basic_map_is_subset(
4374 __isl_keep isl_basic_map *bmap1,
4375 __isl_keep isl_basic_map *bmap2);
4376 isl_bool isl_basic_map_is_strict_subset(
4377 __isl_keep isl_basic_map *bmap1,
4378 __isl_keep isl_basic_map *bmap2);
4379 isl_bool isl_map_is_subset(
4380 __isl_keep isl_map *map1,
4381 __isl_keep isl_map *map2);
4382 isl_bool isl_map_is_strict_subset(
4383 __isl_keep isl_map *map1,
4384 __isl_keep isl_map *map2);
4385 isl_bool isl_union_map_is_subset(
4386 __isl_keep isl_union_map *umap1,
4387 __isl_keep isl_union_map *umap2);
4388 isl_bool isl_union_map_is_strict_subset(
4389 __isl_keep isl_union_map *umap1,
4390 __isl_keep isl_union_map *umap2);
4392 Check whether the first argument is a (strict) subset of the
4397 Every comparison function returns a negative value if the first
4398 argument is considered smaller than the second, a positive value
4399 if the first argument is considered greater and zero if the two
4400 constraints are considered the same by the comparison criterion.
4402 #include <isl/constraint.h>
4403 int isl_constraint_plain_cmp(
4404 __isl_keep isl_constraint *c1,
4405 __isl_keep isl_constraint *c2);
4407 This function is useful for sorting C<isl_constraint>s.
4408 The order depends on the internal representation of the inputs.
4409 The order is fixed over different calls to the function (assuming
4410 the internal representation of the inputs has not changed), but may
4411 change over different versions of C<isl>.
4413 #include <isl/constraint.h>
4414 int isl_constraint_cmp_last_non_zero(
4415 __isl_keep isl_constraint *c1,
4416 __isl_keep isl_constraint *c2);
4418 This function can be used to sort constraints that live in the same
4419 local space. Constraints that involve ``earlier'' dimensions or
4420 that have a smaller coefficient for the shared latest dimension
4421 are considered smaller than other constraints.
4422 This function only defines a B<partial> order.
4424 #include <isl/set.h>
4425 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4426 __isl_keep isl_set *set2);
4428 This function is useful for sorting C<isl_set>s.
4429 The order depends on the internal representation of the inputs.
4430 The order is fixed over different calls to the function (assuming
4431 the internal representation of the inputs has not changed), but may
4432 change over different versions of C<isl>.
4434 #include <isl/aff.h>
4435 int isl_multi_aff_plain_cmp(
4436 __isl_keep isl_multi_aff *ma1,
4437 __isl_keep isl_multi_aff *ma2);
4438 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4439 __isl_keep isl_pw_aff *pa2);
4441 The functions C<isl_multi_aff_plain_cmp> and
4442 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4443 C<isl_pw_aff>s. The order is not strictly defined.
4444 The current order sorts expressions that only involve
4445 earlier dimensions before those that involve later dimensions.
4449 =head2 Unary Operations
4455 __isl_give isl_set *isl_set_complement(
4456 __isl_take isl_set *set);
4457 __isl_give isl_map *isl_map_complement(
4458 __isl_take isl_map *map);
4462 #include <isl/space.h>
4463 __isl_give isl_space *isl_space_reverse(
4464 __isl_take isl_space *space);
4466 #include <isl/map.h>
4467 __isl_give isl_basic_map *isl_basic_map_reverse(
4468 __isl_take isl_basic_map *bmap);
4469 __isl_give isl_map *isl_map_reverse(
4470 __isl_take isl_map *map);
4472 #include <isl/union_map.h>
4473 __isl_give isl_union_map *isl_union_map_reverse(
4474 __isl_take isl_union_map *umap);
4478 #include <isl/space.h>
4479 __isl_give isl_space *isl_space_domain(
4480 __isl_take isl_space *space);
4481 __isl_give isl_space *isl_space_range(
4482 __isl_take isl_space *space);
4483 __isl_give isl_space *isl_space_params(
4484 __isl_take isl_space *space);
4486 #include <isl/local_space.h>
4487 __isl_give isl_local_space *isl_local_space_domain(
4488 __isl_take isl_local_space *ls);
4489 __isl_give isl_local_space *isl_local_space_range(
4490 __isl_take isl_local_space *ls);
4492 #include <isl/set.h>
4493 __isl_give isl_basic_set *isl_basic_set_project_out(
4494 __isl_take isl_basic_set *bset,
4495 enum isl_dim_type type, unsigned first, unsigned n);
4496 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4497 enum isl_dim_type type, unsigned first, unsigned n);
4498 __isl_give isl_map *isl_set_project_onto_map(
4499 __isl_take isl_set *set,
4500 enum isl_dim_type type, unsigned first,
4502 __isl_give isl_basic_set *isl_basic_set_params(
4503 __isl_take isl_basic_set *bset);
4504 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4506 The function C<isl_set_project_onto_map> returns a relation
4507 that projects the input set onto the given set dimensions.
4509 #include <isl/map.h>
4510 __isl_give isl_basic_map *isl_basic_map_project_out(
4511 __isl_take isl_basic_map *bmap,
4512 enum isl_dim_type type, unsigned first, unsigned n);
4513 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4514 enum isl_dim_type type, unsigned first, unsigned n);
4515 __isl_give isl_basic_set *isl_basic_map_domain(
4516 __isl_take isl_basic_map *bmap);
4517 __isl_give isl_basic_set *isl_basic_map_range(
4518 __isl_take isl_basic_map *bmap);
4519 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4520 __isl_give isl_set *isl_map_domain(
4521 __isl_take isl_map *bmap);
4522 __isl_give isl_set *isl_map_range(
4523 __isl_take isl_map *map);
4525 #include <isl/union_set.h>
4526 __isl_give isl_union_set *isl_union_set_project_out(
4527 __isl_take isl_union_set *uset,
4528 enum isl_dim_type type,
4529 unsigned first, unsigned n);
4530 __isl_give isl_set *isl_union_set_params(
4531 __isl_take isl_union_set *uset);
4533 The function C<isl_union_set_project_out> can only project out
4536 #include <isl/union_map.h>
4537 __isl_give isl_union_map *isl_union_map_project_out(
4538 __isl_take isl_union_map *umap,
4539 enum isl_dim_type type, unsigned first, unsigned n);
4540 __isl_give isl_union_map *
4541 isl_union_map_project_out_all_params(
4542 __isl_take isl_union_map *umap);
4543 __isl_give isl_set *isl_union_map_params(
4544 __isl_take isl_union_map *umap);
4545 __isl_give isl_union_set *isl_union_map_domain(
4546 __isl_take isl_union_map *umap);
4547 __isl_give isl_union_set *isl_union_map_range(
4548 __isl_take isl_union_map *umap);
4550 The function C<isl_union_map_project_out> can only project out
4553 #include <isl/aff.h>
4554 __isl_give isl_aff *isl_aff_project_domain_on_params(
4555 __isl_take isl_aff *aff);
4556 __isl_give isl_multi_aff *
4557 isl_multi_aff_project_domain_on_params(
4558 __isl_take isl_multi_aff *ma);
4559 __isl_give isl_pw_aff *
4560 isl_pw_aff_project_domain_on_params(
4561 __isl_take isl_pw_aff *pa);
4562 __isl_give isl_multi_pw_aff *
4563 isl_multi_pw_aff_project_domain_on_params(
4564 __isl_take isl_multi_pw_aff *mpa);
4565 __isl_give isl_pw_multi_aff *
4566 isl_pw_multi_aff_project_domain_on_params(
4567 __isl_take isl_pw_multi_aff *pma);
4568 __isl_give isl_set *isl_pw_aff_domain(
4569 __isl_take isl_pw_aff *pwaff);
4570 __isl_give isl_set *isl_pw_multi_aff_domain(
4571 __isl_take isl_pw_multi_aff *pma);
4572 __isl_give isl_set *isl_multi_pw_aff_domain(
4573 __isl_take isl_multi_pw_aff *mpa);
4574 __isl_give isl_union_set *isl_union_pw_aff_domain(
4575 __isl_take isl_union_pw_aff *upa);
4576 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4577 __isl_take isl_union_pw_multi_aff *upma);
4578 __isl_give isl_union_set *
4579 isl_multi_union_pw_aff_domain(
4580 __isl_take isl_multi_union_pw_aff *mupa);
4581 __isl_give isl_set *isl_pw_aff_params(
4582 __isl_take isl_pw_aff *pwa);
4584 If no explicit domain was set on a zero-dimensional input to
4585 C<isl_multi_union_pw_aff_domain>, then this function will
4586 return a parameter set.
4588 #include <isl/polynomial.h>
4589 __isl_give isl_qpolynomial *
4590 isl_qpolynomial_project_domain_on_params(
4591 __isl_take isl_qpolynomial *qp);
4592 __isl_give isl_pw_qpolynomial *
4593 isl_pw_qpolynomial_project_domain_on_params(
4594 __isl_take isl_pw_qpolynomial *pwqp);
4595 __isl_give isl_pw_qpolynomial_fold *
4596 isl_pw_qpolynomial_fold_project_domain_on_params(
4597 __isl_take isl_pw_qpolynomial_fold *pwf);
4598 __isl_give isl_set *isl_pw_qpolynomial_domain(
4599 __isl_take isl_pw_qpolynomial *pwqp);
4600 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4601 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4602 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4603 __isl_take isl_union_pw_qpolynomial *upwqp);
4605 #include <isl/space.h>
4606 __isl_give isl_space *isl_space_domain_map(
4607 __isl_take isl_space *space);
4608 __isl_give isl_space *isl_space_range_map(
4609 __isl_take isl_space *space);
4611 #include <isl/map.h>
4612 __isl_give isl_map *isl_set_wrapped_domain_map(
4613 __isl_take isl_set *set);
4614 __isl_give isl_basic_map *isl_basic_map_domain_map(
4615 __isl_take isl_basic_map *bmap);
4616 __isl_give isl_basic_map *isl_basic_map_range_map(
4617 __isl_take isl_basic_map *bmap);
4618 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4619 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4621 #include <isl/union_map.h>
4622 __isl_give isl_union_map *isl_union_map_domain_map(
4623 __isl_take isl_union_map *umap);
4624 __isl_give isl_union_pw_multi_aff *
4625 isl_union_map_domain_map_union_pw_multi_aff(
4626 __isl_take isl_union_map *umap);
4627 __isl_give isl_union_map *isl_union_map_range_map(
4628 __isl_take isl_union_map *umap);
4629 __isl_give isl_union_map *
4630 isl_union_set_wrapped_domain_map(
4631 __isl_take isl_union_set *uset);
4633 The functions above construct a (basic, regular or union) relation
4634 that maps (a wrapped version of) the input relation to its domain or range.
4635 C<isl_set_wrapped_domain_map> maps the input set to the domain
4636 of its wrapped relation.
4640 __isl_give isl_basic_set *isl_basic_set_eliminate(
4641 __isl_take isl_basic_set *bset,
4642 enum isl_dim_type type,
4643 unsigned first, unsigned n);
4644 __isl_give isl_set *isl_set_eliminate(
4645 __isl_take isl_set *set, enum isl_dim_type type,
4646 unsigned first, unsigned n);
4647 __isl_give isl_basic_map *isl_basic_map_eliminate(
4648 __isl_take isl_basic_map *bmap,
4649 enum isl_dim_type type,
4650 unsigned first, unsigned n);
4651 __isl_give isl_map *isl_map_eliminate(
4652 __isl_take isl_map *map, enum isl_dim_type type,
4653 unsigned first, unsigned n);
4655 Eliminate the coefficients for the given dimensions from the constraints,
4656 without removing the dimensions.
4658 =item * Constructing a set from a parameter domain
4660 A zero-dimensional (local) space or (basic) set can be constructed
4661 on a given parameter domain using the following functions.
4663 #include <isl/space.h>
4664 __isl_give isl_space *isl_space_set_from_params(
4665 __isl_take isl_space *space);
4667 #include <isl/local_space.h>
4668 __isl_give isl_local_space *
4669 isl_local_space_set_from_params(
4670 __isl_take isl_local_space *ls);
4672 #include <isl/set.h>
4673 __isl_give isl_basic_set *isl_basic_set_from_params(
4674 __isl_take isl_basic_set *bset);
4675 __isl_give isl_set *isl_set_from_params(
4676 __isl_take isl_set *set);
4678 =item * Constructing a relation from one or two sets
4680 Create a relation with the given set(s) as domain and/or range.
4681 If only the domain or the range is specified, then
4682 the range or domain of the created relation is a zero-dimensional
4683 flat anonymous space.
4685 #include <isl/space.h>
4686 __isl_give isl_space *isl_space_from_domain(
4687 __isl_take isl_space *space);
4688 __isl_give isl_space *isl_space_from_range(
4689 __isl_take isl_space *space);
4690 __isl_give isl_space *isl_space_map_from_set(
4691 __isl_take isl_space *space);
4692 __isl_give isl_space *isl_space_map_from_domain_and_range(
4693 __isl_take isl_space *domain,
4694 __isl_take isl_space *range);
4696 #include <isl/local_space.h>
4697 __isl_give isl_local_space *isl_local_space_from_domain(
4698 __isl_take isl_local_space *ls);
4700 #include <isl/map.h>
4701 __isl_give isl_map *isl_map_from_domain(
4702 __isl_take isl_set *set);
4703 __isl_give isl_map *isl_map_from_range(
4704 __isl_take isl_set *set);
4706 #include <isl/union_map.h>
4707 __isl_give isl_union_map *isl_union_map_from_domain(
4708 __isl_take isl_union_set *uset);
4709 __isl_give isl_union_map *isl_union_map_from_range(
4710 __isl_take isl_union_set *uset);
4711 __isl_give isl_union_map *
4712 isl_union_map_from_domain_and_range(
4713 __isl_take isl_union_set *domain,
4714 __isl_take isl_union_set *range);
4716 #include <isl/val.h>
4717 __isl_give isl_multi_val *isl_multi_val_from_range(
4718 __isl_take isl_multi_val *mv);
4720 #include <isl/aff.h>
4721 __isl_give isl_aff *isl_aff_from_range(
4722 __isl_take isl_aff *aff);
4723 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4724 __isl_take isl_multi_aff *ma);
4725 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4726 __isl_take isl_pw_aff *pwa);
4727 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4728 __isl_take isl_multi_pw_aff *mpa);
4729 __isl_give isl_multi_union_pw_aff *
4730 isl_multi_union_pw_aff_from_range(
4731 __isl_take isl_multi_union_pw_aff *mupa);
4732 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4733 __isl_take isl_set *set);
4734 __isl_give isl_union_pw_multi_aff *
4735 isl_union_pw_multi_aff_from_domain(
4736 __isl_take isl_union_set *uset);
4738 #include <isl/polynomial.h>
4739 __isl_give isl_pw_qpolynomial *
4740 isl_pw_qpolynomial_from_range(
4741 __isl_take isl_pw_qpolynomial *pwqp);
4742 __isl_give isl_pw_qpolynomial_fold *
4743 isl_pw_qpolynomial_fold_from_range(
4744 __isl_take isl_pw_qpolynomial_fold *pwf);
4748 #include <isl/set.h>
4749 __isl_give isl_basic_set *isl_basic_set_fix_si(
4750 __isl_take isl_basic_set *bset,
4751 enum isl_dim_type type, unsigned pos, int value);
4752 __isl_give isl_basic_set *isl_basic_set_fix_val(
4753 __isl_take isl_basic_set *bset,
4754 enum isl_dim_type type, unsigned pos,
4755 __isl_take isl_val *v);
4756 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4757 enum isl_dim_type type, unsigned pos, int value);
4758 __isl_give isl_set *isl_set_fix_val(
4759 __isl_take isl_set *set,
4760 enum isl_dim_type type, unsigned pos,
4761 __isl_take isl_val *v);
4763 #include <isl/map.h>
4764 __isl_give isl_basic_map *isl_basic_map_fix_si(
4765 __isl_take isl_basic_map *bmap,
4766 enum isl_dim_type type, unsigned pos, int value);
4767 __isl_give isl_basic_map *isl_basic_map_fix_val(
4768 __isl_take isl_basic_map *bmap,
4769 enum isl_dim_type type, unsigned pos,
4770 __isl_take isl_val *v);
4771 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4772 enum isl_dim_type type, unsigned pos, int value);
4773 __isl_give isl_map *isl_map_fix_val(
4774 __isl_take isl_map *map,
4775 enum isl_dim_type type, unsigned pos,
4776 __isl_take isl_val *v);
4778 #include <isl/aff.h>
4779 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4780 __isl_take isl_pw_multi_aff *pma,
4781 enum isl_dim_type type, unsigned pos, int value);
4783 #include <isl/polynomial.h>
4784 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4785 __isl_take isl_pw_qpolynomial *pwqp,
4786 enum isl_dim_type type, unsigned n,
4787 __isl_take isl_val *v);
4788 __isl_give isl_pw_qpolynomial_fold *
4789 isl_pw_qpolynomial_fold_fix_val(
4790 __isl_take isl_pw_qpolynomial_fold *pwf,
4791 enum isl_dim_type type, unsigned n,
4792 __isl_take isl_val *v);
4794 Intersect the set, relation or function domain
4795 with the hyperplane where the given
4796 dimension has the fixed given value.
4798 #include <isl/set.h>
4799 __isl_give isl_basic_set *
4800 isl_basic_set_lower_bound_val(
4801 __isl_take isl_basic_set *bset,
4802 enum isl_dim_type type, unsigned pos,
4803 __isl_take isl_val *value);
4804 __isl_give isl_basic_set *
4805 isl_basic_set_upper_bound_val(
4806 __isl_take isl_basic_set *bset,
4807 enum isl_dim_type type, unsigned pos,
4808 __isl_take isl_val *value);
4809 __isl_give isl_set *isl_set_lower_bound_si(
4810 __isl_take isl_set *set,
4811 enum isl_dim_type type, unsigned pos, int value);
4812 __isl_give isl_set *isl_set_lower_bound_val(
4813 __isl_take isl_set *set,
4814 enum isl_dim_type type, unsigned pos,
4815 __isl_take isl_val *value);
4816 __isl_give isl_set *isl_set_upper_bound_si(
4817 __isl_take isl_set *set,
4818 enum isl_dim_type type, unsigned pos, int value);
4819 __isl_give isl_set *isl_set_upper_bound_val(
4820 __isl_take isl_set *set,
4821 enum isl_dim_type type, unsigned pos,
4822 __isl_take isl_val *value);
4824 #include <isl/map.h>
4825 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4826 __isl_take isl_basic_map *bmap,
4827 enum isl_dim_type type, unsigned pos, int value);
4828 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4829 __isl_take isl_basic_map *bmap,
4830 enum isl_dim_type type, unsigned pos, int value);
4831 __isl_give isl_map *isl_map_lower_bound_si(
4832 __isl_take isl_map *map,
4833 enum isl_dim_type type, unsigned pos, int value);
4834 __isl_give isl_map *isl_map_upper_bound_si(
4835 __isl_take isl_map *map,
4836 enum isl_dim_type type, unsigned pos, int value);
4838 Intersect the set or relation with the half-space where the given
4839 dimension has a value bounded by the fixed given integer value.
4841 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4842 enum isl_dim_type type1, int pos1,
4843 enum isl_dim_type type2, int pos2);
4844 __isl_give isl_basic_map *isl_basic_map_equate(
4845 __isl_take isl_basic_map *bmap,
4846 enum isl_dim_type type1, int pos1,
4847 enum isl_dim_type type2, int pos2);
4848 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4849 enum isl_dim_type type1, int pos1,
4850 enum isl_dim_type type2, int pos2);
4852 Intersect the set or relation with the hyperplane where the given
4853 dimensions are equal to each other.
4855 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4856 enum isl_dim_type type1, int pos1,
4857 enum isl_dim_type type2, int pos2);
4859 Intersect the relation with the hyperplane where the given
4860 dimensions have opposite values.
4862 __isl_give isl_map *isl_map_order_le(
4863 __isl_take isl_map *map,
4864 enum isl_dim_type type1, int pos1,
4865 enum isl_dim_type type2, int pos2);
4866 __isl_give isl_basic_map *isl_basic_map_order_ge(
4867 __isl_take isl_basic_map *bmap,
4868 enum isl_dim_type type1, int pos1,
4869 enum isl_dim_type type2, int pos2);
4870 __isl_give isl_map *isl_map_order_ge(
4871 __isl_take isl_map *map,
4872 enum isl_dim_type type1, int pos1,
4873 enum isl_dim_type type2, int pos2);
4874 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4875 enum isl_dim_type type1, int pos1,
4876 enum isl_dim_type type2, int pos2);
4877 __isl_give isl_basic_map *isl_basic_map_order_gt(
4878 __isl_take isl_basic_map *bmap,
4879 enum isl_dim_type type1, int pos1,
4880 enum isl_dim_type type2, int pos2);
4881 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4882 enum isl_dim_type type1, int pos1,
4883 enum isl_dim_type type2, int pos2);
4885 Intersect the relation with the half-space where the given
4886 dimensions satisfy the given ordering.
4888 #include <isl/union_set.h>
4889 __isl_give isl_union_map *isl_union_map_remove_map_if(
4890 __isl_take isl_union_map *umap,
4891 isl_bool (*fn)(__isl_keep isl_map *map,
4892 void *user), void *user);
4894 This function calls the callback function once for each
4895 pair of spaces for which there are elements in the input.
4896 If the callback returns C<isl_bool_true>, then all those elements
4897 are removed from the result. The only remaining elements in the output
4898 are then those for which the callback returns C<isl_bool_false>.
4902 #include <isl/aff.h>
4903 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4904 __isl_take isl_aff *aff);
4905 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4906 __isl_take isl_aff *aff);
4907 __isl_give isl_set *isl_pw_aff_pos_set(
4908 __isl_take isl_pw_aff *pa);
4909 __isl_give isl_set *isl_pw_aff_nonneg_set(
4910 __isl_take isl_pw_aff *pwaff);
4911 __isl_give isl_set *isl_pw_aff_zero_set(
4912 __isl_take isl_pw_aff *pwaff);
4913 __isl_give isl_set *isl_pw_aff_non_zero_set(
4914 __isl_take isl_pw_aff *pwaff);
4915 __isl_give isl_union_set *
4916 isl_union_pw_aff_zero_union_set(
4917 __isl_take isl_union_pw_aff *upa);
4918 __isl_give isl_union_set *
4919 isl_multi_union_pw_aff_zero_union_set(
4920 __isl_take isl_multi_union_pw_aff *mupa);
4922 The function C<isl_aff_neg_basic_set> returns a basic set
4923 containing those elements in the domain space
4924 of C<aff> where C<aff> is negative.
4925 The function C<isl_pw_aff_nonneg_set> returns a set
4926 containing those elements in the domain
4927 of C<pwaff> where C<pwaff> is non-negative.
4928 The function C<isl_multi_union_pw_aff_zero_union_set>
4929 returns a union set containing those elements
4930 in the domains of its elements where they are all zero.
4934 __isl_give isl_map *isl_set_identity(
4935 __isl_take isl_set *set);
4936 __isl_give isl_union_map *isl_union_set_identity(
4937 __isl_take isl_union_set *uset);
4938 __isl_give isl_union_pw_multi_aff *
4939 isl_union_set_identity_union_pw_multi_aff(
4940 __isl_take isl_union_set *uset);
4942 Construct an identity relation on the given (union) set.
4944 =item * Function Extraction
4946 A piecewise quasi affine expression that is equal to 1 on a set
4947 and 0 outside the set can be created using the following function.
4949 #include <isl/aff.h>
4950 __isl_give isl_pw_aff *isl_set_indicator_function(
4951 __isl_take isl_set *set);
4953 A piecewise multiple quasi affine expression can be extracted
4954 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4955 and the C<isl_map> is single-valued.
4956 In case of a conversion from an C<isl_union_map>
4957 to an C<isl_union_pw_multi_aff>, these properties need to hold
4958 in each domain space.
4959 A conversion to a C<isl_multi_union_pw_aff> additionally
4960 requires that the input is non-empty and involves only a single
4963 #include <isl/aff.h>
4964 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4965 __isl_take isl_set *set);
4966 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4967 __isl_take isl_map *map);
4969 __isl_give isl_union_pw_multi_aff *
4970 isl_union_pw_multi_aff_from_union_set(
4971 __isl_take isl_union_set *uset);
4972 __isl_give isl_union_pw_multi_aff *
4973 isl_union_pw_multi_aff_from_union_map(
4974 __isl_take isl_union_map *umap);
4976 __isl_give isl_multi_union_pw_aff *
4977 isl_multi_union_pw_aff_from_union_map(
4978 __isl_take isl_union_map *umap);
4982 __isl_give isl_basic_set *isl_basic_map_deltas(
4983 __isl_take isl_basic_map *bmap);
4984 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4985 __isl_give isl_union_set *isl_union_map_deltas(
4986 __isl_take isl_union_map *umap);
4988 These functions return a (basic) set containing the differences
4989 between image elements and corresponding domain elements in the input.
4991 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4992 __isl_take isl_basic_map *bmap);
4993 __isl_give isl_map *isl_map_deltas_map(
4994 __isl_take isl_map *map);
4995 __isl_give isl_union_map *isl_union_map_deltas_map(
4996 __isl_take isl_union_map *umap);
4998 The functions above construct a (basic, regular or union) relation
4999 that maps (a wrapped version of) the input relation to its delta set.
5003 Simplify the representation of a set, relation or functions by trying
5004 to combine pairs of basic sets or relations into a single
5005 basic set or relation.
5007 #include <isl/set.h>
5008 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
5010 #include <isl/map.h>
5011 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5013 #include <isl/union_set.h>
5014 __isl_give isl_union_set *isl_union_set_coalesce(
5015 __isl_take isl_union_set *uset);
5017 #include <isl/union_map.h>
5018 __isl_give isl_union_map *isl_union_map_coalesce(
5019 __isl_take isl_union_map *umap);
5021 #include <isl/aff.h>
5022 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5023 __isl_take isl_pw_aff *pwqp);
5024 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5025 __isl_take isl_pw_multi_aff *pma);
5026 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5027 __isl_take isl_multi_pw_aff *mpa);
5028 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5029 __isl_take isl_union_pw_aff *upa);
5030 __isl_give isl_union_pw_multi_aff *
5031 isl_union_pw_multi_aff_coalesce(
5032 __isl_take isl_union_pw_multi_aff *upma);
5033 __isl_give isl_multi_union_pw_aff *
5034 isl_multi_union_pw_aff_coalesce(
5035 __isl_take isl_multi_union_pw_aff *aff);
5037 #include <isl/polynomial.h>
5038 __isl_give isl_pw_qpolynomial_fold *
5039 isl_pw_qpolynomial_fold_coalesce(
5040 __isl_take isl_pw_qpolynomial_fold *pwf);
5041 __isl_give isl_union_pw_qpolynomial *
5042 isl_union_pw_qpolynomial_coalesce(
5043 __isl_take isl_union_pw_qpolynomial *upwqp);
5044 __isl_give isl_union_pw_qpolynomial_fold *
5045 isl_union_pw_qpolynomial_fold_coalesce(
5046 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5048 One of the methods for combining pairs of basic sets or relations
5049 can result in coefficients that are much larger than those that appear
5050 in the constraints of the input. By default, the coefficients are
5051 not allowed to grow larger, but this can be changed by unsetting
5052 the following option.
5054 isl_stat isl_options_set_coalesce_bounded_wrapping(
5055 isl_ctx *ctx, int val);
5056 int isl_options_get_coalesce_bounded_wrapping(
5059 =item * Detecting equalities
5061 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5062 __isl_take isl_basic_set *bset);
5063 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5064 __isl_take isl_basic_map *bmap);
5065 __isl_give isl_set *isl_set_detect_equalities(
5066 __isl_take isl_set *set);
5067 __isl_give isl_map *isl_map_detect_equalities(
5068 __isl_take isl_map *map);
5069 __isl_give isl_union_set *isl_union_set_detect_equalities(
5070 __isl_take isl_union_set *uset);
5071 __isl_give isl_union_map *isl_union_map_detect_equalities(
5072 __isl_take isl_union_map *umap);
5074 Simplify the representation of a set or relation by detecting implicit
5077 =item * Removing redundant constraints
5079 #include <isl/set.h>
5080 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5081 __isl_take isl_basic_set *bset);
5082 __isl_give isl_set *isl_set_remove_redundancies(
5083 __isl_take isl_set *set);
5085 #include <isl/union_set.h>
5086 __isl_give isl_union_set *
5087 isl_union_set_remove_redundancies(
5088 __isl_take isl_union_set *uset);
5090 #include <isl/map.h>
5091 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5092 __isl_take isl_basic_map *bmap);
5093 __isl_give isl_map *isl_map_remove_redundancies(
5094 __isl_take isl_map *map);
5096 #include <isl/union_map.h>
5097 __isl_give isl_union_map *
5098 isl_union_map_remove_redundancies(
5099 __isl_take isl_union_map *umap);
5103 __isl_give isl_basic_set *isl_set_convex_hull(
5104 __isl_take isl_set *set);
5105 __isl_give isl_basic_map *isl_map_convex_hull(
5106 __isl_take isl_map *map);
5108 If the input set or relation has any existentially quantified
5109 variables, then the result of these operations is currently undefined.
5113 #include <isl/set.h>
5114 __isl_give isl_basic_set *
5115 isl_set_unshifted_simple_hull(
5116 __isl_take isl_set *set);
5117 __isl_give isl_basic_set *isl_set_simple_hull(
5118 __isl_take isl_set *set);
5119 __isl_give isl_basic_set *
5120 isl_set_plain_unshifted_simple_hull(
5121 __isl_take isl_set *set);
5122 __isl_give isl_basic_set *
5123 isl_set_unshifted_simple_hull_from_set_list(
5124 __isl_take isl_set *set,
5125 __isl_take isl_set_list *list);
5127 #include <isl/map.h>
5128 __isl_give isl_basic_map *
5129 isl_map_unshifted_simple_hull(
5130 __isl_take isl_map *map);
5131 __isl_give isl_basic_map *isl_map_simple_hull(
5132 __isl_take isl_map *map);
5133 __isl_give isl_basic_map *
5134 isl_map_plain_unshifted_simple_hull(
5135 __isl_take isl_map *map);
5136 __isl_give isl_basic_map *
5137 isl_map_unshifted_simple_hull_from_map_list(
5138 __isl_take isl_map *map,
5139 __isl_take isl_map_list *list);
5141 #include <isl/union_map.h>
5142 __isl_give isl_union_map *isl_union_map_simple_hull(
5143 __isl_take isl_union_map *umap);
5145 These functions compute a single basic set or relation
5146 that contains the whole input set or relation.
5147 In particular, the output is described by translates
5148 of the constraints describing the basic sets or relations in the input.
5149 In case of C<isl_set_unshifted_simple_hull>, only the original
5150 constraints are used, without any translation.
5151 In case of C<isl_set_plain_unshifted_simple_hull> and
5152 C<isl_map_plain_unshifted_simple_hull>, the result is described
5153 by original constraints that are obviously satisfied
5154 by the entire input set or relation.
5155 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5156 C<isl_map_unshifted_simple_hull_from_map_list>, the
5157 constraints are taken from the elements of the second argument.
5161 (See \autoref{s:simple hull}.)
5167 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5168 __isl_take isl_basic_set *bset);
5169 __isl_give isl_basic_set *isl_set_affine_hull(
5170 __isl_take isl_set *set);
5171 __isl_give isl_union_set *isl_union_set_affine_hull(
5172 __isl_take isl_union_set *uset);
5173 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5174 __isl_take isl_basic_map *bmap);
5175 __isl_give isl_basic_map *isl_map_affine_hull(
5176 __isl_take isl_map *map);
5177 __isl_give isl_union_map *isl_union_map_affine_hull(
5178 __isl_take isl_union_map *umap);
5180 In case of union sets and relations, the affine hull is computed
5183 =item * Polyhedral hull
5185 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5186 __isl_take isl_set *set);
5187 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5188 __isl_take isl_map *map);
5189 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5190 __isl_take isl_union_set *uset);
5191 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5192 __isl_take isl_union_map *umap);
5194 These functions compute a single basic set or relation
5195 not involving any existentially quantified variables
5196 that contains the whole input set or relation.
5197 In case of union sets and relations, the polyhedral hull is computed
5200 =item * Other approximations
5202 #include <isl/set.h>
5203 __isl_give isl_basic_set *
5204 isl_basic_set_drop_constraints_involving_dims(
5205 __isl_take isl_basic_set *bset,
5206 enum isl_dim_type type,
5207 unsigned first, unsigned n);
5208 __isl_give isl_basic_set *
5209 isl_basic_set_drop_constraints_not_involving_dims(
5210 __isl_take isl_basic_set *bset,
5211 enum isl_dim_type type,
5212 unsigned first, unsigned n);
5213 __isl_give isl_set *
5214 isl_set_drop_constraints_involving_dims(
5215 __isl_take isl_set *set,
5216 enum isl_dim_type type,
5217 unsigned first, unsigned n);
5218 __isl_give isl_set *
5219 isl_set_drop_constraints_not_involving_dims(
5220 __isl_take isl_set *set,
5221 enum isl_dim_type type,
5222 unsigned first, unsigned n);
5224 #include <isl/map.h>
5225 __isl_give isl_basic_map *
5226 isl_basic_map_drop_constraints_involving_dims(
5227 __isl_take isl_basic_map *bmap,
5228 enum isl_dim_type type,
5229 unsigned first, unsigned n);
5230 __isl_give isl_basic_map *
5231 isl_basic_map_drop_constraints_not_involving_dims(
5232 __isl_take isl_basic_map *bmap,
5233 enum isl_dim_type type,
5234 unsigned first, unsigned n);
5235 __isl_give isl_map *
5236 isl_map_drop_constraints_involving_dims(
5237 __isl_take isl_map *map,
5238 enum isl_dim_type type,
5239 unsigned first, unsigned n);
5240 __isl_give isl_map *
5241 isl_map_drop_constraints_not_involving_dims(
5242 __isl_take isl_map *map,
5243 enum isl_dim_type type,
5244 unsigned first, unsigned n);
5246 These functions drop any constraints (not) involving the specified dimensions.
5247 Note that the result depends on the representation of the input.
5249 #include <isl/polynomial.h>
5250 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5251 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5252 __isl_give isl_union_pw_qpolynomial *
5253 isl_union_pw_qpolynomial_to_polynomial(
5254 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5256 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5257 the polynomial will be an overapproximation. If C<sign> is negative,
5258 it will be an underapproximation. If C<sign> is zero, the approximation
5259 will lie somewhere in between.
5263 __isl_give isl_basic_set *isl_basic_set_sample(
5264 __isl_take isl_basic_set *bset);
5265 __isl_give isl_basic_set *isl_set_sample(
5266 __isl_take isl_set *set);
5267 __isl_give isl_basic_map *isl_basic_map_sample(
5268 __isl_take isl_basic_map *bmap);
5269 __isl_give isl_basic_map *isl_map_sample(
5270 __isl_take isl_map *map);
5272 If the input (basic) set or relation is non-empty, then return
5273 a singleton subset of the input. Otherwise, return an empty set.
5275 =item * Optimization
5277 #include <isl/ilp.h>
5278 __isl_give isl_val *isl_basic_set_max_val(
5279 __isl_keep isl_basic_set *bset,
5280 __isl_keep isl_aff *obj);
5281 __isl_give isl_val *isl_set_min_val(
5282 __isl_keep isl_set *set,
5283 __isl_keep isl_aff *obj);
5284 __isl_give isl_val *isl_set_max_val(
5285 __isl_keep isl_set *set,
5286 __isl_keep isl_aff *obj);
5287 __isl_give isl_multi_val *
5288 isl_union_set_min_multi_union_pw_aff(
5289 __isl_keep isl_union_set *set,
5290 __isl_keep isl_multi_union_pw_aff *obj);
5292 Compute the minimum or maximum of the integer affine expression C<obj>
5293 over the points in C<set>, returning the result in C<opt>.
5294 The result is C<NULL> in case of an error, the optimal value in case
5295 there is one, negative infinity or infinity if the problem is unbounded and
5296 NaN if the problem is empty.
5298 #include <isl/ilp.h>
5299 __isl_give isl_val *isl_basic_set_dim_max_val(
5300 __isl_take isl_basic_set *bset, int pos);
5302 Return the maximal value attained by the given set dimension,
5303 independently of the parameter values and of any other dimensions.
5304 The result is C<NULL> in case of an error, the optimal value in case
5305 there is one, infinity if the problem is unbounded and
5306 NaN if the input is empty.
5308 =item * Parametric optimization
5310 __isl_give isl_pw_aff *isl_set_dim_min(
5311 __isl_take isl_set *set, int pos);
5312 __isl_give isl_pw_aff *isl_set_dim_max(
5313 __isl_take isl_set *set, int pos);
5314 __isl_give isl_pw_aff *isl_map_dim_min(
5315 __isl_take isl_map *map, int pos);
5316 __isl_give isl_pw_aff *isl_map_dim_max(
5317 __isl_take isl_map *map, int pos);
5319 Compute the minimum or maximum of the given set or output dimension
5320 as a function of the parameters (and input dimensions), but independently
5321 of the other set or output dimensions.
5322 For lexicographic optimization, see L<"Lexicographic Optimization">.
5326 The following functions compute either the set of (rational) coefficient
5327 values of valid constraints for the given set or the set of (rational)
5328 values satisfying the constraints with coefficients from the given set.
5329 Internally, these two sets of functions perform essentially the
5330 same operations, except that the set of coefficients is assumed to
5331 be a cone, while the set of values may be any polyhedron.
5332 The current implementation is based on the Farkas lemma and
5333 Fourier-Motzkin elimination, but this may change or be made optional
5334 in future. In particular, future implementations may use different
5335 dualization algorithms or skip the elimination step.
5337 #include <isl/set.h>
5338 __isl_give isl_basic_set *isl_basic_set_coefficients(
5339 __isl_take isl_basic_set *bset);
5340 __isl_give isl_basic_set_list *
5341 isl_basic_set_list_coefficients(
5342 __isl_take isl_basic_set_list *list);
5343 __isl_give isl_basic_set *isl_set_coefficients(
5344 __isl_take isl_set *set);
5345 __isl_give isl_union_set *isl_union_set_coefficients(
5346 __isl_take isl_union_set *bset);
5347 __isl_give isl_basic_set *isl_basic_set_solutions(
5348 __isl_take isl_basic_set *bset);
5349 __isl_give isl_basic_set *isl_set_solutions(
5350 __isl_take isl_set *set);
5351 __isl_give isl_union_set *isl_union_set_solutions(
5352 __isl_take isl_union_set *bset);
5356 __isl_give isl_map *isl_map_fixed_power_val(
5357 __isl_take isl_map *map,
5358 __isl_take isl_val *exp);
5359 __isl_give isl_union_map *
5360 isl_union_map_fixed_power_val(
5361 __isl_take isl_union_map *umap,
5362 __isl_take isl_val *exp);
5364 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5365 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5366 of C<map> is computed.
5368 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5370 __isl_give isl_union_map *isl_union_map_power(
5371 __isl_take isl_union_map *umap, int *exact);
5373 Compute a parametric representation for all positive powers I<k> of C<map>.
5374 The result maps I<k> to a nested relation corresponding to the
5375 I<k>th power of C<map>.
5376 The result may be an overapproximation. If the result is known to be exact,
5377 then C<*exact> is set to C<1>.
5379 =item * Transitive closure
5381 __isl_give isl_map *isl_map_transitive_closure(
5382 __isl_take isl_map *map, int *exact);
5383 __isl_give isl_union_map *isl_union_map_transitive_closure(
5384 __isl_take isl_union_map *umap, int *exact);
5386 Compute the transitive closure of C<map>.
5387 The result may be an overapproximation. If the result is known to be exact,
5388 then C<*exact> is set to C<1>.
5390 =item * Reaching path lengths
5392 __isl_give isl_map *isl_map_reaching_path_lengths(
5393 __isl_take isl_map *map, int *exact);
5395 Compute a relation that maps each element in the range of C<map>
5396 to the lengths of all paths composed of edges in C<map> that
5397 end up in the given element.
5398 The result may be an overapproximation. If the result is known to be exact,
5399 then C<*exact> is set to C<1>.
5400 To compute the I<maximal> path length, the resulting relation
5401 should be postprocessed by C<isl_map_lexmax>.
5402 In particular, if the input relation is a dependence relation
5403 (mapping sources to sinks), then the maximal path length corresponds
5404 to the free schedule.
5405 Note, however, that C<isl_map_lexmax> expects the maximum to be
5406 finite, so if the path lengths are unbounded (possibly due to
5407 the overapproximation), then you will get an error message.
5411 #include <isl/space.h>
5412 __isl_give isl_space *isl_space_wrap(
5413 __isl_take isl_space *space);
5414 __isl_give isl_space *isl_space_unwrap(
5415 __isl_take isl_space *space);
5417 #include <isl/local_space.h>
5418 __isl_give isl_local_space *isl_local_space_wrap(
5419 __isl_take isl_local_space *ls);
5421 #include <isl/set.h>
5422 __isl_give isl_basic_map *isl_basic_set_unwrap(
5423 __isl_take isl_basic_set *bset);
5424 __isl_give isl_map *isl_set_unwrap(
5425 __isl_take isl_set *set);
5427 #include <isl/map.h>
5428 __isl_give isl_basic_set *isl_basic_map_wrap(
5429 __isl_take isl_basic_map *bmap);
5430 __isl_give isl_set *isl_map_wrap(
5431 __isl_take isl_map *map);
5433 #include <isl/union_set.h>
5434 __isl_give isl_union_map *isl_union_set_unwrap(
5435 __isl_take isl_union_set *uset);
5437 #include <isl/union_map.h>
5438 __isl_give isl_union_set *isl_union_map_wrap(
5439 __isl_take isl_union_map *umap);
5441 The input to C<isl_space_unwrap> should
5442 be the space of a set, while that of
5443 C<isl_space_wrap> should be the space of a relation.
5444 Conversely, the output of C<isl_space_unwrap> is the space
5445 of a relation, while that of C<isl_space_wrap> is the space of a set.
5449 Remove any internal structure of domain (and range) of the given
5450 set or relation. If there is any such internal structure in the input,
5451 then the name of the space is also removed.
5453 #include <isl/space.h>
5454 __isl_give isl_space *isl_space_flatten_domain(
5455 __isl_take isl_space *space);
5456 __isl_give isl_space *isl_space_flatten_range(
5457 __isl_take isl_space *space);
5459 #include <isl/local_space.h>
5460 __isl_give isl_local_space *
5461 isl_local_space_flatten_domain(
5462 __isl_take isl_local_space *ls);
5463 __isl_give isl_local_space *
5464 isl_local_space_flatten_range(
5465 __isl_take isl_local_space *ls);
5467 #include <isl/set.h>
5468 __isl_give isl_basic_set *isl_basic_set_flatten(
5469 __isl_take isl_basic_set *bset);
5470 __isl_give isl_set *isl_set_flatten(
5471 __isl_take isl_set *set);
5473 #include <isl/map.h>
5474 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5475 __isl_take isl_basic_map *bmap);
5476 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5477 __isl_take isl_basic_map *bmap);
5478 __isl_give isl_map *isl_map_flatten_range(
5479 __isl_take isl_map *map);
5480 __isl_give isl_map *isl_map_flatten_domain(
5481 __isl_take isl_map *map);
5482 __isl_give isl_basic_map *isl_basic_map_flatten(
5483 __isl_take isl_basic_map *bmap);
5484 __isl_give isl_map *isl_map_flatten(
5485 __isl_take isl_map *map);
5487 #include <isl/val.h>
5488 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5489 __isl_take isl_multi_val *mv);
5491 #include <isl/aff.h>
5492 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5493 __isl_take isl_multi_aff *ma);
5494 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5495 __isl_take isl_multi_aff *ma);
5496 __isl_give isl_multi_pw_aff *
5497 isl_multi_pw_aff_flatten_range(
5498 __isl_take isl_multi_pw_aff *mpa);
5499 __isl_give isl_multi_union_pw_aff *
5500 isl_multi_union_pw_aff_flatten_range(
5501 __isl_take isl_multi_union_pw_aff *mupa);
5503 #include <isl/map.h>
5504 __isl_give isl_map *isl_set_flatten_map(
5505 __isl_take isl_set *set);
5507 The function above constructs a relation
5508 that maps the input set to a flattened version of the set.
5512 Lift the input set to a space with extra dimensions corresponding
5513 to the existentially quantified variables in the input.
5514 In particular, the result lives in a wrapped map where the domain
5515 is the original space and the range corresponds to the original
5516 existentially quantified variables.
5518 #include <isl/set.h>
5519 __isl_give isl_basic_set *isl_basic_set_lift(
5520 __isl_take isl_basic_set *bset);
5521 __isl_give isl_set *isl_set_lift(
5522 __isl_take isl_set *set);
5523 __isl_give isl_union_set *isl_union_set_lift(
5524 __isl_take isl_union_set *uset);
5526 Given a local space that contains the existentially quantified
5527 variables of a set, a basic relation that, when applied to
5528 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5529 can be constructed using the following function.
5531 #include <isl/local_space.h>
5532 __isl_give isl_basic_map *isl_local_space_lifting(
5533 __isl_take isl_local_space *ls);
5535 #include <isl/aff.h>
5536 __isl_give isl_multi_aff *isl_multi_aff_lift(
5537 __isl_take isl_multi_aff *maff,
5538 __isl_give isl_local_space **ls);
5540 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5541 then it is assigned the local space that lies at the basis of
5542 the lifting applied.
5544 =item * Internal Product
5546 #include <isl/space.h>
5547 __isl_give isl_space *isl_space_zip(
5548 __isl_take isl_space *space);
5550 #include <isl/map.h>
5551 __isl_give isl_basic_map *isl_basic_map_zip(
5552 __isl_take isl_basic_map *bmap);
5553 __isl_give isl_map *isl_map_zip(
5554 __isl_take isl_map *map);
5556 #include <isl/union_map.h>
5557 __isl_give isl_union_map *isl_union_map_zip(
5558 __isl_take isl_union_map *umap);
5560 Given a relation with nested relations for domain and range,
5561 interchange the range of the domain with the domain of the range.
5565 #include <isl/space.h>
5566 __isl_give isl_space *isl_space_curry(
5567 __isl_take isl_space *space);
5568 __isl_give isl_space *isl_space_uncurry(
5569 __isl_take isl_space *space);
5571 #include <isl/map.h>
5572 __isl_give isl_basic_map *isl_basic_map_curry(
5573 __isl_take isl_basic_map *bmap);
5574 __isl_give isl_basic_map *isl_basic_map_uncurry(
5575 __isl_take isl_basic_map *bmap);
5576 __isl_give isl_map *isl_map_curry(
5577 __isl_take isl_map *map);
5578 __isl_give isl_map *isl_map_uncurry(
5579 __isl_take isl_map *map);
5581 #include <isl/union_map.h>
5582 __isl_give isl_union_map *isl_union_map_curry(
5583 __isl_take isl_union_map *umap);
5584 __isl_give isl_union_map *isl_union_map_uncurry(
5585 __isl_take isl_union_map *umap);
5587 Given a relation with a nested relation for domain,
5588 the C<curry> functions
5589 move the range of the nested relation out of the domain
5590 and use it as the domain of a nested relation in the range,
5591 with the original range as range of this nested relation.
5592 The C<uncurry> functions perform the inverse operation.
5594 #include <isl/space.h>
5595 __isl_give isl_space *isl_space_range_curry(
5596 __isl_take isl_space *space);
5598 #include <isl/map.h>
5599 __isl_give isl_map *isl_map_range_curry(
5600 __isl_take isl_map *map);
5602 #include <isl/union_map.h>
5603 __isl_give isl_union_map *isl_union_map_range_curry(
5604 __isl_take isl_union_map *umap);
5606 These functions apply the currying to the relation that
5607 is nested inside the range of the input.
5609 =item * Aligning parameters
5611 Change the order of the parameters of the given set, relation
5613 such that the first parameters match those of C<model>.
5614 This may involve the introduction of extra parameters.
5615 All parameters need to be named.
5617 #include <isl/space.h>
5618 __isl_give isl_space *isl_space_align_params(
5619 __isl_take isl_space *space1,
5620 __isl_take isl_space *space2)
5622 #include <isl/set.h>
5623 __isl_give isl_basic_set *isl_basic_set_align_params(
5624 __isl_take isl_basic_set *bset,
5625 __isl_take isl_space *model);
5626 __isl_give isl_set *isl_set_align_params(
5627 __isl_take isl_set *set,
5628 __isl_take isl_space *model);
5630 #include <isl/map.h>
5631 __isl_give isl_basic_map *isl_basic_map_align_params(
5632 __isl_take isl_basic_map *bmap,
5633 __isl_take isl_space *model);
5634 __isl_give isl_map *isl_map_align_params(
5635 __isl_take isl_map *map,
5636 __isl_take isl_space *model);
5638 #include <isl/val.h>
5639 __isl_give isl_multi_val *isl_multi_val_align_params(
5640 __isl_take isl_multi_val *mv,
5641 __isl_take isl_space *model);
5643 #include <isl/aff.h>
5644 __isl_give isl_aff *isl_aff_align_params(
5645 __isl_take isl_aff *aff,
5646 __isl_take isl_space *model);
5647 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5648 __isl_take isl_multi_aff *multi,
5649 __isl_take isl_space *model);
5650 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5651 __isl_take isl_pw_aff *pwaff,
5652 __isl_take isl_space *model);
5653 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5654 __isl_take isl_pw_multi_aff *pma,
5655 __isl_take isl_space *model);
5656 __isl_give isl_union_pw_aff *
5657 isl_union_pw_aff_align_params(
5658 __isl_take isl_union_pw_aff *upa,
5659 __isl_take isl_space *model);
5660 __isl_give isl_union_pw_multi_aff *
5661 isl_union_pw_multi_aff_align_params(
5662 __isl_take isl_union_pw_multi_aff *upma,
5663 __isl_take isl_space *model);
5664 __isl_give isl_multi_union_pw_aff *
5665 isl_multi_union_pw_aff_align_params(
5666 __isl_take isl_multi_union_pw_aff *mupa,
5667 __isl_take isl_space *model);
5669 #include <isl/polynomial.h>
5670 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5671 __isl_take isl_qpolynomial *qp,
5672 __isl_take isl_space *model);
5674 =item * Unary Arithmetic Operations
5676 #include <isl/set.h>
5677 __isl_give isl_set *isl_set_neg(
5678 __isl_take isl_set *set);
5679 #include <isl/map.h>
5680 __isl_give isl_map *isl_map_neg(
5681 __isl_take isl_map *map);
5683 C<isl_set_neg> constructs a set containing the opposites of
5684 the elements in its argument.
5685 The domain of the result of C<isl_map_neg> is the same
5686 as the domain of its argument. The corresponding range
5687 elements are the opposites of the corresponding range
5688 elements in the argument.
5690 #include <isl/val.h>
5691 __isl_give isl_multi_val *isl_multi_val_neg(
5692 __isl_take isl_multi_val *mv);
5694 #include <isl/aff.h>
5695 __isl_give isl_aff *isl_aff_neg(
5696 __isl_take isl_aff *aff);
5697 __isl_give isl_multi_aff *isl_multi_aff_neg(
5698 __isl_take isl_multi_aff *ma);
5699 __isl_give isl_pw_aff *isl_pw_aff_neg(
5700 __isl_take isl_pw_aff *pwaff);
5701 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5702 __isl_take isl_pw_multi_aff *pma);
5703 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5704 __isl_take isl_multi_pw_aff *mpa);
5705 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5706 __isl_take isl_union_pw_aff *upa);
5707 __isl_give isl_union_pw_multi_aff *
5708 isl_union_pw_multi_aff_neg(
5709 __isl_take isl_union_pw_multi_aff *upma);
5710 __isl_give isl_multi_union_pw_aff *
5711 isl_multi_union_pw_aff_neg(
5712 __isl_take isl_multi_union_pw_aff *mupa);
5713 __isl_give isl_aff *isl_aff_ceil(
5714 __isl_take isl_aff *aff);
5715 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5716 __isl_take isl_pw_aff *pwaff);
5717 __isl_give isl_aff *isl_aff_floor(
5718 __isl_take isl_aff *aff);
5719 __isl_give isl_multi_aff *isl_multi_aff_floor(
5720 __isl_take isl_multi_aff *ma);
5721 __isl_give isl_pw_aff *isl_pw_aff_floor(
5722 __isl_take isl_pw_aff *pwaff);
5723 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5724 __isl_take isl_union_pw_aff *upa);
5725 __isl_give isl_multi_union_pw_aff *
5726 isl_multi_union_pw_aff_floor(
5727 __isl_take isl_multi_union_pw_aff *mupa);
5729 #include <isl/aff.h>
5730 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5731 __isl_take isl_pw_aff_list *list);
5732 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5733 __isl_take isl_pw_aff_list *list);
5735 #include <isl/polynomial.h>
5736 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5737 __isl_take isl_qpolynomial *qp);
5738 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5739 __isl_take isl_pw_qpolynomial *pwqp);
5740 __isl_give isl_union_pw_qpolynomial *
5741 isl_union_pw_qpolynomial_neg(
5742 __isl_take isl_union_pw_qpolynomial *upwqp);
5743 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5744 __isl_take isl_qpolynomial *qp,
5746 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5747 __isl_take isl_pw_qpolynomial *pwqp,
5752 The following functions evaluate a function in a point.
5754 #include <isl/aff.h>
5755 __isl_give isl_val *isl_aff_eval(
5756 __isl_take isl_aff *aff,
5757 __isl_take isl_point *pnt);
5759 #include <isl/polynomial.h>
5760 __isl_give isl_val *isl_pw_qpolynomial_eval(
5761 __isl_take isl_pw_qpolynomial *pwqp,
5762 __isl_take isl_point *pnt);
5763 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5764 __isl_take isl_pw_qpolynomial_fold *pwf,
5765 __isl_take isl_point *pnt);
5766 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5767 __isl_take isl_union_pw_qpolynomial *upwqp,
5768 __isl_take isl_point *pnt);
5769 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5770 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5771 __isl_take isl_point *pnt);
5773 These functions return NaN when evaluated at a void point.
5775 =item * Dimension manipulation
5777 It is usually not advisable to directly change the (input or output)
5778 space of a set or a relation as this removes the name and the internal
5779 structure of the space. However, the functions below can be useful
5780 to add new parameters, assuming
5781 C<isl_set_align_params> and C<isl_map_align_params>
5784 #include <isl/space.h>
5785 __isl_give isl_space *isl_space_add_dims(
5786 __isl_take isl_space *space,
5787 enum isl_dim_type type, unsigned n);
5788 __isl_give isl_space *isl_space_insert_dims(
5789 __isl_take isl_space *space,
5790 enum isl_dim_type type, unsigned pos, unsigned n);
5791 __isl_give isl_space *isl_space_drop_dims(
5792 __isl_take isl_space *space,
5793 enum isl_dim_type type, unsigned first, unsigned n);
5794 __isl_give isl_space *isl_space_move_dims(
5795 __isl_take isl_space *space,
5796 enum isl_dim_type dst_type, unsigned dst_pos,
5797 enum isl_dim_type src_type, unsigned src_pos,
5800 #include <isl/local_space.h>
5801 __isl_give isl_local_space *isl_local_space_add_dims(
5802 __isl_take isl_local_space *ls,
5803 enum isl_dim_type type, unsigned n);
5804 __isl_give isl_local_space *isl_local_space_insert_dims(
5805 __isl_take isl_local_space *ls,
5806 enum isl_dim_type type, unsigned first, unsigned n);
5807 __isl_give isl_local_space *isl_local_space_drop_dims(
5808 __isl_take isl_local_space *ls,
5809 enum isl_dim_type type, unsigned first, unsigned n);
5811 #include <isl/set.h>
5812 __isl_give isl_basic_set *isl_basic_set_add_dims(
5813 __isl_take isl_basic_set *bset,
5814 enum isl_dim_type type, unsigned n);
5815 __isl_give isl_set *isl_set_add_dims(
5816 __isl_take isl_set *set,
5817 enum isl_dim_type type, unsigned n);
5818 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5819 __isl_take isl_basic_set *bset,
5820 enum isl_dim_type type, unsigned pos,
5822 __isl_give isl_set *isl_set_insert_dims(
5823 __isl_take isl_set *set,
5824 enum isl_dim_type type, unsigned pos, unsigned n);
5825 __isl_give isl_basic_set *isl_basic_set_move_dims(
5826 __isl_take isl_basic_set *bset,
5827 enum isl_dim_type dst_type, unsigned dst_pos,
5828 enum isl_dim_type src_type, unsigned src_pos,
5830 __isl_give isl_set *isl_set_move_dims(
5831 __isl_take isl_set *set,
5832 enum isl_dim_type dst_type, unsigned dst_pos,
5833 enum isl_dim_type src_type, unsigned src_pos,
5836 #include <isl/map.h>
5837 __isl_give isl_basic_map *isl_basic_map_add_dims(
5838 __isl_take isl_basic_map *bmap,
5839 enum isl_dim_type type, unsigned n);
5840 __isl_give isl_map *isl_map_add_dims(
5841 __isl_take isl_map *map,
5842 enum isl_dim_type type, unsigned n);
5843 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5844 __isl_take isl_basic_map *bmap,
5845 enum isl_dim_type type, unsigned pos,
5847 __isl_give isl_map *isl_map_insert_dims(
5848 __isl_take isl_map *map,
5849 enum isl_dim_type type, unsigned pos, unsigned n);
5850 __isl_give isl_basic_map *isl_basic_map_move_dims(
5851 __isl_take isl_basic_map *bmap,
5852 enum isl_dim_type dst_type, unsigned dst_pos,
5853 enum isl_dim_type src_type, unsigned src_pos,
5855 __isl_give isl_map *isl_map_move_dims(
5856 __isl_take isl_map *map,
5857 enum isl_dim_type dst_type, unsigned dst_pos,
5858 enum isl_dim_type src_type, unsigned src_pos,
5861 #include <isl/val.h>
5862 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5863 __isl_take isl_multi_val *mv,
5864 enum isl_dim_type type, unsigned first, unsigned n);
5865 __isl_give isl_multi_val *isl_multi_val_add_dims(
5866 __isl_take isl_multi_val *mv,
5867 enum isl_dim_type type, unsigned n);
5868 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5869 __isl_take isl_multi_val *mv,
5870 enum isl_dim_type type, unsigned first, unsigned n);
5872 #include <isl/aff.h>
5873 __isl_give isl_aff *isl_aff_insert_dims(
5874 __isl_take isl_aff *aff,
5875 enum isl_dim_type type, unsigned first, unsigned n);
5876 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5877 __isl_take isl_multi_aff *ma,
5878 enum isl_dim_type type, unsigned first, unsigned n);
5879 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5880 __isl_take isl_pw_aff *pwaff,
5881 enum isl_dim_type type, unsigned first, unsigned n);
5882 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5883 __isl_take isl_multi_pw_aff *mpa,
5884 enum isl_dim_type type, unsigned first, unsigned n);
5885 __isl_give isl_aff *isl_aff_add_dims(
5886 __isl_take isl_aff *aff,
5887 enum isl_dim_type type, unsigned n);
5888 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5889 __isl_take isl_multi_aff *ma,
5890 enum isl_dim_type type, unsigned n);
5891 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5892 __isl_take isl_pw_aff *pwaff,
5893 enum isl_dim_type type, unsigned n);
5894 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5895 __isl_take isl_multi_pw_aff *mpa,
5896 enum isl_dim_type type, unsigned n);
5897 __isl_give isl_aff *isl_aff_drop_dims(
5898 __isl_take isl_aff *aff,
5899 enum isl_dim_type type, unsigned first, unsigned n);
5900 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5901 __isl_take isl_multi_aff *maff,
5902 enum isl_dim_type type, unsigned first, unsigned n);
5903 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5904 __isl_take isl_pw_aff *pwaff,
5905 enum isl_dim_type type, unsigned first, unsigned n);
5906 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5907 __isl_take isl_pw_multi_aff *pma,
5908 enum isl_dim_type type, unsigned first, unsigned n);
5909 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5910 __isl_take isl_union_pw_aff *upa,
5911 enum isl_dim_type type, unsigned first, unsigned n);
5912 __isl_give isl_union_pw_multi_aff *
5913 isl_union_pw_multi_aff_drop_dims(
5914 __isl_take isl_union_pw_multi_aff *upma,
5915 enum isl_dim_type type,
5916 unsigned first, unsigned n);
5917 __isl_give isl_multi_union_pw_aff *
5918 isl_multi_union_pw_aff_drop_dims(
5919 __isl_take isl_multi_union_pw_aff *mupa,
5920 enum isl_dim_type type, unsigned first,
5922 __isl_give isl_aff *isl_aff_move_dims(
5923 __isl_take isl_aff *aff,
5924 enum isl_dim_type dst_type, unsigned dst_pos,
5925 enum isl_dim_type src_type, unsigned src_pos,
5927 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5928 __isl_take isl_multi_aff *ma,
5929 enum isl_dim_type dst_type, unsigned dst_pos,
5930 enum isl_dim_type src_type, unsigned src_pos,
5932 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5933 __isl_take isl_pw_aff *pa,
5934 enum isl_dim_type dst_type, unsigned dst_pos,
5935 enum isl_dim_type src_type, unsigned src_pos,
5937 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5938 __isl_take isl_multi_pw_aff *pma,
5939 enum isl_dim_type dst_type, unsigned dst_pos,
5940 enum isl_dim_type src_type, unsigned src_pos,
5943 #include <isl/polynomial.h>
5944 __isl_give isl_union_pw_qpolynomial *
5945 isl_union_pw_qpolynomial_drop_dims(
5946 __isl_take isl_union_pw_qpolynomial *upwqp,
5947 enum isl_dim_type type,
5948 unsigned first, unsigned n);
5949 __isl_give isl_union_pw_qpolynomial_fold *
5950 isl_union_pw_qpolynomial_fold_drop_dims(
5951 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5952 enum isl_dim_type type,
5953 unsigned first, unsigned n);
5955 The operations on union expressions can only manipulate parameters.
5959 =head2 Binary Operations
5961 The two arguments of a binary operation not only need to live
5962 in the same C<isl_ctx>, they currently also need to have
5963 the same (number of) parameters.
5965 =head3 Basic Operations
5969 =item * Intersection
5971 #include <isl/local_space.h>
5972 __isl_give isl_local_space *isl_local_space_intersect(
5973 __isl_take isl_local_space *ls1,
5974 __isl_take isl_local_space *ls2);
5976 #include <isl/set.h>
5977 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5978 __isl_take isl_basic_set *bset1,
5979 __isl_take isl_basic_set *bset2);
5980 __isl_give isl_basic_set *isl_basic_set_intersect(
5981 __isl_take isl_basic_set *bset1,
5982 __isl_take isl_basic_set *bset2);
5983 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5984 __isl_take struct isl_basic_set_list *list);
5985 __isl_give isl_set *isl_set_intersect_params(
5986 __isl_take isl_set *set,
5987 __isl_take isl_set *params);
5988 __isl_give isl_set *isl_set_intersect(
5989 __isl_take isl_set *set1,
5990 __isl_take isl_set *set2);
5992 #include <isl/map.h>
5993 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5994 __isl_take isl_basic_map *bmap,
5995 __isl_take isl_basic_set *bset);
5996 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5997 __isl_take isl_basic_map *bmap,
5998 __isl_take isl_basic_set *bset);
5999 __isl_give isl_basic_map *isl_basic_map_intersect(
6000 __isl_take isl_basic_map *bmap1,
6001 __isl_take isl_basic_map *bmap2);
6002 __isl_give isl_basic_map *isl_basic_map_list_intersect(
6003 __isl_take isl_basic_map_list *list);
6004 __isl_give isl_map *isl_map_intersect_params(
6005 __isl_take isl_map *map,
6006 __isl_take isl_set *params);
6007 __isl_give isl_map *isl_map_intersect_domain(
6008 __isl_take isl_map *map,
6009 __isl_take isl_set *set);
6010 __isl_give isl_map *isl_map_intersect_range(
6011 __isl_take isl_map *map,
6012 __isl_take isl_set *set);
6013 __isl_give isl_map *isl_map_intersect(
6014 __isl_take isl_map *map1,
6015 __isl_take isl_map *map2);
6016 __isl_give isl_map *
6017 isl_map_intersect_domain_factor_range(
6018 __isl_take isl_map *map,
6019 __isl_take isl_map *factor);
6020 __isl_give isl_map *
6021 isl_map_intersect_range_factor_range(
6022 __isl_take isl_map *map,
6023 __isl_take isl_map *factor);
6025 #include <isl/union_set.h>
6026 __isl_give isl_union_set *isl_union_set_intersect_params(
6027 __isl_take isl_union_set *uset,
6028 __isl_take isl_set *set);
6029 __isl_give isl_union_set *isl_union_set_intersect(
6030 __isl_take isl_union_set *uset1,
6031 __isl_take isl_union_set *uset2);
6033 #include <isl/union_map.h>
6034 __isl_give isl_union_map *isl_union_map_intersect_params(
6035 __isl_take isl_union_map *umap,
6036 __isl_take isl_set *set);
6037 __isl_give isl_union_map *isl_union_map_intersect_domain(
6038 __isl_take isl_union_map *umap,
6039 __isl_take isl_union_set *uset);
6040 __isl_give isl_union_map *isl_union_map_intersect_range(
6041 __isl_take isl_union_map *umap,
6042 __isl_take isl_union_set *uset);
6043 __isl_give isl_union_map *isl_union_map_intersect(
6044 __isl_take isl_union_map *umap1,
6045 __isl_take isl_union_map *umap2);
6046 __isl_give isl_union_map *
6047 isl_union_map_intersect_range_factor_range(
6048 __isl_take isl_union_map *umap,
6049 __isl_take isl_union_map *factor);
6051 #include <isl/aff.h>
6052 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6053 __isl_take isl_pw_aff *pa,
6054 __isl_take isl_set *set);
6055 __isl_give isl_multi_pw_aff *
6056 isl_multi_pw_aff_intersect_domain(
6057 __isl_take isl_multi_pw_aff *mpa,
6058 __isl_take isl_set *domain);
6059 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6060 __isl_take isl_pw_multi_aff *pma,
6061 __isl_take isl_set *set);
6062 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6063 __isl_take isl_union_pw_aff *upa,
6064 __isl_take isl_union_set *uset);
6065 __isl_give isl_union_pw_multi_aff *
6066 isl_union_pw_multi_aff_intersect_domain(
6067 __isl_take isl_union_pw_multi_aff *upma,
6068 __isl_take isl_union_set *uset);
6069 __isl_give isl_multi_union_pw_aff *
6070 isl_multi_union_pw_aff_intersect_domain(
6071 __isl_take isl_multi_union_pw_aff *mupa,
6072 __isl_take isl_union_set *uset);
6073 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6074 __isl_take isl_pw_aff *pa,
6075 __isl_take isl_set *set);
6076 __isl_give isl_multi_pw_aff *
6077 isl_multi_pw_aff_intersect_params(
6078 __isl_take isl_multi_pw_aff *mpa,
6079 __isl_take isl_set *set);
6080 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6081 __isl_take isl_pw_multi_aff *pma,
6082 __isl_take isl_set *set);
6083 __isl_give isl_union_pw_aff *
6084 isl_union_pw_aff_intersect_params(
6085 __isl_take isl_union_pw_aff *upa,
6086 __isl_give isl_union_pw_multi_aff *
6087 isl_union_pw_multi_aff_intersect_params(
6088 __isl_take isl_union_pw_multi_aff *upma,
6089 __isl_take isl_set *set);
6090 __isl_give isl_multi_union_pw_aff *
6091 isl_multi_union_pw_aff_intersect_params(
6092 __isl_take isl_multi_union_pw_aff *mupa,
6093 __isl_take isl_set *params);
6094 isl_multi_union_pw_aff_intersect_range(
6095 __isl_take isl_multi_union_pw_aff *mupa,
6096 __isl_take isl_set *set);
6098 #include <isl/polynomial.h>
6099 __isl_give isl_pw_qpolynomial *
6100 isl_pw_qpolynomial_intersect_domain(
6101 __isl_take isl_pw_qpolynomial *pwpq,
6102 __isl_take isl_set *set);
6103 __isl_give isl_union_pw_qpolynomial *
6104 isl_union_pw_qpolynomial_intersect_domain(
6105 __isl_take isl_union_pw_qpolynomial *upwpq,
6106 __isl_take isl_union_set *uset);
6107 __isl_give isl_union_pw_qpolynomial_fold *
6108 isl_union_pw_qpolynomial_fold_intersect_domain(
6109 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6110 __isl_take isl_union_set *uset);
6111 __isl_give isl_pw_qpolynomial *
6112 isl_pw_qpolynomial_intersect_params(
6113 __isl_take isl_pw_qpolynomial *pwpq,
6114 __isl_take isl_set *set);
6115 __isl_give isl_pw_qpolynomial_fold *
6116 isl_pw_qpolynomial_fold_intersect_params(
6117 __isl_take isl_pw_qpolynomial_fold *pwf,
6118 __isl_take isl_set *set);
6119 __isl_give isl_union_pw_qpolynomial *
6120 isl_union_pw_qpolynomial_intersect_params(
6121 __isl_take isl_union_pw_qpolynomial *upwpq,
6122 __isl_take isl_set *set);
6123 __isl_give isl_union_pw_qpolynomial_fold *
6124 isl_union_pw_qpolynomial_fold_intersect_params(
6125 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6126 __isl_take isl_set *set);
6128 The second argument to the C<_params> functions needs to be
6129 a parametric (basic) set. For the other functions, a parametric set
6130 for either argument is only allowed if the other argument is
6131 a parametric set as well.
6132 The list passed to C<isl_basic_set_list_intersect> needs to have
6133 at least one element and all elements need to live in the same space.
6134 The function C<isl_multi_union_pw_aff_intersect_range>
6135 restricts the input function to those shared domain elements
6136 that map to the specified range.
6140 #include <isl/set.h>
6141 __isl_give isl_set *isl_basic_set_union(
6142 __isl_take isl_basic_set *bset1,
6143 __isl_take isl_basic_set *bset2);
6144 __isl_give isl_set *isl_set_union(
6145 __isl_take isl_set *set1,
6146 __isl_take isl_set *set2);
6147 __isl_give isl_set *isl_set_list_union(
6148 __isl_take isl_set_list *list);
6150 #include <isl/map.h>
6151 __isl_give isl_map *isl_basic_map_union(
6152 __isl_take isl_basic_map *bmap1,
6153 __isl_take isl_basic_map *bmap2);
6154 __isl_give isl_map *isl_map_union(
6155 __isl_take isl_map *map1,
6156 __isl_take isl_map *map2);
6158 #include <isl/union_set.h>
6159 __isl_give isl_union_set *isl_union_set_union(
6160 __isl_take isl_union_set *uset1,
6161 __isl_take isl_union_set *uset2);
6162 __isl_give isl_union_set *isl_union_set_list_union(
6163 __isl_take isl_union_set_list *list);
6165 #include <isl/union_map.h>
6166 __isl_give isl_union_map *isl_union_map_union(
6167 __isl_take isl_union_map *umap1,
6168 __isl_take isl_union_map *umap2);
6170 The list passed to C<isl_set_list_union> needs to have
6171 at least one element and all elements need to live in the same space.
6173 =item * Set difference
6175 #include <isl/set.h>
6176 __isl_give isl_set *isl_set_subtract(
6177 __isl_take isl_set *set1,
6178 __isl_take isl_set *set2);
6180 #include <isl/map.h>
6181 __isl_give isl_map *isl_map_subtract(
6182 __isl_take isl_map *map1,
6183 __isl_take isl_map *map2);
6184 __isl_give isl_map *isl_map_subtract_domain(
6185 __isl_take isl_map *map,
6186 __isl_take isl_set *dom);
6187 __isl_give isl_map *isl_map_subtract_range(
6188 __isl_take isl_map *map,
6189 __isl_take isl_set *dom);
6191 #include <isl/union_set.h>
6192 __isl_give isl_union_set *isl_union_set_subtract(
6193 __isl_take isl_union_set *uset1,
6194 __isl_take isl_union_set *uset2);
6196 #include <isl/union_map.h>
6197 __isl_give isl_union_map *isl_union_map_subtract(
6198 __isl_take isl_union_map *umap1,
6199 __isl_take isl_union_map *umap2);
6200 __isl_give isl_union_map *isl_union_map_subtract_domain(
6201 __isl_take isl_union_map *umap,
6202 __isl_take isl_union_set *dom);
6203 __isl_give isl_union_map *isl_union_map_subtract_range(
6204 __isl_take isl_union_map *umap,
6205 __isl_take isl_union_set *dom);
6207 #include <isl/aff.h>
6208 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6209 __isl_take isl_pw_aff *pa,
6210 __isl_take isl_set *set);
6211 __isl_give isl_pw_multi_aff *
6212 isl_pw_multi_aff_subtract_domain(
6213 __isl_take isl_pw_multi_aff *pma,
6214 __isl_take isl_set *set);
6215 __isl_give isl_union_pw_aff *
6216 isl_union_pw_aff_subtract_domain(
6217 __isl_take isl_union_pw_aff *upa,
6218 __isl_take isl_union_set *uset);
6219 __isl_give isl_union_pw_multi_aff *
6220 isl_union_pw_multi_aff_subtract_domain(
6221 __isl_take isl_union_pw_multi_aff *upma,
6222 __isl_take isl_set *set);
6224 #include <isl/polynomial.h>
6225 __isl_give isl_pw_qpolynomial *
6226 isl_pw_qpolynomial_subtract_domain(
6227 __isl_take isl_pw_qpolynomial *pwpq,
6228 __isl_take isl_set *set);
6229 __isl_give isl_pw_qpolynomial_fold *
6230 isl_pw_qpolynomial_fold_subtract_domain(
6231 __isl_take isl_pw_qpolynomial_fold *pwf,
6232 __isl_take isl_set *set);
6233 __isl_give isl_union_pw_qpolynomial *
6234 isl_union_pw_qpolynomial_subtract_domain(
6235 __isl_take isl_union_pw_qpolynomial *upwpq,
6236 __isl_take isl_union_set *uset);
6237 __isl_give isl_union_pw_qpolynomial_fold *
6238 isl_union_pw_qpolynomial_fold_subtract_domain(
6239 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6240 __isl_take isl_union_set *uset);
6244 #include <isl/space.h>
6245 __isl_give isl_space *isl_space_join(
6246 __isl_take isl_space *left,
6247 __isl_take isl_space *right);
6249 #include <isl/map.h>
6250 __isl_give isl_basic_set *isl_basic_set_apply(
6251 __isl_take isl_basic_set *bset,
6252 __isl_take isl_basic_map *bmap);
6253 __isl_give isl_set *isl_set_apply(
6254 __isl_take isl_set *set,
6255 __isl_take isl_map *map);
6256 __isl_give isl_union_set *isl_union_set_apply(
6257 __isl_take isl_union_set *uset,
6258 __isl_take isl_union_map *umap);
6259 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6260 __isl_take isl_basic_map *bmap1,
6261 __isl_take isl_basic_map *bmap2);
6262 __isl_give isl_basic_map *isl_basic_map_apply_range(
6263 __isl_take isl_basic_map *bmap1,
6264 __isl_take isl_basic_map *bmap2);
6265 __isl_give isl_map *isl_map_apply_domain(
6266 __isl_take isl_map *map1,
6267 __isl_take isl_map *map2);
6268 __isl_give isl_map *isl_map_apply_range(
6269 __isl_take isl_map *map1,
6270 __isl_take isl_map *map2);
6272 #include <isl/union_map.h>
6273 __isl_give isl_union_map *isl_union_map_apply_domain(
6274 __isl_take isl_union_map *umap1,
6275 __isl_take isl_union_map *umap2);
6276 __isl_give isl_union_map *isl_union_map_apply_range(
6277 __isl_take isl_union_map *umap1,
6278 __isl_take isl_union_map *umap2);
6280 #include <isl/aff.h>
6281 __isl_give isl_union_pw_aff *
6282 isl_multi_union_pw_aff_apply_aff(
6283 __isl_take isl_multi_union_pw_aff *mupa,
6284 __isl_take isl_aff *aff);
6285 __isl_give isl_union_pw_aff *
6286 isl_multi_union_pw_aff_apply_pw_aff(
6287 __isl_take isl_multi_union_pw_aff *mupa,
6288 __isl_take isl_pw_aff *pa);
6289 __isl_give isl_multi_union_pw_aff *
6290 isl_multi_union_pw_aff_apply_multi_aff(
6291 __isl_take isl_multi_union_pw_aff *mupa,
6292 __isl_take isl_multi_aff *ma);
6293 __isl_give isl_multi_union_pw_aff *
6294 isl_multi_union_pw_aff_apply_pw_multi_aff(
6295 __isl_take isl_multi_union_pw_aff *mupa,
6296 __isl_take isl_pw_multi_aff *pma);
6298 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6299 over the shared domain of the elements of the input. The dimension is
6300 required to be greater than zero.
6301 The C<isl_multi_union_pw_aff> argument of
6302 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6303 but only if the range of the C<isl_multi_aff> argument
6304 is also zero-dimensional.
6305 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6307 #include <isl/polynomial.h>
6308 __isl_give isl_pw_qpolynomial_fold *
6309 isl_set_apply_pw_qpolynomial_fold(
6310 __isl_take isl_set *set,
6311 __isl_take isl_pw_qpolynomial_fold *pwf,
6313 __isl_give isl_pw_qpolynomial_fold *
6314 isl_map_apply_pw_qpolynomial_fold(
6315 __isl_take isl_map *map,
6316 __isl_take isl_pw_qpolynomial_fold *pwf,
6318 __isl_give isl_union_pw_qpolynomial_fold *
6319 isl_union_set_apply_union_pw_qpolynomial_fold(
6320 __isl_take isl_union_set *uset,
6321 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6323 __isl_give isl_union_pw_qpolynomial_fold *
6324 isl_union_map_apply_union_pw_qpolynomial_fold(
6325 __isl_take isl_union_map *umap,
6326 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6329 The functions taking a map
6330 compose the given map with the given piecewise quasipolynomial reduction.
6331 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6332 over all elements in the intersection of the range of the map
6333 and the domain of the piecewise quasipolynomial reduction
6334 as a function of an element in the domain of the map.
6335 The functions taking a set compute a bound over all elements in the
6336 intersection of the set and the domain of the
6337 piecewise quasipolynomial reduction.
6341 #include <isl/set.h>
6342 __isl_give isl_basic_set *
6343 isl_basic_set_preimage_multi_aff(
6344 __isl_take isl_basic_set *bset,
6345 __isl_take isl_multi_aff *ma);
6346 __isl_give isl_set *isl_set_preimage_multi_aff(
6347 __isl_take isl_set *set,
6348 __isl_take isl_multi_aff *ma);
6349 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6350 __isl_take isl_set *set,
6351 __isl_take isl_pw_multi_aff *pma);
6352 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6353 __isl_take isl_set *set,
6354 __isl_take isl_multi_pw_aff *mpa);
6356 #include <isl/union_set.h>
6357 __isl_give isl_union_set *
6358 isl_union_set_preimage_multi_aff(
6359 __isl_take isl_union_set *uset,
6360 __isl_take isl_multi_aff *ma);
6361 __isl_give isl_union_set *
6362 isl_union_set_preimage_pw_multi_aff(
6363 __isl_take isl_union_set *uset,
6364 __isl_take isl_pw_multi_aff *pma);
6365 __isl_give isl_union_set *
6366 isl_union_set_preimage_union_pw_multi_aff(
6367 __isl_take isl_union_set *uset,
6368 __isl_take isl_union_pw_multi_aff *upma);
6370 #include <isl/map.h>
6371 __isl_give isl_basic_map *
6372 isl_basic_map_preimage_domain_multi_aff(
6373 __isl_take isl_basic_map *bmap,
6374 __isl_take isl_multi_aff *ma);
6375 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6376 __isl_take isl_map *map,
6377 __isl_take isl_multi_aff *ma);
6378 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6379 __isl_take isl_map *map,
6380 __isl_take isl_multi_aff *ma);
6381 __isl_give isl_map *
6382 isl_map_preimage_domain_pw_multi_aff(
6383 __isl_take isl_map *map,
6384 __isl_take isl_pw_multi_aff *pma);
6385 __isl_give isl_map *
6386 isl_map_preimage_range_pw_multi_aff(
6387 __isl_take isl_map *map,
6388 __isl_take isl_pw_multi_aff *pma);
6389 __isl_give isl_map *
6390 isl_map_preimage_domain_multi_pw_aff(
6391 __isl_take isl_map *map,
6392 __isl_take isl_multi_pw_aff *mpa);
6393 __isl_give isl_basic_map *
6394 isl_basic_map_preimage_range_multi_aff(
6395 __isl_take isl_basic_map *bmap,
6396 __isl_take isl_multi_aff *ma);
6398 #include <isl/union_map.h>
6399 __isl_give isl_union_map *
6400 isl_union_map_preimage_domain_multi_aff(
6401 __isl_take isl_union_map *umap,
6402 __isl_take isl_multi_aff *ma);
6403 __isl_give isl_union_map *
6404 isl_union_map_preimage_range_multi_aff(
6405 __isl_take isl_union_map *umap,
6406 __isl_take isl_multi_aff *ma);
6407 __isl_give isl_union_map *
6408 isl_union_map_preimage_domain_pw_multi_aff(
6409 __isl_take isl_union_map *umap,
6410 __isl_take isl_pw_multi_aff *pma);
6411 __isl_give isl_union_map *
6412 isl_union_map_preimage_range_pw_multi_aff(
6413 __isl_take isl_union_map *umap,
6414 __isl_take isl_pw_multi_aff *pma);
6415 __isl_give isl_union_map *
6416 isl_union_map_preimage_domain_union_pw_multi_aff(
6417 __isl_take isl_union_map *umap,
6418 __isl_take isl_union_pw_multi_aff *upma);
6419 __isl_give isl_union_map *
6420 isl_union_map_preimage_range_union_pw_multi_aff(
6421 __isl_take isl_union_map *umap,
6422 __isl_take isl_union_pw_multi_aff *upma);
6424 These functions compute the preimage of the given set or map domain/range under
6425 the given function. In other words, the expression is plugged
6426 into the set description or into the domain/range of the map.
6430 #include <isl/aff.h>
6431 __isl_give isl_aff *isl_aff_pullback_aff(
6432 __isl_take isl_aff *aff1,
6433 __isl_take isl_aff *aff2);
6434 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6435 __isl_take isl_aff *aff,
6436 __isl_take isl_multi_aff *ma);
6437 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6438 __isl_take isl_pw_aff *pa,
6439 __isl_take isl_multi_aff *ma);
6440 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6441 __isl_take isl_pw_aff *pa,
6442 __isl_take isl_pw_multi_aff *pma);
6443 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6444 __isl_take isl_pw_aff *pa,
6445 __isl_take isl_multi_pw_aff *mpa);
6446 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6447 __isl_take isl_multi_aff *ma1,
6448 __isl_take isl_multi_aff *ma2);
6449 __isl_give isl_pw_multi_aff *
6450 isl_pw_multi_aff_pullback_multi_aff(
6451 __isl_take isl_pw_multi_aff *pma,
6452 __isl_take isl_multi_aff *ma);
6453 __isl_give isl_multi_pw_aff *
6454 isl_multi_pw_aff_pullback_multi_aff(
6455 __isl_take isl_multi_pw_aff *mpa,
6456 __isl_take isl_multi_aff *ma);
6457 __isl_give isl_pw_multi_aff *
6458 isl_pw_multi_aff_pullback_pw_multi_aff(
6459 __isl_take isl_pw_multi_aff *pma1,
6460 __isl_take isl_pw_multi_aff *pma2);
6461 __isl_give isl_multi_pw_aff *
6462 isl_multi_pw_aff_pullback_pw_multi_aff(
6463 __isl_take isl_multi_pw_aff *mpa,
6464 __isl_take isl_pw_multi_aff *pma);
6465 __isl_give isl_multi_pw_aff *
6466 isl_multi_pw_aff_pullback_multi_pw_aff(
6467 __isl_take isl_multi_pw_aff *mpa1,
6468 __isl_take isl_multi_pw_aff *mpa2);
6469 __isl_give isl_union_pw_aff *
6470 isl_union_pw_aff_pullback_union_pw_multi_aff(
6471 __isl_take isl_union_pw_aff *upa,
6472 __isl_take isl_union_pw_multi_aff *upma);
6473 __isl_give isl_union_pw_multi_aff *
6474 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6475 __isl_take isl_union_pw_multi_aff *upma1,
6476 __isl_take isl_union_pw_multi_aff *upma2);
6477 __isl_give isl_multi_union_pw_aff *
6478 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6479 __isl_take isl_multi_union_pw_aff *mupa,
6480 __isl_take isl_union_pw_multi_aff *upma);
6482 These functions precompose the first expression by the second function.
6483 In other words, the second function is plugged
6484 into the first expression.
6488 #include <isl/aff.h>
6489 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6490 __isl_take isl_aff *aff1,
6491 __isl_take isl_aff *aff2);
6492 __isl_give isl_set *isl_aff_eq_set(
6493 __isl_take isl_aff *aff1,
6494 __isl_take isl_aff *aff2);
6495 __isl_give isl_set *isl_aff_ne_set(
6496 __isl_take isl_aff *aff1,
6497 __isl_take isl_aff *aff2);
6498 __isl_give isl_basic_set *isl_aff_le_basic_set(
6499 __isl_take isl_aff *aff1,
6500 __isl_take isl_aff *aff2);
6501 __isl_give isl_set *isl_aff_le_set(
6502 __isl_take isl_aff *aff1,
6503 __isl_take isl_aff *aff2);
6504 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6505 __isl_take isl_aff *aff1,
6506 __isl_take isl_aff *aff2);
6507 __isl_give isl_set *isl_aff_lt_set(
6508 __isl_take isl_aff *aff1,
6509 __isl_take isl_aff *aff2);
6510 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6511 __isl_take isl_aff *aff1,
6512 __isl_take isl_aff *aff2);
6513 __isl_give isl_set *isl_aff_ge_set(
6514 __isl_take isl_aff *aff1,
6515 __isl_take isl_aff *aff2);
6516 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6517 __isl_take isl_aff *aff1,
6518 __isl_take isl_aff *aff2);
6519 __isl_give isl_set *isl_aff_gt_set(
6520 __isl_take isl_aff *aff1,
6521 __isl_take isl_aff *aff2);
6522 __isl_give isl_set *isl_pw_aff_eq_set(
6523 __isl_take isl_pw_aff *pwaff1,
6524 __isl_take isl_pw_aff *pwaff2);
6525 __isl_give isl_set *isl_pw_aff_ne_set(
6526 __isl_take isl_pw_aff *pwaff1,
6527 __isl_take isl_pw_aff *pwaff2);
6528 __isl_give isl_set *isl_pw_aff_le_set(
6529 __isl_take isl_pw_aff *pwaff1,
6530 __isl_take isl_pw_aff *pwaff2);
6531 __isl_give isl_set *isl_pw_aff_lt_set(
6532 __isl_take isl_pw_aff *pwaff1,
6533 __isl_take isl_pw_aff *pwaff2);
6534 __isl_give isl_set *isl_pw_aff_ge_set(
6535 __isl_take isl_pw_aff *pwaff1,
6536 __isl_take isl_pw_aff *pwaff2);
6537 __isl_give isl_set *isl_pw_aff_gt_set(
6538 __isl_take isl_pw_aff *pwaff1,
6539 __isl_take isl_pw_aff *pwaff2);
6541 __isl_give isl_set *isl_multi_aff_lex_le_set(
6542 __isl_take isl_multi_aff *ma1,
6543 __isl_take isl_multi_aff *ma2);
6544 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6545 __isl_take isl_multi_aff *ma1,
6546 __isl_take isl_multi_aff *ma2);
6547 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6548 __isl_take isl_multi_aff *ma1,
6549 __isl_take isl_multi_aff *ma2);
6550 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6551 __isl_take isl_multi_aff *ma1,
6552 __isl_take isl_multi_aff *ma2);
6554 __isl_give isl_set *isl_pw_aff_list_eq_set(
6555 __isl_take isl_pw_aff_list *list1,
6556 __isl_take isl_pw_aff_list *list2);
6557 __isl_give isl_set *isl_pw_aff_list_ne_set(
6558 __isl_take isl_pw_aff_list *list1,
6559 __isl_take isl_pw_aff_list *list2);
6560 __isl_give isl_set *isl_pw_aff_list_le_set(
6561 __isl_take isl_pw_aff_list *list1,
6562 __isl_take isl_pw_aff_list *list2);
6563 __isl_give isl_set *isl_pw_aff_list_lt_set(
6564 __isl_take isl_pw_aff_list *list1,
6565 __isl_take isl_pw_aff_list *list2);
6566 __isl_give isl_set *isl_pw_aff_list_ge_set(
6567 __isl_take isl_pw_aff_list *list1,
6568 __isl_take isl_pw_aff_list *list2);
6569 __isl_give isl_set *isl_pw_aff_list_gt_set(
6570 __isl_take isl_pw_aff_list *list1,
6571 __isl_take isl_pw_aff_list *list2);
6573 The function C<isl_aff_ge_basic_set> returns a basic set
6574 containing those elements in the shared space
6575 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6576 The function C<isl_pw_aff_ge_set> returns a set
6577 containing those elements in the shared domain
6578 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6579 greater than or equal to C<pwaff2>.
6580 The function C<isl_multi_aff_lex_le_set> returns a set
6581 containing those elements in the shared domain space
6582 where C<ma1> is lexicographically smaller than or
6584 The functions operating on C<isl_pw_aff_list> apply the corresponding
6585 C<isl_pw_aff> function to each pair of elements in the two lists.
6587 #include <isl/aff.h>
6588 __isl_give isl_map *isl_pw_aff_eq_map(
6589 __isl_take isl_pw_aff *pa1,
6590 __isl_take isl_pw_aff *pa2);
6591 __isl_give isl_map *isl_pw_aff_lt_map(
6592 __isl_take isl_pw_aff *pa1,
6593 __isl_take isl_pw_aff *pa2);
6594 __isl_give isl_map *isl_pw_aff_gt_map(
6595 __isl_take isl_pw_aff *pa1,
6596 __isl_take isl_pw_aff *pa2);
6598 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6599 __isl_take isl_multi_pw_aff *mpa1,
6600 __isl_take isl_multi_pw_aff *mpa2);
6601 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6602 __isl_take isl_multi_pw_aff *mpa1,
6603 __isl_take isl_multi_pw_aff *mpa2);
6604 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6605 __isl_take isl_multi_pw_aff *mpa1,
6606 __isl_take isl_multi_pw_aff *mpa2);
6608 These functions return a map between domain elements of the arguments
6609 where the function values satisfy the given relation.
6611 #include <isl/union_map.h>
6612 __isl_give isl_union_map *
6613 isl_union_map_eq_at_multi_union_pw_aff(
6614 __isl_take isl_union_map *umap,
6615 __isl_take isl_multi_union_pw_aff *mupa);
6616 __isl_give isl_union_map *
6617 isl_union_map_lex_lt_at_multi_union_pw_aff(
6618 __isl_take isl_union_map *umap,
6619 __isl_take isl_multi_union_pw_aff *mupa);
6620 __isl_give isl_union_map *
6621 isl_union_map_lex_gt_at_multi_union_pw_aff(
6622 __isl_take isl_union_map *umap,
6623 __isl_take isl_multi_union_pw_aff *mupa);
6625 These functions select the subset of elements in the union map
6626 that have an equal or lexicographically smaller function value.
6628 =item * Cartesian Product
6630 #include <isl/space.h>
6631 __isl_give isl_space *isl_space_product(
6632 __isl_take isl_space *space1,
6633 __isl_take isl_space *space2);
6634 __isl_give isl_space *isl_space_domain_product(
6635 __isl_take isl_space *space1,
6636 __isl_take isl_space *space2);
6637 __isl_give isl_space *isl_space_range_product(
6638 __isl_take isl_space *space1,
6639 __isl_take isl_space *space2);
6642 C<isl_space_product>, C<isl_space_domain_product>
6643 and C<isl_space_range_product> take pairs or relation spaces and
6644 produce a single relations space, where either the domain, the range
6645 or both domain and range are wrapped spaces of relations between
6646 the domains and/or ranges of the input spaces.
6647 If the product is only constructed over the domain or the range
6648 then the ranges or the domains of the inputs should be the same.
6649 The function C<isl_space_product> also accepts a pair of set spaces,
6650 in which case it returns a wrapped space of a relation between the
6653 #include <isl/set.h>
6654 __isl_give isl_set *isl_set_product(
6655 __isl_take isl_set *set1,
6656 __isl_take isl_set *set2);
6658 #include <isl/map.h>
6659 __isl_give isl_basic_map *isl_basic_map_domain_product(
6660 __isl_take isl_basic_map *bmap1,
6661 __isl_take isl_basic_map *bmap2);
6662 __isl_give isl_basic_map *isl_basic_map_range_product(
6663 __isl_take isl_basic_map *bmap1,
6664 __isl_take isl_basic_map *bmap2);
6665 __isl_give isl_basic_map *isl_basic_map_product(
6666 __isl_take isl_basic_map *bmap1,
6667 __isl_take isl_basic_map *bmap2);
6668 __isl_give isl_map *isl_map_domain_product(
6669 __isl_take isl_map *map1,
6670 __isl_take isl_map *map2);
6671 __isl_give isl_map *isl_map_range_product(
6672 __isl_take isl_map *map1,
6673 __isl_take isl_map *map2);
6674 __isl_give isl_map *isl_map_product(
6675 __isl_take isl_map *map1,
6676 __isl_take isl_map *map2);
6678 #include <isl/union_set.h>
6679 __isl_give isl_union_set *isl_union_set_product(
6680 __isl_take isl_union_set *uset1,
6681 __isl_take isl_union_set *uset2);
6683 #include <isl/union_map.h>
6684 __isl_give isl_union_map *isl_union_map_domain_product(
6685 __isl_take isl_union_map *umap1,
6686 __isl_take isl_union_map *umap2);
6687 __isl_give isl_union_map *isl_union_map_range_product(
6688 __isl_take isl_union_map *umap1,
6689 __isl_take isl_union_map *umap2);
6690 __isl_give isl_union_map *isl_union_map_product(
6691 __isl_take isl_union_map *umap1,
6692 __isl_take isl_union_map *umap2);
6694 #include <isl/val.h>
6695 __isl_give isl_multi_val *isl_multi_val_range_product(
6696 __isl_take isl_multi_val *mv1,
6697 __isl_take isl_multi_val *mv2);
6698 __isl_give isl_multi_val *isl_multi_val_product(
6699 __isl_take isl_multi_val *mv1,
6700 __isl_take isl_multi_val *mv2);
6702 #include <isl/aff.h>
6703 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6704 __isl_take isl_multi_aff *ma1,
6705 __isl_take isl_multi_aff *ma2);
6706 __isl_give isl_multi_aff *isl_multi_aff_product(
6707 __isl_take isl_multi_aff *ma1,
6708 __isl_take isl_multi_aff *ma2);
6709 __isl_give isl_multi_pw_aff *
6710 isl_multi_pw_aff_range_product(
6711 __isl_take isl_multi_pw_aff *mpa1,
6712 __isl_take isl_multi_pw_aff *mpa2);
6713 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6714 __isl_take isl_multi_pw_aff *mpa1,
6715 __isl_take isl_multi_pw_aff *mpa2);
6716 __isl_give isl_pw_multi_aff *
6717 isl_pw_multi_aff_range_product(
6718 __isl_take isl_pw_multi_aff *pma1,
6719 __isl_take isl_pw_multi_aff *pma2);
6720 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6721 __isl_take isl_pw_multi_aff *pma1,
6722 __isl_take isl_pw_multi_aff *pma2);
6723 __isl_give isl_multi_union_pw_aff *
6724 isl_multi_union_pw_aff_range_product(
6725 __isl_take isl_multi_union_pw_aff *mupa1,
6726 __isl_take isl_multi_union_pw_aff *mupa2);
6728 The above functions compute the cross product of the given
6729 sets, relations or functions. The domains and ranges of the results
6730 are wrapped maps between domains and ranges of the inputs.
6731 To obtain a ``flat'' product, use the following functions
6734 #include <isl/set.h>
6735 __isl_give isl_basic_set *isl_basic_set_flat_product(
6736 __isl_take isl_basic_set *bset1,
6737 __isl_take isl_basic_set *bset2);
6738 __isl_give isl_set *isl_set_flat_product(
6739 __isl_take isl_set *set1,
6740 __isl_take isl_set *set2);
6742 #include <isl/map.h>
6743 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6744 __isl_take isl_basic_map *bmap1,
6745 __isl_take isl_basic_map *bmap2);
6746 __isl_give isl_map *isl_map_flat_domain_product(
6747 __isl_take isl_map *map1,
6748 __isl_take isl_map *map2);
6749 __isl_give isl_map *isl_map_flat_range_product(
6750 __isl_take isl_map *map1,
6751 __isl_take isl_map *map2);
6752 __isl_give isl_basic_map *isl_basic_map_flat_product(
6753 __isl_take isl_basic_map *bmap1,
6754 __isl_take isl_basic_map *bmap2);
6755 __isl_give isl_map *isl_map_flat_product(
6756 __isl_take isl_map *map1,
6757 __isl_take isl_map *map2);
6759 #include <isl/union_map.h>
6760 __isl_give isl_union_map *
6761 isl_union_map_flat_domain_product(
6762 __isl_take isl_union_map *umap1,
6763 __isl_take isl_union_map *umap2);
6764 __isl_give isl_union_map *
6765 isl_union_map_flat_range_product(
6766 __isl_take isl_union_map *umap1,
6767 __isl_take isl_union_map *umap2);
6769 #include <isl/val.h>
6770 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6771 __isl_take isl_multi_val *mv1,
6772 __isl_take isl_multi_aff *mv2);
6774 #include <isl/aff.h>
6775 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6776 __isl_take isl_multi_aff *ma1,
6777 __isl_take isl_multi_aff *ma2);
6778 __isl_give isl_pw_multi_aff *
6779 isl_pw_multi_aff_flat_range_product(
6780 __isl_take isl_pw_multi_aff *pma1,
6781 __isl_take isl_pw_multi_aff *pma2);
6782 __isl_give isl_multi_pw_aff *
6783 isl_multi_pw_aff_flat_range_product(
6784 __isl_take isl_multi_pw_aff *mpa1,
6785 __isl_take isl_multi_pw_aff *mpa2);
6786 __isl_give isl_union_pw_multi_aff *
6787 isl_union_pw_multi_aff_flat_range_product(
6788 __isl_take isl_union_pw_multi_aff *upma1,
6789 __isl_take isl_union_pw_multi_aff *upma2);
6790 __isl_give isl_multi_union_pw_aff *
6791 isl_multi_union_pw_aff_flat_range_product(
6792 __isl_take isl_multi_union_pw_aff *mupa1,
6793 __isl_take isl_multi_union_pw_aff *mupa2);
6795 #include <isl/space.h>
6796 __isl_give isl_space *isl_space_factor_domain(
6797 __isl_take isl_space *space);
6798 __isl_give isl_space *isl_space_factor_range(
6799 __isl_take isl_space *space);
6800 __isl_give isl_space *isl_space_domain_factor_domain(
6801 __isl_take isl_space *space);
6802 __isl_give isl_space *isl_space_domain_factor_range(
6803 __isl_take isl_space *space);
6804 __isl_give isl_space *isl_space_range_factor_domain(
6805 __isl_take isl_space *space);
6806 __isl_give isl_space *isl_space_range_factor_range(
6807 __isl_take isl_space *space);
6809 The functions C<isl_space_range_factor_domain> and
6810 C<isl_space_range_factor_range> extract the two arguments from
6811 the result of a call to C<isl_space_range_product>.
6813 The arguments of a call to a product can be extracted
6814 from the result using the following functions.
6816 #include <isl/map.h>
6817 __isl_give isl_map *isl_map_factor_domain(
6818 __isl_take isl_map *map);
6819 __isl_give isl_map *isl_map_factor_range(
6820 __isl_take isl_map *map);
6821 __isl_give isl_map *isl_map_domain_factor_domain(
6822 __isl_take isl_map *map);
6823 __isl_give isl_map *isl_map_domain_factor_range(
6824 __isl_take isl_map *map);
6825 __isl_give isl_map *isl_map_range_factor_domain(
6826 __isl_take isl_map *map);
6827 __isl_give isl_map *isl_map_range_factor_range(
6828 __isl_take isl_map *map);
6830 #include <isl/union_map.h>
6831 __isl_give isl_union_map *isl_union_map_factor_domain(
6832 __isl_take isl_union_map *umap);
6833 __isl_give isl_union_map *isl_union_map_factor_range(
6834 __isl_take isl_union_map *umap);
6835 __isl_give isl_union_map *
6836 isl_union_map_domain_factor_domain(
6837 __isl_take isl_union_map *umap);
6838 __isl_give isl_union_map *
6839 isl_union_map_domain_factor_range(
6840 __isl_take isl_union_map *umap);
6841 __isl_give isl_union_map *
6842 isl_union_map_range_factor_domain(
6843 __isl_take isl_union_map *umap);
6844 __isl_give isl_union_map *
6845 isl_union_map_range_factor_range(
6846 __isl_take isl_union_map *umap);
6848 #include <isl/val.h>
6849 __isl_give isl_multi_val *isl_multi_val_factor_range(
6850 __isl_take isl_multi_val *mv);
6851 __isl_give isl_multi_val *
6852 isl_multi_val_range_factor_domain(
6853 __isl_take isl_multi_val *mv);
6854 __isl_give isl_multi_val *
6855 isl_multi_val_range_factor_range(
6856 __isl_take isl_multi_val *mv);
6858 #include <isl/aff.h>
6859 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6860 __isl_take isl_multi_aff *ma);
6861 __isl_give isl_multi_aff *
6862 isl_multi_aff_range_factor_domain(
6863 __isl_take isl_multi_aff *ma);
6864 __isl_give isl_multi_aff *
6865 isl_multi_aff_range_factor_range(
6866 __isl_take isl_multi_aff *ma);
6867 __isl_give isl_multi_pw_aff *
6868 isl_multi_pw_aff_factor_range(
6869 __isl_take isl_multi_pw_aff *mpa);
6870 __isl_give isl_multi_pw_aff *
6871 isl_multi_pw_aff_range_factor_domain(
6872 __isl_take isl_multi_pw_aff *mpa);
6873 __isl_give isl_multi_pw_aff *
6874 isl_multi_pw_aff_range_factor_range(
6875 __isl_take isl_multi_pw_aff *mpa);
6876 __isl_give isl_multi_union_pw_aff *
6877 isl_multi_union_pw_aff_factor_range(
6878 __isl_take isl_multi_union_pw_aff *mupa);
6879 __isl_give isl_multi_union_pw_aff *
6880 isl_multi_union_pw_aff_range_factor_domain(
6881 __isl_take isl_multi_union_pw_aff *mupa);
6882 __isl_give isl_multi_union_pw_aff *
6883 isl_multi_union_pw_aff_range_factor_range(
6884 __isl_take isl_multi_union_pw_aff *mupa);
6886 The splice functions are a generalization of the flat product functions,
6887 where the second argument may be inserted at any position inside
6888 the first argument rather than being placed at the end.
6889 The functions C<isl_multi_val_factor_range>,
6890 C<isl_multi_aff_factor_range>,
6891 C<isl_multi_pw_aff_factor_range> and
6892 C<isl_multi_union_pw_aff_factor_range>
6893 take functions that live in a set space.
6895 #include <isl/val.h>
6896 __isl_give isl_multi_val *isl_multi_val_range_splice(
6897 __isl_take isl_multi_val *mv1, unsigned pos,
6898 __isl_take isl_multi_val *mv2);
6900 #include <isl/aff.h>
6901 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6902 __isl_take isl_multi_aff *ma1, unsigned pos,
6903 __isl_take isl_multi_aff *ma2);
6904 __isl_give isl_multi_aff *isl_multi_aff_splice(
6905 __isl_take isl_multi_aff *ma1,
6906 unsigned in_pos, unsigned out_pos,
6907 __isl_take isl_multi_aff *ma2);
6908 __isl_give isl_multi_pw_aff *
6909 isl_multi_pw_aff_range_splice(
6910 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6911 __isl_take isl_multi_pw_aff *mpa2);
6912 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6913 __isl_take isl_multi_pw_aff *mpa1,
6914 unsigned in_pos, unsigned out_pos,
6915 __isl_take isl_multi_pw_aff *mpa2);
6916 __isl_give isl_multi_union_pw_aff *
6917 isl_multi_union_pw_aff_range_splice(
6918 __isl_take isl_multi_union_pw_aff *mupa1,
6920 __isl_take isl_multi_union_pw_aff *mupa2);
6922 =item * Simplification
6924 When applied to a set or relation,
6925 the gist operation returns a set or relation that has the
6926 same intersection with the context as the input set or relation.
6927 Any implicit equality in the intersection is made explicit in the result,
6928 while all inequalities that are redundant with respect to the intersection
6930 In case of union sets and relations, the gist operation is performed
6933 When applied to a function,
6934 the gist operation applies the set gist operation to each of
6935 the cells in the domain of the input piecewise expression.
6936 The context is also exploited
6937 to simplify the expression associated to each cell.
6939 #include <isl/set.h>
6940 __isl_give isl_basic_set *isl_basic_set_gist(
6941 __isl_take isl_basic_set *bset,
6942 __isl_take isl_basic_set *context);
6943 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6944 __isl_take isl_set *context);
6945 __isl_give isl_set *isl_set_gist_params(
6946 __isl_take isl_set *set,
6947 __isl_take isl_set *context);
6949 #include <isl/map.h>
6950 __isl_give isl_basic_map *isl_basic_map_gist(
6951 __isl_take isl_basic_map *bmap,
6952 __isl_take isl_basic_map *context);
6953 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6954 __isl_take isl_basic_map *bmap,
6955 __isl_take isl_basic_set *context);
6956 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6957 __isl_take isl_map *context);
6958 __isl_give isl_map *isl_map_gist_params(
6959 __isl_take isl_map *map,
6960 __isl_take isl_set *context);
6961 __isl_give isl_map *isl_map_gist_domain(
6962 __isl_take isl_map *map,
6963 __isl_take isl_set *context);
6964 __isl_give isl_map *isl_map_gist_range(
6965 __isl_take isl_map *map,
6966 __isl_take isl_set *context);
6968 #include <isl/union_set.h>
6969 __isl_give isl_union_set *isl_union_set_gist(
6970 __isl_take isl_union_set *uset,
6971 __isl_take isl_union_set *context);
6972 __isl_give isl_union_set *isl_union_set_gist_params(
6973 __isl_take isl_union_set *uset,
6974 __isl_take isl_set *set);
6976 #include <isl/union_map.h>
6977 __isl_give isl_union_map *isl_union_map_gist(
6978 __isl_take isl_union_map *umap,
6979 __isl_take isl_union_map *context);
6980 __isl_give isl_union_map *isl_union_map_gist_params(
6981 __isl_take isl_union_map *umap,
6982 __isl_take isl_set *set);
6983 __isl_give isl_union_map *isl_union_map_gist_domain(
6984 __isl_take isl_union_map *umap,
6985 __isl_take isl_union_set *uset);
6986 __isl_give isl_union_map *isl_union_map_gist_range(
6987 __isl_take isl_union_map *umap,
6988 __isl_take isl_union_set *uset);
6990 #include <isl/aff.h>
6991 __isl_give isl_aff *isl_aff_gist_params(
6992 __isl_take isl_aff *aff,
6993 __isl_take isl_set *context);
6994 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6995 __isl_take isl_set *context);
6996 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6997 __isl_take isl_multi_aff *maff,
6998 __isl_take isl_set *context);
6999 __isl_give isl_multi_aff *isl_multi_aff_gist(
7000 __isl_take isl_multi_aff *maff,
7001 __isl_take isl_set *context);
7002 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
7003 __isl_take isl_pw_aff *pwaff,
7004 __isl_take isl_set *context);
7005 __isl_give isl_pw_aff *isl_pw_aff_gist(
7006 __isl_take isl_pw_aff *pwaff,
7007 __isl_take isl_set *context);
7008 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
7009 __isl_take isl_pw_multi_aff *pma,
7010 __isl_take isl_set *set);
7011 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
7012 __isl_take isl_pw_multi_aff *pma,
7013 __isl_take isl_set *set);
7014 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
7015 __isl_take isl_multi_pw_aff *mpa,
7016 __isl_take isl_set *set);
7017 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
7018 __isl_take isl_multi_pw_aff *mpa,
7019 __isl_take isl_set *set);
7020 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
7021 __isl_take isl_union_pw_aff *upa,
7022 __isl_take isl_union_set *context);
7023 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
7024 __isl_take isl_union_pw_aff *upa,
7025 __isl_take isl_set *context);
7026 __isl_give isl_union_pw_multi_aff *
7027 isl_union_pw_multi_aff_gist_params(
7028 __isl_take isl_union_pw_multi_aff *upma,
7029 __isl_take isl_set *context);
7030 __isl_give isl_union_pw_multi_aff *
7031 isl_union_pw_multi_aff_gist(
7032 __isl_take isl_union_pw_multi_aff *upma,
7033 __isl_take isl_union_set *context);
7034 __isl_give isl_multi_union_pw_aff *
7035 isl_multi_union_pw_aff_gist_params(
7036 __isl_take isl_multi_union_pw_aff *aff,
7037 __isl_take isl_set *context);
7038 __isl_give isl_multi_union_pw_aff *
7039 isl_multi_union_pw_aff_gist(
7040 __isl_take isl_multi_union_pw_aff *aff,
7041 __isl_take isl_union_set *context);
7043 #include <isl/polynomial.h>
7044 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
7045 __isl_take isl_qpolynomial *qp,
7046 __isl_take isl_set *context);
7047 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
7048 __isl_take isl_qpolynomial *qp,
7049 __isl_take isl_set *context);
7050 __isl_give isl_qpolynomial_fold *
7051 isl_qpolynomial_fold_gist_params(
7052 __isl_take isl_qpolynomial_fold *fold,
7053 __isl_take isl_set *context);
7054 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7055 __isl_take isl_qpolynomial_fold *fold,
7056 __isl_take isl_set *context);
7057 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7058 __isl_take isl_pw_qpolynomial *pwqp,
7059 __isl_take isl_set *context);
7060 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7061 __isl_take isl_pw_qpolynomial *pwqp,
7062 __isl_take isl_set *context);
7063 __isl_give isl_pw_qpolynomial_fold *
7064 isl_pw_qpolynomial_fold_gist(
7065 __isl_take isl_pw_qpolynomial_fold *pwf,
7066 __isl_take isl_set *context);
7067 __isl_give isl_pw_qpolynomial_fold *
7068 isl_pw_qpolynomial_fold_gist_params(
7069 __isl_take isl_pw_qpolynomial_fold *pwf,
7070 __isl_take isl_set *context);
7071 __isl_give isl_union_pw_qpolynomial *
7072 isl_union_pw_qpolynomial_gist_params(
7073 __isl_take isl_union_pw_qpolynomial *upwqp,
7074 __isl_take isl_set *context);
7075 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7076 __isl_take isl_union_pw_qpolynomial *upwqp,
7077 __isl_take isl_union_set *context);
7078 __isl_give isl_union_pw_qpolynomial_fold *
7079 isl_union_pw_qpolynomial_fold_gist(
7080 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7081 __isl_take isl_union_set *context);
7082 __isl_give isl_union_pw_qpolynomial_fold *
7083 isl_union_pw_qpolynomial_fold_gist_params(
7084 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7085 __isl_take isl_set *context);
7087 =item * Binary Arithmetic Operations
7089 #include <isl/set.h>
7090 __isl_give isl_set *isl_set_sum(
7091 __isl_take isl_set *set1,
7092 __isl_take isl_set *set2);
7093 #include <isl/map.h>
7094 __isl_give isl_map *isl_map_sum(
7095 __isl_take isl_map *map1,
7096 __isl_take isl_map *map2);
7098 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7099 i.e., the set containing the sums of pairs of elements from
7100 C<set1> and C<set2>.
7101 The domain of the result of C<isl_map_sum> is the intersection
7102 of the domains of its two arguments. The corresponding range
7103 elements are the sums of the corresponding range elements
7104 in the two arguments.
7106 #include <isl/val.h>
7107 __isl_give isl_multi_val *isl_multi_val_add(
7108 __isl_take isl_multi_val *mv1,
7109 __isl_take isl_multi_val *mv2);
7110 __isl_give isl_multi_val *isl_multi_val_sub(
7111 __isl_take isl_multi_val *mv1,
7112 __isl_take isl_multi_val *mv2);
7114 #include <isl/aff.h>
7115 __isl_give isl_aff *isl_aff_add(
7116 __isl_take isl_aff *aff1,
7117 __isl_take isl_aff *aff2);
7118 __isl_give isl_multi_aff *isl_multi_aff_add(
7119 __isl_take isl_multi_aff *maff1,
7120 __isl_take isl_multi_aff *maff2);
7121 __isl_give isl_pw_aff *isl_pw_aff_add(
7122 __isl_take isl_pw_aff *pwaff1,
7123 __isl_take isl_pw_aff *pwaff2);
7124 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7125 __isl_take isl_multi_pw_aff *mpa1,
7126 __isl_take isl_multi_pw_aff *mpa2);
7127 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7128 __isl_take isl_pw_multi_aff *pma1,
7129 __isl_take isl_pw_multi_aff *pma2);
7130 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7131 __isl_take isl_union_pw_aff *upa1,
7132 __isl_take isl_union_pw_aff *upa2);
7133 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7134 __isl_take isl_union_pw_multi_aff *upma1,
7135 __isl_take isl_union_pw_multi_aff *upma2);
7136 __isl_give isl_multi_union_pw_aff *
7137 isl_multi_union_pw_aff_add(
7138 __isl_take isl_multi_union_pw_aff *mupa1,
7139 __isl_take isl_multi_union_pw_aff *mupa2);
7140 __isl_give isl_pw_aff *isl_pw_aff_min(
7141 __isl_take isl_pw_aff *pwaff1,
7142 __isl_take isl_pw_aff *pwaff2);
7143 __isl_give isl_pw_aff *isl_pw_aff_max(
7144 __isl_take isl_pw_aff *pwaff1,
7145 __isl_take isl_pw_aff *pwaff2);
7146 __isl_give isl_aff *isl_aff_sub(
7147 __isl_take isl_aff *aff1,
7148 __isl_take isl_aff *aff2);
7149 __isl_give isl_multi_aff *isl_multi_aff_sub(
7150 __isl_take isl_multi_aff *ma1,
7151 __isl_take isl_multi_aff *ma2);
7152 __isl_give isl_pw_aff *isl_pw_aff_sub(
7153 __isl_take isl_pw_aff *pwaff1,
7154 __isl_take isl_pw_aff *pwaff2);
7155 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7156 __isl_take isl_multi_pw_aff *mpa1,
7157 __isl_take isl_multi_pw_aff *mpa2);
7158 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7159 __isl_take isl_pw_multi_aff *pma1,
7160 __isl_take isl_pw_multi_aff *pma2);
7161 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7162 __isl_take isl_union_pw_aff *upa1,
7163 __isl_take isl_union_pw_aff *upa2);
7164 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7165 __isl_take isl_union_pw_multi_aff *upma1,
7166 __isl_take isl_union_pw_multi_aff *upma2);
7167 __isl_give isl_multi_union_pw_aff *
7168 isl_multi_union_pw_aff_sub(
7169 __isl_take isl_multi_union_pw_aff *mupa1,
7170 __isl_take isl_multi_union_pw_aff *mupa2);
7172 C<isl_aff_sub> subtracts the second argument from the first.
7174 #include <isl/polynomial.h>
7175 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7176 __isl_take isl_qpolynomial *qp1,
7177 __isl_take isl_qpolynomial *qp2);
7178 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7179 __isl_take isl_pw_qpolynomial *pwqp1,
7180 __isl_take isl_pw_qpolynomial *pwqp2);
7181 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7182 __isl_take isl_pw_qpolynomial *pwqp1,
7183 __isl_take isl_pw_qpolynomial *pwqp2);
7184 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7185 __isl_take isl_pw_qpolynomial_fold *pwf1,
7186 __isl_take isl_pw_qpolynomial_fold *pwf2);
7187 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7188 __isl_take isl_union_pw_qpolynomial *upwqp1,
7189 __isl_take isl_union_pw_qpolynomial *upwqp2);
7190 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7191 __isl_take isl_qpolynomial *qp1,
7192 __isl_take isl_qpolynomial *qp2);
7193 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7194 __isl_take isl_pw_qpolynomial *pwqp1,
7195 __isl_take isl_pw_qpolynomial *pwqp2);
7196 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7197 __isl_take isl_union_pw_qpolynomial *upwqp1,
7198 __isl_take isl_union_pw_qpolynomial *upwqp2);
7199 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7200 __isl_take isl_pw_qpolynomial_fold *pwf1,
7201 __isl_take isl_pw_qpolynomial_fold *pwf2);
7202 __isl_give isl_union_pw_qpolynomial_fold *
7203 isl_union_pw_qpolynomial_fold_fold(
7204 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7205 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7207 #include <isl/aff.h>
7208 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7209 __isl_take isl_pw_aff *pwaff1,
7210 __isl_take isl_pw_aff *pwaff2);
7211 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7212 __isl_take isl_pw_multi_aff *pma1,
7213 __isl_take isl_pw_multi_aff *pma2);
7214 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7215 __isl_take isl_union_pw_aff *upa1,
7216 __isl_take isl_union_pw_aff *upa2);
7217 __isl_give isl_union_pw_multi_aff *
7218 isl_union_pw_multi_aff_union_add(
7219 __isl_take isl_union_pw_multi_aff *upma1,
7220 __isl_take isl_union_pw_multi_aff *upma2);
7221 __isl_give isl_multi_union_pw_aff *
7222 isl_multi_union_pw_aff_union_add(
7223 __isl_take isl_multi_union_pw_aff *mupa1,
7224 __isl_take isl_multi_union_pw_aff *mupa2);
7225 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7226 __isl_take isl_pw_aff *pwaff1,
7227 __isl_take isl_pw_aff *pwaff2);
7228 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7229 __isl_take isl_pw_aff *pwaff1,
7230 __isl_take isl_pw_aff *pwaff2);
7232 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7233 expression with a domain that is the union of those of C<pwaff1> and
7234 C<pwaff2> and such that on each cell, the quasi-affine expression is
7235 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7236 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7237 associated expression is the defined one.
7238 This in contrast to the C<isl_pw_aff_max> function, which is
7239 only defined on the shared definition domain of the arguments.
7241 #include <isl/val.h>
7242 __isl_give isl_multi_val *isl_multi_val_add_val(
7243 __isl_take isl_multi_val *mv,
7244 __isl_take isl_val *v);
7245 __isl_give isl_multi_val *isl_multi_val_mod_val(
7246 __isl_take isl_multi_val *mv,
7247 __isl_take isl_val *v);
7248 __isl_give isl_multi_val *isl_multi_val_scale_val(
7249 __isl_take isl_multi_val *mv,
7250 __isl_take isl_val *v);
7251 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7252 __isl_take isl_multi_val *mv,
7253 __isl_take isl_val *v);
7255 #include <isl/aff.h>
7256 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7257 __isl_take isl_val *mod);
7258 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7259 __isl_take isl_pw_aff *pa,
7260 __isl_take isl_val *mod);
7261 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7262 __isl_take isl_union_pw_aff *upa,
7263 __isl_take isl_val *f);
7264 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7265 __isl_take isl_val *v);
7266 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7267 __isl_take isl_multi_aff *ma,
7268 __isl_take isl_val *v);
7269 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7270 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7271 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7272 __isl_take isl_multi_pw_aff *mpa,
7273 __isl_take isl_val *v);
7274 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7275 __isl_take isl_pw_multi_aff *pma,
7276 __isl_take isl_val *v);
7277 __isl_give isl_union_pw_multi_aff *
7278 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7279 __isl_take isl_union_pw_aff *upa,
7280 __isl_take isl_val *f);
7281 isl_union_pw_multi_aff_scale_val(
7282 __isl_take isl_union_pw_multi_aff *upma,
7283 __isl_take isl_val *val);
7284 __isl_give isl_multi_union_pw_aff *
7285 isl_multi_union_pw_aff_scale_val(
7286 __isl_take isl_multi_union_pw_aff *mupa,
7287 __isl_take isl_val *v);
7288 __isl_give isl_aff *isl_aff_scale_down_ui(
7289 __isl_take isl_aff *aff, unsigned f);
7290 __isl_give isl_aff *isl_aff_scale_down_val(
7291 __isl_take isl_aff *aff, __isl_take isl_val *v);
7292 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7293 __isl_take isl_multi_aff *ma,
7294 __isl_take isl_val *v);
7295 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7296 __isl_take isl_pw_aff *pa,
7297 __isl_take isl_val *f);
7298 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7299 __isl_take isl_multi_pw_aff *mpa,
7300 __isl_take isl_val *v);
7301 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7302 __isl_take isl_pw_multi_aff *pma,
7303 __isl_take isl_val *v);
7304 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7305 __isl_take isl_union_pw_aff *upa,
7306 __isl_take isl_val *v);
7307 __isl_give isl_union_pw_multi_aff *
7308 isl_union_pw_multi_aff_scale_down_val(
7309 __isl_take isl_union_pw_multi_aff *upma,
7310 __isl_take isl_val *val);
7311 __isl_give isl_multi_union_pw_aff *
7312 isl_multi_union_pw_aff_scale_down_val(
7313 __isl_take isl_multi_union_pw_aff *mupa,
7314 __isl_take isl_val *v);
7316 #include <isl/polynomial.h>
7317 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7318 __isl_take isl_qpolynomial *qp,
7319 __isl_take isl_val *v);
7320 __isl_give isl_qpolynomial_fold *
7321 isl_qpolynomial_fold_scale_val(
7322 __isl_take isl_qpolynomial_fold *fold,
7323 __isl_take isl_val *v);
7324 __isl_give isl_pw_qpolynomial *
7325 isl_pw_qpolynomial_scale_val(
7326 __isl_take isl_pw_qpolynomial *pwqp,
7327 __isl_take isl_val *v);
7328 __isl_give isl_pw_qpolynomial_fold *
7329 isl_pw_qpolynomial_fold_scale_val(
7330 __isl_take isl_pw_qpolynomial_fold *pwf,
7331 __isl_take isl_val *v);
7332 __isl_give isl_union_pw_qpolynomial *
7333 isl_union_pw_qpolynomial_scale_val(
7334 __isl_take isl_union_pw_qpolynomial *upwqp,
7335 __isl_take isl_val *v);
7336 __isl_give isl_union_pw_qpolynomial_fold *
7337 isl_union_pw_qpolynomial_fold_scale_val(
7338 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7339 __isl_take isl_val *v);
7340 __isl_give isl_qpolynomial *
7341 isl_qpolynomial_scale_down_val(
7342 __isl_take isl_qpolynomial *qp,
7343 __isl_take isl_val *v);
7344 __isl_give isl_qpolynomial_fold *
7345 isl_qpolynomial_fold_scale_down_val(
7346 __isl_take isl_qpolynomial_fold *fold,
7347 __isl_take isl_val *v);
7348 __isl_give isl_pw_qpolynomial *
7349 isl_pw_qpolynomial_scale_down_val(
7350 __isl_take isl_pw_qpolynomial *pwqp,
7351 __isl_take isl_val *v);
7352 __isl_give isl_pw_qpolynomial_fold *
7353 isl_pw_qpolynomial_fold_scale_down_val(
7354 __isl_take isl_pw_qpolynomial_fold *pwf,
7355 __isl_take isl_val *v);
7356 __isl_give isl_union_pw_qpolynomial *
7357 isl_union_pw_qpolynomial_scale_down_val(
7358 __isl_take isl_union_pw_qpolynomial *upwqp,
7359 __isl_take isl_val *v);
7360 __isl_give isl_union_pw_qpolynomial_fold *
7361 isl_union_pw_qpolynomial_fold_scale_down_val(
7362 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7363 __isl_take isl_val *v);
7365 #include <isl/val.h>
7366 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7367 __isl_take isl_multi_val *mv1,
7368 __isl_take isl_multi_val *mv2);
7369 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7370 __isl_take isl_multi_val *mv1,
7371 __isl_take isl_multi_val *mv2);
7372 __isl_give isl_multi_val *
7373 isl_multi_val_scale_down_multi_val(
7374 __isl_take isl_multi_val *mv1,
7375 __isl_take isl_multi_val *mv2);
7377 #include <isl/aff.h>
7378 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7379 __isl_take isl_multi_aff *ma,
7380 __isl_take isl_multi_val *mv);
7381 __isl_give isl_multi_union_pw_aff *
7382 isl_multi_union_pw_aff_mod_multi_val(
7383 __isl_take isl_multi_union_pw_aff *upma,
7384 __isl_take isl_multi_val *mv);
7385 __isl_give isl_multi_pw_aff *
7386 isl_multi_pw_aff_mod_multi_val(
7387 __isl_take isl_multi_pw_aff *mpa,
7388 __isl_take isl_multi_val *mv);
7389 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7390 __isl_take isl_multi_aff *ma,
7391 __isl_take isl_multi_val *mv);
7392 __isl_give isl_pw_multi_aff *
7393 isl_pw_multi_aff_scale_multi_val(
7394 __isl_take isl_pw_multi_aff *pma,
7395 __isl_take isl_multi_val *mv);
7396 __isl_give isl_multi_pw_aff *
7397 isl_multi_pw_aff_scale_multi_val(
7398 __isl_take isl_multi_pw_aff *mpa,
7399 __isl_take isl_multi_val *mv);
7400 __isl_give isl_multi_union_pw_aff *
7401 isl_multi_union_pw_aff_scale_multi_val(
7402 __isl_take isl_multi_union_pw_aff *mupa,
7403 __isl_take isl_multi_val *mv);
7404 __isl_give isl_union_pw_multi_aff *
7405 isl_union_pw_multi_aff_scale_multi_val(
7406 __isl_take isl_union_pw_multi_aff *upma,
7407 __isl_take isl_multi_val *mv);
7408 __isl_give isl_multi_aff *
7409 isl_multi_aff_scale_down_multi_val(
7410 __isl_take isl_multi_aff *ma,
7411 __isl_take isl_multi_val *mv);
7412 __isl_give isl_multi_pw_aff *
7413 isl_multi_pw_aff_scale_down_multi_val(
7414 __isl_take isl_multi_pw_aff *mpa,
7415 __isl_take isl_multi_val *mv);
7416 __isl_give isl_multi_union_pw_aff *
7417 isl_multi_union_pw_aff_scale_down_multi_val(
7418 __isl_take isl_multi_union_pw_aff *mupa,
7419 __isl_take isl_multi_val *mv);
7421 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7422 by the corresponding elements of C<mv>.
7424 #include <isl/aff.h>
7425 __isl_give isl_aff *isl_aff_mul(
7426 __isl_take isl_aff *aff1,
7427 __isl_take isl_aff *aff2);
7428 __isl_give isl_aff *isl_aff_div(
7429 __isl_take isl_aff *aff1,
7430 __isl_take isl_aff *aff2);
7431 __isl_give isl_pw_aff *isl_pw_aff_mul(
7432 __isl_take isl_pw_aff *pwaff1,
7433 __isl_take isl_pw_aff *pwaff2);
7434 __isl_give isl_pw_aff *isl_pw_aff_div(
7435 __isl_take isl_pw_aff *pa1,
7436 __isl_take isl_pw_aff *pa2);
7437 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7438 __isl_take isl_pw_aff *pa1,
7439 __isl_take isl_pw_aff *pa2);
7440 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7441 __isl_take isl_pw_aff *pa1,
7442 __isl_take isl_pw_aff *pa2);
7444 When multiplying two affine expressions, at least one of the two needs
7445 to be a constant. Similarly, when dividing an affine expression by another,
7446 the second expression needs to be a constant.
7447 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7448 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7451 #include <isl/polynomial.h>
7452 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7453 __isl_take isl_qpolynomial *qp1,
7454 __isl_take isl_qpolynomial *qp2);
7455 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7456 __isl_take isl_pw_qpolynomial *pwqp1,
7457 __isl_take isl_pw_qpolynomial *pwqp2);
7458 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7459 __isl_take isl_union_pw_qpolynomial *upwqp1,
7460 __isl_take isl_union_pw_qpolynomial *upwqp2);
7464 =head3 Lexicographic Optimization
7466 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7467 the following functions
7468 compute a set that contains the lexicographic minimum or maximum
7469 of the elements in C<set> (or C<bset>) for those values of the parameters
7470 that satisfy C<dom>.
7471 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7472 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7474 In other words, the union of the parameter values
7475 for which the result is non-empty and of C<*empty>
7478 #include <isl/set.h>
7479 __isl_give isl_set *isl_basic_set_partial_lexmin(
7480 __isl_take isl_basic_set *bset,
7481 __isl_take isl_basic_set *dom,
7482 __isl_give isl_set **empty);
7483 __isl_give isl_set *isl_basic_set_partial_lexmax(
7484 __isl_take isl_basic_set *bset,
7485 __isl_take isl_basic_set *dom,
7486 __isl_give isl_set **empty);
7487 __isl_give isl_set *isl_set_partial_lexmin(
7488 __isl_take isl_set *set, __isl_take isl_set *dom,
7489 __isl_give isl_set **empty);
7490 __isl_give isl_set *isl_set_partial_lexmax(
7491 __isl_take isl_set *set, __isl_take isl_set *dom,
7492 __isl_give isl_set **empty);
7494 Given a (basic) set C<set> (or C<bset>), the following functions simply
7495 return a set containing the lexicographic minimum or maximum
7496 of the elements in C<set> (or C<bset>).
7497 In case of union sets, the optimum is computed per space.
7499 #include <isl/set.h>
7500 __isl_give isl_set *isl_basic_set_lexmin(
7501 __isl_take isl_basic_set *bset);
7502 __isl_give isl_set *isl_basic_set_lexmax(
7503 __isl_take isl_basic_set *bset);
7504 __isl_give isl_set *isl_set_lexmin(
7505 __isl_take isl_set *set);
7506 __isl_give isl_set *isl_set_lexmax(
7507 __isl_take isl_set *set);
7508 __isl_give isl_union_set *isl_union_set_lexmin(
7509 __isl_take isl_union_set *uset);
7510 __isl_give isl_union_set *isl_union_set_lexmax(
7511 __isl_take isl_union_set *uset);
7513 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7514 the following functions
7515 compute a relation that maps each element of C<dom>
7516 to the single lexicographic minimum or maximum
7517 of the elements that are associated to that same
7518 element in C<map> (or C<bmap>).
7519 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7520 that contains the elements in C<dom> that do not map
7521 to any elements in C<map> (or C<bmap>).
7522 In other words, the union of the domain of the result and of C<*empty>
7525 #include <isl/map.h>
7526 __isl_give isl_map *isl_basic_map_partial_lexmax(
7527 __isl_take isl_basic_map *bmap,
7528 __isl_take isl_basic_set *dom,
7529 __isl_give isl_set **empty);
7530 __isl_give isl_map *isl_basic_map_partial_lexmin(
7531 __isl_take isl_basic_map *bmap,
7532 __isl_take isl_basic_set *dom,
7533 __isl_give isl_set **empty);
7534 __isl_give isl_map *isl_map_partial_lexmax(
7535 __isl_take isl_map *map, __isl_take isl_set *dom,
7536 __isl_give isl_set **empty);
7537 __isl_give isl_map *isl_map_partial_lexmin(
7538 __isl_take isl_map *map, __isl_take isl_set *dom,
7539 __isl_give isl_set **empty);
7541 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7542 return a map mapping each element in the domain of
7543 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7544 of all elements associated to that element.
7545 In case of union relations, the optimum is computed per space.
7547 #include <isl/map.h>
7548 __isl_give isl_map *isl_basic_map_lexmin(
7549 __isl_take isl_basic_map *bmap);
7550 __isl_give isl_map *isl_basic_map_lexmax(
7551 __isl_take isl_basic_map *bmap);
7552 __isl_give isl_map *isl_map_lexmin(
7553 __isl_take isl_map *map);
7554 __isl_give isl_map *isl_map_lexmax(
7555 __isl_take isl_map *map);
7556 __isl_give isl_union_map *isl_union_map_lexmin(
7557 __isl_take isl_union_map *umap);
7558 __isl_give isl_union_map *isl_union_map_lexmax(
7559 __isl_take isl_union_map *umap);
7561 The following functions return their result in the form of
7562 a piecewise multi-affine expression,
7563 but are otherwise equivalent to the corresponding functions
7564 returning a basic set or relation.
7566 #include <isl/set.h>
7567 __isl_give isl_pw_multi_aff *
7568 isl_basic_set_partial_lexmin_pw_multi_aff(
7569 __isl_take isl_basic_set *bset,
7570 __isl_take isl_basic_set *dom,
7571 __isl_give isl_set **empty);
7572 __isl_give isl_pw_multi_aff *
7573 isl_basic_set_partial_lexmax_pw_multi_aff(
7574 __isl_take isl_basic_set *bset,
7575 __isl_take isl_basic_set *dom,
7576 __isl_give isl_set **empty);
7577 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7578 __isl_take isl_set *set);
7579 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7580 __isl_take isl_set *set);
7582 #include <isl/map.h>
7583 __isl_give isl_pw_multi_aff *
7584 isl_basic_map_lexmin_pw_multi_aff(
7585 __isl_take isl_basic_map *bmap);
7586 __isl_give isl_pw_multi_aff *
7587 isl_basic_map_partial_lexmin_pw_multi_aff(
7588 __isl_take isl_basic_map *bmap,
7589 __isl_take isl_basic_set *dom,
7590 __isl_give isl_set **empty);
7591 __isl_give isl_pw_multi_aff *
7592 isl_basic_map_partial_lexmax_pw_multi_aff(
7593 __isl_take isl_basic_map *bmap,
7594 __isl_take isl_basic_set *dom,
7595 __isl_give isl_set **empty);
7596 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7597 __isl_take isl_map *map);
7598 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7599 __isl_take isl_map *map);
7601 The following functions return the lexicographic minimum or maximum
7602 on the shared domain of the inputs and the single defined function
7603 on those parts of the domain where only a single function is defined.
7605 #include <isl/aff.h>
7606 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7607 __isl_take isl_pw_multi_aff *pma1,
7608 __isl_take isl_pw_multi_aff *pma2);
7609 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7610 __isl_take isl_pw_multi_aff *pma1,
7611 __isl_take isl_pw_multi_aff *pma2);
7613 If the input to a lexicographic optimization problem has
7614 multiple constraints with the same coefficients for the optimized
7615 variables, then, by default, this symmetry is exploited by
7616 replacing those constraints by a single constraint with
7617 an abstract bound, which is in turn bounded by the corresponding terms
7618 in the original constraints.
7619 Without this optimization, the solver would typically consider
7620 all possible orderings of those original bounds, resulting in a needless
7621 decomposition of the domain.
7622 However, the optimization can also result in slowdowns since
7623 an extra parameter is introduced that may get used in additional
7625 The following option determines whether symmetry detection is applied
7626 during lexicographic optimization.
7628 #include <isl/options.h>
7629 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7631 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7635 See also \autoref{s:offline}.
7639 =head2 Ternary Operations
7641 #include <isl/aff.h>
7642 __isl_give isl_pw_aff *isl_pw_aff_cond(
7643 __isl_take isl_pw_aff *cond,
7644 __isl_take isl_pw_aff *pwaff_true,
7645 __isl_take isl_pw_aff *pwaff_false);
7647 The function C<isl_pw_aff_cond> performs a conditional operator
7648 and returns an expression that is equal to C<pwaff_true>
7649 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7650 where C<cond> is zero.
7654 Lists are defined over several element types, including
7655 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7656 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7657 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7658 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7659 Here we take lists of C<isl_set>s as an example.
7660 Lists can be created, copied, modified and freed using the following functions.
7662 #include <isl/set.h>
7663 __isl_give isl_set_list *isl_set_list_from_set(
7664 __isl_take isl_set *el);
7665 __isl_give isl_set_list *isl_set_list_alloc(
7666 isl_ctx *ctx, int n);
7667 __isl_give isl_set_list *isl_set_list_copy(
7668 __isl_keep isl_set_list *list);
7669 __isl_give isl_set_list *isl_set_list_insert(
7670 __isl_take isl_set_list *list, unsigned pos,
7671 __isl_take isl_set *el);
7672 __isl_give isl_set_list *isl_set_list_add(
7673 __isl_take isl_set_list *list,
7674 __isl_take isl_set *el);
7675 __isl_give isl_set_list *isl_set_list_drop(
7676 __isl_take isl_set_list *list,
7677 unsigned first, unsigned n);
7678 __isl_give isl_set_list *isl_set_list_set_set(
7679 __isl_take isl_set_list *list, int index,
7680 __isl_take isl_set *set);
7681 __isl_give isl_set_list *isl_set_list_concat(
7682 __isl_take isl_set_list *list1,
7683 __isl_take isl_set_list *list2);
7684 __isl_give isl_set_list *isl_set_list_map(
7685 __isl_take isl_set_list *list,
7686 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7689 __isl_give isl_set_list *isl_set_list_sort(
7690 __isl_take isl_set_list *list,
7691 int (*cmp)(__isl_keep isl_set *a,
7692 __isl_keep isl_set *b, void *user),
7694 __isl_null isl_set_list *isl_set_list_free(
7695 __isl_take isl_set_list *list);
7697 C<isl_set_list_alloc> creates an empty list with an initial capacity
7698 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7699 add elements to a list, increasing its capacity as needed.
7700 C<isl_set_list_from_set> creates a list with a single element.
7702 Lists can be inspected using the following functions.
7704 #include <isl/set.h>
7705 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7706 __isl_give isl_set *isl_set_list_get_set(
7707 __isl_keep isl_set_list *list, int index);
7708 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7709 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7711 isl_stat isl_set_list_foreach_scc(
7712 __isl_keep isl_set_list *list,
7713 isl_bool (*follows)(__isl_keep isl_set *a,
7714 __isl_keep isl_set *b, void *user),
7716 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7719 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7720 strongly connected components of the graph with as vertices the elements
7721 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7722 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7723 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7725 Lists can be printed using
7727 #include <isl/set.h>
7728 __isl_give isl_printer *isl_printer_print_set_list(
7729 __isl_take isl_printer *p,
7730 __isl_keep isl_set_list *list);
7732 =head2 Associative arrays
7734 Associative arrays map isl objects of a specific type to isl objects
7735 of some (other) specific type. They are defined for several pairs
7736 of types, including (C<isl_map>, C<isl_basic_set>),
7737 (C<isl_id>, C<isl_ast_expr>),
7738 (C<isl_id>, C<isl_id>) and
7739 (C<isl_id>, C<isl_pw_aff>).
7740 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7743 Associative arrays can be created, copied and freed using
7744 the following functions.
7746 #include <isl/id_to_ast_expr.h>
7747 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7748 isl_ctx *ctx, int min_size);
7749 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7750 __isl_keep isl_id_to_ast_expr *id2expr);
7751 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7752 __isl_take isl_id_to_ast_expr *id2expr);
7754 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7755 to specify the expected size of the associative array.
7756 The associative array will be grown automatically as needed.
7758 Associative arrays can be inspected using the following functions.
7760 #include <isl/id_to_ast_expr.h>
7761 __isl_give isl_maybe_isl_ast_expr
7762 isl_id_to_ast_expr_try_get(
7763 __isl_keep isl_id_to_ast_expr *id2expr,
7764 __isl_keep isl_id *key);
7765 isl_bool isl_id_to_ast_expr_has(
7766 __isl_keep isl_id_to_ast_expr *id2expr,
7767 __isl_keep isl_id *key);
7768 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7769 __isl_keep isl_id_to_ast_expr *id2expr,
7770 __isl_take isl_id *key);
7771 isl_stat isl_id_to_ast_expr_foreach(
7772 __isl_keep isl_id_to_ast_expr *id2expr,
7773 isl_stat (*fn)(__isl_take isl_id *key,
7774 __isl_take isl_ast_expr *val, void *user),
7777 The function C<isl_id_to_ast_expr_try_get> returns a structure
7778 containing two elements, C<valid> and C<value>.
7779 If there is a value associated to the key, then C<valid>
7780 is set to C<isl_bool_true> and C<value> contains a copy of
7781 the associated value. Otherwise C<value> is C<NULL> and
7782 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7783 on whether some error has occurred or there simply is no associated value.
7784 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7785 in the structure and
7786 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7788 Associative arrays can be modified using the following functions.
7790 #include <isl/id_to_ast_expr.h>
7791 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7792 __isl_take isl_id_to_ast_expr *id2expr,
7793 __isl_take isl_id *key,
7794 __isl_take isl_ast_expr *val);
7795 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7796 __isl_take isl_id_to_ast_expr *id2expr,
7797 __isl_take isl_id *key);
7799 Associative arrays can be printed using the following function.
7801 #include <isl/id_to_ast_expr.h>
7802 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7803 __isl_take isl_printer *p,
7804 __isl_keep isl_id_to_ast_expr *id2expr);
7808 Vectors can be created, copied and freed using the following functions.
7810 #include <isl/vec.h>
7811 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7813 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
7815 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7816 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7818 Note that the elements of a vector created by C<isl_vec_alloc>
7819 may have arbitrary values.
7820 A vector created by C<isl_vec_zero> has elements with value zero.
7821 The elements can be changed and inspected using the following functions.
7823 int isl_vec_size(__isl_keep isl_vec *vec);
7824 __isl_give isl_val *isl_vec_get_element_val(
7825 __isl_keep isl_vec *vec, int pos);
7826 __isl_give isl_vec *isl_vec_set_element_si(
7827 __isl_take isl_vec *vec, int pos, int v);
7828 __isl_give isl_vec *isl_vec_set_element_val(
7829 __isl_take isl_vec *vec, int pos,
7830 __isl_take isl_val *v);
7831 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7833 __isl_give isl_vec *isl_vec_set_val(
7834 __isl_take isl_vec *vec, __isl_take isl_val *v);
7835 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7836 __isl_keep isl_vec *vec2, int pos);
7838 C<isl_vec_get_element> will return a negative value if anything went wrong.
7839 In that case, the value of C<*v> is undefined.
7841 The following function can be used to concatenate two vectors.
7843 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7844 __isl_take isl_vec *vec2);
7848 Matrices can be created, copied and freed using the following functions.
7850 #include <isl/mat.h>
7851 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7852 unsigned n_row, unsigned n_col);
7853 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7854 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7856 Note that the elements of a newly created matrix may have arbitrary values.
7857 The elements can be changed and inspected using the following functions.
7859 int isl_mat_rows(__isl_keep isl_mat *mat);
7860 int isl_mat_cols(__isl_keep isl_mat *mat);
7861 __isl_give isl_val *isl_mat_get_element_val(
7862 __isl_keep isl_mat *mat, int row, int col);
7863 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7864 int row, int col, int v);
7865 __isl_give isl_mat *isl_mat_set_element_val(
7866 __isl_take isl_mat *mat, int row, int col,
7867 __isl_take isl_val *v);
7869 The following function computes the rank of a matrix.
7870 The return value may be -1 if some error occurred.
7872 #include <isl/mat.h>
7873 int isl_mat_rank(__isl_keep isl_mat *mat);
7875 The following function can be used to compute the (right) inverse
7876 of a matrix, i.e., a matrix such that the product of the original
7877 and the inverse (in that order) is a multiple of the identity matrix.
7878 The input matrix is assumed to be of full row-rank.
7880 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7882 The following function can be used to compute the (right) kernel
7883 (or null space) of a matrix, i.e., a matrix such that the product of
7884 the original and the kernel (in that order) is the zero matrix.
7886 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7888 The following function computes a basis for the space spanned
7889 by the rows of a matrix.
7891 __isl_give isl_mat *isl_mat_row_basis(
7892 __isl_take isl_mat *mat);
7894 The following function computes rows that extend a basis of C<mat1>
7895 to a basis that also covers C<mat2>.
7897 __isl_give isl_mat *isl_mat_row_basis_extension(
7898 __isl_take isl_mat *mat1,
7899 __isl_take isl_mat *mat2);
7901 The following function checks whether there is no linear dependence
7902 among the combined rows of "mat1" and "mat2" that is not already present
7903 in "mat1" or "mat2" individually.
7904 If "mat1" and "mat2" have linearly independent rows by themselves,
7905 then this means that there is no linear dependence among all rows together.
7907 isl_bool isl_mat_has_linearly_independent_rows(
7908 __isl_keep isl_mat *mat1,
7909 __isl_keep isl_mat *mat2);
7911 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7913 The following functions determine
7914 an upper or lower bound on a quasipolynomial over its domain.
7916 __isl_give isl_pw_qpolynomial_fold *
7917 isl_pw_qpolynomial_bound(
7918 __isl_take isl_pw_qpolynomial *pwqp,
7919 enum isl_fold type, int *tight);
7921 __isl_give isl_union_pw_qpolynomial_fold *
7922 isl_union_pw_qpolynomial_bound(
7923 __isl_take isl_union_pw_qpolynomial *upwqp,
7924 enum isl_fold type, int *tight);
7926 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7927 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7928 is the returned bound is known be tight, i.e., for each value
7929 of the parameters there is at least
7930 one element in the domain that reaches the bound.
7931 If the domain of C<pwqp> is not wrapping, then the bound is computed
7932 over all elements in that domain and the result has a purely parametric
7933 domain. If the domain of C<pwqp> is wrapping, then the bound is
7934 computed over the range of the wrapped relation. The domain of the
7935 wrapped relation becomes the domain of the result.
7937 =head2 Parametric Vertex Enumeration
7939 The parametric vertex enumeration described in this section
7940 is mainly intended to be used internally and by the C<barvinok>
7943 #include <isl/vertices.h>
7944 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7945 __isl_keep isl_basic_set *bset);
7947 The function C<isl_basic_set_compute_vertices> performs the
7948 actual computation of the parametric vertices and the chamber
7949 decomposition and stores the result in an C<isl_vertices> object.
7950 This information can be queried by either iterating over all
7951 the vertices or iterating over all the chambers or cells
7952 and then iterating over all vertices that are active on the chamber.
7954 isl_stat isl_vertices_foreach_vertex(
7955 __isl_keep isl_vertices *vertices,
7956 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7957 void *user), void *user);
7959 isl_stat isl_vertices_foreach_cell(
7960 __isl_keep isl_vertices *vertices,
7961 isl_stat (*fn)(__isl_take isl_cell *cell,
7962 void *user), void *user);
7963 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7964 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7965 void *user), void *user);
7967 Other operations that can be performed on an C<isl_vertices> object are
7970 int isl_vertices_get_n_vertices(
7971 __isl_keep isl_vertices *vertices);
7972 __isl_null isl_vertices *isl_vertices_free(
7973 __isl_take isl_vertices *vertices);
7975 Vertices can be inspected and destroyed using the following functions.
7977 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7978 __isl_give isl_basic_set *isl_vertex_get_domain(
7979 __isl_keep isl_vertex *vertex);
7980 __isl_give isl_multi_aff *isl_vertex_get_expr(
7981 __isl_keep isl_vertex *vertex);
7982 void isl_vertex_free(__isl_take isl_vertex *vertex);
7984 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7985 describing the vertex in terms of the parameters,
7986 while C<isl_vertex_get_domain> returns the activity domain
7989 Chambers can be inspected and destroyed using the following functions.
7991 __isl_give isl_basic_set *isl_cell_get_domain(
7992 __isl_keep isl_cell *cell);
7993 void isl_cell_free(__isl_take isl_cell *cell);
7995 =head1 Polyhedral Compilation Library
7997 This section collects functionality in C<isl> that has been specifically
7998 designed for use during polyhedral compilation.
8000 =head2 Schedule Trees
8002 A schedule tree is a structured representation of a schedule,
8003 assigning a relative order to a set of domain elements.
8004 The relative order expressed by the schedule tree is
8005 defined recursively. In particular, the order between
8006 two domain elements is determined by the node that is closest
8007 to the root that refers to both elements and that orders them apart.
8008 Each node in the tree is of one of several types.
8009 The root node is always of type C<isl_schedule_node_domain>
8010 (or C<isl_schedule_node_extension>)
8011 and it describes the (extra) domain elements to which the schedule applies.
8012 The other types of nodes are as follows.
8016 =item C<isl_schedule_node_band>
8018 A band of schedule dimensions. Each schedule dimension is represented
8019 by a union piecewise quasi-affine expression. If this expression
8020 assigns a different value to two domain elements, while all previous
8021 schedule dimensions in the same band assign them the same value,
8022 then the two domain elements are ordered according to these two
8024 Each expression is required to be total in the domain elements
8025 that reach the band node.
8027 =item C<isl_schedule_node_expansion>
8029 An expansion node maps each of the domain elements that reach the node
8030 to one or more domain elements. The image of this mapping forms
8031 the set of domain elements that reach the child of the expansion node.
8032 The function that maps each of the expanded domain elements
8033 to the original domain element from which it was expanded
8034 is called the contraction.
8036 =item C<isl_schedule_node_filter>
8038 A filter node does not impose any ordering, but rather intersects
8039 the set of domain elements that the current subtree refers to
8040 with a given union set. The subtree of the filter node only
8041 refers to domain elements in the intersection.
8042 A filter node is typically only used as a child of a sequence or
8045 =item C<isl_schedule_node_leaf>
8047 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
8049 =item C<isl_schedule_node_mark>
8051 A mark node can be used to attach any kind of information to a subtree
8052 of the schedule tree.
8054 =item C<isl_schedule_node_sequence>
8056 A sequence node has one or more children, each of which is a filter node.
8057 The filters on these filter nodes form a partition of
8058 the domain elements that the current subtree refers to.
8059 If two domain elements appear in distinct filters then the sequence
8060 node orders them according to the child positions of the corresponding
8063 =item C<isl_schedule_node_set>
8065 A set node is similar to a sequence node, except that
8066 it expresses that domain elements appearing in distinct filters
8067 may have any order. The order of the children of a set node
8068 is therefore also immaterial.
8072 The following node types are only supported by the AST generator.
8076 =item C<isl_schedule_node_context>
8078 The context describes constraints on the parameters and
8079 the schedule dimensions of outer
8080 bands that the AST generator may assume to hold. It is also the only
8081 kind of node that may introduce additional parameters.
8082 The space of the context is that of the flat product of the outer
8083 band nodes. In particular, if there are no outer band nodes, then
8084 this space is the unnamed zero-dimensional space.
8085 Since a context node references the outer band nodes, any tree
8086 containing a context node is considered to be anchored.
8088 =item C<isl_schedule_node_extension>
8090 An extension node instructs the AST generator to add additional
8091 domain elements that need to be scheduled.
8092 The additional domain elements are described by the range of
8093 the extension map in terms of the outer schedule dimensions,
8094 i.e., the flat product of the outer band nodes.
8095 Note that domain elements are added whenever the AST generator
8096 reaches the extension node, meaning that there are still some
8097 active domain elements for which an AST needs to be generated.
8098 The conditions under which some domain elements are still active
8099 may however not be completely described by the outer AST nodes
8100 generated at that point.
8101 Since an extension node references the outer band nodes, any tree
8102 containing an extension node is considered to be anchored.
8104 An extension node may also appear as the root of a schedule tree,
8105 when it is intended to be inserted into another tree
8106 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8107 In this case, the domain of the extension node should
8108 correspond to the flat product of the outer band nodes
8109 in this other schedule tree at the point where the extension tree
8112 =item C<isl_schedule_node_guard>
8114 The guard describes constraints on the parameters and
8115 the schedule dimensions of outer
8116 bands that need to be enforced by the outer nodes
8117 in the generated AST.
8118 That is, the part of the AST that is generated from descendants
8119 of the guard node can assume that these constraints are satisfied.
8120 The space of the guard is that of the flat product of the outer
8121 band nodes. In particular, if there are no outer band nodes, then
8122 this space is the unnamed zero-dimensional space.
8123 Since a guard node references the outer band nodes, any tree
8124 containing a guard node is considered to be anchored.
8128 Except for the C<isl_schedule_node_context> nodes,
8129 none of the nodes may introduce any parameters that were not
8130 already present in the root domain node.
8132 A schedule tree is encapsulated in an C<isl_schedule> object.
8133 The simplest such objects, those with a tree consisting of single domain node,
8134 can be created using the following functions with either an empty
8135 domain or a given domain.
8137 #include <isl/schedule.h>
8138 __isl_give isl_schedule *isl_schedule_empty(
8139 __isl_take isl_space *space);
8140 __isl_give isl_schedule *isl_schedule_from_domain(
8141 __isl_take isl_union_set *domain);
8143 The function C<isl_schedule_constraints_compute_schedule> described
8144 in L</"Scheduling"> can also be used to construct schedules.
8146 C<isl_schedule> objects may be copied and freed using the following functions.
8148 #include <isl/schedule.h>
8149 __isl_give isl_schedule *isl_schedule_copy(
8150 __isl_keep isl_schedule *sched);
8151 __isl_null isl_schedule *isl_schedule_free(
8152 __isl_take isl_schedule *sched);
8154 The following functions checks whether two C<isl_schedule> objects
8155 are obviously the same.
8157 #include <isl/schedule.h>
8158 isl_bool isl_schedule_plain_is_equal(
8159 __isl_keep isl_schedule *schedule1,
8160 __isl_keep isl_schedule *schedule2);
8162 The domain of the schedule, i.e., the domain described by the root node,
8163 can be obtained using the following function.
8165 #include <isl/schedule.h>
8166 __isl_give isl_union_set *isl_schedule_get_domain(
8167 __isl_keep isl_schedule *schedule);
8169 An extra top-level band node (right underneath the domain node) can
8170 be introduced into the schedule using the following function.
8171 The schedule tree is assumed not to have any anchored nodes.
8173 #include <isl/schedule.h>
8174 __isl_give isl_schedule *
8175 isl_schedule_insert_partial_schedule(
8176 __isl_take isl_schedule *schedule,
8177 __isl_take isl_multi_union_pw_aff *partial);
8179 A top-level context node (right underneath the domain node) can
8180 be introduced into the schedule using the following function.
8182 #include <isl/schedule.h>
8183 __isl_give isl_schedule *isl_schedule_insert_context(
8184 __isl_take isl_schedule *schedule,
8185 __isl_take isl_set *context)
8187 A top-level guard node (right underneath the domain node) can
8188 be introduced into the schedule using the following function.
8190 #include <isl/schedule.h>
8191 __isl_give isl_schedule *isl_schedule_insert_guard(
8192 __isl_take isl_schedule *schedule,
8193 __isl_take isl_set *guard)
8195 A schedule that combines two schedules either in the given
8196 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8197 or an C<isl_schedule_node_set> node,
8198 can be created using the following functions.
8200 #include <isl/schedule.h>
8201 __isl_give isl_schedule *isl_schedule_sequence(
8202 __isl_take isl_schedule *schedule1,
8203 __isl_take isl_schedule *schedule2);
8204 __isl_give isl_schedule *isl_schedule_set(
8205 __isl_take isl_schedule *schedule1,
8206 __isl_take isl_schedule *schedule2);
8208 The domains of the two input schedules need to be disjoint.
8210 The following function can be used to restrict the domain
8211 of a schedule with a domain node as root to be a subset of the given union set.
8212 This operation may remove nodes in the tree that have become
8215 #include <isl/schedule.h>
8216 __isl_give isl_schedule *isl_schedule_intersect_domain(
8217 __isl_take isl_schedule *schedule,
8218 __isl_take isl_union_set *domain);
8220 The following function can be used to simplify the domain
8221 of a schedule with a domain node as root with respect to the given
8224 #include <isl/schedule.h>
8225 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8226 __isl_take isl_schedule *schedule,
8227 __isl_take isl_set *context);
8229 The following function resets the user pointers on all parameter
8230 and tuple identifiers referenced by the nodes of the given schedule.
8232 #include <isl/schedule.h>
8233 __isl_give isl_schedule *isl_schedule_reset_user(
8234 __isl_take isl_schedule *schedule);
8236 The following function aligns the parameters of all nodes
8237 in the given schedule to the given space.
8239 #include <isl/schedule.h>
8240 __isl_give isl_schedule *isl_schedule_align_params(
8241 __isl_take isl_schedule *schedule,
8242 __isl_take isl_space *space);
8244 The following function allows the user to plug in a given function
8245 in the iteration domains. The input schedule is not allowed to contain
8246 any expansion nodes.
8248 #include <isl/schedule.h>
8249 __isl_give isl_schedule *
8250 isl_schedule_pullback_union_pw_multi_aff(
8251 __isl_take isl_schedule *schedule,
8252 __isl_take isl_union_pw_multi_aff *upma);
8254 The following function can be used to plug in the schedule C<expansion>
8255 in the leaves of C<schedule>, where C<contraction> describes how
8256 the domain elements of C<expansion> map to the domain elements
8257 at the original leaves of C<schedule>.
8258 The resulting schedule will contain expansion nodes, unless
8259 C<contraction> is an identity function.
8261 #include <isl/schedule.h>
8262 __isl_give isl_schedule *isl_schedule_expand(
8263 __isl_take isl_schedule *schedule,
8264 __isl_take isl_union_pw_multi_aff *contraction,
8265 __isl_take isl_schedule *expansion);
8267 An C<isl_union_map> representation of the schedule can be obtained
8268 from an C<isl_schedule> using the following function.
8270 #include <isl/schedule.h>
8271 __isl_give isl_union_map *isl_schedule_get_map(
8272 __isl_keep isl_schedule *sched);
8274 The resulting relation encodes the same relative ordering as
8275 the schedule by mapping the domain elements to a common schedule space.
8276 If the schedule_separate_components option is set, then the order
8277 of the children of a set node is explicitly encoded in the result.
8278 If the tree contains any expansion nodes, then the relation
8279 is formulated in terms of the expanded domain elements.
8281 Schedules can be read from input using the following functions.
8283 #include <isl/schedule.h>
8284 __isl_give isl_schedule *isl_schedule_read_from_file(
8285 isl_ctx *ctx, FILE *input);
8286 __isl_give isl_schedule *isl_schedule_read_from_str(
8287 isl_ctx *ctx, const char *str);
8289 A representation of the schedule can be printed using
8291 #include <isl/schedule.h>
8292 __isl_give isl_printer *isl_printer_print_schedule(
8293 __isl_take isl_printer *p,
8294 __isl_keep isl_schedule *schedule);
8295 __isl_give char *isl_schedule_to_str(
8296 __isl_keep isl_schedule *schedule);
8298 C<isl_schedule_to_str> prints the schedule in flow format.
8300 The schedule tree can be traversed through the use of
8301 C<isl_schedule_node> objects that point to a particular
8302 position in the schedule tree. Whenever a C<isl_schedule_node>
8303 is used to modify a node in the schedule tree, the original schedule
8304 tree is left untouched and the modifications are performed to a copy
8305 of the tree. The returned C<isl_schedule_node> then points to
8306 this modified copy of the tree.
8308 The root of the schedule tree can be obtained using the following function.
8310 #include <isl/schedule.h>
8311 __isl_give isl_schedule_node *isl_schedule_get_root(
8312 __isl_keep isl_schedule *schedule);
8314 A pointer to a newly created schedule tree with a single domain
8315 node can be created using the following functions.
8317 #include <isl/schedule_node.h>
8318 __isl_give isl_schedule_node *
8319 isl_schedule_node_from_domain(
8320 __isl_take isl_union_set *domain);
8321 __isl_give isl_schedule_node *
8322 isl_schedule_node_from_extension(
8323 __isl_take isl_union_map *extension);
8325 C<isl_schedule_node_from_extension> creates a tree with an extension
8328 Schedule nodes can be copied and freed using the following functions.
8330 #include <isl/schedule_node.h>
8331 __isl_give isl_schedule_node *isl_schedule_node_copy(
8332 __isl_keep isl_schedule_node *node);
8333 __isl_null isl_schedule_node *isl_schedule_node_free(
8334 __isl_take isl_schedule_node *node);
8336 The following functions can be used to check if two schedule
8337 nodes point to the same position in the same schedule.
8339 #include <isl/schedule_node.h>
8340 isl_bool isl_schedule_node_is_equal(
8341 __isl_keep isl_schedule_node *node1,
8342 __isl_keep isl_schedule_node *node2);
8344 The following properties can be obtained from a schedule node.
8346 #include <isl/schedule_node.h>
8347 enum isl_schedule_node_type isl_schedule_node_get_type(
8348 __isl_keep isl_schedule_node *node);
8349 enum isl_schedule_node_type
8350 isl_schedule_node_get_parent_type(
8351 __isl_keep isl_schedule_node *node);
8352 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8353 __isl_keep isl_schedule_node *node);
8355 The function C<isl_schedule_node_get_type> returns the type of
8356 the node, while C<isl_schedule_node_get_parent_type> returns
8357 type of the parent of the node, which is required to exist.
8358 The function C<isl_schedule_node_get_schedule> returns a copy
8359 to the schedule to which the node belongs.
8361 The following functions can be used to move the schedule node
8362 to a different position in the tree or to check if such a position
8365 #include <isl/schedule_node.h>
8366 isl_bool isl_schedule_node_has_parent(
8367 __isl_keep isl_schedule_node *node);
8368 __isl_give isl_schedule_node *isl_schedule_node_parent(
8369 __isl_take isl_schedule_node *node);
8370 __isl_give isl_schedule_node *isl_schedule_node_root(
8371 __isl_take isl_schedule_node *node);
8372 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8373 __isl_take isl_schedule_node *node,
8375 int isl_schedule_node_n_children(
8376 __isl_keep isl_schedule_node *node);
8377 __isl_give isl_schedule_node *isl_schedule_node_child(
8378 __isl_take isl_schedule_node *node, int pos);
8379 isl_bool isl_schedule_node_has_children(
8380 __isl_keep isl_schedule_node *node);
8381 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8382 __isl_take isl_schedule_node *node);
8383 isl_bool isl_schedule_node_has_previous_sibling(
8384 __isl_keep isl_schedule_node *node);
8385 __isl_give isl_schedule_node *
8386 isl_schedule_node_previous_sibling(
8387 __isl_take isl_schedule_node *node);
8388 isl_bool isl_schedule_node_has_next_sibling(
8389 __isl_keep isl_schedule_node *node);
8390 __isl_give isl_schedule_node *
8391 isl_schedule_node_next_sibling(
8392 __isl_take isl_schedule_node *node);
8394 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8395 is the node itself, the ancestor of generation 1 is its parent and so on.
8397 It is also possible to query the number of ancestors of a node,
8398 the position of the current node
8399 within the children of its parent, the position of the subtree
8400 containing a node within the children of an ancestor
8401 or to obtain a copy of a given
8402 child without destroying the current node.
8403 Given two nodes that point to the same schedule, their closest
8404 shared ancestor can be obtained using
8405 C<isl_schedule_node_get_shared_ancestor>.
8407 #include <isl/schedule_node.h>
8408 int isl_schedule_node_get_tree_depth(
8409 __isl_keep isl_schedule_node *node);
8410 int isl_schedule_node_get_child_position(
8411 __isl_keep isl_schedule_node *node);
8412 int isl_schedule_node_get_ancestor_child_position(
8413 __isl_keep isl_schedule_node *node,
8414 __isl_keep isl_schedule_node *ancestor);
8415 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8416 __isl_keep isl_schedule_node *node, int pos);
8417 __isl_give isl_schedule_node *
8418 isl_schedule_node_get_shared_ancestor(
8419 __isl_keep isl_schedule_node *node1,
8420 __isl_keep isl_schedule_node *node2);
8422 All nodes in a schedule tree or
8423 all descendants of a specific node (including the node) can be visited
8424 in depth-first pre-order using the following functions.
8426 #include <isl/schedule.h>
8427 isl_stat isl_schedule_foreach_schedule_node_top_down(
8428 __isl_keep isl_schedule *sched,
8429 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8430 void *user), void *user);
8432 #include <isl/schedule_node.h>
8433 isl_stat isl_schedule_node_foreach_descendant_top_down(
8434 __isl_keep isl_schedule_node *node,
8435 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8436 void *user), void *user);
8438 The callback function is slightly different from the usual
8439 callbacks in that it not only indicates success (non-negative result)
8440 or failure (negative result), but also indicates whether the children
8441 of the given node should be visited. In particular, if the callback
8442 returns a positive value, then the children are visited, but if
8443 the callback returns zero, then the children are not visited.
8445 The following functions checks whether
8446 all descendants of a specific node (including the node itself)
8447 satisfy a user-specified test.
8449 #include <isl/schedule_node.h>
8450 isl_bool isl_schedule_node_every_descendant(
8451 __isl_keep isl_schedule_node *node,
8452 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8453 void *user), void *user)
8455 The ancestors of a node in a schedule tree can be visited from
8456 the root down to and including the parent of the node using
8457 the following function.
8459 #include <isl/schedule_node.h>
8460 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8461 __isl_keep isl_schedule_node *node,
8462 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8463 void *user), void *user);
8465 The following functions allows for a depth-first post-order
8466 traversal of the nodes in a schedule tree or
8467 of the descendants of a specific node (including the node
8468 itself), where the user callback is allowed to modify the
8471 #include <isl/schedule.h>
8472 __isl_give isl_schedule *
8473 isl_schedule_map_schedule_node_bottom_up(
8474 __isl_take isl_schedule *schedule,
8475 __isl_give isl_schedule_node *(*fn)(
8476 __isl_take isl_schedule_node *node,
8477 void *user), void *user);
8479 #include <isl/schedule_node.h>
8480 __isl_give isl_schedule_node *
8481 isl_schedule_node_map_descendant_bottom_up(
8482 __isl_take isl_schedule_node *node,
8483 __isl_give isl_schedule_node *(*fn)(
8484 __isl_take isl_schedule_node *node,
8485 void *user), void *user);
8487 The traversal continues from the node returned by the callback function.
8488 It is the responsibility of the user to ensure that this does not
8489 lead to an infinite loop. It is safest to always return a pointer
8490 to the same position (same ancestors and child positions) as the input node.
8492 The following function removes a node (along with its descendants)
8493 from a schedule tree and returns a pointer to the leaf at the
8494 same position in the updated tree.
8495 It is not allowed to remove the root of a schedule tree or
8496 a child of a set or sequence node.
8498 #include <isl/schedule_node.h>
8499 __isl_give isl_schedule_node *isl_schedule_node_cut(
8500 __isl_take isl_schedule_node *node);
8502 The following function removes a single node
8503 from a schedule tree and returns a pointer to the child
8504 of the node, now located at the position of the original node
8505 or to a leaf node at that position if there was no child.
8506 It is not allowed to remove the root of a schedule tree,
8507 a set or sequence node, a child of a set or sequence node or
8508 a band node with an anchored subtree.
8510 #include <isl/schedule_node.h>
8511 __isl_give isl_schedule_node *isl_schedule_node_delete(
8512 __isl_take isl_schedule_node *node);
8514 Most nodes in a schedule tree only contain local information.
8515 In some cases, however, a node may also refer to the schedule dimensions
8516 of its outer band nodes.
8517 This means that the position of the node within the tree should
8518 not be changed, or at least that no changes are performed to the
8519 outer band nodes. The following function can be used to test
8520 whether the subtree rooted at a given node contains any such nodes.
8522 #include <isl/schedule_node.h>
8523 isl_bool isl_schedule_node_is_subtree_anchored(
8524 __isl_keep isl_schedule_node *node);
8526 The following function resets the user pointers on all parameter
8527 and tuple identifiers referenced by the given schedule node.
8529 #include <isl/schedule_node.h>
8530 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8531 __isl_take isl_schedule_node *node);
8533 The following function aligns the parameters of the given schedule
8534 node to the given space.
8536 #include <isl/schedule_node.h>
8537 __isl_give isl_schedule_node *
8538 isl_schedule_node_align_params(
8539 __isl_take isl_schedule_node *node,
8540 __isl_take isl_space *space);
8542 Several node types have their own functions for querying
8543 (and in some cases setting) some node type specific properties.
8545 #include <isl/schedule_node.h>
8546 __isl_give isl_space *isl_schedule_node_band_get_space(
8547 __isl_keep isl_schedule_node *node);
8548 __isl_give isl_multi_union_pw_aff *
8549 isl_schedule_node_band_get_partial_schedule(
8550 __isl_keep isl_schedule_node *node);
8551 __isl_give isl_union_map *
8552 isl_schedule_node_band_get_partial_schedule_union_map(
8553 __isl_keep isl_schedule_node *node);
8554 unsigned isl_schedule_node_band_n_member(
8555 __isl_keep isl_schedule_node *node);
8556 isl_bool isl_schedule_node_band_member_get_coincident(
8557 __isl_keep isl_schedule_node *node, int pos);
8558 __isl_give isl_schedule_node *
8559 isl_schedule_node_band_member_set_coincident(
8560 __isl_take isl_schedule_node *node, int pos,
8562 isl_bool isl_schedule_node_band_get_permutable(
8563 __isl_keep isl_schedule_node *node);
8564 __isl_give isl_schedule_node *
8565 isl_schedule_node_band_set_permutable(
8566 __isl_take isl_schedule_node *node, int permutable);
8567 enum isl_ast_loop_type
8568 isl_schedule_node_band_member_get_ast_loop_type(
8569 __isl_keep isl_schedule_node *node, int pos);
8570 __isl_give isl_schedule_node *
8571 isl_schedule_node_band_member_set_ast_loop_type(
8572 __isl_take isl_schedule_node *node, int pos,
8573 enum isl_ast_loop_type type);
8574 __isl_give isl_union_set *
8575 enum isl_ast_loop_type
8576 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8577 __isl_keep isl_schedule_node *node, int pos);
8578 __isl_give isl_schedule_node *
8579 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8580 __isl_take isl_schedule_node *node, int pos,
8581 enum isl_ast_loop_type type);
8582 isl_schedule_node_band_get_ast_build_options(
8583 __isl_keep isl_schedule_node *node);
8584 __isl_give isl_schedule_node *
8585 isl_schedule_node_band_set_ast_build_options(
8586 __isl_take isl_schedule_node *node,
8587 __isl_take isl_union_set *options);
8588 __isl_give isl_set *
8589 isl_schedule_node_band_get_ast_isolate_option(
8590 __isl_keep isl_schedule_node *node);
8592 The function C<isl_schedule_node_band_get_space> returns the space
8593 of the partial schedule of the band.
8594 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8595 returns a representation of the partial schedule of the band node
8596 in the form of an C<isl_union_map>.
8597 The coincident and permutable properties are set by
8598 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8600 A scheduling dimension is considered to be ``coincident''
8601 if it satisfies the coincidence constraints within its band.
8602 That is, if the dependence distances of the coincidence
8603 constraints are all zero in that direction (for fixed
8604 iterations of outer bands).
8605 A band is marked permutable if it was produced using the Pluto-like scheduler.
8606 Note that the scheduler may have to resort to a Feautrier style scheduling
8607 step even if the default scheduler is used.
8608 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8609 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8610 For the meaning of these loop AST generation types and the difference
8611 between the regular loop AST generation type and the isolate
8612 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8613 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8614 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8615 may return C<isl_ast_loop_error> if an error occurs.
8616 The AST build options govern how an AST is generated for
8617 the individual schedule dimensions during AST generation.
8618 See L</"AST Generation Options (Schedule Tree)">.
8619 The isolate option for the given node can be extracted from these
8620 AST build options using the function
8621 C<isl_schedule_node_band_get_ast_isolate_option>.
8623 #include <isl/schedule_node.h>
8624 __isl_give isl_set *
8625 isl_schedule_node_context_get_context(
8626 __isl_keep isl_schedule_node *node);
8628 #include <isl/schedule_node.h>
8629 __isl_give isl_union_set *
8630 isl_schedule_node_domain_get_domain(
8631 __isl_keep isl_schedule_node *node);
8633 #include <isl/schedule_node.h>
8634 __isl_give isl_union_map *
8635 isl_schedule_node_expansion_get_expansion(
8636 __isl_keep isl_schedule_node *node);
8637 __isl_give isl_union_pw_multi_aff *
8638 isl_schedule_node_expansion_get_contraction(
8639 __isl_keep isl_schedule_node *node);
8641 #include <isl/schedule_node.h>
8642 __isl_give isl_union_map *
8643 isl_schedule_node_extension_get_extension(
8644 __isl_keep isl_schedule_node *node);
8646 #include <isl/schedule_node.h>
8647 __isl_give isl_union_set *
8648 isl_schedule_node_filter_get_filter(
8649 __isl_keep isl_schedule_node *node);
8651 #include <isl/schedule_node.h>
8652 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8653 __isl_keep isl_schedule_node *node);
8655 #include <isl/schedule_node.h>
8656 __isl_give isl_id *isl_schedule_node_mark_get_id(
8657 __isl_keep isl_schedule_node *node);
8659 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8660 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8661 partial schedules related to the node.
8663 #include <isl/schedule_node.h>
8664 __isl_give isl_multi_union_pw_aff *
8665 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8666 __isl_keep isl_schedule_node *node);
8667 __isl_give isl_union_pw_multi_aff *
8668 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8669 __isl_keep isl_schedule_node *node);
8670 __isl_give isl_union_map *
8671 isl_schedule_node_get_prefix_schedule_union_map(
8672 __isl_keep isl_schedule_node *node);
8673 __isl_give isl_union_map *
8674 isl_schedule_node_get_prefix_schedule_relation(
8675 __isl_keep isl_schedule_node *node);
8676 __isl_give isl_union_map *
8677 isl_schedule_node_get_subtree_schedule_union_map(
8678 __isl_keep isl_schedule_node *node);
8680 In particular, the functions
8681 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8682 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8683 and C<isl_schedule_node_get_prefix_schedule_union_map>
8684 return a relative ordering on the domain elements that reach the given
8685 node determined by its ancestors.
8686 The function C<isl_schedule_node_get_prefix_schedule_relation>
8687 additionally includes the domain constraints in the result.
8688 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8689 returns a representation of the partial schedule defined by the
8690 subtree rooted at the given node.
8691 If the tree contains any expansion nodes, then the subtree schedule
8692 is formulated in terms of the expanded domain elements.
8693 The tree passed to functions returning a prefix schedule
8694 may only contain extension nodes if these would not affect
8695 the result of these functions. That is, if one of the ancestors
8696 is an extension node, then all of the domain elements that were
8697 added by the extension node need to have been filtered out
8698 by filter nodes between the extension node and the input node.
8699 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8700 may not contain in extension nodes in the selected subtree.
8702 The expansion/contraction defined by an entire subtree, combining
8703 the expansions/contractions
8704 on the expansion nodes in the subtree, can be obtained using
8705 the following functions.
8707 #include <isl/schedule_node.h>
8708 __isl_give isl_union_map *
8709 isl_schedule_node_get_subtree_expansion(
8710 __isl_keep isl_schedule_node *node);
8711 __isl_give isl_union_pw_multi_aff *
8712 isl_schedule_node_get_subtree_contraction(
8713 __isl_keep isl_schedule_node *node);
8715 The total number of outer band members of given node, i.e.,
8716 the shared output dimension of the maps in the result
8717 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8718 using the following function.
8720 #include <isl/schedule_node.h>
8721 int isl_schedule_node_get_schedule_depth(
8722 __isl_keep isl_schedule_node *node);
8724 The following functions return the elements that reach the given node
8725 or the union of universes in the spaces that contain these elements.
8727 #include <isl/schedule_node.h>
8728 __isl_give isl_union_set *
8729 isl_schedule_node_get_domain(
8730 __isl_keep isl_schedule_node *node);
8731 __isl_give isl_union_set *
8732 isl_schedule_node_get_universe_domain(
8733 __isl_keep isl_schedule_node *node);
8735 The input tree of C<isl_schedule_node_get_domain>
8736 may only contain extension nodes if these would not affect
8737 the result of this function. That is, if one of the ancestors
8738 is an extension node, then all of the domain elements that were
8739 added by the extension node need to have been filtered out
8740 by filter nodes between the extension node and the input node.
8742 The following functions can be used to introduce additional nodes
8743 in the schedule tree. The new node is introduced at the point
8744 in the tree where the C<isl_schedule_node> points to and
8745 the results points to the new node.
8747 #include <isl/schedule_node.h>
8748 __isl_give isl_schedule_node *
8749 isl_schedule_node_insert_partial_schedule(
8750 __isl_take isl_schedule_node *node,
8751 __isl_take isl_multi_union_pw_aff *schedule);
8753 This function inserts a new band node with (the greatest integer
8754 part of) the given partial schedule.
8755 The subtree rooted at the given node is assumed not to have
8758 #include <isl/schedule_node.h>
8759 __isl_give isl_schedule_node *
8760 isl_schedule_node_insert_context(
8761 __isl_take isl_schedule_node *node,
8762 __isl_take isl_set *context);
8764 This function inserts a new context node with the given context constraints.
8766 #include <isl/schedule_node.h>
8767 __isl_give isl_schedule_node *
8768 isl_schedule_node_insert_filter(
8769 __isl_take isl_schedule_node *node,
8770 __isl_take isl_union_set *filter);
8772 This function inserts a new filter node with the given filter.
8773 If the original node already pointed to a filter node, then the
8774 two filter nodes are merged into one.
8776 #include <isl/schedule_node.h>
8777 __isl_give isl_schedule_node *
8778 isl_schedule_node_insert_guard(
8779 __isl_take isl_schedule_node *node,
8780 __isl_take isl_set *guard);
8782 This function inserts a new guard node with the given guard constraints.
8784 #include <isl/schedule_node.h>
8785 __isl_give isl_schedule_node *
8786 isl_schedule_node_insert_mark(
8787 __isl_take isl_schedule_node *node,
8788 __isl_take isl_id *mark);
8790 This function inserts a new mark node with the give mark identifier.
8792 #include <isl/schedule_node.h>
8793 __isl_give isl_schedule_node *
8794 isl_schedule_node_insert_sequence(
8795 __isl_take isl_schedule_node *node,
8796 __isl_take isl_union_set_list *filters);
8797 __isl_give isl_schedule_node *
8798 isl_schedule_node_insert_set(
8799 __isl_take isl_schedule_node *node,
8800 __isl_take isl_union_set_list *filters);
8802 These functions insert a new sequence or set node with the given
8803 filters as children.
8805 #include <isl/schedule_node.h>
8806 __isl_give isl_schedule_node *isl_schedule_node_group(
8807 __isl_take isl_schedule_node *node,
8808 __isl_take isl_id *group_id);
8810 This function introduces an expansion node in between the current
8811 node and its parent that expands instances of a space with tuple
8812 identifier C<group_id> to the original domain elements that reach
8813 the node. The group instances are identified by the prefix schedule
8814 of those domain elements. The ancestors of the node are adjusted
8815 to refer to the group instances instead of the original domain
8816 elements. The return value points to the same node in the updated
8817 schedule tree as the input node, i.e., to the child of the newly
8818 introduced expansion node. Grouping instances of different statements
8819 ensures that they will be treated as a single statement by the
8820 AST generator up to the point of the expansion node.
8822 The following function can be used to flatten a nested
8825 #include <isl/schedule_node.h>
8826 __isl_give isl_schedule_node *
8827 isl_schedule_node_sequence_splice_child(
8828 __isl_take isl_schedule_node *node, int pos);
8830 That is, given a sequence node C<node> that has another sequence node
8831 in its child at position C<pos> (in particular, the child of that filter
8832 node is a sequence node), attach the children of that other sequence
8833 node as children of C<node>, replacing the original child at position
8836 The partial schedule of a band node can be scaled (down) or reduced using
8837 the following functions.
8839 #include <isl/schedule_node.h>
8840 __isl_give isl_schedule_node *
8841 isl_schedule_node_band_scale(
8842 __isl_take isl_schedule_node *node,
8843 __isl_take isl_multi_val *mv);
8844 __isl_give isl_schedule_node *
8845 isl_schedule_node_band_scale_down(
8846 __isl_take isl_schedule_node *node,
8847 __isl_take isl_multi_val *mv);
8848 __isl_give isl_schedule_node *
8849 isl_schedule_node_band_mod(
8850 __isl_take isl_schedule_node *node,
8851 __isl_take isl_multi_val *mv);
8853 The spaces of the two arguments need to match.
8854 After scaling, the partial schedule is replaced by its greatest
8855 integer part to ensure that the schedule remains integral.
8857 The partial schedule of a band node can be shifted by an
8858 C<isl_multi_union_pw_aff> with a domain that is a superset
8859 of the domain of the partial schedule using
8860 the following function.
8862 #include <isl/schedule_node.h>
8863 __isl_give isl_schedule_node *
8864 isl_schedule_node_band_shift(
8865 __isl_take isl_schedule_node *node,
8866 __isl_take isl_multi_union_pw_aff *shift);
8868 A band node can be tiled using the following function.
8870 #include <isl/schedule_node.h>
8871 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8872 __isl_take isl_schedule_node *node,
8873 __isl_take isl_multi_val *sizes);
8875 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8877 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8878 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8880 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8882 The C<isl_schedule_node_band_tile> function tiles
8883 the band using the given tile sizes inside its schedule.
8884 A new child band node is created to represent the point loops and it is
8885 inserted between the modified band and its children.
8886 The subtree rooted at the given node is assumed not to have
8888 The C<tile_scale_tile_loops> option specifies whether the tile
8889 loops iterators should be scaled by the tile sizes.
8890 If the C<tile_shift_point_loops> option is set, then the point loops
8891 are shifted to start at zero.
8893 A band node can be split into two nested band nodes
8894 using the following function.
8896 #include <isl/schedule_node.h>
8897 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8898 __isl_take isl_schedule_node *node, int pos);
8900 The resulting outer band node contains the first C<pos> dimensions of
8901 the schedule of C<node> while the inner band contains the remaining dimensions.
8902 The schedules of the two band nodes live in anonymous spaces.
8903 The loop AST generation type options and the isolate option
8904 are split over the two band nodes.
8906 A band node can be moved down to the leaves of the subtree rooted
8907 at the band node using the following function.
8909 #include <isl/schedule_node.h>
8910 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8911 __isl_take isl_schedule_node *node);
8913 The subtree rooted at the given node is assumed not to have
8915 The result points to the node in the resulting tree that is in the same
8916 position as the node pointed to by C<node> in the original tree.
8918 #include <isl/schedule_node.h>
8919 __isl_give isl_schedule_node *
8920 isl_schedule_node_order_before(
8921 __isl_take isl_schedule_node *node,
8922 __isl_take isl_union_set *filter);
8923 __isl_give isl_schedule_node *
8924 isl_schedule_node_order_after(
8925 __isl_take isl_schedule_node *node,
8926 __isl_take isl_union_set *filter);
8928 These functions split the domain elements that reach C<node>
8929 into those that satisfy C<filter> and those that do not and
8930 arranges for the elements that do satisfy the filter to be
8931 executed before (in case of C<isl_schedule_node_order_before>)
8932 or after (in case of C<isl_schedule_node_order_after>)
8933 those that do not. The order is imposed by
8934 a sequence node, possibly reusing the grandparent of C<node>
8935 on two copies of the subtree attached to the original C<node>.
8936 Both copies are simplified with respect to their filter.
8938 Return a pointer to the copy of the subtree that does not
8939 satisfy C<filter>. If there is no such copy (because all
8940 reaching domain elements satisfy the filter), then return
8941 the original pointer.
8943 #include <isl/schedule_node.h>
8944 __isl_give isl_schedule_node *
8945 isl_schedule_node_graft_before(
8946 __isl_take isl_schedule_node *node,
8947 __isl_take isl_schedule_node *graft);
8948 __isl_give isl_schedule_node *
8949 isl_schedule_node_graft_after(
8950 __isl_take isl_schedule_node *node,
8951 __isl_take isl_schedule_node *graft);
8953 This function inserts the C<graft> tree into the tree containing C<node>
8954 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8955 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8956 The root node of C<graft>
8957 should be an extension node where the domain of the extension
8958 is the flat product of all outer band nodes of C<node>.
8959 The root node may also be a domain node.
8960 The elements of the domain or the range of the extension may not
8961 intersect with the domain elements that reach "node".
8962 The schedule tree of C<graft> may not be anchored.
8964 The schedule tree of C<node> is modified to include an extension node
8965 corresponding to the root node of C<graft> as a child of the original
8966 parent of C<node>. The original node that C<node> points to and the
8967 child of the root node of C<graft> are attached to this extension node
8968 through a sequence, with appropriate filters and with the child
8969 of C<graft> appearing before or after the original C<node>.
8971 If C<node> already appears inside a sequence that is the child of
8972 an extension node and if the spaces of the new domain elements
8973 do not overlap with those of the original domain elements,
8974 then that extension node is extended with the new extension
8975 rather than introducing a new segment of extension and sequence nodes.
8977 Return a pointer to the same node in the modified tree that
8978 C<node> pointed to in the original tree.
8980 A representation of the schedule node can be printed using
8982 #include <isl/schedule_node.h>
8983 __isl_give isl_printer *isl_printer_print_schedule_node(
8984 __isl_take isl_printer *p,
8985 __isl_keep isl_schedule_node *node);
8986 __isl_give char *isl_schedule_node_to_str(
8987 __isl_keep isl_schedule_node *node);
8989 C<isl_schedule_node_to_str> prints the schedule node in block format.
8991 =head2 Dependence Analysis
8993 C<isl> contains specialized functionality for performing
8994 array dataflow analysis. That is, given a I<sink> access relation,
8995 a collection of possible I<source> accesses and
8996 a collection of I<kill> accesses,
8997 C<isl> can compute relations that describe
8998 for each iteration of the sink access, which iterations
8999 of which of the source access relations may have
9000 accessed the same data element before the given iteration
9001 of the sink access without any intermediate kill of that data element.
9002 The resulting dependence relations map source iterations
9003 to either the corresponding sink iterations or
9004 pairs of corresponding sink iterations and accessed data elements.
9005 To compute standard flow dependences, the sink should be
9006 a read, while the sources should be writes.
9007 If no kills are specified,
9008 then memory based dependence analysis is performed.
9009 If, on the other hand, all sources are also kills,
9010 then value based dependence analysis is performed.
9011 If any of the source accesses are marked as being I<must>
9012 accesses, then they are also treated as kills.
9013 Furthermore, the specification of must-sources results
9014 in the computation of must-dependences.
9015 Only dependences originating in a must access not coscheduled
9016 with any other access to the same element and without
9017 any may accesses between the must access and the sink access
9018 are considered to be must dependences.
9020 =head3 High-level Interface
9022 A high-level interface to dependence analysis is provided
9023 by the following function.
9025 #include <isl/flow.h>
9026 __isl_give isl_union_flow *
9027 isl_union_access_info_compute_flow(
9028 __isl_take isl_union_access_info *access);
9030 The input C<isl_union_access_info> object describes the sink
9031 access relations, the source access relations and a schedule,
9032 while the output C<isl_union_flow> object describes
9033 the resulting dependence relations and the subsets of the
9034 sink relations for which no source was found.
9036 An C<isl_union_access_info> is created, modified, copied and freed using
9037 the following functions.
9039 #include <isl/flow.h>
9040 __isl_give isl_union_access_info *
9041 isl_union_access_info_from_sink(
9042 __isl_take isl_union_map *sink);
9043 __isl_give isl_union_access_info *
9044 isl_union_access_info_set_kill(
9045 __isl_take isl_union_access_info *access,
9046 __isl_take isl_union_map *kill);
9047 __isl_give isl_union_access_info *
9048 isl_union_access_info_set_may_source(
9049 __isl_take isl_union_access_info *access,
9050 __isl_take isl_union_map *may_source);
9051 __isl_give isl_union_access_info *
9052 isl_union_access_info_set_must_source(
9053 __isl_take isl_union_access_info *access,
9054 __isl_take isl_union_map *must_source);
9055 __isl_give isl_union_access_info *
9056 isl_union_access_info_set_schedule(
9057 __isl_take isl_union_access_info *access,
9058 __isl_take isl_schedule *schedule);
9059 __isl_give isl_union_access_info *
9060 isl_union_access_info_set_schedule_map(
9061 __isl_take isl_union_access_info *access,
9062 __isl_take isl_union_map *schedule_map);
9063 __isl_give isl_union_access_info *
9064 isl_union_access_info_copy(
9065 __isl_keep isl_union_access_info *access);
9066 __isl_null isl_union_access_info *
9067 isl_union_access_info_free(
9068 __isl_take isl_union_access_info *access);
9070 The may sources set by C<isl_union_access_info_set_may_source>
9071 do not need to include the must sources set by
9072 C<isl_union_access_info_set_must_source> as a subset.
9073 The kills set by C<isl_union_access_info_set_kill> may overlap
9074 with the may-sources and/or must-sources.
9075 The user is free not to call one (or more) of these functions,
9076 in which case the corresponding set is kept to its empty default.
9077 Similarly, the default schedule initialized by
9078 C<isl_union_access_info_from_sink> is empty.
9079 The current schedule is determined by the last call to either
9080 C<isl_union_access_info_set_schedule> or
9081 C<isl_union_access_info_set_schedule_map>.
9082 The domain of the schedule corresponds to the domains of
9083 the access relations. In particular, the domains of the access
9084 relations are effectively intersected with the domain of the schedule
9085 and only the resulting accesses are considered by the dependence analysis.
9087 An C<isl_union_access_info> object can be read from input
9088 using the following function.
9090 #include <isl/flow.h>
9091 __isl_give isl_union_access_info *
9092 isl_union_access_info_read_from_file(isl_ctx *ctx,
9095 A representation of the information contained in an object
9096 of type C<isl_union_access_info> can be obtained using
9098 #include <isl/flow.h>
9099 __isl_give isl_printer *
9100 isl_printer_print_union_access_info(
9101 __isl_take isl_printer *p,
9102 __isl_keep isl_union_access_info *access);
9103 __isl_give char *isl_union_access_info_to_str(
9104 __isl_keep isl_union_access_info *access);
9106 C<isl_union_access_info_to_str> prints the information in flow format.
9108 The output of C<isl_union_access_info_compute_flow> can be examined,
9109 copied, and freed using the following functions.
9111 #include <isl/flow.h>
9112 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9113 __isl_keep isl_union_flow *flow);
9114 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9115 __isl_keep isl_union_flow *flow);
9116 __isl_give isl_union_map *
9117 isl_union_flow_get_full_must_dependence(
9118 __isl_keep isl_union_flow *flow);
9119 __isl_give isl_union_map *
9120 isl_union_flow_get_full_may_dependence(
9121 __isl_keep isl_union_flow *flow);
9122 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9123 __isl_keep isl_union_flow *flow);
9124 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9125 __isl_keep isl_union_flow *flow);
9126 __isl_give isl_union_flow *isl_union_flow_copy(
9127 __isl_keep isl_union_flow *flow);
9128 __isl_null isl_union_flow *isl_union_flow_free(
9129 __isl_take isl_union_flow *flow);
9131 The relation returned by C<isl_union_flow_get_must_dependence>
9132 relates domain elements of must sources to domain elements of the sink.
9133 The relation returned by C<isl_union_flow_get_may_dependence>
9134 relates domain elements of must or may sources to domain elements of the sink
9135 and includes the previous relation as a subset.
9136 The relation returned by C<isl_union_flow_get_full_must_dependence>
9137 relates domain elements of must sources to pairs of domain elements of the sink
9138 and accessed data elements.
9139 The relation returned by C<isl_union_flow_get_full_may_dependence>
9140 relates domain elements of must or may sources to pairs of
9141 domain elements of the sink and accessed data elements.
9142 This relation includes the previous relation as a subset.
9143 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9144 of the sink relation for which no dependences have been found.
9145 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9146 of the sink relation for which no definite dependences have been found.
9147 That is, it contains those sink access that do not contribute to any
9148 of the elements in the relation returned
9149 by C<isl_union_flow_get_must_dependence>.
9151 A representation of the information contained in an object
9152 of type C<isl_union_flow> can be obtained using
9154 #include <isl/flow.h>
9155 __isl_give isl_printer *isl_printer_print_union_flow(
9156 __isl_take isl_printer *p,
9157 __isl_keep isl_union_flow *flow);
9158 __isl_give char *isl_union_flow_to_str(
9159 __isl_keep isl_union_flow *flow);
9161 C<isl_union_flow_to_str> prints the information in flow format.
9163 =head3 Low-level Interface
9165 A lower-level interface is provided by the following functions.
9167 #include <isl/flow.h>
9169 typedef int (*isl_access_level_before)(void *first, void *second);
9171 __isl_give isl_access_info *isl_access_info_alloc(
9172 __isl_take isl_map *sink,
9173 void *sink_user, isl_access_level_before fn,
9175 __isl_give isl_access_info *isl_access_info_add_source(
9176 __isl_take isl_access_info *acc,
9177 __isl_take isl_map *source, int must,
9179 __isl_null isl_access_info *isl_access_info_free(
9180 __isl_take isl_access_info *acc);
9182 __isl_give isl_flow *isl_access_info_compute_flow(
9183 __isl_take isl_access_info *acc);
9185 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9186 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9187 void *dep_user, void *user),
9189 __isl_give isl_map *isl_flow_get_no_source(
9190 __isl_keep isl_flow *deps, int must);
9191 void isl_flow_free(__isl_take isl_flow *deps);
9193 The function C<isl_access_info_compute_flow> performs the actual
9194 dependence analysis. The other functions are used to construct
9195 the input for this function or to read off the output.
9197 The input is collected in an C<isl_access_info>, which can
9198 be created through a call to C<isl_access_info_alloc>.
9199 The arguments to this functions are the sink access relation
9200 C<sink>, a token C<sink_user> used to identify the sink
9201 access to the user, a callback function for specifying the
9202 relative order of source and sink accesses, and the number
9203 of source access relations that will be added.
9205 The callback function has type C<int (*)(void *first, void *second)>.
9206 The function is called with two user supplied tokens identifying
9207 either a source or the sink and it should return the shared nesting
9208 level and the relative order of the two accesses.
9209 In particular, let I<n> be the number of loops shared by
9210 the two accesses. If C<first> precedes C<second> textually,
9211 then the function should return I<2 * n + 1>; otherwise,
9212 it should return I<2 * n>.
9213 The low-level interface assumes that no sources are coscheduled.
9214 If the information returned by the callback does not allow
9215 the relative order to be determined, then one of the sources
9216 is arbitrarily taken to be executed after the other(s).
9218 The sources can be added to the C<isl_access_info> object by performing
9219 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9220 C<must> indicates whether the source is a I<must> access
9221 or a I<may> access. Note that a multi-valued access relation
9222 should only be marked I<must> if every iteration in the domain
9223 of the relation accesses I<all> elements in its image.
9224 The C<source_user> token is again used to identify
9225 the source access. The range of the source access relation
9226 C<source> should have the same dimension as the range
9227 of the sink access relation.
9228 The C<isl_access_info_free> function should usually not be
9229 called explicitly, because it is already called implicitly by
9230 C<isl_access_info_compute_flow>.
9232 The result of the dependence analysis is collected in an
9233 C<isl_flow>. There may be elements of
9234 the sink access for which no preceding source access could be
9235 found or for which all preceding sources are I<may> accesses.
9236 The relations containing these elements can be obtained through
9237 calls to C<isl_flow_get_no_source>, the first with C<must> set
9238 and the second with C<must> unset.
9239 In the case of standard flow dependence analysis,
9240 with the sink a read and the sources I<must> writes,
9241 the first relation corresponds to the reads from uninitialized
9242 array elements and the second relation is empty.
9243 The actual flow dependences can be extracted using
9244 C<isl_flow_foreach>. This function will call the user-specified
9245 callback function C<fn> for each B<non-empty> dependence between
9246 a source and the sink. The callback function is called
9247 with four arguments, the actual flow dependence relation
9248 mapping source iterations to sink iterations, a boolean that
9249 indicates whether it is a I<must> or I<may> dependence, a token
9250 identifying the source and an additional C<void *> with value
9251 equal to the third argument of the C<isl_flow_foreach> call.
9252 A dependence is marked I<must> if it originates from a I<must>
9253 source and if it is not followed by any I<may> sources.
9255 After finishing with an C<isl_flow>, the user should call
9256 C<isl_flow_free> to free all associated memory.
9258 =head3 Interaction with the Low-level Interface
9260 During the dependence analysis, we frequently need to perform
9261 the following operation. Given a relation between sink iterations
9262 and potential source iterations from a particular source domain,
9263 what is the last potential source iteration corresponding to each
9264 sink iteration. It can sometimes be convenient to adjust
9265 the set of potential source iterations before or after each such operation.
9266 The prototypical example is fuzzy array dataflow analysis,
9267 where we need to analyze if, based on data-dependent constraints,
9268 the sink iteration can ever be executed without one or more of
9269 the corresponding potential source iterations being executed.
9270 If so, we can introduce extra parameters and select an unknown
9271 but fixed source iteration from the potential source iterations.
9272 To be able to perform such manipulations, C<isl> provides the following
9275 #include <isl/flow.h>
9277 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9278 __isl_keep isl_map *source_map,
9279 __isl_keep isl_set *sink, void *source_user,
9281 __isl_give isl_access_info *isl_access_info_set_restrict(
9282 __isl_take isl_access_info *acc,
9283 isl_access_restrict fn, void *user);
9285 The function C<isl_access_info_set_restrict> should be called
9286 before calling C<isl_access_info_compute_flow> and registers a callback function
9287 that will be called any time C<isl> is about to compute the last
9288 potential source. The first argument is the (reverse) proto-dependence,
9289 mapping sink iterations to potential source iterations.
9290 The second argument represents the sink iterations for which
9291 we want to compute the last source iteration.
9292 The third argument is the token corresponding to the source
9293 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9294 The callback is expected to return a restriction on either the input or
9295 the output of the operation computing the last potential source.
9296 If the input needs to be restricted then restrictions are needed
9297 for both the source and the sink iterations. The sink iterations
9298 and the potential source iterations will be intersected with these sets.
9299 If the output needs to be restricted then only a restriction on the source
9300 iterations is required.
9301 If any error occurs, the callback should return C<NULL>.
9302 An C<isl_restriction> object can be created, freed and inspected
9303 using the following functions.
9305 #include <isl/flow.h>
9307 __isl_give isl_restriction *isl_restriction_input(
9308 __isl_take isl_set *source_restr,
9309 __isl_take isl_set *sink_restr);
9310 __isl_give isl_restriction *isl_restriction_output(
9311 __isl_take isl_set *source_restr);
9312 __isl_give isl_restriction *isl_restriction_none(
9313 __isl_take isl_map *source_map);
9314 __isl_give isl_restriction *isl_restriction_empty(
9315 __isl_take isl_map *source_map);
9316 __isl_null isl_restriction *isl_restriction_free(
9317 __isl_take isl_restriction *restr);
9319 C<isl_restriction_none> and C<isl_restriction_empty> are special
9320 cases of C<isl_restriction_input>. C<isl_restriction_none>
9321 is essentially equivalent to
9323 isl_restriction_input(isl_set_universe(
9324 isl_space_range(isl_map_get_space(source_map))),
9326 isl_space_domain(isl_map_get_space(source_map))));
9328 whereas C<isl_restriction_empty> is essentially equivalent to
9330 isl_restriction_input(isl_set_empty(
9331 isl_space_range(isl_map_get_space(source_map))),
9333 isl_space_domain(isl_map_get_space(source_map))));
9337 #include <isl/schedule.h>
9338 __isl_give isl_schedule *
9339 isl_schedule_constraints_compute_schedule(
9340 __isl_take isl_schedule_constraints *sc);
9342 The function C<isl_schedule_constraints_compute_schedule> can be
9343 used to compute a schedule that satisfies the given schedule constraints.
9344 These schedule constraints include the iteration domain for which
9345 a schedule should be computed and dependences between pairs of
9346 iterations. In particular, these dependences include
9347 I<validity> dependences and I<proximity> dependences.
9348 By default, the algorithm used to construct the schedule is similar
9349 to that of C<Pluto>.
9350 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9352 The generated schedule respects all validity dependences.
9353 That is, all dependence distances over these dependences in the
9354 scheduled space are lexicographically positive.
9356 The default algorithm tries to ensure that the dependence distances
9357 over coincidence constraints are zero and to minimize the
9358 dependence distances over proximity dependences.
9359 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9360 for groups of domains where the dependence distances over validity
9361 dependences have only non-negative values.
9362 Note that when minimizing the maximal dependence distance
9363 over proximity dependences, a single affine expression in the parameters
9364 is constructed that bounds all dependence distances. If no such expression
9365 exists, then the algorithm will fail and resort to an alternative
9366 scheduling algorithm. In particular, this means that adding proximity
9367 dependences may eliminate valid solutions. A typical example where this
9368 phenomenon may occur is when some subset of the proximity dependences
9369 has no restriction on some parameter, forcing the coefficient of that
9370 parameter to be zero, while some other subset forces the dependence
9371 distance to depend on that parameter, requiring the same coefficient
9373 When using Feautrier's algorithm, the coincidence and proximity constraints
9374 are only taken into account during the extension to a
9375 full-dimensional schedule.
9377 An C<isl_schedule_constraints> object can be constructed
9378 and manipulated using the following functions.
9380 #include <isl/schedule.h>
9381 __isl_give isl_schedule_constraints *
9382 isl_schedule_constraints_copy(
9383 __isl_keep isl_schedule_constraints *sc);
9384 __isl_give isl_schedule_constraints *
9385 isl_schedule_constraints_on_domain(
9386 __isl_take isl_union_set *domain);
9387 __isl_give isl_schedule_constraints *
9388 isl_schedule_constraints_set_context(
9389 __isl_take isl_schedule_constraints *sc,
9390 __isl_take isl_set *context);
9391 __isl_give isl_schedule_constraints *
9392 isl_schedule_constraints_set_validity(
9393 __isl_take isl_schedule_constraints *sc,
9394 __isl_take isl_union_map *validity);
9395 __isl_give isl_schedule_constraints *
9396 isl_schedule_constraints_set_coincidence(
9397 __isl_take isl_schedule_constraints *sc,
9398 __isl_take isl_union_map *coincidence);
9399 __isl_give isl_schedule_constraints *
9400 isl_schedule_constraints_set_proximity(
9401 __isl_take isl_schedule_constraints *sc,
9402 __isl_take isl_union_map *proximity);
9403 __isl_give isl_schedule_constraints *
9404 isl_schedule_constraints_set_conditional_validity(
9405 __isl_take isl_schedule_constraints *sc,
9406 __isl_take isl_union_map *condition,
9407 __isl_take isl_union_map *validity);
9408 __isl_give isl_schedule_constraints *
9409 isl_schedule_constraints_apply(
9410 __isl_take isl_schedule_constraints *sc,
9411 __isl_take isl_union_map *umap);
9412 __isl_null isl_schedule_constraints *
9413 isl_schedule_constraints_free(
9414 __isl_take isl_schedule_constraints *sc);
9416 The initial C<isl_schedule_constraints> object created by
9417 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9418 That is, it has an empty set of dependences.
9419 The function C<isl_schedule_constraints_set_context> allows the user
9420 to specify additional constraints on the parameters that may
9421 be assumed to hold during the construction of the schedule.
9422 The function C<isl_schedule_constraints_set_validity> replaces the
9423 validity dependences, mapping domain elements I<i> to domain
9424 elements that should be scheduled after I<i>.
9425 The function C<isl_schedule_constraints_set_coincidence> replaces the
9426 coincidence dependences, mapping domain elements I<i> to domain
9427 elements that should be scheduled together with I<I>, if possible.
9428 The function C<isl_schedule_constraints_set_proximity> replaces the
9429 proximity dependences, mapping domain elements I<i> to domain
9430 elements that should be scheduled either before I<I>
9431 or as early as possible after I<i>.
9433 The function C<isl_schedule_constraints_set_conditional_validity>
9434 replaces the conditional validity constraints.
9435 A conditional validity constraint is only imposed when any of the corresponding
9436 conditions is satisfied, i.e., when any of them is non-zero.
9437 That is, the scheduler ensures that within each band if the dependence
9438 distances over the condition constraints are not all zero
9439 then all corresponding conditional validity constraints are respected.
9440 A conditional validity constraint corresponds to a condition
9441 if the two are adjacent, i.e., if the domain of one relation intersect
9442 the range of the other relation.
9443 The typical use case of conditional validity constraints is
9444 to allow order constraints between live ranges to be violated
9445 as long as the live ranges themselves are local to the band.
9446 To allow more fine-grained control over which conditions correspond
9447 to which conditional validity constraints, the domains and ranges
9448 of these relations may include I<tags>. That is, the domains and
9449 ranges of those relation may themselves be wrapped relations
9450 where the iteration domain appears in the domain of those wrapped relations
9451 and the range of the wrapped relations can be arbitrarily chosen
9452 by the user. Conditions and conditional validity constraints are only
9453 considered adjacent to each other if the entire wrapped relation matches.
9454 In particular, a relation with a tag will never be considered adjacent
9455 to a relation without a tag.
9457 The function C<isl_schedule_constraints_apply> takes
9458 schedule constraints that are defined on some set of domain elements
9459 and transforms them to schedule constraints on the elements
9460 to which these domain elements are mapped by the given transformation.
9462 An C<isl_schedule_constraints> object can be inspected
9463 using the following functions.
9465 #include <isl/schedule.h>
9466 __isl_give isl_union_set *
9467 isl_schedule_constraints_get_domain(
9468 __isl_keep isl_schedule_constraints *sc);
9469 __isl_give isl_set *isl_schedule_constraints_get_context(
9470 __isl_keep isl_schedule_constraints *sc);
9471 __isl_give isl_union_map *
9472 isl_schedule_constraints_get_validity(
9473 __isl_keep isl_schedule_constraints *sc);
9474 __isl_give isl_union_map *
9475 isl_schedule_constraints_get_coincidence(
9476 __isl_keep isl_schedule_constraints *sc);
9477 __isl_give isl_union_map *
9478 isl_schedule_constraints_get_proximity(
9479 __isl_keep isl_schedule_constraints *sc);
9480 __isl_give isl_union_map *
9481 isl_schedule_constraints_get_conditional_validity(
9482 __isl_keep isl_schedule_constraints *sc);
9483 __isl_give isl_union_map *
9484 isl_schedule_constraints_get_conditional_validity_condition(
9485 __isl_keep isl_schedule_constraints *sc);
9487 An C<isl_schedule_constraints> object can be read from input
9488 using the following functions.
9490 #include <isl/schedule.h>
9491 __isl_give isl_schedule_constraints *
9492 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9494 __isl_give isl_schedule_constraints *
9495 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9498 The contents of an C<isl_schedule_constraints> object can be printed
9499 using the following functions.
9501 #include <isl/schedule.h>
9502 __isl_give isl_printer *
9503 isl_printer_print_schedule_constraints(
9504 __isl_take isl_printer *p,
9505 __isl_keep isl_schedule_constraints *sc);
9506 __isl_give char *isl_schedule_constraints_to_str(
9507 __isl_keep isl_schedule_constraints *sc);
9509 The following function computes a schedule directly from
9510 an iteration domain and validity and proximity dependences
9511 and is implemented in terms of the functions described above.
9512 The use of C<isl_union_set_compute_schedule> is discouraged.
9514 #include <isl/schedule.h>
9515 __isl_give isl_schedule *isl_union_set_compute_schedule(
9516 __isl_take isl_union_set *domain,
9517 __isl_take isl_union_map *validity,
9518 __isl_take isl_union_map *proximity);
9520 The generated schedule represents a schedule tree.
9521 For more information on schedule trees, see
9522 L</"Schedule Trees">.
9526 #include <isl/schedule.h>
9527 isl_stat isl_options_set_schedule_max_coefficient(
9528 isl_ctx *ctx, int val);
9529 int isl_options_get_schedule_max_coefficient(
9531 isl_stat isl_options_set_schedule_max_constant_term(
9532 isl_ctx *ctx, int val);
9533 int isl_options_get_schedule_max_constant_term(
9535 isl_stat isl_options_set_schedule_serialize_sccs(
9536 isl_ctx *ctx, int val);
9537 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9538 isl_stat isl_options_set_schedule_whole_component(
9539 isl_ctx *ctx, int val);
9540 int isl_options_get_schedule_whole_component(
9542 isl_stat isl_options_set_schedule_maximize_band_depth(
9543 isl_ctx *ctx, int val);
9544 int isl_options_get_schedule_maximize_band_depth(
9546 isl_stat isl_options_set_schedule_maximize_coincidence(
9547 isl_ctx *ctx, int val);
9548 int isl_options_get_schedule_maximize_coincidence(
9550 isl_stat isl_options_set_schedule_outer_coincidence(
9551 isl_ctx *ctx, int val);
9552 int isl_options_get_schedule_outer_coincidence(
9554 isl_stat isl_options_set_schedule_split_scaled(
9555 isl_ctx *ctx, int val);
9556 int isl_options_get_schedule_split_scaled(
9558 isl_stat isl_options_set_schedule_treat_coalescing(
9559 isl_ctx *ctx, int val);
9560 int isl_options_get_schedule_treat_coalescing(
9562 isl_stat isl_options_set_schedule_algorithm(
9563 isl_ctx *ctx, int val);
9564 int isl_options_get_schedule_algorithm(
9566 isl_stat isl_options_set_schedule_carry_self_first(
9567 isl_ctx *ctx, int val);
9568 int isl_options_get_schedule_carry_self_first(
9570 isl_stat isl_options_set_schedule_separate_components(
9571 isl_ctx *ctx, int val);
9572 int isl_options_get_schedule_separate_components(
9577 =item * schedule_max_coefficient
9579 This option enforces that the coefficients for variable and parameter
9580 dimensions in the calculated schedule are not larger than the specified value.
9581 This option can significantly increase the speed of the scheduling calculation
9582 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9583 this option does not introduce bounds on the variable or parameter
9586 =item * schedule_max_constant_term
9588 This option enforces that the constant coefficients in the calculated schedule
9589 are not larger than the maximal constant term. This option can significantly
9590 increase the speed of the scheduling calculation and may also prevent fusing of
9591 unrelated dimensions. A value of -1 means that this option does not introduce
9592 bounds on the constant coefficients.
9594 =item * schedule_serialize_sccs
9596 If this option is set, then all strongly connected components
9597 in the dependence graph are serialized as soon as they are detected.
9598 This means in particular that instances of statements will only
9599 appear in the same band node if these statements belong
9600 to the same strongly connected component at the point where
9601 the band node is constructed.
9603 =item * schedule_whole_component
9605 If this option is set, then entire (weakly) connected
9606 components in the dependence graph are scheduled together
9608 Otherwise, each strongly connected component within
9609 such a weakly connected component is first scheduled separately
9610 and then combined with other strongly connected components.
9611 This option has no effect if C<schedule_serialize_sccs> is set.
9613 =item * schedule_maximize_band_depth
9615 If this option is set, then the scheduler tries to maximize
9616 the width of the bands. Wider bands give more possibilities for tiling.
9617 In particular, if the C<schedule_whole_component> option is set,
9618 then bands are split if this might result in wider bands.
9619 Otherwise, the effect of this option is to only allow
9620 strongly connected components to be combined if this does
9621 not reduce the width of the bands.
9622 Note that if the C<schedule_serialize_sccs> options is set, then
9623 the C<schedule_maximize_band_depth> option therefore has no effect.
9625 =item * schedule_maximize_coincidence
9627 This option is only effective if the C<schedule_whole_component>
9628 option is turned off.
9629 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9630 strongly connected components are only combined with each other
9631 if this does not reduce the number of coincident band members.
9633 =item * schedule_outer_coincidence
9635 If this option is set, then we try to construct schedules
9636 where the outermost scheduling dimension in each band
9637 satisfies the coincidence constraints.
9639 =item * schedule_algorithm
9641 Selects the scheduling algorithm to be used.
9642 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9643 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9645 =item * schedule_split_scaled
9647 If this option is set, then we try to construct schedules in which the
9648 constant term is split off from the linear part if the linear parts of
9649 the scheduling rows for all nodes in the graph have a common non-trivial
9651 The constant term is then dropped and the linear
9653 This option is only effective when the Feautrier style scheduler is
9654 being used, either as the main scheduler or as a fallback for the
9655 Pluto-like scheduler.
9657 =item * schedule_treat_coalescing
9659 If this option is set, then the scheduler will try and avoid
9660 producing schedules that perform loop coalescing.
9661 In particular, for the Pluto-like scheduler, this option places
9662 bounds on the schedule coefficients based on the sizes of the instance sets.
9663 For the Feautrier style scheduler, this option detects potentially
9664 coalescing schedules and then tries to adjust the schedule to avoid
9667 =item * schedule_carry_self_first
9669 If this option is set, then the Feautrier style scheduler
9670 (when used as a fallback for the Pluto-like scheduler) will
9671 first try to only carry self-dependences.
9673 =item * schedule_separate_components
9675 If this option is set then the function C<isl_schedule_get_map>
9676 will treat set nodes in the same way as sequence nodes.
9680 =head2 AST Generation
9682 This section describes the C<isl> functionality for generating
9683 ASTs that visit all the elements
9684 in a domain in an order specified by a schedule tree or
9686 In case the schedule given as a C<isl_union_map>, an AST is generated
9687 that visits all the elements in the domain of the C<isl_union_map>
9688 according to the lexicographic order of the corresponding image
9689 element(s). If the range of the C<isl_union_map> consists of
9690 elements in more than one space, then each of these spaces is handled
9691 separately in an arbitrary order.
9692 It should be noted that the schedule tree or the image elements
9693 in a schedule map only specify the I<order>
9694 in which the corresponding domain elements should be visited.
9695 No direct relation between the partial schedule values
9696 or the image elements on the one hand and the loop iterators
9697 in the generated AST on the other hand should be assumed.
9699 Each AST is generated within a build. The initial build
9700 simply specifies the constraints on the parameters (if any)
9701 and can be created, inspected, copied and freed using the following functions.
9703 #include <isl/ast_build.h>
9704 __isl_give isl_ast_build *isl_ast_build_alloc(
9706 __isl_give isl_ast_build *isl_ast_build_from_context(
9707 __isl_take isl_set *set);
9708 __isl_give isl_ast_build *isl_ast_build_copy(
9709 __isl_keep isl_ast_build *build);
9710 __isl_null isl_ast_build *isl_ast_build_free(
9711 __isl_take isl_ast_build *build);
9713 The C<set> argument is usually a parameter set with zero or more parameters.
9714 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9715 this set is required to be a parameter set.
9716 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9717 specify any parameter constraints.
9718 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9719 and L</"Fine-grained Control over AST Generation">.
9720 Finally, the AST itself can be constructed using one of the following
9723 #include <isl/ast_build.h>
9724 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9725 __isl_keep isl_ast_build *build,
9726 __isl_take isl_schedule *schedule);
9727 __isl_give isl_ast_node *
9728 isl_ast_build_node_from_schedule_map(
9729 __isl_keep isl_ast_build *build,
9730 __isl_take isl_union_map *schedule);
9732 =head3 Inspecting the AST
9734 The basic properties of an AST node can be obtained as follows.
9736 #include <isl/ast.h>
9737 enum isl_ast_node_type isl_ast_node_get_type(
9738 __isl_keep isl_ast_node *node);
9740 The type of an AST node is one of
9741 C<isl_ast_node_for>,
9743 C<isl_ast_node_block>,
9744 C<isl_ast_node_mark> or
9745 C<isl_ast_node_user>.
9746 An C<isl_ast_node_for> represents a for node.
9747 An C<isl_ast_node_if> represents an if node.
9748 An C<isl_ast_node_block> represents a compound node.
9749 An C<isl_ast_node_mark> introduces a mark in the AST.
9750 An C<isl_ast_node_user> represents an expression statement.
9751 An expression statement typically corresponds to a domain element, i.e.,
9752 one of the elements that is visited by the AST.
9754 Each type of node has its own additional properties.
9756 #include <isl/ast.h>
9757 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9758 __isl_keep isl_ast_node *node);
9759 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9760 __isl_keep isl_ast_node *node);
9761 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9762 __isl_keep isl_ast_node *node);
9763 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9764 __isl_keep isl_ast_node *node);
9765 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9766 __isl_keep isl_ast_node *node);
9767 isl_bool isl_ast_node_for_is_degenerate(
9768 __isl_keep isl_ast_node *node);
9770 An C<isl_ast_for> is considered degenerate if it is known to execute
9773 #include <isl/ast.h>
9774 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9775 __isl_keep isl_ast_node *node);
9776 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9777 __isl_keep isl_ast_node *node);
9778 isl_bool isl_ast_node_if_has_else(
9779 __isl_keep isl_ast_node *node);
9780 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9781 __isl_keep isl_ast_node *node);
9783 __isl_give isl_ast_node_list *
9784 isl_ast_node_block_get_children(
9785 __isl_keep isl_ast_node *node);
9787 __isl_give isl_id *isl_ast_node_mark_get_id(
9788 __isl_keep isl_ast_node *node);
9789 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9790 __isl_keep isl_ast_node *node);
9792 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9793 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9795 #include <isl/ast.h>
9796 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9797 __isl_keep isl_ast_node *node);
9799 All descendants of a specific node in the AST (including the node itself)
9801 in depth-first pre-order using the following function.
9803 #include <isl/ast.h>
9804 isl_stat isl_ast_node_foreach_descendant_top_down(
9805 __isl_keep isl_ast_node *node,
9806 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9807 void *user), void *user);
9809 The callback function should return C<isl_bool_true> if the children
9810 of the given node should be visited and C<isl_bool_false> if they should not.
9811 It should return C<isl_bool_error> in case of failure, in which case
9812 the entire traversal is aborted.
9814 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9815 the following functions.
9817 #include <isl/ast.h>
9818 enum isl_ast_expr_type isl_ast_expr_get_type(
9819 __isl_keep isl_ast_expr *expr);
9821 The type of an AST expression is one of
9823 C<isl_ast_expr_id> or
9824 C<isl_ast_expr_int>.
9825 An C<isl_ast_expr_op> represents the result of an operation.
9826 An C<isl_ast_expr_id> represents an identifier.
9827 An C<isl_ast_expr_int> represents an integer value.
9829 Each type of expression has its own additional properties.
9831 #include <isl/ast.h>
9832 enum isl_ast_op_type isl_ast_expr_get_op_type(
9833 __isl_keep isl_ast_expr *expr);
9834 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9835 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9836 __isl_keep isl_ast_expr *expr, int pos);
9837 isl_stat isl_ast_expr_foreach_ast_op_type(
9838 __isl_keep isl_ast_expr *expr,
9839 isl_stat (*fn)(enum isl_ast_op_type type,
9840 void *user), void *user);
9841 isl_stat isl_ast_node_foreach_ast_op_type(
9842 __isl_keep isl_ast_node *node,
9843 isl_stat (*fn)(enum isl_ast_op_type type,
9844 void *user), void *user);
9846 C<isl_ast_expr_get_op_type> returns the type of the operation
9847 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9848 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9850 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9851 C<isl_ast_op_type> that appears in C<expr>.
9852 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9853 C<isl_ast_op_type> that appears in C<node>.
9854 The operation type is one of the following.
9858 =item C<isl_ast_op_and>
9860 Logical I<and> of two arguments.
9861 Both arguments can be evaluated.
9863 =item C<isl_ast_op_and_then>
9865 Logical I<and> of two arguments.
9866 The second argument can only be evaluated if the first evaluates to true.
9868 =item C<isl_ast_op_or>
9870 Logical I<or> of two arguments.
9871 Both arguments can be evaluated.
9873 =item C<isl_ast_op_or_else>
9875 Logical I<or> of two arguments.
9876 The second argument can only be evaluated if the first evaluates to false.
9878 =item C<isl_ast_op_max>
9880 Maximum of two or more arguments.
9882 =item C<isl_ast_op_min>
9884 Minimum of two or more arguments.
9886 =item C<isl_ast_op_minus>
9890 =item C<isl_ast_op_add>
9892 Sum of two arguments.
9894 =item C<isl_ast_op_sub>
9896 Difference of two arguments.
9898 =item C<isl_ast_op_mul>
9900 Product of two arguments.
9902 =item C<isl_ast_op_div>
9904 Exact division. That is, the result is known to be an integer.
9906 =item C<isl_ast_op_fdiv_q>
9908 Result of integer division, rounded towards negative
9911 =item C<isl_ast_op_pdiv_q>
9913 Result of integer division, where dividend is known to be non-negative.
9915 =item C<isl_ast_op_pdiv_r>
9917 Remainder of integer division, where dividend is known to be non-negative.
9919 =item C<isl_ast_op_zdiv_r>
9921 Equal to zero iff the remainder on integer division is zero.
9923 =item C<isl_ast_op_cond>
9925 Conditional operator defined on three arguments.
9926 If the first argument evaluates to true, then the result
9927 is equal to the second argument. Otherwise, the result
9928 is equal to the third argument.
9929 The second and third argument may only be evaluated if
9930 the first argument evaluates to true and false, respectively.
9931 Corresponds to C<a ? b : c> in C.
9933 =item C<isl_ast_op_select>
9935 Conditional operator defined on three arguments.
9936 If the first argument evaluates to true, then the result
9937 is equal to the second argument. Otherwise, the result
9938 is equal to the third argument.
9939 The second and third argument may be evaluated independently
9940 of the value of the first argument.
9941 Corresponds to C<a * b + (1 - a) * c> in C.
9943 =item C<isl_ast_op_eq>
9947 =item C<isl_ast_op_le>
9949 Less than or equal relation.
9951 =item C<isl_ast_op_lt>
9955 =item C<isl_ast_op_ge>
9957 Greater than or equal relation.
9959 =item C<isl_ast_op_gt>
9961 Greater than relation.
9963 =item C<isl_ast_op_call>
9966 The number of arguments of the C<isl_ast_expr> is one more than
9967 the number of arguments in the function call, the first argument
9968 representing the function being called.
9970 =item C<isl_ast_op_access>
9973 The number of arguments of the C<isl_ast_expr> is one more than
9974 the number of index expressions in the array access, the first argument
9975 representing the array being accessed.
9977 =item C<isl_ast_op_member>
9980 This operation has two arguments, a structure and the name of
9981 the member of the structure being accessed.
9985 #include <isl/ast.h>
9986 __isl_give isl_id *isl_ast_expr_get_id(
9987 __isl_keep isl_ast_expr *expr);
9989 Return the identifier represented by the AST expression.
9991 #include <isl/ast.h>
9992 __isl_give isl_val *isl_ast_expr_get_val(
9993 __isl_keep isl_ast_expr *expr);
9995 Return the integer represented by the AST expression.
9997 =head3 Properties of ASTs
9999 #include <isl/ast.h>
10000 isl_bool isl_ast_expr_is_equal(
10001 __isl_keep isl_ast_expr *expr1,
10002 __isl_keep isl_ast_expr *expr2);
10004 Check if two C<isl_ast_expr>s are equal to each other.
10006 =head3 Manipulating and printing the AST
10008 AST nodes can be copied and freed using the following functions.
10010 #include <isl/ast.h>
10011 __isl_give isl_ast_node *isl_ast_node_copy(
10012 __isl_keep isl_ast_node *node);
10013 __isl_null isl_ast_node *isl_ast_node_free(
10014 __isl_take isl_ast_node *node);
10016 AST expressions can be copied and freed using the following functions.
10018 #include <isl/ast.h>
10019 __isl_give isl_ast_expr *isl_ast_expr_copy(
10020 __isl_keep isl_ast_expr *expr);
10021 __isl_null isl_ast_expr *isl_ast_expr_free(
10022 __isl_take isl_ast_expr *expr);
10024 New AST expressions can be created either directly or within
10025 the context of an C<isl_ast_build>.
10027 #include <isl/ast.h>
10028 __isl_give isl_ast_expr *isl_ast_expr_from_val(
10029 __isl_take isl_val *v);
10030 __isl_give isl_ast_expr *isl_ast_expr_from_id(
10031 __isl_take isl_id *id);
10032 __isl_give isl_ast_expr *isl_ast_expr_neg(
10033 __isl_take isl_ast_expr *expr);
10034 __isl_give isl_ast_expr *isl_ast_expr_address_of(
10035 __isl_take isl_ast_expr *expr);
10036 __isl_give isl_ast_expr *isl_ast_expr_add(
10037 __isl_take isl_ast_expr *expr1,
10038 __isl_take isl_ast_expr *expr2);
10039 __isl_give isl_ast_expr *isl_ast_expr_sub(
10040 __isl_take isl_ast_expr *expr1,
10041 __isl_take isl_ast_expr *expr2);
10042 __isl_give isl_ast_expr *isl_ast_expr_mul(
10043 __isl_take isl_ast_expr *expr1,
10044 __isl_take isl_ast_expr *expr2);
10045 __isl_give isl_ast_expr *isl_ast_expr_div(
10046 __isl_take isl_ast_expr *expr1,
10047 __isl_take isl_ast_expr *expr2);
10048 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
10049 __isl_take isl_ast_expr *expr1,
10050 __isl_take isl_ast_expr *expr2);
10051 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
10052 __isl_take isl_ast_expr *expr1,
10053 __isl_take isl_ast_expr *expr2);
10054 __isl_give isl_ast_expr *isl_ast_expr_and(
10055 __isl_take isl_ast_expr *expr1,
10056 __isl_take isl_ast_expr *expr2)
10057 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10058 __isl_take isl_ast_expr *expr1,
10059 __isl_take isl_ast_expr *expr2)
10060 __isl_give isl_ast_expr *isl_ast_expr_or(
10061 __isl_take isl_ast_expr *expr1,
10062 __isl_take isl_ast_expr *expr2)
10063 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10064 __isl_take isl_ast_expr *expr1,
10065 __isl_take isl_ast_expr *expr2)
10066 __isl_give isl_ast_expr *isl_ast_expr_eq(
10067 __isl_take isl_ast_expr *expr1,
10068 __isl_take isl_ast_expr *expr2);
10069 __isl_give isl_ast_expr *isl_ast_expr_le(
10070 __isl_take isl_ast_expr *expr1,
10071 __isl_take isl_ast_expr *expr2);
10072 __isl_give isl_ast_expr *isl_ast_expr_lt(
10073 __isl_take isl_ast_expr *expr1,
10074 __isl_take isl_ast_expr *expr2);
10075 __isl_give isl_ast_expr *isl_ast_expr_ge(
10076 __isl_take isl_ast_expr *expr1,
10077 __isl_take isl_ast_expr *expr2);
10078 __isl_give isl_ast_expr *isl_ast_expr_gt(
10079 __isl_take isl_ast_expr *expr1,
10080 __isl_take isl_ast_expr *expr2);
10081 __isl_give isl_ast_expr *isl_ast_expr_access(
10082 __isl_take isl_ast_expr *array,
10083 __isl_take isl_ast_expr_list *indices);
10084 __isl_give isl_ast_expr *isl_ast_expr_call(
10085 __isl_take isl_ast_expr *function,
10086 __isl_take isl_ast_expr_list *arguments);
10088 The function C<isl_ast_expr_address_of> can be applied to an
10089 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10090 to represent the address of the C<isl_ast_expr_access>. The function
10091 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10092 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10094 #include <isl/ast_build.h>
10095 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10096 __isl_keep isl_ast_build *build,
10097 __isl_take isl_set *set);
10098 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10099 __isl_keep isl_ast_build *build,
10100 __isl_take isl_pw_aff *pa);
10101 __isl_give isl_ast_expr *
10102 isl_ast_build_access_from_pw_multi_aff(
10103 __isl_keep isl_ast_build *build,
10104 __isl_take isl_pw_multi_aff *pma);
10105 __isl_give isl_ast_expr *
10106 isl_ast_build_access_from_multi_pw_aff(
10107 __isl_keep isl_ast_build *build,
10108 __isl_take isl_multi_pw_aff *mpa);
10109 __isl_give isl_ast_expr *
10110 isl_ast_build_call_from_pw_multi_aff(
10111 __isl_keep isl_ast_build *build,
10112 __isl_take isl_pw_multi_aff *pma);
10113 __isl_give isl_ast_expr *
10114 isl_ast_build_call_from_multi_pw_aff(
10115 __isl_keep isl_ast_build *build,
10116 __isl_take isl_multi_pw_aff *mpa);
10119 the domains of C<pa>, C<mpa> and C<pma> should correspond
10120 to the schedule space of C<build>.
10121 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10122 the function being called.
10123 If the accessed space is a nested relation, then it is taken
10124 to represent an access of the member specified by the range
10125 of this nested relation of the structure specified by the domain
10126 of the nested relation.
10128 The following functions can be used to modify an C<isl_ast_expr>.
10130 #include <isl/ast.h>
10131 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10132 __isl_take isl_ast_expr *expr, int pos,
10133 __isl_take isl_ast_expr *arg);
10135 Replace the argument of C<expr> at position C<pos> by C<arg>.
10137 #include <isl/ast.h>
10138 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10139 __isl_take isl_ast_expr *expr,
10140 __isl_take isl_id_to_ast_expr *id2expr);
10142 The function C<isl_ast_expr_substitute_ids> replaces the
10143 subexpressions of C<expr> of type C<isl_ast_expr_id>
10144 by the corresponding expression in C<id2expr>, if there is any.
10147 User specified data can be attached to an C<isl_ast_node> and obtained
10148 from the same C<isl_ast_node> using the following functions.
10150 #include <isl/ast.h>
10151 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10152 __isl_take isl_ast_node *node,
10153 __isl_take isl_id *annotation);
10154 __isl_give isl_id *isl_ast_node_get_annotation(
10155 __isl_keep isl_ast_node *node);
10157 Basic printing can be performed using the following functions.
10159 #include <isl/ast.h>
10160 __isl_give isl_printer *isl_printer_print_ast_expr(
10161 __isl_take isl_printer *p,
10162 __isl_keep isl_ast_expr *expr);
10163 __isl_give isl_printer *isl_printer_print_ast_node(
10164 __isl_take isl_printer *p,
10165 __isl_keep isl_ast_node *node);
10166 __isl_give char *isl_ast_expr_to_str(
10167 __isl_keep isl_ast_expr *expr);
10168 __isl_give char *isl_ast_node_to_str(
10169 __isl_keep isl_ast_node *node);
10170 __isl_give char *isl_ast_expr_to_C_str(
10171 __isl_keep isl_ast_expr *expr);
10172 __isl_give char *isl_ast_node_to_C_str(
10173 __isl_keep isl_ast_node *node);
10175 The functions C<isl_ast_expr_to_C_str> and
10176 C<isl_ast_node_to_C_str> are convenience functions
10177 that return a string representation of the input in C format.
10179 More advanced printing can be performed using the following functions.
10181 #include <isl/ast.h>
10182 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10183 __isl_take isl_printer *p,
10184 enum isl_ast_op_type type,
10185 __isl_keep const char *name);
10186 isl_stat isl_options_set_ast_print_macro_once(
10187 isl_ctx *ctx, int val);
10188 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10189 __isl_give isl_printer *isl_ast_op_type_print_macro(
10190 enum isl_ast_op_type type,
10191 __isl_take isl_printer *p);
10192 __isl_give isl_printer *isl_ast_expr_print_macros(
10193 __isl_keep isl_ast_expr *expr,
10194 __isl_take isl_printer *p);
10195 __isl_give isl_printer *isl_ast_node_print_macros(
10196 __isl_keep isl_ast_node *node,
10197 __isl_take isl_printer *p);
10198 __isl_give isl_printer *isl_ast_node_print(
10199 __isl_keep isl_ast_node *node,
10200 __isl_take isl_printer *p,
10201 __isl_take isl_ast_print_options *options);
10202 __isl_give isl_printer *isl_ast_node_for_print(
10203 __isl_keep isl_ast_node *node,
10204 __isl_take isl_printer *p,
10205 __isl_take isl_ast_print_options *options);
10206 __isl_give isl_printer *isl_ast_node_if_print(
10207 __isl_keep isl_ast_node *node,
10208 __isl_take isl_printer *p,
10209 __isl_take isl_ast_print_options *options);
10211 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10212 C<isl> may print out an AST that makes use of macros such
10213 as C<floord>, C<min> and C<max>.
10214 The names of these macros may be modified by a call
10215 to C<isl_ast_op_type_set_print_name>. The user-specified
10216 names are associated to the printer object.
10217 C<isl_ast_op_type_print_macro> prints out the macro
10218 corresponding to a specific C<isl_ast_op_type>.
10219 If the print-macro-once option is set, then a given macro definition
10220 is only printed once to any given printer object.
10221 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10222 for subexpressions where these macros would be used and prints
10223 out the required macro definitions.
10224 Essentially, C<isl_ast_expr_print_macros> calls
10225 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10226 as function argument.
10227 C<isl_ast_node_print_macros> does the same
10228 for expressions in its C<isl_ast_node> argument.
10229 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10230 C<isl_ast_node_if_print> print an C<isl_ast_node>
10231 in C<ISL_FORMAT_C>, but allow for some extra control
10232 through an C<isl_ast_print_options> object.
10233 This object can be created using the following functions.
10235 #include <isl/ast.h>
10236 __isl_give isl_ast_print_options *
10237 isl_ast_print_options_alloc(isl_ctx *ctx);
10238 __isl_give isl_ast_print_options *
10239 isl_ast_print_options_copy(
10240 __isl_keep isl_ast_print_options *options);
10241 __isl_null isl_ast_print_options *
10242 isl_ast_print_options_free(
10243 __isl_take isl_ast_print_options *options);
10245 __isl_give isl_ast_print_options *
10246 isl_ast_print_options_set_print_user(
10247 __isl_take isl_ast_print_options *options,
10248 __isl_give isl_printer *(*print_user)(
10249 __isl_take isl_printer *p,
10250 __isl_take isl_ast_print_options *options,
10251 __isl_keep isl_ast_node *node, void *user),
10253 __isl_give isl_ast_print_options *
10254 isl_ast_print_options_set_print_for(
10255 __isl_take isl_ast_print_options *options,
10256 __isl_give isl_printer *(*print_for)(
10257 __isl_take isl_printer *p,
10258 __isl_take isl_ast_print_options *options,
10259 __isl_keep isl_ast_node *node, void *user),
10262 The callback set by C<isl_ast_print_options_set_print_user>
10263 is called whenever a node of type C<isl_ast_node_user> needs to
10265 The callback set by C<isl_ast_print_options_set_print_for>
10266 is called whenever a node of type C<isl_ast_node_for> needs to
10268 Note that C<isl_ast_node_for_print> will I<not> call the
10269 callback set by C<isl_ast_print_options_set_print_for> on the node
10270 on which C<isl_ast_node_for_print> is called, but only on nested
10271 nodes of type C<isl_ast_node_for>. It is therefore safe to
10272 call C<isl_ast_node_for_print> from within the callback set by
10273 C<isl_ast_print_options_set_print_for>.
10275 The following option determines the type to be used for iterators
10276 while printing the AST.
10278 isl_stat isl_options_set_ast_iterator_type(
10279 isl_ctx *ctx, const char *val);
10280 const char *isl_options_get_ast_iterator_type(
10283 The AST printer only prints body nodes as blocks if these
10284 blocks cannot be safely omitted.
10285 For example, a C<for> node with one body node will not be
10286 surrounded with braces in C<ISL_FORMAT_C>.
10287 A block will always be printed by setting the following option.
10289 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10291 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10295 #include <isl/ast_build.h>
10296 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10297 isl_ctx *ctx, int val);
10298 int isl_options_get_ast_build_atomic_upper_bound(
10300 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10302 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10303 isl_stat isl_options_set_ast_build_detect_min_max(
10304 isl_ctx *ctx, int val);
10305 int isl_options_get_ast_build_detect_min_max(
10307 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10308 isl_ctx *ctx, int val);
10309 int isl_options_get_ast_build_exploit_nested_bounds(
10311 isl_stat isl_options_set_ast_build_group_coscheduled(
10312 isl_ctx *ctx, int val);
10313 int isl_options_get_ast_build_group_coscheduled(
10315 isl_stat isl_options_set_ast_build_scale_strides(
10316 isl_ctx *ctx, int val);
10317 int isl_options_get_ast_build_scale_strides(
10319 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10321 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10322 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10324 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10328 =item * ast_build_atomic_upper_bound
10330 Generate loop upper bounds that consist of the current loop iterator,
10331 an operator and an expression not involving the iterator.
10332 If this option is not set, then the current loop iterator may appear
10333 several times in the upper bound.
10334 For example, when this option is turned off, AST generation
10337 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10341 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10344 When the option is turned on, the following AST is generated
10346 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10349 =item * ast_build_prefer_pdiv
10351 If this option is turned off, then the AST generation will
10352 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10353 operators, but no C<isl_ast_op_pdiv_q> or
10354 C<isl_ast_op_pdiv_r> operators.
10355 If this option is turned on, then C<isl> will try to convert
10356 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10357 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10359 =item * ast_build_detect_min_max
10361 If this option is turned on, then C<isl> will try and detect
10362 min or max-expressions when building AST expressions from
10363 piecewise affine expressions.
10365 =item * ast_build_exploit_nested_bounds
10367 Simplify conditions based on bounds of nested for loops.
10368 In particular, remove conditions that are implied by the fact
10369 that one or more nested loops have at least one iteration,
10370 meaning that the upper bound is at least as large as the lower bound.
10371 For example, when this option is turned off, AST generation
10374 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10380 for (int c0 = 0; c0 <= N; c0 += 1)
10381 for (int c1 = 0; c1 <= M; c1 += 1)
10384 When the option is turned on, the following AST is generated
10386 for (int c0 = 0; c0 <= N; c0 += 1)
10387 for (int c1 = 0; c1 <= M; c1 += 1)
10390 =item * ast_build_group_coscheduled
10392 If two domain elements are assigned the same schedule point, then
10393 they may be executed in any order and they may even appear in different
10394 loops. If this options is set, then the AST generator will make
10395 sure that coscheduled domain elements do not appear in separate parts
10396 of the AST. This is useful in case of nested AST generation
10397 if the outer AST generation is given only part of a schedule
10398 and the inner AST generation should handle the domains that are
10399 coscheduled by this initial part of the schedule together.
10400 For example if an AST is generated for a schedule
10402 { A[i] -> [0]; B[i] -> [0] }
10404 then the C<isl_ast_build_set_create_leaf> callback described
10405 below may get called twice, once for each domain.
10406 Setting this option ensures that the callback is only called once
10407 on both domains together.
10409 =item * ast_build_separation_bounds
10411 This option specifies which bounds to use during separation.
10412 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10413 then all (possibly implicit) bounds on the current dimension will
10414 be used during separation.
10415 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10416 then only those bounds that are explicitly available will
10417 be used during separation.
10419 =item * ast_build_scale_strides
10421 This option specifies whether the AST generator is allowed
10422 to scale down iterators of strided loops.
10424 =item * ast_build_allow_else
10426 This option specifies whether the AST generator is allowed
10427 to construct if statements with else branches.
10429 =item * ast_build_allow_or
10431 This option specifies whether the AST generator is allowed
10432 to construct if conditions with disjunctions.
10436 =head3 AST Generation Options (Schedule Tree)
10438 In case of AST construction from a schedule tree, the options
10439 that control how an AST is created from the individual schedule
10440 dimensions are stored in the band nodes of the tree
10441 (see L</"Schedule Trees">).
10443 In particular, a schedule dimension can be handled in four
10444 different ways, atomic, separate, unroll or the default.
10445 This loop AST generation type can be set using
10446 C<isl_schedule_node_band_member_set_ast_loop_type>.
10448 the first three can be selected by including a one-dimensional
10449 element with as value the position of the schedule dimension
10450 within the band and as name one of C<atomic>, C<separate>
10451 or C<unroll> in the options
10452 set by C<isl_schedule_node_band_set_ast_build_options>.
10453 Only one of these three may be specified for
10454 any given schedule dimension within a band node.
10455 If none of these is specified, then the default
10456 is used. The meaning of the options is as follows.
10462 When this option is specified, the AST generator will make
10463 sure that a given domains space only appears in a single
10464 loop at the specified level.
10466 For example, for the schedule tree
10468 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10470 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10471 options: "{ atomic[x] }"
10473 the following AST will be generated
10475 for (int c0 = 0; c0 <= 10; c0 += 1) {
10482 On the other hand, for the schedule tree
10484 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10486 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10487 options: "{ separate[x] }"
10489 the following AST will be generated
10493 for (int c0 = 1; c0 <= 9; c0 += 1) {
10500 If neither C<atomic> nor C<separate> is specified, then the AST generator
10501 may produce either of these two results or some intermediate form.
10505 When this option is specified, the AST generator will
10506 split the domain of the specified schedule dimension
10507 into pieces with a fixed set of statements for which
10508 instances need to be executed by the iterations in
10509 the schedule domain part. This option tends to avoid
10510 the generation of guards inside the corresponding loops.
10511 See also the C<atomic> option.
10515 When this option is specified, the AST generator will
10516 I<completely> unroll the corresponding schedule dimension.
10517 It is the responsibility of the user to ensure that such
10518 unrolling is possible.
10519 To obtain a partial unrolling, the user should apply an additional
10520 strip-mining to the schedule and fully unroll the inner schedule
10525 The C<isolate> option is a bit more involved. It allows the user
10526 to isolate a range of schedule dimension values from smaller and
10527 greater values. Additionally, the user may specify a different
10528 atomic/separate/unroll choice for the isolated part and the remaining
10529 parts. The typical use case of the C<isolate> option is to isolate
10530 full tiles from partial tiles.
10531 The part that needs to be isolated may depend on outer schedule dimensions.
10532 The option therefore needs to be able to reference those outer schedule
10533 dimensions. In particular, the space of the C<isolate> option is that
10534 of a wrapped map with as domain the flat product of all outer band nodes
10535 and as range the space of the current band node.
10536 The atomic/separate/unroll choice for the isolated part is determined
10537 by an option that lives in an unnamed wrapped space with as domain
10538 a zero-dimensional C<isolate> space and as range the regular
10539 C<atomic>, C<separate> or C<unroll> space.
10540 This option may also be set directly using
10541 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10542 The atomic/separate/unroll choice for the remaining part is determined
10543 by the regular C<atomic>, C<separate> or C<unroll> option.
10544 Since the C<isolate> option references outer schedule dimensions,
10545 its use in a band node causes any tree containing the node
10546 to be considered anchored.
10548 As an example, consider the isolation of full tiles from partial tiles
10549 in a tiling of a triangular domain. The original schedule is as follows.
10551 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10553 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10554 { A[i,j] -> [floor(j/10)] }, \
10555 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10559 for (int c0 = 0; c0 <= 10; c0 += 1)
10560 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10561 for (int c2 = 10 * c0;
10562 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10563 for (int c3 = 10 * c1;
10564 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10567 Isolating the full tiles, we have the following input
10569 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10571 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10572 { A[i,j] -> [floor(j/10)] }, \
10573 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10574 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10575 10a+9+10b+9 <= 100 }"
10580 for (int c0 = 0; c0 <= 8; c0 += 1) {
10581 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10582 for (int c2 = 10 * c0;
10583 c2 <= 10 * c0 + 9; c2 += 1)
10584 for (int c3 = 10 * c1;
10585 c3 <= 10 * c1 + 9; c3 += 1)
10587 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10588 for (int c2 = 10 * c0;
10589 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10590 for (int c3 = 10 * c1;
10591 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10594 for (int c0 = 9; c0 <= 10; c0 += 1)
10595 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10596 for (int c2 = 10 * c0;
10597 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10598 for (int c3 = 10 * c1;
10599 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10603 We may then additionally unroll the innermost loop of the isolated part
10605 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10607 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10608 { A[i,j] -> [floor(j/10)] }, \
10609 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10610 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10611 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10616 for (int c0 = 0; c0 <= 8; c0 += 1) {
10617 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10618 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10620 A(c2, 10 * c1 + 1);
10621 A(c2, 10 * c1 + 2);
10622 A(c2, 10 * c1 + 3);
10623 A(c2, 10 * c1 + 4);
10624 A(c2, 10 * c1 + 5);
10625 A(c2, 10 * c1 + 6);
10626 A(c2, 10 * c1 + 7);
10627 A(c2, 10 * c1 + 8);
10628 A(c2, 10 * c1 + 9);
10630 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10631 for (int c2 = 10 * c0;
10632 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10633 for (int c3 = 10 * c1;
10634 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10637 for (int c0 = 9; c0 <= 10; c0 += 1)
10638 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10639 for (int c2 = 10 * c0;
10640 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10641 for (int c3 = 10 * c1;
10642 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10647 =head3 AST Generation Options (Schedule Map)
10649 In case of AST construction using
10650 C<isl_ast_build_node_from_schedule_map>, the options
10651 that control how an AST is created from the individual schedule
10652 dimensions are stored in the C<isl_ast_build>.
10653 They can be set using the following function.
10655 #include <isl/ast_build.h>
10656 __isl_give isl_ast_build *
10657 isl_ast_build_set_options(
10658 __isl_take isl_ast_build *build,
10659 __isl_take isl_union_map *options);
10661 The options are encoded in an C<isl_union_map>.
10662 The domain of this union relation refers to the schedule domain,
10663 i.e., the range of the schedule passed
10664 to C<isl_ast_build_node_from_schedule_map>.
10665 In the case of nested AST generation (see L</"Nested AST Generation">),
10666 the domain of C<options> should refer to the extra piece of the schedule.
10667 That is, it should be equal to the range of the wrapped relation in the
10668 range of the schedule.
10669 The range of the options can consist of elements in one or more spaces,
10670 the names of which determine the effect of the option.
10671 The values of the range typically also refer to the schedule dimension
10672 to which the option applies. In case of nested AST generation
10673 (see L</"Nested AST Generation">), these values refer to the position
10674 of the schedule dimension within the innermost AST generation.
10675 The constraints on the domain elements of
10676 the option should only refer to this dimension and earlier dimensions.
10677 We consider the following spaces.
10681 =item C<separation_class>
10683 B<This option has been deprecated. Use the isolate option on
10684 schedule trees instead.>
10686 This space is a wrapped relation between two one dimensional spaces.
10687 The input space represents the schedule dimension to which the option
10688 applies and the output space represents the separation class.
10689 While constructing a loop corresponding to the specified schedule
10690 dimension(s), the AST generator will try to generate separate loops
10691 for domain elements that are assigned different classes.
10692 If only some of the elements are assigned a class, then those elements
10693 that are not assigned any class will be treated as belonging to a class
10694 that is separate from the explicitly assigned classes.
10695 The typical use case for this option is to separate full tiles from
10697 The other options, described below, are applied after the separation
10700 As an example, consider the separation into full and partial tiles
10701 of a tiling of a triangular domain.
10702 Take, for example, the domain
10704 { A[i,j] : 0 <= i,j and i + j <= 100 }
10706 and a tiling into tiles of 10 by 10. The input to the AST generator
10707 is then the schedule
10709 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10712 Without any options, the following AST is generated
10714 for (int c0 = 0; c0 <= 10; c0 += 1)
10715 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10716 for (int c2 = 10 * c0;
10717 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10719 for (int c3 = 10 * c1;
10720 c3 <= min(10 * c1 + 9, -c2 + 100);
10724 Separation into full and partial tiles can be obtained by assigning
10725 a class, say C<0>, to the full tiles. The full tiles are represented by those
10726 values of the first and second schedule dimensions for which there are
10727 values of the third and fourth dimensions to cover an entire tile.
10728 That is, we need to specify the following option
10730 { [a,b,c,d] -> separation_class[[0]->[0]] :
10731 exists b': 0 <= 10a,10b' and
10732 10a+9+10b'+9 <= 100;
10733 [a,b,c,d] -> separation_class[[1]->[0]] :
10734 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10736 which simplifies to
10738 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10739 a >= 0 and b >= 0 and b <= 8 - a;
10740 [a, b, c, d] -> separation_class[[0] -> [0]] :
10741 a >= 0 and a <= 8 }
10743 With this option, the generated AST is as follows
10746 for (int c0 = 0; c0 <= 8; c0 += 1) {
10747 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10748 for (int c2 = 10 * c0;
10749 c2 <= 10 * c0 + 9; c2 += 1)
10750 for (int c3 = 10 * c1;
10751 c3 <= 10 * c1 + 9; c3 += 1)
10753 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10754 for (int c2 = 10 * c0;
10755 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10757 for (int c3 = 10 * c1;
10758 c3 <= min(-c2 + 100, 10 * c1 + 9);
10762 for (int c0 = 9; c0 <= 10; c0 += 1)
10763 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10764 for (int c2 = 10 * c0;
10765 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10767 for (int c3 = 10 * c1;
10768 c3 <= min(10 * c1 + 9, -c2 + 100);
10775 This is a single-dimensional space representing the schedule dimension(s)
10776 to which ``separation'' should be applied. Separation tries to split
10777 a loop into several pieces if this can avoid the generation of guards
10779 See also the C<atomic> option.
10783 This is a single-dimensional space representing the schedule dimension(s)
10784 for which the domains should be considered ``atomic''. That is, the
10785 AST generator will make sure that any given domain space will only appear
10786 in a single loop at the specified level.
10788 Consider the following schedule
10790 { a[i] -> [i] : 0 <= i < 10;
10791 b[i] -> [i+1] : 0 <= i < 10 }
10793 If the following option is specified
10795 { [i] -> separate[x] }
10797 then the following AST will be generated
10801 for (int c0 = 1; c0 <= 9; c0 += 1) {
10808 If, on the other hand, the following option is specified
10810 { [i] -> atomic[x] }
10812 then the following AST will be generated
10814 for (int c0 = 0; c0 <= 10; c0 += 1) {
10821 If neither C<atomic> nor C<separate> is specified, then the AST generator
10822 may produce either of these two results or some intermediate form.
10826 This is a single-dimensional space representing the schedule dimension(s)
10827 that should be I<completely> unrolled.
10828 To obtain a partial unrolling, the user should apply an additional
10829 strip-mining to the schedule and fully unroll the inner loop.
10833 =head3 Fine-grained Control over AST Generation
10835 Besides specifying the constraints on the parameters,
10836 an C<isl_ast_build> object can be used to control
10837 various aspects of the AST generation process.
10838 In case of AST construction using
10839 C<isl_ast_build_node_from_schedule_map>,
10840 the most prominent way of control is through ``options'',
10841 as explained above.
10843 Additional control is available through the following functions.
10845 #include <isl/ast_build.h>
10846 __isl_give isl_ast_build *
10847 isl_ast_build_set_iterators(
10848 __isl_take isl_ast_build *build,
10849 __isl_take isl_id_list *iterators);
10851 The function C<isl_ast_build_set_iterators> allows the user to
10852 specify a list of iterator C<isl_id>s to be used as iterators.
10853 If the input schedule is injective, then
10854 the number of elements in this list should be as large as the dimension
10855 of the schedule space, but no direct correspondence should be assumed
10856 between dimensions and elements.
10857 If the input schedule is not injective, then an additional number
10858 of C<isl_id>s equal to the largest dimension of the input domains
10860 If the number of provided C<isl_id>s is insufficient, then additional
10861 names are automatically generated.
10863 #include <isl/ast_build.h>
10864 __isl_give isl_ast_build *
10865 isl_ast_build_set_create_leaf(
10866 __isl_take isl_ast_build *build,
10867 __isl_give isl_ast_node *(*fn)(
10868 __isl_take isl_ast_build *build,
10869 void *user), void *user);
10872 C<isl_ast_build_set_create_leaf> function allows for the
10873 specification of a callback that should be called whenever the AST
10874 generator arrives at an element of the schedule domain.
10875 The callback should return an AST node that should be inserted
10876 at the corresponding position of the AST. The default action (when
10877 the callback is not set) is to continue generating parts of the AST to scan
10878 all the domain elements associated to the schedule domain element
10879 and to insert user nodes, ``calling'' the domain element, for each of them.
10880 The C<build> argument contains the current state of the C<isl_ast_build>.
10881 To ease nested AST generation (see L</"Nested AST Generation">),
10882 all control information that is
10883 specific to the current AST generation such as the options and
10884 the callbacks has been removed from this C<isl_ast_build>.
10885 The callback would typically return the result of a nested
10886 AST generation or a
10887 user defined node created using the following function.
10889 #include <isl/ast.h>
10890 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10891 __isl_take isl_ast_expr *expr);
10893 #include <isl/ast_build.h>
10894 __isl_give isl_ast_build *
10895 isl_ast_build_set_at_each_domain(
10896 __isl_take isl_ast_build *build,
10897 __isl_give isl_ast_node *(*fn)(
10898 __isl_take isl_ast_node *node,
10899 __isl_keep isl_ast_build *build,
10900 void *user), void *user);
10901 __isl_give isl_ast_build *
10902 isl_ast_build_set_before_each_for(
10903 __isl_take isl_ast_build *build,
10904 __isl_give isl_id *(*fn)(
10905 __isl_keep isl_ast_build *build,
10906 void *user), void *user);
10907 __isl_give isl_ast_build *
10908 isl_ast_build_set_after_each_for(
10909 __isl_take isl_ast_build *build,
10910 __isl_give isl_ast_node *(*fn)(
10911 __isl_take isl_ast_node *node,
10912 __isl_keep isl_ast_build *build,
10913 void *user), void *user);
10914 __isl_give isl_ast_build *
10915 isl_ast_build_set_before_each_mark(
10916 __isl_take isl_ast_build *build,
10917 isl_stat (*fn)(__isl_keep isl_id *mark,
10918 __isl_keep isl_ast_build *build,
10919 void *user), void *user);
10920 __isl_give isl_ast_build *
10921 isl_ast_build_set_after_each_mark(
10922 __isl_take isl_ast_build *build,
10923 __isl_give isl_ast_node *(*fn)(
10924 __isl_take isl_ast_node *node,
10925 __isl_keep isl_ast_build *build,
10926 void *user), void *user);
10928 The callback set by C<isl_ast_build_set_at_each_domain> will
10929 be called for each domain AST node.
10930 The callbacks set by C<isl_ast_build_set_before_each_for>
10931 and C<isl_ast_build_set_after_each_for> will be called
10932 for each for AST node. The first will be called in depth-first
10933 pre-order, while the second will be called in depth-first post-order.
10934 Since C<isl_ast_build_set_before_each_for> is called before the for
10935 node is actually constructed, it is only passed an C<isl_ast_build>.
10936 The returned C<isl_id> will be added as an annotation (using
10937 C<isl_ast_node_set_annotation>) to the constructed for node.
10938 In particular, if the user has also specified an C<after_each_for>
10939 callback, then the annotation can be retrieved from the node passed to
10940 that callback using C<isl_ast_node_get_annotation>.
10941 The callbacks set by C<isl_ast_build_set_before_each_mark>
10942 and C<isl_ast_build_set_after_each_mark> will be called for each
10943 mark AST node that is created, i.e., for each mark schedule node
10944 in the input schedule tree. The first will be called in depth-first
10945 pre-order, while the second will be called in depth-first post-order.
10946 Since the callback set by C<isl_ast_build_set_before_each_mark>
10947 is called before the mark AST node is actually constructed, it is passed
10948 the identifier of the mark node.
10949 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
10950 The given C<isl_ast_build> can be used to create new
10951 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10952 or C<isl_ast_build_call_from_pw_multi_aff>.
10954 =head3 Nested AST Generation
10956 C<isl> allows the user to create an AST within the context
10957 of another AST. These nested ASTs are created using the
10958 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10959 the outer AST. The C<build> argument should be an C<isl_ast_build>
10960 passed to a callback set by
10961 C<isl_ast_build_set_create_leaf>.
10962 The space of the range of the C<schedule> argument should refer
10963 to this build. In particular, the space should be a wrapped
10964 relation and the domain of this wrapped relation should be the
10965 same as that of the range of the schedule returned by
10966 C<isl_ast_build_get_schedule> below.
10967 In practice, the new schedule is typically
10968 created by calling C<isl_union_map_range_product> on the old schedule
10969 and some extra piece of the schedule.
10970 The space of the schedule domain is also available from
10971 the C<isl_ast_build>.
10973 #include <isl/ast_build.h>
10974 __isl_give isl_union_map *isl_ast_build_get_schedule(
10975 __isl_keep isl_ast_build *build);
10976 __isl_give isl_space *isl_ast_build_get_schedule_space(
10977 __isl_keep isl_ast_build *build);
10978 __isl_give isl_ast_build *isl_ast_build_restrict(
10979 __isl_take isl_ast_build *build,
10980 __isl_take isl_set *set);
10982 The C<isl_ast_build_get_schedule> function returns a (partial)
10983 schedule for the domains elements for which part of the AST still needs to
10984 be generated in the current build.
10985 In particular, the domain elements are mapped to those iterations of the loops
10986 enclosing the current point of the AST generation inside which
10987 the domain elements are executed.
10988 No direct correspondence between
10989 the input schedule and this schedule should be assumed.
10990 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10991 to create a set for C<isl_ast_build_restrict> to intersect
10992 with the current build. In particular, the set passed to
10993 C<isl_ast_build_restrict> can have additional parameters.
10994 The ids of the set dimensions in the space returned by
10995 C<isl_ast_build_get_schedule_space> correspond to the
10996 iterators of the already generated loops.
10997 The user should not rely on the ids of the output dimensions
10998 of the relations in the union relation returned by
10999 C<isl_ast_build_get_schedule> having any particular value.
11001 =head1 Applications
11003 Although C<isl> is mainly meant to be used as a library,
11004 it also contains some basic applications that use some
11005 of the functionality of C<isl>.
11006 For applications that take one or more polytopes or polyhedra
11007 as input, this input may be specified in either the L<isl format>
11008 or the L<PolyLib format>.
11010 =head2 C<isl_polyhedron_sample>
11012 C<isl_polyhedron_sample> takes a polyhedron as input and prints
11013 an integer element of the polyhedron, if there is any.
11014 The first column in the output is the denominator and is always
11015 equal to 1. If the polyhedron contains no integer points,
11016 then a vector of length zero is printed.
11020 C<isl_pip> takes the same input as the C<example> program
11021 from the C<piplib> distribution, i.e., a set of constraints
11022 on the parameters, a line containing only -1 and finally a set
11023 of constraints on a parametric polyhedron.
11024 The coefficients of the parameters appear in the last columns
11025 (but before the final constant column).
11026 The output is the lexicographic minimum of the parametric polyhedron.
11027 As C<isl> currently does not have its own output format, the output
11028 is just a dump of the internal state.
11030 =head2 C<isl_polyhedron_minimize>
11032 C<isl_polyhedron_minimize> computes the minimum of some linear
11033 or affine objective function over the integer points in a polyhedron.
11034 If an affine objective function
11035 is given, then the constant should appear in the last column.
11037 =head2 C<isl_polytope_scan>
11039 Given a polytope, C<isl_polytope_scan> prints
11040 all integer points in the polytope.
11044 Given an C<isl_union_access_info> object as input,
11045 C<isl_flow> prints out the corresponding dependences,
11046 as computed by C<isl_union_access_info_compute_flow>.
11048 =head2 C<isl_codegen>
11050 Given either a schedule tree or a sequence consisting of
11051 a schedule map, a context set and an options relation,
11052 C<isl_codegen> prints out an AST that scans the domain elements
11053 of the schedule in the order of their image(s) taking into account
11054 the constraints in the context set.
11056 =head2 C<isl_schedule>
11058 Given an C<isl_schedule_constraints> object as input,
11059 C<isl_schedule> prints out a schedule that satisfies the given